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1 Spectrograph Optical Design

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					1 Spectrograph Optical Design

1.1 Overview
The NIFS science instrument is a near-infrared, integral-field spectrograph. The optical design consists
of three sub-systems; 1) an input sub-system forms an image of the telescope exit pupil at the system
cold stop and reimages the telescope focal plane at a scale appropriate for the IFU, 2) the IFU sub-
system reformats the 3.03.0 central region of the image into a long “staircase” slit, and 3) the
spectrograph sub-system forms a dispersed image of the reformatted slit at the detector.

Two options have been considered for the input sub-system; an Offner relay followed by a focal ratio
converter, and a single concave mirror. Two options for the IFU geometry have been investigated; a
concentric IFU and a linear IFU. The choice of IFU geometry leads to two different designs for the
spectrograph collimator; the concentric IFU naturally feeds a reflective Bouwers collimator, while the
linear IFU naturally feeds a refractive collimator. Both spectrograph concepts can use the same
refractive camera.

The baseline optical design for NIFS consists of a single concave mirror input sub-system, a concentric
IFU, and a refractive spectrograph camera.

Near-infrared, integral-field spectrographs have been developed only recently. The first such
instrument was 3D (Weitzel et al. 1996). This used a 16-element reflective IFU consisting of a stack of
tilted, plane image slicer mirrors at focus and a hyperbolic array of plane mirrors to steer beams into
the spectrograph from a virtual pupil that was coincident with the telescope exit pupil. This approach
works well for small fields and small detector arrays. However, the ray footprints on the beam steering
mirrors rapidly overlap when this design is scaled to the longer virtual slits required to feed the full
fields of 20482048 pixel detectors. The solution is to use fore-optics or power on the image slicer
mirrors to form an array of pupil images on the beam steering mirrors (Content 1997). This eliminates
beam overlap, but requires a second array of field mirrors to reform a single grating pupil. This is the
approach that is taken in the NIFS optical design.

Fiber optic IFUs were considered. However, these were rejected for several reasons: 1) Operation to
2.5 m would require cooling the optical fiber IFU, with uncertain consequences. This risk was
deemed to be incompatible with the rapid development timescale required for NIFS. 2) Fiber optic
IFUs have lower spatial fill factor than reflective IFUs. The light loss affects sensitivity but, more
significantly, it complicates data interpretation. 3) Small diameter fibers would be required to achieve
even moderate fill factor on the detector. Handling small diameter optical fibers to achieve this fill
factor was considered risky. 4) RSAA has only limited experience with optical fiber instruments. We
do not consider optical fiber IFUs further.

1.2 Optical Layout
Two alternative optical designs are discussed in this section; one is based on a single concave mirror
input sub-system and the concentric IFU design, and the other is based on the use of an Offner relay for
the input sub-system and the linear IFU design. The concentric IFU design is the baseline option so it is
discussed in greater detail (§1.3). Relatively, the concentric IFU design is simpler, has fewer optical
surfaces, and is easier to manufacture, but it also has a longer optical path that makes it more difficult
to accommodate in the duplicate NIRI cryostat. The simpler input sub-system will be more difficult to
baffle. However, this is not an essential feature of the IFU design; in principle, either input sub-system
could be applied to either IFU sub-system.

1.2.1 Concentric IFU Design
The optical layout for the concentric IFU design is shown in Figure 1 and Figure 2. For the sake of
clarity, the folds required to fit the system into the duplicate NIRI cryostat are omitted. The trimetric
view (Figure 1) shows a ray bundle that passes through an end (far) channel of the IFU, whereas the
side view (Figure 2) shows only a section through the central channel, with rays to suit. Figure 1 and
Figure 2 show the telescope beam entering the NIFS science instrument at left at the telescope focus.
The beam is reflected back by the focal ratio converter mirror to the cold stop mirror at left and then
traverses the instrument to the image slicer mirrors located at upper-right in these figures. From there
the sliced beams pass to the pupil mirror array and then to the field mirror array at top-middle and back
to the large collimator mirror at left. The collimated beams pass through the Bouwers corrector shell on
their way to the grating at middle-right before entering the spectrograph camera and forming a
dispersed image at bottom-middle.




Figure 1: Optical layout of the concentric IFU design, in trimetric view, with fold mirrors
omitted. The rays shown are for the far channel of the IFU.




Figure 2: Optical layout of the concentric IFU design, shown for the central channel of the IFU,
in side view with fold mirrors omitted.



The essential feature of the concentric IFU design is the placement of the pupil mirror array and field
mirror array elements on separate continuous arcs that are each concentric with the image slicer axis.
The collimator mirror is also concentric with this axis. Thus the optical paths for every slice of the
image slicer appear to be identical and on-axis from the image slicer to the grating. This avoids
aberration problems in the outer channels. To achieve this, the distance between the collimator mirror
and the grating (the exit pupil of the collimator) must be twice the collimator focal length and the
distance between the image slicer and the field mirror array must equal the collimator focal length. This
makes the system long and hence difficult to accommodate within the duplicate NIRI cryostat.

In both views of the optical layout, there is a discontinuity in the ray bundle at the image slicer. Up to
the slicer, the marginal rays are those for the f/16.2 Cassegrain input beam provided by the telescope.
Beyond the image slicer, the instrument is designed to capture all the radiation from within an enlarged
rectangular aperture at the pupil images, so accounting for some of the diffractive spread caused by the
narrow slitlets of the image slicer (see §1.4). The ray bundle shown after the image slicer is for this
rectangular aperture. Its width (spatial direction) matches the diameter of the round geometrical pupil,
but its length (spectral direction) is enlarged relative to this. As described in the diffraction analysis
(§1.4), the enlargement factor, K, is taken to be 1.6. In the spatial projection, the beam corresponds to
the original f/16.2 telescope input, but in the spectral projection it corresponds to an f/10 input. The
optical performance described in this document is for this enlarged pupil.

The full Zemax prescription for the concentric IFU design is listed in Appendix §Error! Reference
source not found..

1.2.2 Linear IFU System
The layout of the linear IFU design is shown in Figure 3. This includes the fold mirrors necessary to fit
the design in the duplicate NIRI cryostat. The object at the top of the diagram is the cryostat window.
Below that, there is an Offner relay system shown in end-view, before a mirror folds the layout into the
plane of the figure. The Offner relay is used to create the system cold stop. This is incidental to the IFU
design, but requires that a further concave mirror be used to reimage the focal plane at f/160 on the
image slicer. The beams then pass to a pupil mirror array and a field mirror array, as in the concentric
IFU design, and then to a refractive collimator, grating, refractive camera, and come to focus at the
detector.




           Figure 3: Optical layout of the linear IFU design, with fold mirrors included.

The essential feature of the linear IFU design is that the elements of the pupil mirror array and field
mirror array are located on separate flat planes. Consequently, the linear IFU design presents a flat,
telecentric, reformatted “staircase” slit to the spectrograph. This is best accommodated with a refractive
spectrograph collimator. The linear pupil and field mirror arrays require a different manufacturing
approach to the concentric IFU mirror arrays. The trade-offs associated with the two manufacturing
approaches are discussed in §1.21.1. The pupil mirror array elements are toroids to reduce aberrations
and require discontinuous steps between each element. The field mirror array elements are also toroids
to control pupil aberrations for each channel on the grating. Each field mirror array element must also
be decentered perpendicular to the array by differing amounts to control its pupil location on the
grating.

The linear IFU design has the advantage that constraints on packaging in the duplicate NIRI cryostat
are less demanding than for the concentric IFU; there is no constraint on the separation between the
image slicer and field mirror array, and folding is easier because larger fold angles do not introduce
large off-axis angles. This system can be more thoroughly baffled than the concentric IFU system.
However, all channels of the IFU are optically different with the outer channels being increasingly off-
axis and varying in optical path length. This makes field aberrations and pupil imagery more difficult to
control.

The discontinuous pupil mirror array elements present a challenge for diamond turning technology
which is not shared with the concentric IFU design. The need to contain the width of the steps within
the pupil mirror array elements means that a tip radius smaller than the usual 1 mm must be used on the
diamond tool if the array is manufactured as a monolith. Use of a small tip radius is expected to
increase surface roughness and hence scatter. An alternative appraoch is to diamond machine each
pupil mirror element in a separate metal block. Smooth surfaces then result from the use of a standard
diamond tip. However, this approach presents a different challenge in mounting all 29 individul pupil
mirror elements to the required accuracy.

The full Zemax prescription for the linear IFU design is listed in Appendix §Error! Reference source
not found..

1.2.3 Concentric IFU or Linear IFU?
At this stage of the design process, both the concentric IFU and the linear IFU designs are regarded as
viable. Further study is required to decide between them. The concentric IFU is presented in this
document as the baseline design because it has been more thoroughly investigated, has superior optical
performance, and its use of monolithic mirror arrays will simplify alignment. However, several aspects
of the concentric design remain to be resolved. The mirror arrays must be manufactured on a three-axis
diamond machine using a fly cutting technique that approximates the desired optical surface figure
(§1.21.1). The surface quality achieved by these three-axis diamond machines is yet to be quantified.
The ability of the single focal ratio converter mirror to effectively baffle the input beam is yet to be
adequately demonstrated. The degree to which scattered light can be suppressed in the folded
concentric IFU design has yet to be explored. The beam footprint on the order blocking filter is only
3.6 mm in an f/256 beam. The small size of this footprint is of minor concern. The following sections
should be read with these issues in mind.

1.3 Baseline Optical Design Detail
The various components of the baseline optical design for NIFS are now discussed in more detail.
Detailed calculations of the design parameters are deferred to an Appendix (§Error! Reference source
not found.).

1.3.1 Pick-off Mirror, Field Mask, Focal Ratio Converter, and Cold Stop
The pick-off mirror, field mask, focal ratio converter, and cold stop form the input sub-system (Figure
4). A small pick-off mirror protrudes over the OIWFS field and deflects rays at the field center towards
the NIFS science instrument. Light enters the NIFS science instrument through a small, almost square
aperture in a field mask located at the f/16.2 telescope focus. The function of this field mask is to baffle
the instrument from out-of-field radiation. The active area of the aperture is determined by the field
size at the image slicer to be 1.8561.860 mm (2.993.00). The field mask itself is slightly oversized
relative to the active field to accommodate any misalignment. The field mask occupies one position in
an indexable Focal Plane Mask Wheel. This allows the field mask to be replaced by other masks
containing occulting disks of different size, calibration slits, and masks for optical testing.
Figure 4: Field mask, focal ratio converter, and cold stop, with rays shown for the far channel of
the IFU.

The focal ratio converter is located 68 mm beyond the field mask. It is a spherically concave, tilted
mirror with a focal length of 64 mm. The main function of the focal ratio converter is to reimage the
telescope field on the image slicer at 16 times larger scale (i.e., f/256). This is needed to ease
manufacture of the image slicer mirrors, and to meet certain geometrical requirements of the IFU and
collimator. The focal ratio converter mirror also produces a 4.0 mm diameter image of the pupil close
to the field mask. The fold mirror needed to turn the beam back into the spectrograph is conveniently
placed at this location, and so functions as the system cold stop. The vicinity of the fold mirror must be
carefully baffled in order for it to act as an efficient cold stop.

1.3.2 Image Slicer
The image slicer is the first component of the IFU. It is a stack of 29 slitlet mirrors, each 1.024 mm
wide (Figure 5). The focal length of the system at this point is 2048 m (16128 m), so the angular
slitlet width is 0.5 rad (~0.103). In general, the field captured by the image slicer is rectangular, with
the aspect ratio determined by the number of slices chosen, the number of pixels in the detector, and
the anamorphic factor of the grating. For NIFS, 29 slitlets are chosen to make the field as nearly square
as possible. The field size is then 29.696 mm (~2.99) in the spectral direction, and 29.757 mm (3.00)
in the spatial direction. Detailed analysis of this field geometry is given in §Error! Reference source
not found..
Figure 5: Image slicer, comprising 29 slitlet mirrors, each 1.024 mm wide and having an active
length of 29.8 mm. The mirrors are fanned about a vertical axis by ~ 0.127° per slice. The rays
shown are for the far IFU channel.

The mirror stack is fanned about an axis which is tangential to the center of the central slice, so that
each reflected beam is directed to a different element of the following pupil mirror array. Each slitlet
mirror is spherically concave so that it produces a pupil image on the corresponding element of the
pupil mirror array. The pupil images are arranged to under-fill the elements of the pupil mirror array
with a comfortable margin. Without fanning, the slitlet surfaces of the image slicer would each be part
of a common concave spherical surface having a radius of curvature of ~ 623 mm. Detailed analysis of
the fanning geometry is given in §Error! Reference source not found..

1.3.3 Pupil Mirror Array, Field Mirror Array, and Collimator
The pupil and field mirror arrays form the second and third components of the IFU (Figure 6). Each
element of the pupil mirror array is torically concaved by as much as is needed to produce a good
image of its image slicer slitlet on the corresponding element of the field mirror array. The images of
adjacent slitlets on the field mirror array are stacked in staircase fashion (i.e., corner-to-corner) along
the mirror array. Each element of the field mirror array is a spherically concave mirror which reflects
its beam to the collimator from a virtual pupil located on the fanning axis of the IFU. The fanning
geometry is arranged so that the ends of the slitlet images fall on the boundaries between adjacent
elements of the field mirror array. This optimizes use of detector real-estate and minimizes cross-talk
between channels.
Figure 6: The pupil (left) and field (right) mirror arrays with center lines shown on the central,
far and near channels. The rays shown are for the far channel. The beams enter from right and
exit to left.

The elements of both the pupil and field mirror arrays are tilted by 5° with respect to the central ray to
allow for entry and exit beam clearance. The off-axis angle is kept to a minimum because it causes
astigmatism, which is the dominant image aberration. The criterion used in establishing the tilt angle is
that clearance between the active area of the element surface and the passing beam should be > 2 mm.

The IFU and collimator are designed in concert as a concentric system in order to deliver good optical
performance in all IFU channels through to the grating. The elements of the pupil and field mirror
arrays are displaced by equal angular increments about circular arcs that are centered on the fanning
axis of the image slicer. That is, a common fanning axis is used for image slicer, pupil mirror array, and
field mirror array. In similar fashion, the collimator is a concentric Bouwers system, with the centers of
curvature of its three spherical surfaces (one for the mirror and two for the refractive corrector) being
coincident, and located on the fanning axis of the image slicer. As a result, all channels of the IFU are
optically identical through to the grating. The output pupils of all channels are coincident, and located
on the fanning axis. The grating is centered on this common pupil.

The principle of this concentric geometry is illustrated in Figure 7. The two components at the far right
are the image slicer and grating (coincident in the plan view). The other components are, from left to
right, the collimator mirror, the pupil mirror array, the field mirror array, and the collimator corrector.
The fanning axis of the system is the line through the center of the image slicer and the center of the
grating (marked by a small circle in the plan view). In the plan view, the mirror array arcs and the
collimator components are all concentric, and their common curvature center is coincident with the
fanning axis.




Figure 7: The concentric IFU and collimator shown in plan and elevation. The rays are for the
far channel.
For the far channel, a slender f/256 beam is shown in Figure 7 emerging from the center of the image
slicer, travelling left. It passes over the collimator corrector and field mirror array, and is reflected by
the pupil mirror array back onto the field mirror array at f/16. It is then reflected back to the collimator
mirror, still at f/16. The beam reflected from the collimator mirror is roughly collimated, and passes
back though the collimator corrector (which removes spherical aberration). It then continues on to a
pupil image on the grating. Throughout its travel, the beam has remained on the same radial line from
the image slicer. Each channel follows a different radial line, but the concentric geometry makes the
optics identical for all of them.

A characteristic of this concentric geometry is that the field mirror array must be separated from the
image slicer by a specific distance, which is approximately equal to the focal length of the collimator.
The length of the combined IFU and collimator system is large because it must be approximately twice
the focal length of the collimator. The spatial envelope of the duplicate NIRI cryostat requires that this
be folded.

The geometrical (without diffractive spreading) diameter of the collimator output beam is fixed by
spectroscopic requirements at 26.3 mm, as is explained in §1.3.4. The length of this system is therefore
proportional to the common focal ratio used for the output of the pupil mirror array and the input of the
collimator. To minimize length, this focal ratio is chosen to be the smallest that gives good image
quality. The major factors determining this are astigmatism in the IFU and chromatic defocus in the
collimator. The adopted focal ratio is f/16, and it follows from this that the collimator focal length is
421 mm, and the combined length of the IFU and collimator is ~ 842 mm. The IFU and collimator are
actually designed to deliver a rectangular beam to the grating which is 26.3 mm wide (in the spatial
direction) and 42.1 mm long (in the spectral direction) to take account of the diffractive beam spread
discussed in §1.4

IFU aberrations were investigated algebraically to reveal the effect of various parameters and to
facilitate optimization of the design (see §Error! Reference source not found.). The refractive
corrector meniscus of the collimator is made from calcium fluoride to control chromatic defocus. The
low dispersion of this material limits the defocus to about one third of one pixel at the ends of the
wavelength range (0.94-2.50 m). This avoids the need for refocus between spectral bands. Even this
residual chromatic defocus can be largely corrected by compensating in the camera design.

1.3.4 Grating
The Ebert angle at the grating is chosen to be 30° to achieve adequate clearance between the collimator
and camera. The grating angle is ~ 20° for all gratings proposed (§1.6). The resolving power of the
spectrograph is proportional to the geometrical diameter of the collimated beam for given values of the
Ebert angle, grating angle, angular slitlet width, and telescope aperture diameter. A beam diameter of ~
24.8 mm is required to achieve the desired resolving power of ~ 5000.

However, there is a further criterion for selecting the exact beam diameter, provided that this
approximate resolving power requirement is met. Once the diffraction order and groove density have
been chosen for the grating (in addition to the above parameters), the need to match a specific
wavelength range to the detector width determines the exact beam diameter (a larger wavelength range
requires a smaller beam diameter). For NIFS, it is proposed that the H band (1.49-1.80 m) be matched
to the detector width using a 400 l mm-1 grating operating in first order. To achieve this, the
geometrical diameter of the collimator beam must be 26.3 mm and the grating angle is 19.919°. The
corresponding resolving power is ~ 5280. Details of the beam diameter analysis are given in §Error!
Reference source not found..

1.3.5 Camera
The camera focal length must be set to 288 mm to match the width of the monochromatic slitlet image
to two pixels at the detector (36 m). No acceptably simple reflective design was found that would give
satisfactory performance, so a five element refractive camera design is proposed (Figure 8). The
materials employed for the five elements are, from first to last, calcium fluoride, silica, zinc selenide,
calcium fluoride, and silica. All are readily available in the required sizes. Optical parameters for the
camera are presented in §Error! Reference source not found. and §Error! Reference source not
found..




Figure 8: The five-element camera with rays shown for the central channel from the grating to
the detector.

The first camera surface is placed 140 mm from the grating center to provide adequate clearance from
the collimator beam. The distance from grating center to the detector is 507 mm. This can be
comfortably accommodated in the available cryostat space. A smaller value is not desirable because it
would degrade optical performance. No remotely controllable focus mechanism is proposed (§1.17).

The spectrograph camera design produces sub-pixel images over the whole area of the detector for all
wavelength bands without refocusing when used in combination with the rest of the optical system.
Some chromatic defocus could be incorporated to compensate for the small chromatic defocus caused
by the collimator, but this has not been done. Distortion can be adequately controlled (§1.5.5.2).

1.4 Diffraction Effects

NIFS will use an IFU with 0.1 wide slitlets which are only slightly larger than the ~ 0.07 FWHM of
the telescope diffraction pattern at 2.2 m. Such narrow slits cause diffraction effects in the
spectrograph dispersion direction that broaden the beam beyond its geometrical size. These effects
must be considered in arriving at suitable dimensions for the NIFS pupil mirrors and diffraction
gratings. The finite lengths of the pupil mirrors and diffraction gratings also mask the pupil images.
This causes a second diffraction effect that alters the profiles of monochromatic slit images at the
detector. This effect must be assessed to ensure that diffraction effects do not limit the rejection
efficiency of OH airglow line emission.

The optical parameters described in the following diffraction model differ somewhat from those
described in §1.3. This is because the diffraction analysis was done with respect to an earlier optical
design. The analysis concludes that the pupil apertures must be over-sized in the spectral direction by a
certain factor with respect to the geometrically determined size in order to capture sufficient of the
radiation diffracted by the narrow slitlets. This factor is also applicable to the currently proposed
optical design.

1.4.1 Diffraction Model
Diffraction effects in NIFS have been modeled using a Fourier technique that assumes perfect
geometrical optics. Fast Fourier transformations (FFTs) are used to progress from the telescope pupil
plane through the telescope image plane, the pupil mirror plane, the field mirror image plane, the
grating pupil plane, and finally to the detector image plane. The image and pupil planes are both
sampled on a 512512 pixel grid. Transformations from pupil planes to image planes are performed
with a forward FFT, and transformations from image planes to pupil planes are performed with an
inverse FFT. The sampling resolution is 80 mm/pixel at the telescope pupil, 13.5 m/pixel at the pupil
mirror plane, and 312 m/pixel at the grating. The image scale is 0.005 arcsec/pixel where  is the
wavelength in microns. The transmitted transforms are masked as appropriate at each plane. The
telescope pupil is modeled as a 7900 mm diameter circular aperture with a central obstruction 1023
mm in diameter and a four vane spider with 5 mm thick vanes. An effective telescope focal length of
712,580 mm was used to produce an f/90 image on the IFU image slicer mirrors. The image plane at
the image slicer was masked with a 0.10 wide slit representing one slitlet of the IFU. A pupil image is
formed 120 mm from the image slicer at the pupil mirror array. This pupil image is masked by a
rectangular aperture 2.0 mm wide (in the slit direction) and 4.0 mm long (in the dispersion direction)
representing a single pupil mirror. The pupil mirrors reimage each IFU slitlet onto its corresponding
mirror in the field mirror array where the reformatted “staircase” slit image is formed. The field mirrors
are each 2.0 mm4.0 mm and do not vignette the image. The 500 mm focal length collimator reimages
the pupil on to the diffraction grating. The adopted geometrical grating pupil diameter is 30.85 mm.
Since the angle of incidence at the grating is approximately 35, the physical length of the grating must
be at least a factor sec 35 larger than this pupil image in the dispersion direction. The reformatted slit
image is reimaged on to the detector by the 290 mm focal length camera. It is assumed throughout that
the telescope optics produce a perfect diffraction-limited image at the image slicer with no distortion
due to atmospheric seeing or optical aberrations. To first order, it is the purpose of the ALTAIR
adaptive optics system to deliver such an image. The reflectivities of all surfaces, including the grating,
are assumed to be unity.

The pupil images formed at the pupil mirrors are reimaged at the grating with the image dimensions
scaling as the ratio of the collimator to field mirror focal lengths. The 2.0 mm  4.0 mm pupil mirrors
then map to 46.4 mm  92.8 mm at the grating pupil. The sec 35 projection factor due to the grating
inclination requires that the gratings be at least 113 mm long to prevent further vignetting at the grating
pupil. Geometrical constraints on the size of the grating wheel and camera optics limit the grating size
to less than this value. Consequently, it is the grating rather than the pupil mirrors which limit the
extent of the diffracted pupil image.

1.4.2 Diffraction Analysis

1.4.2.1 On-Axis Source

The effects of diffraction due to slit and pupil masking at a wavelength of 2.5 m are shown in the
sequence of images in Figure 9. The images shown for an on-axis source are the telescope pupil image,
the image at the IFU image slicer, this image seen through a single 0.1 wide slitlet, the pupil image at
the pupil mirror, the masked pupil at the grating, and the image at the detector. The telescope
diffraction rings are seen clearly, along with the smearing of the pupil images in the dispersion
(horizontal) direction and the diffraction effect due to the finite lengths of the pupil mirrors and the
grating on the final slit image at the detector. The latter effect is manifest as a faint slit diffraction
pattern in the dispersion direction.
         Telescope Pupil                 Telescope Image                 Single Slitlet




         Pupil Mirror                     Grating Pupil                  Image at Detector




Figure 9: Pupil and image planes for an on-axis source at 2.5 m, seen through a 0.1 wide slitlet
with 46.4 mm  90 mm grating.


1.4.2.2 Off-Axis Source
Objects of scientific interest will generally not be accurately centered in the NIFS IFU slitlets; most
science objects will either be point sources distributed randomly across the field-of-view or they will be
extended. It is therefore necessary to examine diffraction effects as a function of the source position in
an IFU slitlet.

The sequence of images shown in Figure 9 is repeated in Figure 10 for a source offset 0.05 from the
slitlet center. This places the center of the Airy disk on the edge of the slitlet. Comparison of Figure 9
and Figure 10 shows that the distribution of light at the pupil mirror is broader for the off-axis source.
This is to be expected because of the sharp discontinuity in the image plane at the slitlet edge. The
same effect is seen when this pupil image is reimaged onto the grating. More severe masking of the
pupil image by the finite extent of the grating then causes a more prominent slit diffraction pattern in
the dispersion direction at the detector.
         Telescope Pupil                 Telescope Image                    Single Slitlet




         Pupil Mirror                      Grating Pupil                 Image at Detector




Figure 10: Pupil and image planes for a 0.05 off-axis source at 2.5 m, seen through a 0.1 wide
slitlet with 46.4 mm  90 mm grating.



1.4.2.3 System Throughput
The broadening of the collimated beam relative to the geometrical beam size caused by diffraction will
lead to light loss unless large optical elements are used in the collimated beam. The throughput
degradation due to light loss at the pupil mirrors and grating has been calculated as a function of the
physical grating length (including the projection factor) since this sets the scale of the collimated beam
optics. Both on-axis and 0.05 off-axis point sources were considered because the light distribution at
the pupil mirrors varies with the off-axis position of the source. The curves in Figure 11 and Figure 12
show the system throughput at a wavelength of 2.5 m as a function of the physical length of the
grating. This wavelength represents the worst case for diffraction losses in NIFS. The throughput rises
more steeply with increasing grating length for the on-axis source because the pupil image is more
centrally concentrated in this case. The system throughput reaches a maximum in both cases for
gratings longer than ~ 113 mm. Beyond this length the throughput is set by the length of the pupil
mirrors rather than by the length of the grating. For the 4.0 mm long pupil mirrors assumed here, it is
clear from Figure 11 and Figure 12 that a grating length of ~ 60 mm, or approximately twice the
geometrical pupil size, provides an acceptable trade between system throughput degradation, optical
complexity, and expense.
Figure 11: System throughput at 2.5 m due to diffraction losses for an on-axis point source.




Figure 12: System throughput at 2.5 m due to diffraction losses for a point source offset 0.05
from the slitlet center.



1.4.2.4 Emission-Line Profile
Diffraction effects at the pupil images produce wings on the profiles of point sources in the dispersion
direction (Figure 9 and Figure 10). Extended sources will produce the same effect, with airglow from
OH emission lines being the most problematic in this regard because of the extreme brightness of many
of these lines compared to the faint sources that NIFS will measure. The profiles of OH airglow lines
have been modeled by considering the image profile at the detector of a source of uniform illumination.
A uniform source is modeled by summing the contributions from twenty-one point sources that are
equally spaced by 0.01 along a 0.2 long line in the image slicer plane perpendicular to and centered
on the 0.1 wide slitlet. Since the phases of OH airglow emissions from different positions on the sky
are uncorrelated (i.e., the emission is incoherent across the slitlet), light from each position in the slit
must be propagated through the system independently. The image intensity at the detector is calculated
for each slit position and co-added and summed along the slit image to produce the final OH emission-
line profile.

OH emission-line profiles were calculated for grating lengths of 60 mm and 100 mm at a wavelength of
1.3 m appropriate to science measurements of H at a redshift of z = 1. These profiles are shown in
Figure 13and Figure 14, respectively. The fringing seen in the wings of the profiles is probably due to
numerical instabilities in the FFT at the Nyquist frequency. It is apparent that the attenuation of the
signal at more than ~ 3 pixels (~ 0.15) either side of the line center is a factor of > 660 for a 60 mm
grating length and a factor of > 2500 for a 100 mm grating length.




           Figure 13: OH emission-line profile at 1.3 m for a grating length of 60 mm.




           Figure 14: OH emission-line profile at 1.3 m for a grating length of 100 mm.


1.4.3 Design Consequences
NIFS will be a near-diffraction-limited imaging spectrograph. As such, it will use slits comparable in
width to the telescope diffraction size. Slit diffraction then broadens (i.e., speeds) the beam emerging
from the IFU slitlets which increases the size of the pupil image in the dispersion direction. The finite
size of the collimated beam optics then results in a throughput loss. Diffraction effects at the pupil
image subsequently broaden the slit image formed at the detector. These effects can be controlled by
ensuring that the beam footprint on the grating is about twice as large in the spectral direction as it is in
the spatial direction. Accounting for the anamorphic effect of the grating, the required pupil aperture
over-sizing factor in the spectral direction is taken to be K = 1.6.

1.5 Image Quality
Image quality is examined at each of the relevant surfaces through the optical system. Field and pupil
images are considered. For the field images which occur after the image slicer (i.e., at the field mirror
array and the detector), the objects are taken to be points on the image slicer, and hence do not involve
the telescope or the focal ratio converter optics. This imagery uses a rectangular feed pupil to account
for the diffractive beam spread caused by the narrow image slicer slitlets.

1.5.1 Cold Stop Image Quality
The entrance pupil of the telescope is the secondary mirror. An image of this mirror is formed by the
focal ratio converter mirror in NIFS, and is cast onto the 4 mm diameter cold stop mirror. The pupil of
the telescope becomes the field for this imaging process. The square field mask at the telescope focus
becomes the pupil. This mask is made slightly larger than the field, which is ~ 1.86 mm square (14.5
rad, or 3.0 square).

This masking imposes a diffraction limit on the quality of the pupil image, against which the
geometrical aberration must be judged. In linear terms, the diffraction limit for a square aperture is the
product of the focal ratio and the wavelength. Given that the focal length of the focal ratio converter
mirror is 64 mm, the focal ratio producing the pupil image is about f/34. The diffraction limit is ~ 34
m even for the shortest wavelength of ~ 1 m.

The purpose of the cold stop (apart from folding the beam) is to cleanly pass light which comes from
within the boundary of the secondary mirror, but mask light which does not. The aberration of interest,
therefore, is that for the edge of the pupil in the tangential (but not sagittal) direction. For simplicity the
figure of the focal ratio converter mirror is made spherical. The dominant aberration is astigmatism
because this mirror is tilted, so the pupil image is worst at its most off-axis point (i.e., the bottom edge
shown in Figure 4). At this point, the tangential spread of the image is 7 m (Figure 15), which is small
compared to the diffraction limit. In fact, much of the aberration is caused by de-focus, because the
pupil mirror has been positioned for an infinitely distant secondary mirror. This approximation results
in a blur of about 7 m. The geometrical image quality could be dramatically improved by correct
focus positioning, and using a toric figure for the focal ratio converter, but the aberration is not
significant in any case.




Figure 15: Spot diagram for the most off-axis point on the cold stop perimeter. Box size is 10 m.


1.5.2 Image Slicer Image Quality
The focal ratio converter mirror re-images the f/16.2 field at the field mask to f/256 on the image slicer.
This field is ~ 30 mm square and is sliced into 29 slitlet strips each with a width of 1.024 mm (0.5
rad). Image aberration should be small compared to this width.

The focal ratio converter is a tilted mirror with spherical figure. This and the changing field angles
around the image slicer result in image aberration. Spot diagrams of images at the image slicer are
shown in Figure 16 for the center and ends of the far, middle, and near IFU channels. In general, the
full extent of the blurring is ~ 0.10 mm, which is considerably smaller than the slitlet width (and the
corresponding pixel size). The geometrical image quality could be improved somewhat by using a toric
figure on the focal ratio converter mirror , but there is no need for this complication.
                                                                                            NEAR
                                                                                            SLICE




                                                                                            MID
                                                                                            SLICE




                                                                                             FAR
                                                                                             SLICE




Figure 16: Spot diagram at the image slicer for the center and ends (columns) of the far, middle,
and near IFU channels (rows). Boxes are 0.512 mm (corresponding to one pixel in the spectral
direction).


1.5.3 Pupil Mirror Array Image Quality
The cold stop is imaged onto each element of the pupil mirror array by the corresponding curved slitlet
mirror in the image slicer. The IFU geometry is arranged so that the pupil image under-fills the mirror
element in the fanning direction by a factor of 0.825 (§Error! Reference source not found.). Given
that the circumferential pitch of the mirror pupil mirror elements is 1.984 mm, the margin is 0.174 mm.
Geometrical aberrations in the pupil image, and the diffraction limit, should be small compared to this.

The slitlets of the image slicer become the pupil for this re-imaging process. The linear diffraction limit
they impose is the product of the focal ratio with which they form the pupil images and the wavelength.
The separation between the image slicer and the pupil mirror array is 448 mm, and the slitlet mirrors
are 1.024 mm thick and ~ 30 mm long. The spectral and spatial focal ratios are therefore ~ f/440 and
f/15, respectively. For the longest wavelength applicable (2.5 m), the diffraction limit is ~ 1.1 mm
perpendicular to the pupil mirror array, and ~ 38 m along the array. This latter value is small
compared to the clearance margin of 0.174 mm.

The large diffraction limit in the spectral direction has already been accounted for elsewhere with the
adoption of the pupil aperture enlargement factor of K = 1.6 (§1.4.3).

The geometrical aberration in the pupil image varies from channel to channel (slitlet to slitlet). For the
central channel, the extent of the blur in the direction of the array is 8 m. For the far channel (bottom
slitlet), it is 13 m. For the near channel (top slitlet), it is 22 m. This is small compared to both the
clearance margin and the diffraction limit. Aberration perpendicular to the direction of the array is
comparable, but of no importance. These values are for the center of the pupil image, but because the
angle subtended by the image about the image slicer is small, quality does not vary greatly around the
pupil.
                FAR                             MID                            NEAR

Figure 17: Spot diagrams at the center of the pupil on the pupil mirror array. Array direction is
vertical. Box size is 40 m.


1.5.4 Field Mirror Array Image Quality
For each channel of the IFU, a slitlet in the image slicer is re-imaged onto an element of the field
mirror array by an element in the pupil mirror array at a focal ratio of f/16. The width of the slitlet
image is 64 m, and one pixel corresponds to 32 m in the spectral direction. To control astigmatism,
the pupil mirror array elements have a toric figure.

The image quality varies a little with position in each slitlet, and with the position of the slitlet.
Typically it is worst at the extremes of both, but the rectangular blur envelope is never more than ~ 18
m long. Spot diagrams are shown in Figure 18 for the center and ends of the far, middle, and near IFU
channels. Third order analysis of this image quality is presented in §Error! Reference source not
found., and shows its dependency on the various IFU parameters.
                                                                                           NEAR
                                                                                           SLICE




                                                                                           MID
                                                                                           SLICE




                                                                                            FAR
                                                                                            SLICE




Figure 18: Spot diagrams at the field mirror array for the center and ends (columns) of the far,
middle, and near IFU channels (rows). Boxes are 0.032 m (corresponding to one pixel in the
spectral direction).


1.5.5 Detector Field Image Quality

1.5.5.1 Point Spread
Image aberrations at the detector are the combined effects of the IFU, collimator, and camera. Spot
diagrams are shown for the H, K and J1 gratings in Figure 19, Figure 20 and Figure 21, respectively,
for the central, far, and near channels of the IFU. For each of these channels, object points at the center,
far, and near ends of the slitlet are considered. For all nine of these object positions, three wavelengths
are considered (the center and ends of the wavelength band).

For the most part, blurring is sub-pixel without any re-focussing.

Separate analysis of the collimator has shown that it contributes very little aberration, apart from about
one third of a pixel of chromatic defocus at the ends of the wavelength range.
                                                                  NEAR

                                                                  SLICE




                                                                  MID

                                                                  SLICE




                                                                   FAR

                                                                   SLICE




                         1.49          1.645          1.8          WAVELENGTH


Figure 19: Spot diagram at the detector for the H grating. Spots for the near, middle, and far
channels of the IFU are shown at wavelengths corresponding to the middle and ends of the
spectrum (columns) for positions at the center and ends of each slitlet (rows). Boxes are 18 m
(one pixel) square.
                                                                 NEAR

                                                                 SLICE




                                                                 MID

                                                                 SLICE




                                                                 FAR

                                                                 SLICE




                  2.0              2.2              2.4          WAVELENGTH
                                                                 (MICRONS)


Figure 20: Spot diagram at the detector for the K grating. Spots for the near, middle, and far
channels of the IFU are shown at wavelengths corresponding to the middle and ends of the
spectrum (columns) for positions at the center and ends of each slitlet (rows). Boxes are 18 m
(one pixel) square.
                                                                             NEAR

                                                                             SLICE




                                                                             MID

                                                                             SLICE




                                                                              FAR

                                                                              SLICE




                              0.95            1.05            1.15            WAVELENGTH
                                                                              (MICRONS)

Figure 21: Spot diagram at the detector for the J1 grating. Spots for the near, middle, and far
channels of the IFU are shown at wavelengths corresponding to the middle and ends of the
spectrum (columns) for positions at the center and ends of each slitlet (rows). Boxes are 18 m
(one pixel) square.


1.5.5.2 Distortion
Distortion control is important to ensure that spectra for all spatial points in the object field align with
the detector pixel array. Figure 22 shows the distortion at the detector for the baseline optical design.
The two curves show deviations in Y position on the detector relative to the central Y value for the far
and near channels. Curves for the intermediate channels lie between these extremes. All of this
distortion is introduced by the camera. As can be seen, spectra on the edges of the detector deviate
from their desired positions by nearly two pixels in the spatial direction. Although not documented
here, recent reoptimization of the camera design has shown that the deviation can be readily reduced to
about 0.5 pixels.

                     3




                     2




                     1
  Delta Y (Pixels)




                     0




                     -1




                     -2




                     -3
                      1.495   1.545   1.595            1.645               1.695    1.745           1.795
                                               Wavelength (microns)

                                                Near Slice     Far slice


Figure 22: Distortion at the detector in the spatial direction for the two end IFU channels. Curves
for other channels lie between the two shown.



1.6 Grating Suite
As a low-cost, fast-tracked instrument, the choice of reflection gratings for NIFS has been restricted to
commercially available catalog gratings. The selection of grating parameters and camera focal length
are a trade between spectral coverage, spectral resolving power, signal-to-noise ratio, and OH airglow
emission-line rejection efficiency. The science drivers for NIFS require spectral resolving powers of R
= 4000-5000 in the J and H bands to significantly separate OH airglow lines, and velocity resolutions
of ~ 100 km s-1 (corresponding to spectral resolving powers R ~ 3000) in the K band to measure stellar
velocity dispersions in nearby galactic nuclei. NIFS is also required to provide coverage of as much as
possible of the 0.95-2.50 m wavelength range having atmospheric transmission above ~ 50% from
Mauna Kea (see §Error! Reference source not found.).

1.6.1 Grating Selection Criteria
NIFS is designed with a minimum of cryogenic mechanisms in order to simplify and speed its
construction, assembly, and commissioning phases. It was decided early-on to include only one grating
wheel carrying fixed-angle gratings, rather than to develop a complex cryogenic mechanism for
selecting different gratings and setting and accurately maintaining the required grating angle.
Consequently, each NIFS grating is optimized for its particular pass band. All gratings are selected to
operate in first order for maximum efficiency. Only gratings with groove spacings significantly larger
than the maximum required wavelength have been considered initially; groove densities of 600, 400,
and 300 l mm-1 are the finest considered for the J, H, and K bands, respectively. Gratings are chosen to
operate at low grating angle, , to maintain high grating efficiency and minimize polarization effects.
With the above constraints on the groove density and the mechanical constraint that the Ebert angle, ,
must be ~ 30°, grating angles of ~ 20° are required to center each of the H and K bands on the detector.
     The angles used for all gratings should be similar to ensure that the monochromatic slitlet image width
     is always matched to two detector pixels.

     For grating angles of up to 20°, the spectral resolving power is determined by the angular slitlet width
     as
                                                d col sin  cos 2 1
                                         R2
                                                d tel cos   2  x
     where the symbols are explained in §Error! Reference source not found.. For grating angles of more
     than 20°, the spectral resolving power is determined by the pixel size as
                                                f cam sin  cos 2 
                                           R                         .
                                                hx cos   2 
     The resolving power using a grating angle  = 20° is therefore ~ 5300. As explained in §Error!
     Reference source not found., the collimator beam diameter, dcol, has been chosen so that the H band
     fills the detector with a 400 l mm-1 grating. A 300 l mm-1 grating operating at an angle of 20° in the K
     band then delivers the wavelength range 2.00–2.41 m to the detector, which covers about 75% of the
     K band available from Mauna Kea. Two gratings are required to cover the available J band, with the
     selection being dictated by the availability of suitable blaze functions.

     Applying the pupil aperture over-sizing factor specified in the diffraction analysis (§1.4) gives an
     active grating length of 51 mm. Gratings with smaller ruled masters were not considered. The gratings
     will be mounted on the face of a 300 mm diameter wheel. The size of this wheel is limited by the
     duplicate NIRI cryostat dimensions. Eight gratings of this length can be accommodated on the grating
     wheel. One of these positions will be allocated to a mirror for direct viewing of the undispersed image
     (§1.18).

     1.6.2 Grating Selection

     1.6.2.1 Grating Option A: 26.3 mm Beam Configuration
     The 26.3 mm beam configuration is the baseline design described in this document. A suitable grating
     set delivering R ~ 5300 is listed in Table 1. Littrow relative efficiency curves for these gratings have
     been obtained from the Richardson Grating Laboratory; these are all > 80% in their operating bands
     (Figure 23). However, the K grating does not cover the full atmospheric window.

                      Table 1: R ~ 5300 Gratings for the 26.3 mm Beam Configuration
              CENTRAL                       GRATING       GRATING         RESOLVING    VELOCITY       SPECTRAL
GRATING      WAVELENGTH        GROOVES        BLAZE         ANGLE           POWER     RESOLUTION      COVERAGE
                (m)            (l/mm)       (degrees)     (degrees)                     (km/s)          (m)
J1                1.05            600         17.5          19.0            4990          60.1         0.94-1.15
J2                1.25            600         22.0          22.8            6040          49.6         1.15-1.35
H                 1.65            400         18.6          19.9            5280          56.8         1.49-1.80
K                 2.20            300         17.5          20.0            5300          56.6         2.00-2.41
     Figure 23: Littrow relative efficiency curves for gratings in Table 1 in s-plane (solid line) and p-
     plane (dashed line) polarized light. The wavelength range used for each grating is shaded. The
     reflectivity of aluminum is plotted as a heavy solid line.

     Broader spectral coverage in the K atmospheric window can be achieved at the expense of spectral
     resolving power by substituting the coarser Kw grating in Table 2 for the K grating listed in Table 1.
     The Kw grating offers wavelength coverage over the full K band available from Mauna Kea. The
     poorer velocity resolution delivered by this grating is appropriate for stellar velocity dispersion
     measurements in nearby galactic nuclei, but is not sufficiently high for Galactic interstellar medium
     studies such as resolving velocity structure in jets from young stellar objects. Furthermore, the Kw
     grating has poor efficiency over the required operating band (Figure 24) with a peak in-band efficiency
     (polarized at 45º to the grooves) of ~ 78% at 1.9 m and a minimum of ~ 32% at 2.5 m. The low
     efficiency of the Kw grating means that this lower resolution grating would produce a lower signal-to-
     noise ratio per pixel than the higher resolution K grating.

                      Table 2: Optional Gratings for the 26.3 mm Beam Configuration
              CENTRAL                      GRATING      GRATING       RESOLVING       VELOCITY      SPECTRAL
GRATING      WAVELENGTH       GROOVES        BLAZE        ANGLE         POWER        RESOLUTION     COVERAGE
                (m)           (l/mm)       (degrees)    (degrees)                      (km/s)         (m)
Kw                2.17           200         10.0          13.0          3240            92.7        1.84-2.51
J                 1.15           300         10.4          10.3          2510           119.4        0.92-1.38
HK                2.08           150          8.6           9.3          2250           133.2        1.62-2.54




     Figure 24: Littrow relative efficiency curves for the lower resolution K band gratings listed in
     Table 2. The curve for the Kw grating is for light polarized at 45º to the grooves. Other features
     are as for Figure 23.
     Broader wavelength coverage with approximately half the resolving power of the gratings in Table 1
     can also be achieved using the J and HK gratings listed in Table 2. The whole J atmospheric window is
     recorded in one exposure of a HAWAII-2 20482048 array with the J grating, and all of the K band
     along with half of the H band is recorded with the HK grating. The HK grating would also permit the
     measurement of P at low redshift on nights with suitable transparency, but the coverage does not
     extend sufficiently shortward to reach the important [Fe II] 1.644 m emission-line. The relative
     efficiency of the J grating has not been measured by the Richardson Grating Laboratory. The relative
     efficiency of the HK grating is poor (Figure 24) with large s- and p-plane polarization differences
     reminiscent of the Kw grating. Consequently, this grating will not realize the potential signal-to-noise
     ratio improvement from halving the spectral resolving power. Furthermore, performance modeling
     done with NIFSSIM (§Error! Reference source not found.) suggests that spectra obtained with the
     low resolving power J and HK gratings will be severely contaminated by OH airglow emission-lines.

     1.6.2.2 Grating Option B: 19.7 mm Beam Configuration
     An alternative way of broadening the K band wavelength coverage is to scale the whole spectrograph
     to a smaller size. The full K band accessible from Mauna Kea is made available with the K grating
     listed in Table 1 if this scale factor is 0.748. The collimated beam diameter is then 19.7 mm, the
     collimator focal length is 315 mm, and the camera focal length is 215 mm. The four gratings from
     Table 1 perform in the way listed in Table 3 in this configuration. The wavelength coverage of each
     grating is increased by ~ 30%, causing the H grating to extend well into regions of poor atmospheric
     transmission, and broadening the coverage of the J1 and J2 gratings so that they can overlap
     significantly in the region of poor atmospheric transmission around 1.12 m. Indeed, the coverage of
     the J2 grating is sufficient that it may be unnecessary to include the J1 grating. The resolving power
     achieved with each grating is also reduced by the scaling factor and is ~ 3970 for grating angles of ~
     20°. Values of R  4000 are still sufficient to adequately separate OH airglow line emission (§Error!
     Reference source not found.). The lower resolving power also helps overcome dark current noise in
     the J and H bands. Relative efficiency curves for these gratings are repeated in Figure 25 with their
     now wider operating bands.

                      Table 3: R ~ 4000 Gratings for the 19.7 mm Beam Configuration
              CENTRAL                       GRATING      GRATING       RESOLVING       VELOCITY       SPECTRAL
GRATING      WAVELENGTH       GROOVES         BLAZE        ANGLE         POWER        RESOLUTION      COVERAGE
                (m)           (l/mm)        (degrees)    (degrees)                      (km/s)          (m)
J1                1.07           600          17.5          19.4          3830            78.4         0.93-1.21
J2                1.22           600          22.0          22.3          4420            67.8         1.09-1.35
H                 1.62           400          18.6          19.6          3870            77.5         1.41-1.83
K                 2.22           300          17.5          20.2          4020            74.7         1.95-2.50
     Figure 25: Littrow relative efficiency curves for the gratings listed in Table 3. Other features are
     as for Figure 23.

     The combined H and K bands can now be covered at R ~ 1600 with the low efficiency HK grating
     (Table 4). Similarly, the entire J band can be covered at R ~ 1800 with the J’ grating listed in Table 4,
     with large overlap into the optical. The relative efficiency curves for these gratings are shown in Figure
     26. The main advantage of these gratings is their large wavelength coverage.

                      Table 4: Optional Gratings for the 19.7 mm Beam Configuration
              CENTRAL                       GRATING       GRATING       RESOLVING       VELOCITY        SPECTRAL
GRATING      WAVELENGTH        GROOVES        BLAZE         ANGLE         POWER        RESOLUTION       COVERAGE
                (m)            (l/mm)       (degrees)     (degrees)                      (km/s)           (m)
J                1.10            300           8.6           9.8          1780             168         0.79-1.40
HK                1.95            150           8.6           8.7          1570             191         1.34-2.57
K1                2.12            497          34.0          33.0          6620             45.3        1.98-2.25
K2                2.32            497          34.0          36.6          7410             40.5        2.19-2.44
Jh                1.25            830          30.0          32.5          6500             46.2        1.15-1.35
Hh                1.62            600          28.7          30.2          6015             49.9        1.48-1.76
Figure 26: Littrow relative efficiency curves for the gratings listed in Table 4. The curve for the
J grating is for light polarized at 45° to the grooves. Other features are as for Figure 23.

The overall lower resolving powers of the moderate resolution gratings (Table 3) are primarily a
concern in the K band where higher resolution is required to measure Br 2.166 m and H2 1-0 S(1)
2.122 m emission-line profiles and stellar velocity dispersions in cool systems using the 2.3 m CO
first-overtone bands. However, there is also a need for higher resolving power in the J2 and H bands
for measuring rotation curves of small z ~ 1 galaxies. Somewhat higher resolving powers can be
achieved in the K band using the K1 and K2 gratings listed in Table 4. The same grating master
delivers R ~ 7000 over the K atmospheric window in two grating settings with good efficiency (Figure
26). The Jh grating listed in Table 4 delivers a similarly high resolving power in the wavelength region
of H in z = 0.75-1.05 galaxies. The Hh grating listed in Table 4 delivers only slightly higher resolving
power than the H grating, so is probably not worthy of inclusion. Efficiency curves for the Jh and Hh
gratings are yet to be obtained.

An advantage of this configuration is that the spectrograph would be significantly smaller and therefore
easier to accommodate in the duplicate NIRI cryostat.

1.6.2.3 OH Rejection Efficiency
NIFSSIM has been used to determine the percentage of the wavelength range of each grating that is
occupied by OH airglow emission-lines (excluding the OH-free long wavelength end of the K band).
These percentages are listed in Table 5 and Table 6 for grating option A and B, respectively. It is
desirable to limit the percentage of pixels contaminated by OH airglow emission to less than ~ 20%
(§Error! Reference source not found.). Gratings with resolving powers lower than the J and HK
gratings exceed this contamination level.
                    Table 5: OH Airglow Contamination for Option A Gratings
                  c        l/mm         R         v        Range         Percentage OH Lines
                 (m)                            (km s-1)     (m)          J        H        K

    J1           1.05        600       4990        60.1     0.94-1.15    6.9%
    J2           1.25        600       6040        49.6     1.15-1.35    10.6%
    H            1.65        400       5280        56.8     1.49-1.80               13.3%
    K            2.20        300       5300        56.6     2.00-2.41                           9.8%

    J            1.15        300       2510        119      0.92-1.38    18.1%
    HK           2.08        150       2250        133      1.62-2.54               31.1%      19.6%

                    Table 6: OH Airglow Contamination for Option B Gratings
                  c        l/mm         R         v        Range         Percentage OH Lines
                 (m)                            (km s-1)     (m)          J        H        K

    J1           1.07        600       3830        78.4     0.93-1.21    10.3%
    J2           1.22        600       4420        67.8     1.09-1.35    13.8%
    H            1.62        400       3870        77.5     1.41-1.83               15.7%
    K            2.22        300       4020        74.7     1.95-2.50                          10.6%

    J’           1.10        300       1780        168      0.79-1.40    17.8%
    HK           1.95        150       1570        191      1.34-2.57               39.0%      21.2%

    K1           2.12        497       6620        45.3     1.98-2.25                           6.7%
    K2           2.32        497       7410        40.5     2.19-2.44                           4.4%


1.6.2.4 Which Grating Option?
NIFS will accommodate seven gratings and a direct viewing mirror. Option A uses a selection of six
gratings. Option B uses up to eight gratings, but with scope for significantly reducing this number. The
grating selection has not been constrained further for the purpose of the Conceptual Design Review.
Instead, we seek input from the review committee in making the decision between grating options A
and B, and on which of the option B gratings should be omitted. Obvious choices for the latter are a)
omit the low resolution J’ and HK gratings on the basis of low efficiency and poor OH rejection
potential, b) omit the high resolution K1 and K2 gratings on the basis of insufficient discrimination
from the K grating, or c) omit the J1 grating on the basis of inappropriate wavelength range.

It should be noted that the spectrograph required for option B is only about 0.75 times the size of that
for option A. The larger spectrograph is the baseline design described in this report.

The Richardson Grating laboratory catalog numbers and master dimensions of the gratings discussed
are listed in Table 7 for future reference.
                    Table 7: Grating Catalog Numbers and Master Dimensions.
                                         GRATING          CATALOG
               GRATING     GROOVES         BLAZE          NUMBER             RULED AREA
                            (l/mm)        (degrees)                           (mmmm)
               J1             600          17.5         35-53-*-520            154206
               J2             600          22.0         35-53-*-560            154206
               H              400          18.6         35-53-*-650            102102
               K              300          17.5         35-53-*-770            154206
               Kw             200          10.0         35-53-*-630             8484
               J              300          10.4         35-53-*-640             8484
               HK             150           8.6         35-53-*-760            154206
               J’             300           8.6         35-53-*-510            102128
               K1,K2          497          34.0         35-53-*-231            102102
               Jh             830          30.0         35-53-*-525            154206
               Hh             600          28.7         35-53-*-550            154206


1.6.3 Grating Anamorphic Magnification Effects
The spectrograph described in this document has the gratings in blaze-to-collimator configuration. It
has an Ebert angle  = 30° and is optimized for grating angles  ~ 20°. The anamorphic magnification
of these gratings is then:
                                                  cos   2
                                          M
                                                  cos   2
which for the adopted parameters gives M = 0.82. An alternative approach is to operate the gratings in
blaze-to-camera configuration. Then  = 30° and  ~ -20°, and the anamorphic magnification value is
inverted to give M = 1.22.

Either way, the angular resolution in the spatial direction cannot be the same as it is in the spectral
direction. For the angular slitlet width x = 0.5 rad (~0.1), the two-pixel angular resolution in the
spatial direction is 0.41 rad (~ 0.082) for the former case, and 0.61 rad (~ 0.122) for the latter case.

A consequence of this is that both the field size and the number of image slicer slitlets required to
produce a square field, N, are altered by the anamorphic magnification of the grating, M. From the
analysis of the image slicer field geometry (§Error! Reference source not found.), it can be seen that
for a square field and a fixed number of detector pixels
                                              N M .
For the blaze-to-camera configuration, the number of image slicer slitlets changes from 29 to 35, and
the field size changes from ~ 14.5 rad (~ 3.0) square to ~ 17.5 rad (~ 3.6) square.

To maintain spectral resolution with this change, the length of the beam footprint on the grating must
stay the same. In terms of beam diameter, the collimator and camera beams are swapped. The
collimator beam becomes larger, and the camera beam becomes smaller. To maintain aberrations at the
same level in the IFU and collimator and the pixel scale in the camera, the focal ratios of both would be
retained. The IFU and collimator would therefore be longer, and the camera shorter. This would make
the already long IFU and collimator of the baseline spectrograph design difficult to accommodate in the
duplicate NIRI cryostat, unless the lower-resolution option (§1.6.2.2) was also adopted.

In consideration of these issues, it has been decided that the blaze-to-collimator configuration is
preferable.

1.6.4 Scattered Light
Scattering at the grating may prove to contribute significantly to near-angle scattering of OH airglow
line emission into the adjacent continuum. This would degrade the efficiency with which airglow
emission-lines can be rejected. The Richardson Grating Laboratory has been asked to quantify this
effect. No data are currently available. However, replicated gratings may actually have lower scattered
light levels due to the smoothing of surface defects by the epoxy and inversion of the grooves. In any
event, short of ruling new master gratings, there is nothing that can be done to reduce this scatter.

1.6.5 Grating Manufacture
Richardson Grating Laboratories can produce replica gratings on client supplied substrates. The
recommended substrate for cryogenic applications is aluminum. The surface roughness tolerance is 25
m RMS. The perpendicularity tolerance between adjacent sides is 0.1. The grating side of the
substrate must have a 45 bevel edge, with 1.5 mm face width.

1.7 Order Blocking Filters
Order blocking filters are required to prevent out-of-band light reaching the detector. Order blocking
filters suitable for the H and K gratings have already been purchased from NDC Infrared Engineering
as part of a joint NIRI/GNIRS/NIFS acquisition. Parameters for these filters are listed in Table 8.
Transmission curves are plotted in Figure 27. Availability of order sorting filters for other gratings
depend on the grating option selected (§1.6.2). The J2 grating in option A can use the photometric J
filter offered as a catalog item by OCLI (Table 8). Order blocking filters for other gratings will have to
be custom manufactured. Barr Associates Inc. will do this for ~ $US4000 per filter.

                          Table 8: NIFS Order Blocking Filter Parameters
                                       J2                  H                   K

        Supplier                       OCLI                NDC IR Eng.         NDC IR Eng.
        50% Cut-On (m)                1.1  0.01          1.47  0.015        1.92  0.019
        50% Cut-Off (m)               1.4  0.01          1.80  0.018        2.52  0.025
        Peak Transmission              >60%                >75%                >75%
        Blocking                       10-3                10-4                10-4
        Diameter (mm)                  25                  25                  25
        Status                         Catalog item        In-hand             In-hand




Figure 27: Transmission curves for H (left) and K (right) grating order blocking filters purchased
from NDC Infrared Engineering. The band passes of the H and K gratings (option A) are shaded.


1.8 Optical Coatings

1.8.1 Mirrors and Gratings
The NIFS optical path includes a large number of mirrors. High reflectivity mirror coatings must be
specified to maximize the system throughput. In making the choice of coatings, consideration should
also be given to the cryogenic vacuum environment and the choice of substrate material. Grade 6061
aluminum alloy is proposed for the IFU components because diamond machined is required to produce
the surfaces. Fused silica or diamond turned aluminum alloy is proposed for other mirror substrates.
Given that the coatings will be protected by their vacuum environment, the preferred coatings are bare
gold and silver. Reflectivities for these metals are shown in Table 9 (R. N. Wilson, Reflecting
Telescopes, Optics II, Table 6.1). Silica and aluminum alloy are both suitable substrates for these
coatings. Consideration should also be given to protected silver coatings where reflectivities are
equivalent to fresh bare silver. Examples of protected silver and gold coatings are the FSS-99 and FSG-
98 coatings from Denton Vacuum. Similar coatings can be applied in Australia by at least two vendors.
The baseline mirror coating should be ion-assisted deposited (IAD) gold, as this will give a low scatter,
durable, coated surface with reflectance values as listed in Table 9. For metal substrates, such as
diamond turned aluminum with nickel coating, a further option is the new electrochemical process
trademarked as LaserGold. This is available in the USA from Epner Co. It produces a hard, durable
coating, again with the reflectance values listed in Table 9.

                                  Table 9: Reflectivity of Freshly Evaporated Metals
                            Wavelength                Ag Reflectivity              Au Reflectivity
                              (m)                        (%)                          (%)

                                0.9                        99.3                         98.4
                                1.0                        99.4                         98.6
                                1.5                        99.4                         99.0
                                2.0                        99.4                         99.1
                                3.0                        99.4                         99.3


1.8.2 Lenses
The concentric IFU system uses lenses made from CaF2, silica, and ZnSe. The linear IFU system also
uses BaF2 and sapphire. Standard anti-reflection (AR) coatings are proposed for the CaF2 and BaF2
elements (96% transmission) and silica (96% transmission) elements. These can be applied at
Avtronics in Australia.

Special AR coatings are available from Janos Technology Inc for ZnSe and sapphire. Their
performance is shown in Figure 28 and Figure 29, respectively.


                  10
                  9
                  8
Reflectance (%)




                  7
                  6
                  5
                  4
                  3
                  2
                  1
                  0
                    750      1000     1250     1500     1750      2000    2250     2500     2750       3000
                                                      Wavelength (nm)

                  Figure 28: Reflectance of AR coating for ZnSe available from Janos Technology Inc.
                     10
                     9
                     8
 Reflectance (%)


                     7
                     6
                     5
                     4
                     3
                     2
                     1
                     0
                       750      1000     1250     1500     1750     2000     2250     2500    2750     3000
                                                         Wavelength (nm)

                   Figure 29: Reflectance of AR coating for sapphire available from Janos Technology Inc.


1.9 System Throughput

NIFS is required to have an optical throughput of > 15% in the wavelength range 1-2.5 m for the
complete optical train, including, but not limited to, the telescope, gratings, filters and the detector, but
not including the adaptive optics train. Optical throughput is calculated for the concentric IFU design
assuming 3.2 mm high pupil mirrors and 50 mm long gratings.

1.9.1 Throughput Model Assumptions
The optical throughput has been modeled by considering the reflection losses at each optical surface.
All mirrors outside the cryostat are assumed to be coated with protected silver. Except for the ZnSe
meniscus lens in the camera, all lenses are assumed to be AR coated with a single layer of MgF 2 with a
design wavelength of 1.50 m. Reflection losses for these surfaces are modeled based on the
wavelength-dependent refractive indices of the coating and lens materials using single layer AR
coating theory (Melles Griot Optics Guide 5). The coating for the ZnSe lens is assumed to be a
proprietary system available from Janos Technology Inc. (Figure 28). The order blocking filters are
required to have optical throughputs > 80% over their spectral bands. We adopt a value of 80%,
independent of wavelength. Diffraction losses at the NIFS pupil mirrors and grating are discussed in
§1.4. These depend on wavelength and field position across each slitlet; they are typically <3%, and
always less than 10% for 50 mm long gratings.

The diffraction grating efficiencies are a major uncertainty in the throughput budget (see §1.6).
Relative efficiency curves for several of the proposed moderate resolving power gratings obtained from
the Richardson Grating Lab. are > 80% over the wavelength range of interest for NIFS. However,
relative efficiencies for the low resolving power grating options are typically ~ 50%, and the high
resolving power gratings probably have intermediate efficiencies. We therefore adopt a typical grating
efficiency of 75% for the present purpose.

We adopt the detector quantum efficiency function for a HAWAII-1 array published on the Rockwell
Science Center FPA web pages (Error! Reference source not found.). As mentioned in §Error!
Reference source not found., the HAWAII-2 array to be used in NIFS is expected to have similar
quantum efficiency, and Rockwell arrays based on CdZnTe technology may have higher quantum
efficiencies of ~ 85%.

We assume that the bulk absorption properties of the transmissive components are negligible. No
allowance is made for absorption or scattering in the Earth’s atmosphere.
1.9.2 System Throughput Summary
The NIFS system throughput budgets are summarized in Table 10 for the concentric IFU design with a
single mirror focal ratio converter, and in Table 11 for the linear IFU design with an Offner relay input.
            Table 10: NIFS System Throughput Budget for the Concentric IFU Design
                 Component                     Coating               Transmission
                                                                1.00m   1.65m   2.20m


                 Telescope Primary             O/C Silver       0.979    0.986    0.987
                 Telescope Secondary           O/C Silver       0.979    0.986    0.987
                 ISS Fold Mirror               O/C Silver       0.979    0.986    0.987
                 Cryostat Window               CaF2/MgF2        0.949    0.960    0.955
                 Pick-Off Mirror               Gold             0.986    0.990    0.991
                 F/# Converter Mirror          Gold             0.986    0.990    0.991
                 Cold Stop Mirror              Gold             0.986    0.990    0.991
                 Filter                        …                0.80     0.80     0.80
                 Fold 1 Mirror                 Gold             0.986    0.990    0.991
                 Fold 2 Mirror                 Gold             0.986    0.990    0.991
                 Fold 3 Mirror                 Gold             0.986    0.990    0.991
                 Image Slicer: Reflectivity    Gold             0.986    0.990    0.991
                 Image Slicer: Diffraction     …                0.99     0.98     0.97
                 Pupil Mirror Array Mirror     Gold             0.986    0.990    0.991
                 Field Mirror Array Mirror     Gold             0.986    0.990    0.991
                 Fold 4 Mirror                 Gold             0.986    0.990    0.991
                 Collimator Mirror             Gold             0.986    0.990    0.991
                 Fold 5 Mirror                 Gold             0.986    0.990    0.991
                 Collimator Corrector Lens     CaF2/MgF2        0.949    0.960    0.955
                 Grating: Efficiency           …                0.75     0.75     0.75
                 Grating: Reflectivity         Gold             0.986    0.990    0.991
                 Camera Lens 1                 CaF2/MgF2        0.949    0.960    0.955
                 Camera Lens 2                 Silica/MgF2      0.950    0.951    0.950
                 Camera Lens 3                 ZnSe/Janos       0.994    0.998    0.986
                 Camera Lens 4                 CaF2/MgF2        0.949    0.960    0.955
                 Camera Lens 5                 Silica/MgF2      0.950    0.951    0.950
                 Detector QE                   …                0.518    0.583    0.623

                 TOTAL (without AO)                             0.175    0.221    0.229

                 ALTAIR                                         0.773    0.825    0.843
                 TOTAL (with AO)                                0.135    0.182    0.193
              Table 11: NIFS System Throughput Budget for the Linear IFU Design
                Component                     Coating               Transmission
                                                               1.00m   1.65m   2.20m


                Telescope Primary             O/C Silver       0.979    0.986    0.987
                Telescope Secondary           O/C Silver       0.979    0.986    0.987
                ISS Fold Mirror               O/C Silver       0.979    0.986    0.987
                Cryostat Window               CaF2/MgF2        0.949    0.960    0.955
                Pick-Off Mirror               Gold             0.986    0.990    0.991
                Offner Primary                Gold             0.986    0.990    0.991
                Offner Secondary              Gold             0.986    0.990    0.991
                Offner Primary                Gold             0.986    0.990    0.991
                Filter                        …                0.80     0.80     0.80
                Fold Mirror                   Gold             0.986    0.990    0.991
                F/# Converter Mirror          Gold             0.986    0.990    0.991
                Image Slicer: Reflectivity    Gold             0.986    0.990    0.991
                Image Slicer: Diffraction     …                0.99     0.98     0.97
                Pupil Mirror Array Mirror     Gold             0.986    0.990    0.991
                Field Mirror Array Mirror     Gold             0.986    0.990    0.991
                Field Lens 1                  Sapph./Janos     0.987    0.982    0.994
                Field Lens 2                  Silica/MgF2      0.950    0.951    0.950
                Collimator Fold Mirror        Gold             0.986    0.990    0.991
                Collimator Lens 1             Silica/MgF2      0.950    0.951    0.950
                Collimator Lens 2             ZnSe/Janos       0.994    0.998    0.986
                Collimator Lens 3             BaF2/MgF2        0.948    0.966    0.958
                Grating: Efficiency           …                0.75     0.75     0.75
                Grating: Reflectivity         Gold             0.986    0.990    0.980
                Camera Lens 1                 CaF2/MgF2        0.949    0.960    0.955
                Camera Lens 2                 Silica/MgF2      0.950    0.951    0.950
                Camera Lens 3                 CaF2/MgF2        0.949    0.960    0.955
                Camera Lens 4                 ZnSe/Janos       0.994    0.998    0.986
                Camera Lens 5                 Sapph./Janos     0.950    0.951    0.950
                Detector QE                   …                0.518    0.583    0.623

                TOTAL (without AO)                             0.159    0.201    0.205

                ALTAIR                                         0.773    0.825    0.843
                TOTAL (with AO)                                0.123    0.166    0.173


1.10 System Emissivity
The cryostat window is the dominant component to the instrumental effective emissivity. The
absorption coefficient of crystal CaF2 varies from ~ 0.4910-3 cm-1 to ~ 5.210-3 cm-1 depending on
supplier. Adopting the high value leads to an emissivity of ~ 0.010 for the 20 mm thick cryotat
window. Assuming that the pick-off mirror, baffles, and other optical components each have a
contribution an order of magnitude lower than the window (i.e., 0.001 emissivity), the total emissivity
should be ~ 0.10-0.11%.

1.11 Ghost Images
Ghost images can be a problem in axially symmetric refractive systems, such as the NIFS camera. In
general, several different effects produce ghosts:
 A proximity focused halo is produced when light from a bright point image is reflected off the
    detector and then reflected back onto the detector by a close refractive surface.
 When the detector lies close to the reflected focal surface of a refractive system, some of the field
    light reflected from the detector forms a ghost image of the field that is rotate by 180°.
   Some light from the whole field forms a bright spot at the center of the field when reflections from
    refractive surfaces form a pupil image on the detector.

The camera design shown for the concentric IFU system has been checked for ghosts of these types,
and no significant effects have been found. This is demonstrated in Table 12 which shows the ratio of
ghost intensity to image intensity for a one-pixel image in the center of the field for each camera
surface. This assumes that the detector quantum efficiency is 60% and that the reflectivity of each
camera lens surface is 2%. The camera surfaces are numbered from the grating.

             Table 12: Ghost Image Intensities for the Concentric IFU Design Camera
                                 Camera                Ghost Intensity
                                 Surface                   Ratio

                                     10                   4.510-8
                                     9                    9.110-9
                                     8                    7.910-10
                                     7                    5.710-9
                                     6                    1.910-10
                                     5                    2.510-10
                                     4                    3.210-10
                                     3                    5.310-11
                                     2                    5.310-11
                                     1                    1.410-10


1.12 Scattered Light
The main concern with scattered light is the effect of the diamond turned surfaces. The use of diamond
turned surfaces is practically unavoidable for the three IFU components, and it also offers advantages
for other mirrors in the system. By the nature of the process, diamond machining produces surface
irregularity in the form of regularly spaced grooves. The effect is minimized by using a small tool feed
and large tool tip radius. Conventionally, the feasible limits for these are taken to be ~ 1 m for the
feed, and ~ 1 mm for the tip radius. Geometrically, the maximum surface slope error that this produces
is about 0.5 mrad.

This grooving effect tends to be reduced by burnishing because aluminum alloy is a soft material. On
the other hand, alloying elements tend to segregate and form hard inclusions, and it is these that
apparently cause much of the surface roughness seen on diamond machined aluminum alloy mirrors.
The alloy grade L111 is proposed to minimize this effect.

For the mirrors placed at field images (i.e., the image slicer and the field mirror array), scatter is of
little consequence because it produces only a slight degradation of focal ratio. For mirrors not placed at
field images (i.e., the pupil mirror array, and any other mirror for which diamond machining is chosen),
this roughness will cause field image degradation at some level. Detailed assessment of this has not
been done, but conventionally the effect is regarded as acceptable for instruments operating at near-
infrared wavelengths.

Diamond turned surfaces are expected to have an RMS surface roughness of ~ 10 nm. The total
integrated scatter, TIS, from a random surface of RMS roughness  is given by
                                                   4 
                                                            2

                                            TIS       
                                                    
which for  = 10 nm and  = 1.65 m gives TIS = 0.006. This has negligible effect on system
throughput.

Near-angle scatter is more relevant than total integrated scatter because light scattered at small angles
to the optical axis may illuminate the detector. The dominant source of near-angle scatter is expected to
be the diffraction grating. The intensity of this scattered light is more difficult to estimate and will
ultimately depend on the detailed nature of the surface and the quality of diffraction gratings used. The
Richardson Grating Lab. can measure the scattering properties of gratings they replicate.

1.13 Baffling
Light scattered at surfaces must be blocked by baffles to prevent it reaching the detector. It is proposed
to baffle the instrument chamber by partitioning it into many zones by means of thin blackened panels,
with the beam being passed though holes with no more clearance than is necessary. The rational for
this is that it forms large cavities with small apertures, and the entering radiation is widely spread to
reduce flux, as for a black body cavity at low temperature. Baffles closely conforming to the beam
should be avoided where possible because stray light tends to be intercepted at grazing incidence,
reflected, and contained within the beam space. The folded nature of the spectrograph will require
some close baffling between adjacent beams.

An area of particular concern is the zone containing the input field mask and the cold stop in the
proposed concentric IFU system, because the former is the source of all spurious radiation, and the
latter is the main means of excluding it. These components are in close proximity, and their baffling
isolation needs further careful consideration. An alternative approach is to add an Offner relay system
to form a more isolated cold stop, as is done in the linear IFU system. The cost of this is more
complexity and more optical surfaces.

1.14 Blackening
Surfaces within the cooled chamber of the instrument should have high emissivity to suppress scattered
radiation. Many proprietary infrared blacks are available for this purpose, such as Chemglaze Z306 and
3M Black Velvet paint1. Conventional matt black acrylic paint has also be used at RSAA for this
purpose, and found to be effective.

1.15 Thermal Stability
Considerable thermal strain will occur in the cooled structure of the instrument between ambient and
operating temperatures. To minimize the additional difficulties caused by differential strain, as much of
the instrument as possible should be made of a common material. The material of the cold work surface
is already specified to be grade 6061 aluminum alloy. This has many properties that are desirable for an
instrument of this type, including its high conductivity and suitability for diamond machining, so this is
proposed as the common structural material. Based on data for this material presented in the American
Institute of Physics Handbook, the thermal strain with respect to ambient temperature at an operating
temperature of T is given by

  4.187 10 3  7.9988 10 10 T 3  4.10149 10 12 T 4  8.53866 10 15 T 5  6.5634 10 18 T 6

accurate to five decimal places for temperatures from 0 to 400 K. This thermal strain is –0.00406 K-1 at
T = 60 K. The strain equation can be differentiated to give the corresponding coefficient of expansion.
At T = 60 K the coefficient of expansion is 5.610-6. Over characteristic path lengths within the
instrument of about 500 mm, the contraction will be ~ 2.0 mm. Over a characteristic lens housing
diameter of 100 mm, the contraction will be ~ 0.4 mm. Other materials used for optical components
have considerably lower contraction, so it is clear that the difference must be accounted for in design
with regard to both optical performance and optical component mounting. Temperature effects on
refractive index must also be accounted for. Cryogenic refractive indices for CaF 2, BaF2, and ZnSe
have been published by Tropf (1995).

1.16 Thermal Radiation
The spectrograph chamber is almost a fully enclosed cavity held at a constant temperature, so the
thermal radiation flux within it will be that of a black body. Analysis on this basis (see §Error!

1
    http://electro-optical.com/bb_rad/emissivity/matlemisivty.htm,
    http://www.tak2000.com/data/finish.htm#Black
Reference source not found.) indicates that the spectrograph temperature must be held below ~ 135 K
to ensure that the total radiation flux remains significantly below the expected detector dark current for
a 2.5 m cut-off detector. No problems are foreseen in achieving this spectrograph temperature. A
more stringent limit of < 65 K would be imposed if NIFS were to use a 5.5 m cut-off detector.

1.17 Focus Requirements
The chromatic correction in the proposed camera allows the spectrograph to operate over the whole
wavelength range without re-focus. To achieve this, the camera was designed for a collimated input
beam. In fact, the input beam has slight chromatic de-focus at the ends of the wavelength range (about
± 1/3 pixel) caused by the refractive corrector of the collimator. Revision of the camera design should
allow even this effect to be compensated.

It is therefore proposed that no remote focus control facility be included. Rather, it is intended that the
system be designed for correct focus, with the facility for manual correction based on initial cold focus
position measurement.

The objective is to simultaneously achieve three focus conditions.

   The field mask should be focussed on the detector to provide sharp masking and facilitate optical
    tests using special field masks.
   The field mirror array should be focussed on the detector to provide sharp IFU channel separation.
   The grating beam should be properly collimated to avoid astigmatism.

The depth of focus corresponding to a fixed angular blur on the sky is proportional to the square of the
focal ratio at the focus concerned. For a blur of 0.25 rad (1 pixel), the depth of focus is 0.51 mm at the
field mask and at the field mirror array (f/16.2), 130 mm at the image slicer (f/256), and 0.24 mm at the
detector (f/10.9). For corresponding collimation accuracy, the axial position accuracy for the collimator
is also 0.24 mm. The locations of these components can be readily controlled to finer accuracy than
indicated here.

1.18 Field Acquisition
The case for a field-viewing plane mirror in the grating wheel is twofold; it would allow the
undispersed “staircase” slit image to be recorded to aid in acquiring faint objects, and it could also be
used to check the alignment of the IFU. Of course, a field-viewing mirror is unnecessary if sufficiently
accurate object and guide star coordinates are known in advance. However, many situations can be
envisaged where it will be advantageous to image the sky directly through NIFS to confirm critical
positioning or alignments. The data cube generated from NIFS spectral data can be collapsed in the
spectral direction to produce an image of the sky. However, this image inherits the dark current and
read noise from all 2048 spectral pixels recorded at each spatial location. It is more efficient to obtain
an image by replacing the grating with a plane mirror and directly recording the undispersed image of
the “staircase” slit. Wavelength stability should not be affected by rotating the grating wheel between
science observations since the grating angles will be fixed and the wavelength calibration should not be
sensitive to small positioning errors of the grating perpendicular to the optical axis.

Imaging the “staircase” slit directly will allow the alignment of the IFU to be inspected as well as
providing a spatial calibration of the IFU pattern on the detector. This is not a strong motivation for
including a field-viewing mirror since similar information can be obtained from an arc lamp spectral
image without using a field-viewing mirror.

1.19 Optical Tolerances

1.19.1 Focal Ratio Converter and IFU Optics
As proposed, the pupil and field mirror arrays will be diamond turned as monoliths. The relative
alignment of the elements will therefore match the surface figure accuracy (~ 40 nm) that this
technology produces for a single surface, and not limit performance. The mirror arrays can then be
treated as single components with regard to alignment.
Likewise, the proposed method of manufacture for the image slicer makes relative alignment of the
slitlets intrinsically accurate with regard to tilt in the spectral direction. However, fanning angle errors
in the spatial direction must not cause significant pupil image displacements on the pupil mirror array.
Limiting these displacements to about 15% of the clearance between the pupil image and the pupil
mirror array element boundaries requires a fanning angle tolerance of ±30 rad. This must be
maintained during cooldown to cryogenic temperatures.

Many dimensions of the focal ratio converter and IFU mirrors are not critical because they perform
their functions as single elements. For example, a deviation from the design curvature causes a focus
displacement that can be compensated for in the mounting position. They are also arranged to achieve
adequate performance with the substantial tilts required for beam clearance, and their aberrations are
therefore very tolerant of the small tilt errors that can be expected after alignment. The alignment
tolerances are determined by beam capture requirements rather than aberrations.

1.19.2 Collimator
A tolerancing analysis has not yet been done for the collimator, but no problems are expected because
it takes a simple concentric form.

1.19.3 Camera Optics
A tolerance analysis of the camera optics indicates that the only demanding elements are the ZnSe
meniscus element and, to a lesser extent, the silica field flattener. Otherwise, the required tolerances are
easily achieved by standard techniques for precision optics. The standard tolerances proposed include
±0.1% for curvature radius, 1/8 wave p-v figure error at 0.6 m wavelength, ±0.1 mm for thickness,
and ±0.03 mm for runout.

Some tolerances for the ZnSe element are critical unless the design of the other elements is re-
optimized for the actual dimensions of this element. Otherwise, the curvature tolerance must be
reduced to ±0.05%, the thickness tolerance to ±0.025 mm, and the runout tolerance to ±0.01 mm. A
similar tolerance is required for the runout of the silica field flattener.

Mounting the lenses in an aluminum alloy barrel, arranged to provide close fits after thermal
contraction, with a reasonably precise housing tolerance of ±0.015 mm will provide adequate control of
lens decenter and tilt. Standard instrument making tolerances for spacer thicknesses will provide
adequate axial positioning accuracy. Mounting accuracy is most critical for the ZnSe meniscus
element, but is easily met.

1.19.4 Optical Tolerance Budget
The procedures outlined in the Gemini System Error Budget Plan (Oschmann 1997, SPE-S-G0041)
have been followed in defining a preliminary optical tolerance budget for the concentric IFU design.
Optical aberrations are specified in terms of RMS wavefront error in nm. The Strehl ratio, S, achieved
is given by
                                                                 2
                                                        2 
                                                           
                                                         
                                               S ~e
where  is the RMS wavefront error in nm and  is the wavelength in nm, and the approximation is
valid for Strehl ratios larger than ~0.2. The bottom-up error budget is defined assuming that all
reflective elements use raw diamond machined surfaces (no post-polishing) with an RMS surface error
of 40 nm. The associated wavefront error is doubled on reflection. Commercial transmissive elements
(i.e., the cryostat window and the ZnSe camera lens) are assumed to have a RMS figure error of /30 in
the visible or ~ 20 nm. Transmissive elements manufactured in the RSAA Optical Workshop can be
tested to an RMS accuracy of ~ /30 (~ /8 p-v). We adopt this figure error for the camera lenses,
assuming they will be manufactured at RSAA. The order sorting filters have been specified to have a
/4 flatness at the central wavelength of the filter (i.e., ~ 1.6 m). The grating is assigned an arbitrarily
higher figure error due to the replication process. Different optical elements contribute to wavefront
errors at the detector in different ways (e.g., an element at a pupil has more effect than an element at a
focus). A detailed sensitivity analysis has not been performed yet. Instead, we assume that figure errors
  contribute to wavefront errors in proportion to the fractional area of the element illuminated by the
  beam. The concentric IFU optical design produces a RMS wavefront error at the detector of ~ 30 nm.
  This ignores the complicating effects of enlarged pupil sizes due to slit diffraction. The error budget
  includes an allowance for overall optical alignment of /10 in the visible or ~ 60 nm. The individual
  RMS wavefront errors are combined to form the RSS sum listed in Table 13.

           Table 13: Preliminary Optical Tolerance Budget for the Concentric IFU Design
Component                                    RMS Figure Error                           RMS Wavefront
                                                                                           Error
                                      Quality                      (nm)                     (nm)

Cryostat Window                     /30 (vis)                     20                           2
Pick-Off Mirror                 Diamond machined                   40                           20
F/# Converter Mirror            Diamond machined                   40                           60
Cold Stop Mirror                Diamond machined                   40                           80
Filter                               /4 (IR)                      400                          10
Fold 1 Mirror                   Diamond machined                   40                           8
Fold 2 Mirror                   Diamond machined                   40                           8
Fold 3 Mirror                   Diamond machined                   40                           8
Image Slicer Mirror             Diamond machined                   40                           0
Pupil Mirror Array Mirror       Diamond machined                   40                           80
Field Mirror Array Mirror       Diamond machined                   40                           0
Fold 4 Mirror                   Diamond machined                   40                           8
Collimator Mirror               Diamond machined                   40                           80
Fold 5 Mirror                   Diamond machined                   40                           80
Collimator Corrector Lens           /30 (vis)                     20                           20
Grating                            Replicated                      25                           50
Camera Lens 1                       /30 (vis)                     20                           20
Camera Lens 2                       /30 (vis)                     20                           20
Camera Lens 3                       /30 (vis)                     20                           20
Camera Lens 4                       /30 (vis)                     20                           12
Camera Lens 5                       /30 (vis)                     20                           6

Optical Design                                                                                  30
Optical Alignment                                                                               60
OIWFS Stability                                                                                 20

RSS TOTAL                                                                                      198


  A top-down optical tolerance budget can be defined using the general scaling (Oschmann 1997, SPE-S-
  G0041) that a 50 nm RMS wavefront error corresponds approximately to a 0.01 degradation in 50%
  encircled energy diameter at 2.2 m2. Spot diagrams for the concentric IFU design, including
  diffraction effects, place 90% of the light within one 0.04 pixel (§1.5). Manufacturing tolerances and
  alignment errors may degrade this to 50% encircled energy within 0.04, which is converted to a RMS
  wavefront error of ~ 200 nm using the general scaling approximation. The NIFS FPRD specifies a
  flexure between the OIWFS and the science detector of < 0.1 pixel/hr, i.e., < 0.004/hr. This is equated
  to a wavefront error of ~ 20 nm/hr using the general scaling relation. This tracking error makes little
  difference to either tolerance estimate, but is included in the bottom-up RSS total in Table 13. Both the
  bottom-up and the top-down optical tolerance estimates suggest that image qualities suitable for the
  near diffraction-limited sampling of NIFS can be achieved with routine, high quality optical surfaces
  and alignment procedures.


  2
    We adopt 50 nm RMS wavefront error (Oschmann 1999, priv. comm.) rather than the 100 nm quoted
  in Oschmann 1997, SPE-S-G0041.
1.20 Alignment Procedures
It is proposed that the optical system be aligned with methods similar to those developed for CASPIR
(a cryogenic near-infrared imager built by RSAA). Two general techniques are applicable. One
involves sightings made through a micro-alignment telescope. The second involves the recording of
images on the detector with various test arrangements placed in the beam. Detailed planning must
await further instrument design, but some basic principles are described as follows.

The locations of some components can be determined by precision machining of the mount, without
adjustment, because of the broad tolerance. For example, the separation tolerances for the field mask,
focal ratio converter, cold stop, and image slicer are generous.

Tilt error of the focal ratio converter mirror can be seen by mounting an alignment telescope in front of
the field mask station and sighting the cold stop image formed by the focal ratio converter. The micro-
alignment telescope can then be re-focused on the field mask, where there will also be an image of the
image slicer. Eccentricity between the field mask and image slicer image is then a measure of cold stop
tilt error.

The IFU arrays are manufactured as precise monoliths, so avoiding the problem of relative alignment.
For bulk alignment, the component location can be set by means of mechanical measurement, with the
orientations then adjusted to annul sighting errors, as seen with the micro-alignment telescope still
mounted at the front of the instrument. The pupil array mirror orientations might best be adjusted by
replacing the image slicer with a single mirror of the same curvature and sighting a target point on the
central element of the field mirror array. Within limits, this sighting is not affected by the tilt of the
replacement image slicer mirror.

The image slicer could then be restored and its orientation adjusted to annul eccentricity of the pupil
mirror array image. This might best be done with all but the central slitlet masked. Likewise, the
orientation of the field mirror array could then be adjusted to annul eccentricity of a grating image.
Suitably illuminated targets would have to be provided at each of these object points.

The Bouwers collimator has no axis, and the only alignment requirement is that its two elements have
their curvature centers coincident on the grating center. With appropriate allowance made for thermal
strain, this can be set at ambient temperature by mounting the micro-alignment telescope at the grating
station and sighting auto-reflection images formed by the elements. The auto-reflection image formed
by the AR-coated corrector will be dim, but should still be visible with dark masking of the
background.

Alignment of the camera lenses can be achieved by relying on th mechanical precision of the mounting
barrel. The mounting surfaces in this will be lathe turned about a single spin axis, and so will be
intrinsically accurate.

Axial position errors can be measured in cold conditions by using the detector. Focus error at the
detector could be measured by using a slit in the field mask and a two-aperture Hartmann mask over
the mirror available in the grating turret. Errors in the collimation of the grating beam can be
determined by placing a pin hole at the field mask position, deploying the mirror in the grating turret,
and measuring astigmatism in the image.

1.21 Manufacturing Feasibility

1.21.1 IFU Optics
One of the challenges with this project is to produce the IFU. It has been concluded that diamond
machining is the most suitable method of producing the optical surfaces required for all three
components (image slicer, pupil mirror array, and field mirror array). A suitable grade of aluminum
alloy (6061 or L111) is proposed as the material. Discussions held with the diamond turning company
P-O E indicate that the proposed machining methods are all feasible.
1.21.1.1 Image Slicer
For the concentric IFU system design, the image slicer mirrors are each 1.024 mm thick, and have an
active length of ~ 30 mm. They each have a spherically concaved surface with the radius of curvature
being ~ 623 mm. The stack of mirrors is fanned at a rate of ~ 0.127° per slitlet. The geometry of the
surfaces is such that, without fanning, they would all be part of a single sphere. This is a feature that
facilitates manufacture. It is proposed that the stack of aluminum alloy plates be equipped with an
accurate dual-mode registration system, one corresponding to the un-fanned configuration, and the
other to the fanned configuration. The face of the stack would be diamond turned to the common
spherical figure while clamped in the first mode, then re-assembled in the second mode.

The positions of the slitlet curvature centers should be controlled to ~ 20 m with respect to each other.
Given that the radius of curvature is ~ 623 mm, the tilt tolerance is ~ 30 rad.

Several registration systems are feasible. One that has already been successfully applied to a
mechanical prototype uses two pairs of precision dowel pins. With careful design, pin position can be
controlled to about 1 m, so a pin separation of ~ 30 mm should achieve the required tilt precision of
30 rad. Pin separations somewhat greater than this are feasible.

A similar effect could be achieved with a dual-mode ramp.

An alternative approach is that adopted for the UIST IFU design. Here, the slitlet plates would all be
made to different lengths, with the increment being ~ 1.38 mm. They would be mounted in a
rectangular recess. For diamond turning the common spherical surface, they would be clamped against
one end of the recess. To fan the surfaces, they would then be slid to the other end of the recess and re-
clamped. The difference in length between the shortest and longest plates would be ~ 38.67 mm. The
lengths would have to be controlled to an accuracy of ~ 20 m.

Control of the slitlet plate thickness can be had by the rolling of slightly oversized stock sheet. A
supplier of laboratory grade metal materials has already offered this service. There is some doubt about
the suitability of rolled sheet for diamond turning, and so an alternative approach is to adjust the
spectrograph design to use a stock product, after the exact thickness has been determined.

1.21.1.2 Mirror Arrays
The alignment of the array elements must be accurate. The tilt error corresponding to one pixel of
image shift is ~ 570 rad for the pupil mirror array elements. It is proposed that each mirror array be
machined as a monolith to achieve adequate alignment control of the mirror array elements. By
machining in a single set-up, the accuracy that can be achieved across a single optical element can be
applied to the whole array, and so relative misalignment within the array is effectively eliminated.

An additional consideration in adopting a monolith is that the depth of the array elements must be well
controlled. The position of the boundary between adjacent elements is very sensitive to depth
differences because the curved elements are shallow. For the field mirror array, the depth error
corresponding to a boundary displacement of one pixel (18 m) is only 0.64 m. Again, however, this
is not a problem if the machining is done in one set-up.

The monolith would take the form of a rectangular plate with the array surfaces machined into one of
the long narrow faces. Such plates can be mounted and adjusted relatively easily.

An obvious method of machining a monolithic array is to mount the blank to a lathe chuck so that it
lies parallel to the axis of rotation, but is radially offset by about the required radius of curvature of the
element surfaces. As the chuck is spun, the tool is traversed along the required longitudinal profile of
the array. This procedure can be used to generate truly spherical (or toric) surfaces, but only if the
centers of curvature all lie in a straight line (coincident with the chuck axis). Unfortunately, this
condition is not satisfied for either the concentric IFU system or the linear IFU system. For the former,
the centers of curvature are distributed along an arc that is concentric with the fanning axis of the
image slicer. For the field mirror array of the latter, the centers of curvature are all the same distance
from the face of the blank into which they are machined, but they have to be offset by different
amounts in the direction perpendicular to the plate in order to control the exit pupil position.

An alternative method that is applicable to only the concentric IFU system is to mount the array plate
in a jig on the face of the chuck so that it lies perpendicular to the chuck axis. The jig would allow the
plate to be manually re-positioned through a series of precise steps along an arc matching that of the
array elements. The spherical (or toric) surface would be machined at each location. The stepping
direction would be opposite to the tool direction to avoid having burrs pulled over previously machined
element. With careful jig design, the steps could be accurately controlled, but this would not have the
intrinsic accuracy of a single set-up method.

A third (and favored) method that is applicable to both IFU systems is to fly-cut the surfaces. Here, the
cutter tip spins about the spindle axis. The blank does not rotate, but rather is traversed in all three
translational axes. The curvature radius is determined in one projection as the radius with which the
cutter tip spins. In the perpendicular projection, it is determined by the locus of the traverse. This is the
machining configuration commonly used for fly-cutting in conventional milling machines. Diamond
machining facilities of this type are now available, for example, at the University of Bremen. The more
traditional diamond turning lathes, such as those operated by P-OE, can also be adapted to work in this
manner. For this, a third translational axis must be added to the tool post of the machine. P-OE have a
computer controlled platform of this type which they use for such purposes. Because it is controlled
independently of the lathe, its movement cannot be coordinated with that of the other two axes to
produce a compound locus. Rather the third axis can only be used to change the level of the work piece
between separate surface cutting operations for each element of the array. This is not sufficient for the
preferred fly-cutting method (configuration C of §1.21.1.2.1).

A limitation of this fly-cutting method is that it does not produce truly spherical (or toric) surfaces.
Rather, the surface is tangential to the intended sphere along two orthogonal lines on the surface.
Elsewhere the deviation follows a “quad-foil” pattern, somewhat like the 17th or 18th order Zernike
polynomial terms. A diagram of the whole fly-cutter envelope is shown in Figure 30. The
approximately spherical zones are at the top and bottom.




                        Figure 30: Wireframe diagram of fly-cutter envelope.


1.21.1.2.1 Fly-Cutter Aberrations
The fly-cut pupil mirror array produces aberrations because it is not spherical (or toric). Figure 31
shows one of several possible fly-cutting configurations. Here, the array plate is traversed in its own
plane to follow the horizontal profile of the array. The radial line through the origin of the coordinate
system is the diameter of the fly-cutter circle that is parallel to the traverse plane. The surface is only
coincident with the intended sphere (or toric) along the x and y-axes. In general, the error introduced to
a ray reflected off the surface corresponds to an angular deviation on the sky of
                                                   1 r
                                            x         x y
                                                            2

                                                   2 f

                                                   1 r 2
                                            y         x y
                                                   2 f

where symbols are defined in Figure 31 and Appendix §Error! Reference source not found.. The
angular size of the rectangular pupil on the mirror element is

                                                        1
                                                x 
                                                       2 F4

                                                        K
                                                y 
                                                       2F4

which for F4 = 16 and K = 1.6 gives x = 0.03125 rad and y = 0.05000 rad. If the coordinates of the
pupil center are x0 and y0, those of the four corner points can be found by adding or subtracting half
the corresponding  values. Applying these relationships, aberrations are determined for three possible
fly-cutting configurations.




                              Figure 31: Fly-cutter generation geometry.

Configuration A

This configuration is as shown in Figure 31. The fly-cutter axis is aligned parallel to the face of the
array blank. For the worst case of the end elements, x0 = 0.06199 rad. For all elements y0 = 0.08727
rad. The ray deviations are calculated for the center of the pupil, and for the four corners, and the extent
of the aberration is determined as the range of these deviations. Then Ex = 0.175 rad (~ 0.70 pixel)
and Ey = 0.119 rad (~ 0.48 pixel). These high values are not acceptable.
Configuration B

In this configuration the fly-cutter axis is aligned perpendicular to the plane of the array blank, so
annulling the x0 value and making all elements of the array identical. The array is traversed in all
three axes, which means that this cannot be done on a lathe with an independently controlled tool post
platform. For this x0 = 0 and y0 = 0.08727 rad. The extent of the aberration is then Ex = 0.086 rad
(~ 0.34 pixel) and Ey = 0.003 rad (~0.01 pixel). Smaller aberrations are desirable.

Configuration C

This configuration is similar to configuration B, except that the fly-cutter axis is tilted to match that of
the elements (5°). To first order, this additionally annuls the y0 value. With x0 = 0 and y0 = 0, the
extent of the aberration becomes Ex = 0.004 rad (~ 0.02 pixel) and Ey = 0.003 rad (~0.01 pixel).
These aberrations are negligible. However, a three-axis diamond turning machine is required which
increases risk.

1.21.2 Lens Material Availability
Apart from the CaF2 cryostat window, all refractive element materials proposed in both the concentric
IFU and linear IFU systems are readily available in the required grades and sizes. A large enough blank
for the window (180 mm diameter) is available by special order. Facilities required for lens
manufacture are available at RSAA, except for the ZnSE item. Suitable AR coatings are available in all
cases.

A list of the materials required for the concentric IFU system, and their possible suppliers is given in
Table 14. Additional materials are required for the collimator elements of the linear IFU system.
Potential suppliers of these are also listed in Table 14.

                           Table 14: Potential Optical Materials Suppliers
Material                                                 Company

CaF2 optical crystal lens blanks                         Optovac, Corning Inc, USA
Silica, IR grade blanks of Inf 302                       Heraeus Amersil, USA
ZnSe, CVD material, purchased as finished lens           Janos Technology Inc, USA
CaF2 for dewar window, by special order                  Optovac, Corning Inc, USA
BaF2 optical crystal lens blanks                         Sloan Harshaw USA
Sapphire C axis optical crystal lens blank               Janos Technology Inc, USA


1.22 Optical Design Risks

1.22.1 IFU manufacture
The manufacture of the IFU is problematic. We are strongly of the opinion that diamond machining is
the most promising method of construction. In fact, it is difficult to identify a viable alternative. The
particular approach that we have developed for NIFS seems to be as practical as any of those proposed
for similar instruments. Nevertheless, none of these designs is yet proven.

1.22.1.1 Image Slicer
The tolerance on the angular displacement of the image slicer elements is very small, and there is some
risk of it not being achieved. This risk will be mitigated by:
 Maintaining the option of several angle-setting methods during the development program.
 Using a large base length for the angle-setting mechanism.

1.22.1.2 Mirror Arrays
The preferred method of manufacturing both mirror arrays is to diamond machine them as monoliths
using a fly-cutter in a machine with three translational axes. We know of only two companies who are
prepared to undertake this work. One of these would be very expensive, and the other has only recently
commissioned the necessary machine. The lack of proven capability means there is some doubt about
the surface quality that can be achieved with this type of machine. This risk will be mitigated by:
 Maintaining the option of using a more complex procedure that can utilise the more common
     turning technique. The preferred supplier would then be P-OE, who have experience in the
     development of IFUs.
 Exploring the option of making the array elements as separate pieces, and assembling them as a
     stack. This avoids some problems, but introduces others.

1.22.1.3 Alignment
Alignment of the IFU is expected to be difficult, and require some experimental development. The
possibilities of this causing delay during the assembly of the instrument may be mitigated by:
 Having two sets of IFU components manufactured at the earliest possible time.
 Using one set of IFU components for development of the alignment process while keeping the
    other set in safe storage for final installation.

1.22.2 Optical Manufacture
Infrared lenses are difficult to manufacture. Risks include scratching, chipping, thermal shock,
mechanical shock, and dimensional errors. Spare blanks may be purchased in case rework is necessary.

1.22.3 Scattered Light
Scattered light is expected to be a problem at the level required for performance to be limited by
detector dark current in the wavelength regions between bright OH airglow emission-lines. This
problem is caused by small-angle scatter from optical surfaces. Further work is required to quantify
performance.

1.22.4 Baffling
The effectiveness with which the proposed optical layouts can be baffled has not been fully
determined. Areas of particular concern are the proximity of the field mask and cold stop for the
arrangement shown in the concentric IFU system. A possible redress for this is the adoption of an
Offner relay system to form the cold stop.

A further concern is the possibility of stray light leakage at the multiple fold mirror block shown in the
concentric IFU system. An obvious means of avoiding this is the use of a more widely spread folding
arrangement, but cryostat geometry limits this option. An alternative is the adoption of the linear IFU
system.

Further work is required to quantify performance.

1.22.5 Costing
The cost estimates made during this study are based on preliminary design information, and are
therefore uncertain. This is particularly so for the labour component of the estimate. The concern here
is that onerous commitment must be made on this basis.

				
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