WHITE PAPER
Fly’s Eye Arrays for Uniform Illumination
in Digital Projector Optics
Zemax
A Radiant Zemax Company
WHITE PAPER
Fly’s Eye Arrays for Uniform Illumination in Digital Projector Optics
Authored by: Michael Pate
Introduction
In 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
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.
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
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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 Work
Fly’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 Tradeoffs
One 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 Example
The 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 1Case 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:
Summary
Fly’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.
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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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