# UofA College of Optical Sciences Computer Generated Holography

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http://www.arizona.edu   http://spie.org

UofA College of Optical Sciences
Computer Generated
Holography Workshop
March 15-19, 2010

Lab A – Simple DOEs                        1   Anoop George

http://www.arizona.edu     http://spie.org

Overall Purpose: To explore and characterize zone plates created by the maskless
lithography tool.

Background

a
ρ
Z1                         Z2

f/5               f/3                             f

Zone Plate:
A zone plate is a device that changes the amplitude or phase of every other annular zone
in the pupil that corresponds to a half wavelength change of optical path difference defined for a
particular wavelength and a particular source point and an observation point. A parameter L is
used to combine information about both source and observation point:
zz
L = 1 2 (z1 and z2 both defined as positive).
z1 + z 2

Since each zone corresponds to a definite optical path difference range, each zone
consequently shares the same area: An = πλL Each zone boundary is located at ρ n = nλL . The
number of Fresnel zones (or Fresnel #) is then given by the following useful relationship:
a2
FN =
λL

Light from the odd zones will cancel with light from the even zones. Therefore, if there
are an even total # of zones in the aperture, the observation spot will be dark. If there are an odd
number of zones in the aperture, the location of interest will be bright.

Lab A – Simple DOEs                               2                                   Anoop George

http://www.arizona.edu      http://spie.org

What happens when all the zones of one sense are blocked? (This type of zone plate is called a
Fresnel zone plate) All zones interfere constructively and form a bright spot, or (if z1 is at
infinity), a focal point.
ρ12
fn =
nλ

As the observation point is moved toward the lens, at certain locations there will be two
zones in the aperture per patterned zone, resulting in a dark spot. Similarly, at another location,
there are three zones resulting in a bright spot. This corresponds to a second ‘focal point’. There
are also bright spots that correspond to 5 zones, 7 zones, etc. These focal points are called
diffracted orders. If the primary focal length is f, each focal point is located at f/3, f/5, f/7, etc.

Since the number of zones (and consequently, the focal length) is defined for a particular
wavelength, changing wavelength changes the focal length.
λ1
f 2 = f1
λ2

Fresnel Lens:
Another way of constructing a zone plate (and the zone plates we will be testing) is not
by blocking the even or odd zones but by shifting the phase of one set of zones by π. This
increases the energy throughput of the zone plate by a factor of 4. If the irradiance (W/m2) prior
to the zone plate is given by I0, a normal Fresnel zone plate creates at the primary focal point an
irradiance of I o FN 2 . A binary phase zone plate gives 4 I o FN 2 .

By removing or altering the phase in a beam, a zone plate focuses light, and can also be
thought of as a simple lens that follows the basic imaging equations, namely:
1 1 1            z   h′
+ = and 2 = = m
z1 z2 f          z1 h

Just as an electronic signal requires high bandwidth to create a very short signal in time,
the focus spot size in a beam free of aberration depends on the spatial bandwidth of the beam.
This bandwidth corresponds to the angular spread of the beam. The greater the focus cone angle
of the beam, the smaller the spot. The FWHM size is approximated by w ≈ λ            . We can
NA
approximate the numerical aperture of the beam with a small angle approximation (which might
not be true in many cases in this lab, but will suffice for today) by NA≈a/z2 which gives
w ≈ λz 2 for a zone plate. As the spot size decreases, so does the total energy. However, the
a
peak irradiance stays the same for each order.
[
An = π (ρn + tn )2 − ρn
2
]
Area of an annulus:

Lab A – Simple DOEs                                3                                    Anoop George

http://www.arizona.edu          http://spie.org

Part I (30 min): General Inspection & Imaging properties
1) Place the zone plate in the holder provided and using an illuminated target, take a piece of paper and locate the
resulting first order image. Measure the object and images distances along with the height of the object and image.
Then calculate the focal length and magnification:

object:           z1 =                                          f =
h =
image:            z2 =                                          m=
h’ =

2) Use the microscope (Milst-O-Vision) to inspect the zone plate more closely. Describe the zone boundaries at the
inner and outer radii.

3) Using ‘Milst-o-Vision’, measure the radius of the first zone and the radius and thickness of an outer zone.
Calculate the area for each zone and the theoretical area of the zone plate:

ρ1 =                                Area of zone 1 =
ρn =                                Area of zone n =
tn =                                Theoretical area for each zone =

Part II (30 min): Closer Inspection & Wavelength Dependence
1) Measure the primary focal length using red light versus green light.

fred =
fgreen =                            Theoretical fgreen given fred =

2) Measure the locations of as many diffraction order focal points as possible. Plot the location as a function of
diffraction order. Make sure all locations are wrt to the plate.

Lab A – Simple DOEs                                        4                                         Anoop George

http://www.arizona.edu          http://spie.org

Location              Scaled Position
Plate
m=1
m=2
m=3
m=4
m=5
m=6
m=7
m=8
m=9
Position

0
1       2           3       4          5         6         7         8         9
Diffraction order

3) Replace the binary phase zone plate with a smooth zone Fresnel lens. What do you notice? How does this mimic
the effect of a blazed grating?

Questions:
You should have noticed many ‘images’ through the zone plate. Why do some images seem smaller and some
larger?

Why does blocking or changing the phase in an aperture make it behave like a lens?

When examining the zone plate closely, did the zones (both inner and outer) closely match a smooth circular
boundary of a theoretical zone plate? If not, try to account for the difference and think about what effect it might
have on the formation of the foci.

Lab A – Simple DOEs                                          5                                        Anoop George

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