The fly’s eye array is a useful optical element in illuminations systems, which can be used to create uniform irradiance distributions from non-uniform sources. This article applies the design of a fly's eye spactial light integrator to a digital projector and discusses the advantages and disadvantages of using such a system.
Authored By Michael Pate
Introduction
In digital projector design, we want to ensure that the digital source matches the projected image when it comes to the irradiance profile. This constraint therefore requires a projector design to encompass a uniformly illuminated spatial light modulator - usually in the form of an LCD panel. In theory, this sounds easy, but in reality, the source beams on such a panel are typically Gaussian (i.e. not uniform). Thus, a device is required to "de-Gauss", or, spatially transform the non-uniform beam profile into a uniform one. One such device with this capability is a pair of fly's eyes light integrator arrays. In this article, we will investigate these devices and their optimal settings.
What is a fly’s eye array?
A fly’s eye array is a two-dimensional array of individual optical elements assembled into a single optical element. It is used to spatially transform light from a nonuniform distribution to a uniform irradiance distribution at the image plane. Digital projection systems that use fly’s eye arrays are often used in conjunction with lamp assemblies which have a parabolic reflector providing semi-collimated incident light. At the present time, they are mostly used in LCD digital projector light engines to deliver homogenous illumination to the spatial light modulator illumination plane.
A 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 elements can be spherical or anamorphic (different optical power in the vertical and horizontal meridians). The optical power is typically only on one surface of the array with the second surface usually being planar.
One of the easiest ways to model this setup in OpticStudio is through the use of an array object. For the provided example, a Lenslet Array 1 object was chosen which consists of an array of rectangular volumes, each with a flat front face and a user-definable number of repeating curved back faces. The back surface may be planar, spheric, conic, polynomial aspheric, or toroidal. This allows great flexibility in defining - and optimizing - the precise surface shape of the lens elements in the array. The graphic below 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. You can read more about these arrays and their specifications in the help documentation: The Setup Tab...Editors Group (Setup Tab)...Non-Sequential Component Editor...Non-Sequential Geometry Objects.
Lens arrays are also supported in Sequential optical design, via the User-Defined Surface capability.
How do 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 objective array acts like an objective lens on a camera and forms an image of the 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 we had a collimated light source, generating uniform irradiance would be easy. As shown above, if an objective array is used with collimated light and we place a condenser lens at the focal plane of the objective array, we will obtain uniform irradiance at the illumination plane, as can be seen in the above Detector Viewer. Unfortunately, we are not lucky enough to have point sources of light, which makes obtaining collimated light difficult. The light from lamp assemblies with a parabolic reflector, like the one typically found in a digital projector, has some divergence or angle because the source has a finite volume, not a point. We can see the results of using only an objective array and condenser lens with a slightly divergent (around 3.75 degrees) source, and sources with multiple field angles in the screenshots below.
Nominally, the axial rays are imaged to overlap at the illumination plane and provide uniform illumination. In reality, diverging rays (shown as the green rays in the top figure) are imaged to a different location, and therefore do not overlap with the collimated rays at the illumination plane. This causes a non-uniformity at the illumination plane because, while the full beams from the axial rays are overlapping, only half of the diverging rays are illuminating the same planar location as the on-axis rays.
For the second system 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 pattern like what is shown in the Detector Viewer.
In both cases we can improve the uniformity of illumination by adding a field array. As discussed above, a 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 final image plane illuminated at the same time by both the axial and diverging rays. We can see what the addition of the field array does for the two cases listed in the figures below, even with just minimal optimization. In both, the field array acts in conjunction with the objective array and the condenser lens to ensure that both the diverging and on-axis rays overlap at the illumination plane.
Fly’s eye array design tradeoffs
When setting up the design, the user needs to decide 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 worse this scattering becomes.
An odd or even number of channels is another choice. Using an odd number of channels means that the center channel is always on center and the channels on either side 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. Similarly, eleven is about the maximum. These are not hard boundaries; as such, 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, focal length, and spacing of the two arrays determine the size of the illumination plane in both the horizontal and vertical direction. 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.
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 planar 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. This sample file can be found in {Zemax}\Samples\Non-Sequential\Miscellaneous\Digital_projector_flys_eye_homogenizer.zmx.
The source is an ellipsoidal volume, centered at the focus of a parabolic mirror. The resulting output from the parabolic mirror is very non-uniform:
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 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: a 6x4 array of lenslets:
Case 2: a 7x5 array of lenslets:
Case 3: an 11x9 array of lenslets:
It can be easily seen that the 11x9 case gives the best uniformity. OpticStudio makes it easy to change the number of lenslets, their radius of curvature, aspheric coefficients, etc. It is also possible to optimize for uniformity using the pixel = -4 data item from the NSDD optimization operand. Please see the OpticStudio Help Files for full details.
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 seen:
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