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Scanning Fabry Perot Imager cavity

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					 Submitted for Photon „04 Special Issue


      High Spatial Spectral Resolution VIS-NIR Scanning Fabry Perot
            Imager for Geostationary spaceborne applications
          Viviana Vladutescu, Mustapha Abdulfattah, Fred Moshary, Barry Gross
       Optical Remote Sensing Lab, City College of the City University of New York
                              New York, New York 10031

                                               Abstract

 A scanning Fabry Perot Imager design is proposed based on combinations of Fabry Perot
 etalons and/or broadband interference filters that can in principle be used as a
 hyperspectral sensors from geostationary spaceborne platforms. In a single stage etalon
 design, a number of interference filters are required that can be rotated in front of the
 ethalon to eliminate overlapping orders. A procedure is developed to optimize the
 number and bandwidth of filters for a given Fabry Perot cavity length and spectral
 coverage requirements. An alternate approach utilizing multiple etalons in a cascade
 geometry is also investigated as a means to achieve both high spectral resolution and
 large free spectral range required for the proposed application. It is shown that the S/N
 can be made sufficiently large with only moderate decoupling of the etalon cavities. In
 addition, preliminary studies of the affects of cavity misalignment for both single etalons
 and multiple etalons are carried out.

 Keywords: Fabry Perot, interferometry, multiple etalon, spectrometer,



 I. Introduction                                       limited spectral range to probe a particular
                                                       spectral line. However, there is no
High      spatio-spectral     space   based            fundamental limit in adapting this
observation of VIS-NIR reflectance is                  technique to the VIS-NIR portion of the
required for a variety of remote sensing               spectrum except for the cavity size (<
applications including ocean color, land               1um) and the resulting tuning sensitivity.
surface classification, and atmospheric                On the other hand, for larger cavity
monitoring. In conventional approaches,                lengths, in broad band (VIS-NIR)
the spectral selectivity is accomplished by            applications, multiple resonance orders
means of interferometry, a series of pass-             will overlap and some seperation
band filters (channels), or grating based              methodology is needed.
spectrometers selectively designed to                    To handle the case of multiple
cover the spetral domain of interest for a             resonances, we purpose two possible
given application [1-7]. More recently, an             systems. The first is based on the simple
alternative technique based on the use of a            approach of designing a set of
mid-ir (MIR) Planar Fabry-Perot (PFP)                  interference filters which will each pass
filter with a array imager has been                    only a single resonance order within the
proposed for monitoring tropospheric                   spectral region of interest. The
gases such as ozone [2-3]. Here the main               specification of the interference filters in
interest was pico-meter resolution over a              this case will depend on the specified
minimum cavity length. The use of                     The light collection/reducing telescope
multiple interference filters requires a              (30 cm primary) has a collimated output
rotating filter wheel that can place one              beam of 6 cm diameter (5x compression)
filter at a time in the optical train, and            which will increase the angular spread
adds complexity to the design.                        before the ethalon to 5 times the field of
In a second approach, similar to the                  view of the imager. The most important
method proposed in [2-3], a synchronized              aspect to observe is that the rays going to
set of etalons are employed whose optical             different CCD pixels pass the Fabry Perot
pathlengths are chosen to allow                       Filter at different angles and that
constructive interference of the periodic             differernt angles will affect the spectral
pass bands of each etalon at a single                 response.
resonance while destructively canceling                 To see the magnitude of these affects we
other transmission resonances.          This          can take an idealized imaging system as
method effectively increases the free                 given in figure 2 with 60 mm diameter
spectral range of the muti-stage ethalon              optics. For a 1” CCD with 512x512
system while allowing for high spectral               effective resolution, the CCD field of
resolution.       Similar to the multiple             view (FOV) after an f/# =3 imaging lens
interference filter design, a system can be           is 50 mrads. Each spatial pixel would
designed in this way to operate over the              capture an effective FOV of 100
entire VIS-NIR range from 400-800nm.                  μrad/pixel. For a geostationary satellite at
The complexity in this case is to                     30,000 km, this would result in a 1200
accommodate synchronized scanning                     meter/pixel     footprint.    The     FOV
while maintaining alignment of multiple               specifications are critical since beam
ethalon system.                                       anglar dispersion leads to spectral shifts
  The systems described in this paper are             which may be approximately calculated
preliminary       conceptual      instrument               1 2
                                                      as        max . For the system in figure
designs that address the main issues                           2
needed for a flexible multi- or hyper-                1, maximum wave number shifts are
spectral sensor with high spatial                     below 1 nm, an order of magnitude
resolution from a geostationary platform.             superior to current specifications for
                                                      existing or planned instruments. Even
II. Imaging Specifications.                           then, such spectral shifts may be
                                                      compensated by pre-calibration with a
A conceptual schematic of the imaging                 narrow laser source.
instrument is illustrated in figure 1
              10 mrad
                                FP/Filter   Imaging
                                elements    Lens            H  30,000 km    x
                                                                                 f  18cm ( D  6cm)

           30cm         6cm
                                                                                                       X=1cm
                                                                                      
                                                                
                              50 mrad          CCD




      Figure 1. Fabry Perot Schematic                   Figure 2. Imaging angles
III. System Configuration
                                               III A.1 Results
III A.    Single cavity Fabry Perot
Interferometer in series with a                This observation allows us to define a
passband filter                                simple algorithm to determine the
                                               passbands for each order that will allow
In order to extend the free spectreal range    continuous single resonance operation
(FSR) from 400-1000 nm using an etalon         over the range of interest. The main
of reasonable length requires a large          point of this algorithm is that the
number of synchronized pass- bands to          minimum wavelength of a resonance
reject multiple resonance orders. To see       order n must larger than the maximum
the constraints on the pass band filters for   wavelength of the next resonance order
maintain single                                (n+1). The procedure is as follows:

                                               1. Input as a limiting value, the
                                                  minimum FP cavity length Lmin
                                                                            cav

                                               2. Starting at the minimum wavelength
                                                  of the passband required, determine
                                                  the minimum resonance number
                                                  needed for the first filter stage
                                                        
                                                   n1  2 Lmin 1
                                                            cav   min
                                                   for the desired cavity length

 Figure 3: Resonance Boundaries of FP          3. Determine the maximum wavelength
                                                  for the first stage as

                                                  1  n1  1 n1   bound
                                                   max
resonance operation, we plot in figure 3,
the boundaries of the different resonance         where a buffer of bandwidth
orders for a given etalon.                         bound   FP     is added to
                                                  account for the finite bandwidth of
Simple algebra shows that the single              the FP etalon.
resonance conditions
                                               4. Once the maximum wavelength of
 2 Lmin 2 Lmax                                    the first section is determined, the
                                                 next section is considered where the
  n 1     n
                                                  minimum wavelength of this stage is
 2 Lmin 2 Lmax
                                       (1)       given as
    n    n 1
 lead to max  n  1 min  n min                min  1  bound
                                                           max
                                                    2
                   n          n 1
                 2 Lmax       2L               This algorithm is then iterated over the
 where min            max  max      (2)    stages until we fill the entire passband.
                    n           n
                                               Each filter stage (k) calculated above,
would then require an interference filter                                                  In this configuration, it is clear that no
covering the stage bandwidth. By                                                           changes have to be made to the cavity
rotating over all interference filters,                                                    length sweep. Therefore, all that is
complete single resonance coverage is                                                      required is a filter wheel mechanism to
obtained.                                                                                  select each relevent passband over the
        In figure 4, we plot both the                                                      same operational scan.
order of each Fabry Perot stage and the                                                    IIIB.    Multicavity      Fabry      Perot
cavity length needed to cover each                                                         Interferometer Design
stage‟s passband assuming that the
minimum cavity length is limited to                                                        A high resolution single wavelength
                                                                                           Fabry Perot Interferometer with no
LLimit  2500nm
  cav                                                                                      interferenc filters will result in multiple
We can see that a minimum of 8 stages                                                      resonance orders. However, it has been
are needed to cover the range from                                                         show that multiple cascade etalons can
400nm to 1000 nm where each stage                                                          increase the free-spectral range [5]. In
covers a subsequently larger spectral                                                      our scheme, the wide tunability and the
band.                                                                                      need for high side band suppression with
                                                                                           S/N > 100 leads us to consider three
                                    14
                                                                              k=1
                                                                              k=2
                                                                                           weakly coupled etalons. Reduction of
                                    12                                        k=3          the coupling due to multiple interference
                                                                              k=4
                                    10                                                     is obtained by suitable placement of a
                  resonance order




                                                                              k=5

                                     8
                                                                              k=6
                                                                              k=7
                                                                                           neutral desnity filter. As one can see in
                                                                              k=8          figure 5, the three etalons are positioned
                                     6
                                                                                           in series with the isolating medium
                                     4                                                     attenuating the possible reflections
                                     2                                                     between cavities.
                                    0                                                                t        t
                                    400    500   600      700     800   900     1000
                                                       wavelength                          Ein                               T1T2T3Eint2
Figure 4a Filter stage resonance order for each
                                                                                                                             T1T2T3EinR1R22R3t6
passband
                                                                                                                             T1T2T3EinR12R24R32t10
                                                                                                   R1        R2   R3

                  3000
                                                                                           Figure. 5. Three-etalon series configuration.
                  2500
section lengths




                  2000
                                                                                           The transmission of the attenuating
                  1500
                                                                                           medium between consecutive cavities is
                  1000                                                                     denoted as t, the etalons reflectivities are
                                                                                           denoted by Rj and the input spectrum by
                           500
                                                                                           Ein. The transmissions of each cavity are
                                     0                                                     represented by Tj.
                                     400   500   600      700     800    900        1000
                                                       wavelength                                  The      derived      transmission
                                                                                           function for a triple etalon system taking
Figure 4b Filter stage length range for each                                               in consideration all multiple reflections
passband                                                                                   R1,2,3 between parallel cavities used at
                                                                                           normal incidence is given as
                     T1T2T3t 2                                         2Lp       2 Lq p       Lp
T                                              (3)          res                      (4)       
     (1  R1R2t 2 )(1  R2 R3t 2 )  R1R3T22t 4                    p     q      Lq q
                                                      Therefore, we see that a transmission
where t is the attenuation of the isolating           resonance of the coupled system
medium and Rj=(1-Tj) the reflection of                requires that the cavity lengths are
cavity j.                                             chosen correctly. The lengths are
                                                      connected by the so called “vernier”
                                                      ratio whose value is near unity for
III.B.1 Simulation Results                            sufficiently high resonance orders
                                                      (which is the case for the cavity lengths
To see the conditions imposed on the                  considered).    Therefore if p=n and
FPIs in series, to maintain single                    q=n+1, it is easy to prove that all
resonance operation, we superimpose in                neighboring resonances are eliminated
figure 6, the independent etalon                      until
transmission spectra . It is evident that
                                                      2L p       2Lq             2 L2 p       2 L2 q        res
we may tune the cavities so that a                                     
                                                                                                               (5)
particular set of resonances overlap.                 p 1       q 1             2p           2q           2
However, all neighboring resonances                   It also follows that the maximum tuning
will no longer overlap, greatly                       range is limited so that λmax<2λmin and
supressing any sidelobes. Furthemore,                 only the region between 400 and 800nm
the degreee of supression obviously                   can operate in a single resonance mode.
depends on the resonance linewidth.                   Operation in this mode requires only a
                                                      single fixed filter covering the entire
                                                      passband. The resulting transmission of
                                                      both a double and triple etalon system
                                                      are represented in figure 7 where t=.8
                                                      between the elements. It is clear that the
                                                      sidelobe supression increases for three
                                                      etalons by an order of magnitude.




Figure 6. Single cavity etalon transmissions for
three different spacings . The three etalons agree
on the central resonance tuned to 600nm

To examine the limits of single mode
operation for a multiple etalon system,
we note that at a particular wavelength
(in our case 600nm) a (p) order
                                                      Figure 7 Transmissions of 2 respectively 3
resonance     of    one    cavity   will              cavities etalons.
constructively interfere with the (q)
resonance of a second cavity when the                 On the other hand, it should be pointed
following relationship holds:                         out that as we vary the neutral density
filters between the elements, the ratio of           the transmission for a single etalon as we
passband to sidelobe transmission will               vary the length trough one complete
change so a tradeoff between S/N and                 scan. It is clear that for any scan
total power must be made.                            position, multiple resonances will occur.
                                                     In contrast, in figure 10, implementation
                                                     of the three etalon configuration
                                                     completely eliminates and multiple
                                                     resonances




Figure 8 a) Main resonance transmission b) S/N
between main and side band.

To increase the S/N, it is necessary to
decrease the transmission as seen in                 Figure 10. All multiple resonances eliminated
figure 8. For example, a value t=.6 is               and single wavelength is almost achieved
sufficient for S/N~100. Once the
condition is met for one resonance                   Therefore, we achieve single wavelength
wavelength, by synchronizing the length              operation over the full bandwidth of
shifts in all the cavities to maintain the           interest and only one fixed broadband
same vernier ratio, we can tune the                  filter is needed. It should also be noted
system over the entire band of interest.             that in this configuration, misallignment
To illustrate the difference an increased            errors will tend to compensate and the
FSR will provide using multiple etalons,             spectral shifts may be somewhat
we plot in figure 9,                                 reduced.

                                                     IV. Conclusions

                                                     We illustrate in principle designs for a
                                                     VIS/NIR       Fabry      Perot     Imaging
                                                     Spectrometer and develop a proceedure
                                                     to calculate the characteristics of the
                                                     needed pass band filters. It is shown that
                                                     a set of 8 cascading filters can be used to
                                                     cover the spectral range from 400nm to
                                                     1000nm with the same sweep. It is
                                                     shown that for sufficiently small
Figure 9 Spectral response of a single etalon. The   imaging systems, the spectral shifts in
diagonals    represent    multiple     resonances    the response across the CCD are
occurring with same intensity                        significant but should be easy to
compensate for. We have also shown           References
that if we use synchronously scanned
multiple etalon cavities, we may             [1]. Larar A M., Hays P B., and Drayson S.
significantly increase the FSR without       R “Global tropospheric and total ozone
decreasing the bandwidht of the              monitoring with a double-etalon Fabry–
resonance allowing single mode               Perot interferometer.I. Instrument concept”,
operation over the 400nm-800nm band          ( 1998)
with only a single fixed interferenxce       [2]. Larar A; and S. Drayson, “Global
filter.   The S/N between the main           tropospheric and total ozone monitoring
resonance and the sideband resonance is      with     a    double-etalon    Fabry–Perot
somewhat impacted by the multiple            interferometer. II. Feasibility analysis”,
reflections of the cavities but we show      Applied Optics, 37, 21 (1998)
that a moderate decoupling of the etalons
is sufficient to achieve S/N ~100. Trade     [3]. Lee J.Y; and J. W. Hahn, H-W. Lee,
offs between S/N and exposure time,          “Spatiospectral transmission of a plane
beam compression versus optical              mirror Fabry- Perot interferometer with
element size, aperturing and detector        nonuniform finite-size diffraction beam
S/N still need to be considered but the      illumination”, J.Opt.Soc.Am.A 19 #5,
                                             (2002).
methodology appears quite promising
due to it‟s simplicity and flexibility.      [4]. Hecht E.; “Optic”s, 3rd Ed. Addison
                                             Wesley (1998)
Acknowledgements
                                             [5]. Mack J.E., McNutt D.P., Roesler F.L.,
This work was in part supported under        and Chabbal R.,”The PEPSIOS Purely
the NASA Center for Optical Sensing          Interferometric High-Resolution Scanning
and Imaging (COSI) under grant number        Spectrometer. I. The Pilot Model” (1963)
NCC-1-03009. We would also like to
thank Raytheon and in particular Jeff        [6].Marinelli, W; C. Gittins, A. Gelb, and B.
                                             Green, “A Tunable Fabry-Perot Etalon-
Puschell for his assistance and support of
                                             Based Long-Wavelength Infrared Imaging
this project.                                spectroradiometer” , Applied Optics 38(16),
                                             2594-2604 (2000)

                                             [7]. Netterfield R. P., Freund C. H.,
                                             Seckold J. A., and Walsh C. J., “Design
                                             of a lithium niobate Fabry–Perot e´
                                             talon-based spectrometer”(1997)

				
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Description: Scanning Fabry Perot Imager cavity