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Fly’s Eye Arrays for Uniform Illumination in Digital Projector Optics

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Authored by: Michael Pate

IntroductionIn digital projector design, when we want to display a still or video image where the

digital source is uniform in radiance, we want the corresponding projected image to

be uniform in irradiance on the screen. In order to achieve this uniformity of irradiance

of the projected image we need to have the spatial light modulator, such as an LCD

panel, uniformly illuminated. The uniform illumination at the spatial light modulator

plane cannot come directly from the light source because the irradiance profile of the

source from the lamp assembly is (typically) a Gaussian-type irradiance profile. We must

somehow “degauss” this irradiance profile or spatially transform it from nonuniform to

uniform irradiance profile. This can be accomplished with a pair of fly’s eyes arrays spatial

light integrators and we will take a look at how these devices work in this white paper.

What Is A Fly’s Eye Array?A fly’s eye array is a two dimensional array of individual optical elements assembled

or formed into a single optical element and used to spatially transform light from a

nonuniform distribution to a uniform irradiance distribution at an illumination plane.

Digital projectors that use fly’s eye arrays are almost always used with lamp assemblies

with a parabolic reflector that provides semi-collimated light. At the present time they

are mostly used in LCD digital projector light engines in the illumination section to

deliver spatially uniform or homogenized illumination to the spatial light modulator

illumination plane.

The fly’s eye array can be seen in the above figure. This photograph is provided

courtesy of In Vision, www.in-vision.at. Each of the individual optical elements in the

array can be square or rectangular in shape. The surface shape of individual optical

Fly’s Eye Arrays for Uniform Illumina-tion in Digital Projector Optics

WHITE PAPER

This white paper discusses the design

issues involved in designing fly’s eye

spatial light integrators, with specific

application to the design of digital

projectors.

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elements can be spherical or anamorphic (different optical power in the vertical and

horizontal meridians) and the optical power is typically only on one surface of the array,

the second surface being most often plano.

In terms of modeling these components in Zemax, probably the easiest way is to use

the Lenslet Array 1 object. A Lenslet Array 1 object consists of an array of rectangular

volumes, each with a flat front face and a user-definable number of repeating curved

surfaces. The array surface may be plane, sphere, conic, or polynomial asphere; or a

spherical, conic, or polynomial aspheric toroid. This allows great flexibility in defining,

and optimizing, the precise surface shape of the lens elements in the array.

The above graphic shows a single Lenslet Array 1 object, which comprises a 7 x 5 array

of rectangular lenses, each of which is a rectangular section of a spherical lens. Other

objects which may be useful for this application include the Lenslet Array 2 object and

the Hexagonal Lenslet Array object. Note that any object can be replicated and placed

on an array easily using Tools -> Replicate Object.

Lens arrays are also supported in sequential optical design, via the user-defined surface

capability. Samples are provided for arrays of spherical, conic aspheric, even-aspheric

and cylindrical lens arrays.

How They WorkFly’s eye arrays are typically used in pairs along with a condenser lens to provide

uniform irradiance at the illumination plane. The first fly’s eye array is often called the

objective array and the second array along the optical axis is called the field array. For

now we will consider only the objective array. The function of the objective array is to

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act like an objective lens on a camera and form an image of an object, or light source

in our case, at the focal plane of the objective lens, as shown below. In our case we will

form an image of the collimated light source at the focal plane of the objective array.

If an objective array is used with collimated light and we place a condenser lens at the

focal plane of the objective array as shown above, we will obtain a uniform irradiance

at the illumination plane as shown in Figure 5. Unfortunately we are not lucky enough

to have point sources of light so it is very difficult to obtain collimated light from a lamp

assembly with a parabolic reflector. The light from lamp assemblies with a parabolic

reflector has some divergence or angle because the fire ball of the lamp is a volume

light source and not a point. We can see the results of using only an objective array and

condenser lens with a diverging source and a source with two field angles in the two

screenshots below.

The axial rays are imaged to overlap at the illumination plane and provide uniform

illumination. The diverging rays shown in the left figure above as green rays are imaged

to a different location, and therefore do not overlap with the collimated beam rays at the

illumination plane. This imaging at a different axial location causes a nonuniformity at

the illumination plane because the full beams from the axial rays are overlapping, and

only half of the illumination from the diverging rays illuminates the same plane as the

on-axis (blue) rays.

For the figure on the right above, the two field angles get imaged to different object

heights at the condenser lens, and therefore get imaged to a different object height

by the condenser lens at the illumination plane. If the images from all fields are not

overlapped at the illumination plane we will have a nonuniform illumination plane.

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In both cases we can improve the uniformity at the illumination by adding a second

fly’s eye array called a field array. This field array is a second fly’s eye array and is located

at the image plane of the objective array. The function of the field array is to provide

overlapping images at the illumination plane for different fields from the source. To be

uniform at the same plane we need the full width of the illumination plane illuminated by

both the axial and diverging rays to be the same. We can see what the addition of the field

arrays do for our two situations in the figures below. In both, the diverging rays and the

field rays of fly’s eye lenses act like a field lens and work with the condenser lens to keep

the illumination so that it will still overlap at the illumination plane.

Fly’s Eye Array Design TradeoffsOne of the design tradeoffs is how many channels to have in the vertical and horizontal

directions in the array. The larger the number of channels the more uniform the

illumination at the illumination plane. However, the edges between the lenslets are not

infinitely sharp, and so light gets scattered by these edges out of the beam. The more

lenslets, the greater the scattering.

Using an odd or even number of channels is another choice. An odd number of

channels mean that the center channel is always on center, and the channels to either

side of the center channel are optically folded onto the center channel. This is where

the spatial homogenization comes from. Even numbers of lenslets can lead to a dip in

intensity at the center.

As a generalization, approximately seven channels is the minimum amount required to

achieve a uniform irradiance at the illumination plane of a digital projector, while about

eleven is the maximum. Since these are general numbers, make sure you model the

illumination system from the source to the illumination plane to determine precisely how

many channels are required in your fly’s eye arrays.

The focal length of the lenslets determines the spacing between the two arrays. The

aperture of each channel and the focal length of the objective array determines the

field of view that the field array can transmit. The channel aperture and focal length

and spacing of the two arrays determine the size of the illumination plane in both

vertical and horizontal directions. One way to think of the field array is that the job of

an individual lenslet is to image the aperture of that channel’s objective array to the

illumination plane with a certain magnification.

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In LCD and LCoS digital projector light engines where the light source must be

polarized prior to reaching the illumination plane, a polarization conversion assembly or

PCS is often used. The PCS array is often cemented to the plano side of the field array

to provide a common mounting and rigid support for the PCS array rhombus.

An ExampleThe following is a simple example of a real fly’s eye illumination system for digital projector use.

The source is an ellipsoidal volume, centered at the focus of a parabolic mirror.

The resulting output from the parabolic mirror is very nonuniform:

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Note that if the lamp can be modeled in more detail, even with a simple lamp model,

the scale of the problem can be clearly seen. The rays are then traced through two

Lenslet Array objects and the condenser lens, and are then analyzed on a detector

object positioned at the location of the spatial light modulator in the digital projector.

The following shows the results of different numbers of lenslets in the two arrays (both

arrays have the same number of lenslets in all cases):

Case 1 Case 2 A 6 x 4 Array of Lenslets A 11 x 9 Array of Lenslets

Case 3 A 11 x 9 Array of Lenslets

It can be easily seen that the 11 x 9 case gives the best uniformity. Zemax makes it easy

to change the number of lenslets, their radius of curvature and apsheric coefficients,

etc. It is also possible to optimize for uniformity using the pixel = -4 data item from the

NSDD optimization operand. Please see the Zemax manual for full details.

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If we set the detector viewer to show luminous intensity (i.e. power as a function of angle),

the effect of the array of the angular spectrum of the light can also be clearly seen:

SummaryFly’s eye arrays are used in pairs to spatially homogenize or make a light source uniform

at the illumination plane. The two arrays are called the objective array and the field array

and are used with a condenser lens. The objective array images the source at the field

array. The field array reimages all of the fields with the condenser lens so they overlap at

the illumination plane and create a uniform irradiance. A typical fly’s eye array has seven

to eleven channels in each direction. Each of these channels are optically overlapped at

the illumination plane to achieve uniform light from a nonuniform source.

© 2013 Radiant Zemax LLC. Radiant Zemax, ProMetric, TrueTest and Zemax are trademarks of Radiant Zemax LLC. All other marks are the property of their respective owners.770-9002-01 1/13

This white paper discusses the design issues involved in designing fl y’s eye spatial

light integrators, with specifi c application to the design of digital projectors.

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