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 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 eye array spatial light integrators and we will take a look at how these devices work in this article.
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. In digital projectors that use fly’s eye arrays they 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 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 Array1 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.
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 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 an 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 is 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.
In both of these 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 the field array of fly’s eye lenses acts like a field lens and works with the condenser lens to keep the illumination so that it will still overlap at the illumination plane.
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 worse this scattering becomes.
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 and 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 7 channels is the minimum number required to achieve a uniform irradiance at the illumination plane of a digital projector and about 11 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 directions horizontal and vertical. 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 plano side of the field array to provide a common mounting and rigid support for the PCS array rhombs.
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 non-uniform:
Note that if the lamp can be modelled in more detail: but with even 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 condensor 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. 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.
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:
