Multi-Channel Optic Light Concentrator

© Bob Field 2002

Physics major Ben Tarr worked under my supervision on his senior project to design, fabricate, and evaluate a multi-channel light concentrator that was inspired by the reflective optical elements of the superposition compound eye of a deep-sea lobster. The scientific goal was to determine how well such an optical system would concentrate a beam of light. The project exemplified the Cal Poly learn by doing educational philosophy: developing an unconventional optical system provided my student with experiences with all the key elements of my experience in the aerospace industry, where I developed advanced high energy laser optics based on new and unproven technologies. It also provided a lesson in looking to nature for guidance in optics, because organisms have evolved many highly specialized and efficient light detection systems over millions of years.

There are many advanced vision systems among the arthropods, all of them based on the compound eye that is different than the vertebrate eye humans have. Most arthropod eyes have apposition compound eyes that collect light in isolated channels. These eyes have a wide field of view but a low spatial resolution compared to vertebrate eyes. Evolutionary processes have also produced superposition compound eyes in certain arthropods that function in low light conditions by concentrating the light collected by multiple apertures onto a single visual sensor. These species include nocturnal insects and deep-sea crustaceans since sunlight is highly absorbed in the first hundred meters of the sea.

Most compound eyes have one lens in each channel. The eye of interest to us is based on reflection rather than refraction and is found in a deep-sea lobster. This enabled us to use mirrors to construct an optical system. These mirrors are oriented at a steep angle so that the light passes through the optical system and collects behind it rather than returning toward the light source as many mirror systems do. I was interested in this optical system because of similarities to my previous work with grazing incidence optics for free electron lasers and conical optics for chemical lasers. I was also highly suspicious of the optical characteristics commonly reported and illustrated in the biological literature. It turns out that these optical systems produce more complex concentration patterns than early reports indicated. Furthermore, refractive as well as reflective features probably influence the performance of the lobster eye.

Lobster eye optics are arranged on a nearly hemispherical surface with each element looking outward from the center. Our design positioned all of the optical channels in a plane rather than on a sphere in order to simplify the fabrication process. Instead of using a two-dimensional array of channels, our design is based on a row of 18 mirrors that have their trailing edge in a common plane. Our mirrors are polished stainless steel sheets that are six inches long and one inch wide. They are held in place by a Plexiglas frame and lie in planes that intersect eight inches from the leading edge in a common line. One mirror is one degree from the center of the system and each successive mirror is an additional two degrees from its adjacent mirror.

The design is intended to concentrate light from a point source into a plane approximately halfway to the common intersection or about four inches behind the front of the row of mirrors. The mirrors are flat so there is no focusing of beams, simply an overlapping. The design was optimized for a light source 40 inches away, but was also designed to work well for more distant sources including the sun whose rays are nearly parallel over the aperture of the optical assembly. The amount of light intercepted by the mirrors depends on their orientation. A mirror near the center collects very little light while an outer mirror collects almost all light between it and its neighboring mirrors. The collected light falls along a line parallel to the long dimension of the mirrors.

A second row of 18 mirrors was added to the first row and held in place in the same Plexiglas frame. These mirrors are the same as the first set except that they lie in planes that intercept ten inches behind their front edge and they are spaced 1.75 degrees apart. They are designed to concentrate light in the same plane as the other row of mirrors. The big difference is that this row is oriented at right angles to the other row. As you view the multi-channel optic (MCO) from the source side, you will observe that the optic appears to be a square array with 17 channels on each side of the square, or a total of 289 channels. This arrangement functions similar to an array of intersecting mirrors without producing the technical problems associated with fabricating and assembling interlaced mirrors.

The second row also concentrates light along a line that is parallel to its mirrors. This produces a cross bar light pattern in the concentration plane behind the MCO. Furthermore, there is an opportunity for some light to hit mirrors in both rows. These rays not only end up on the cross bar, but are actually directed to the intersection of the cross bar light pattern, producing a central peak similar to what an ordinary lens does. Based on my analytical estimates, an ideal MCO will distribute incident light into the concentration plane as follows: about one third will fall in the cross bar intersection, about one fourth will fall on each of the two bars of the cross bar, but not in the intersection, and about one sixth will miss the cross bar completely either because it misses all of the mirrors or because it hits two mirrors in the same row, causing it to reflect in a direction similar to the incident direction.

Although the light concentrated in the center is a fraction of the incident light, it is very intense because it is concentrated in a small area until it spreads out beyond the concentration plane. The light on the bars is spread over areas that are about sixteen times greater. The remaining light is generally not concentrated at all. Consequently, the bars of light are about four times brighter than the background light that misses the mirrors. The intersection of the bars that would be eight times brighter turns out to be about eighty times brighter because of the contributions from the light that is reflected from both rows of the MCO. In the ideal optic, the central peak is about twenty times more intense than the light in the cross bars. If similar results occurred in nature, then an animal operating in a low light environment would have an eighty times greater intensity on their primary photoreceptor and a cross bar stray light background from each point of light twenty times less than the peak. This seems like enough to enhance the function of a vision system.

Our MCO is not ideal in several respects. First of all the mirror reflectance is far less than 100%. This particularly degrades the contributions due to reflections from both rows of mirrors. Second the mirrors are not perfectly aligned, so the reflections do not line up in the concentration plane completely. This is also particularly significant for the light that reflected from both rows. Small effects can add up quickly: if light is spread over a width three times the width of the bar, the peak decreases by a factor of nine.

Because of these complications and severe time constraints, the project was deemed successful because it produced the characteristic cross bar light pattern in the concentration plane and because the intersection appears to have more light than would be present from the crossing bars alone, in other words, some light reflected from mirrors in both rows. The final measure of success was to attempt to account for all of the incident light.

The optical engineering literature has numerous references to lobster-eye optics and multi-channel plate optical systems. Generally, these refer to x-ray systems. X-rays cannot be focused by lenses or reflected at ordinary angles by conventional metal mirrors. Grazing incidence metal mirrors can reflect x-rays. Consequently plates have been built with channels in them to concentrate x-rays. Furthermore, the concept of two rows of mirrors oriented at right angles is well known in the x-ray optical field. There are two main applications of x-ray optics. One is for telescopes to collect x-rays for astronomical investigation of distant stars. The other is to concentrate x-rays for medical applications including diagnostic imaging (radiology) and radiation therapy.

The design of the MCO was based on many considerations including availability of materials and fabrication processes, sizing the system for convenience, ease of assembly, durability, and similarity to natural or manufactured systems reported in the literature. A six-inch square MCO seemed about as large as we could handle and afford. A smaller system was likely to be harder to assemble to good tolerances and the mirror thickness losses would increase. A portion of the incident light strikes the edges of the mirrors and is lost, so thin is better. Too thin can result in bending or breaking risks depending on mirror material. Stainless steel is locally available already polished at a reasonable price in 0.028-inch thick sheets that are rigid but only block a portion of the light that would reach an adjacent mirror. Other materials such as aluminum or coated glass may have better optical properties but less attractive mechanical properties.

Plexiglas was chosen for the frame because it can be machined without the risk of a structural failure due to any granular structure and it has the added bonus of transparency that is helpful during testing. The slots to hold the mirrors in the frame were 1/16th inch wide, which is consistent with an inexpensive locally available jig saw blade and is wide enough to allow the mirrors to be adjusted with shims within the slots. Choosing a wide slot reduces the manufacturing tolerances and provides for an adjustability to correct for any number of design or manufacturing limitations. The reflected beams from the mirrors were overlapped by visually observing them on a cardboard screen placed in the concentration plane while using shims to adjust the mirror positions.

A Mathcad model was created in order to compare different designs and to predict the potential performance of the optimized design that was fabricated. The model included a single row of mirrors. The performance of two perpendicular rows of mirrors was inferred by examining the analysis of a single row. This made the analysis manageable in the limited time available. The model specified the length of the mirrors, their positions, and the location of the point source of light. The model then calculated the direction of light rays that reflect off the mirrors. Since the light source is a point, each ray is incident on the mirror at a different angle. Each mirror is also tilted at a different angle. The model draws the extreme rays incident and reflected by each mirror.

There are four ray path cases of interest. In the first case, rays hit a mirror and are reflected toward the center of the row of mirrors. In Case 2, a mirror blocks some rays from hitting the intended mirror, so less of that surface is available for reflections. In Case 3, rays pass through the row of mirrors without hitting any mirror. In Case 4, rays that hit near the leading edge of the mirror hit the back of the adjacent mirror and reflect away from the centerline. Only the first case contributes to the concentration of light, except for some additional light that is on axis to begin with and is not reflected. The model calculates the amount of light collected in this case. This tool allowed us to evaluate a number of design variables and select a fairly optimal design.

This process is performed for both rows of mirrors. If one row concentrates 60% of the light and the other concentrates 50%, then we can estimate that about (100%-60%)*(100%-50%) = 20% of the light misses the cross bars and 80% hits them. The amount concentrated in the peak where the bars cross is estimated to be 60%*50% = 30%. Therefore the cross bars collect about 50%. Since the area of the bars is about 32 times the area of the central channel, the bar intensity is based on 1.5% of the available 289 channels or about five times the original beam intensity. The peak is 30% of 289 channels or almost 90 times the original beam. Because of the single reflection contributions, 100 times is a better estimate. The "signal to noise ratio" of the peak to the cross bar is about 20. This calculation is one factor leading to the estimate reported in a previous paragraph for an ideal MCO.

Misalignment of mirrors or other optical elements can degrade many optical systems unless steps are taken to minimize the effect. In our case, the reflections from both rows proved to be uncorrectable using the alignment procedure that was used, but the reflections of the two rows were individually optimized. Additional time would have enabled us to use more comprehensive alignment methods and may have significantly increased the peak height.

Subaperture testing is commonly used to evaluate large or complex optical elements. In our case, it is natural to test portions of the MCO while masking off other portions in order to identify which elements are contributing successfully to the concentration of light on the cross bars. Examples of masks include masking off the four corners or masking off the central area in each row. It is also possible to align one row of mirrors before adding the second row and even to align some mirrors within a row before adding the rest of the mirrors in that row. Several of these techniques were successfully employed. Light sensors can be used to evaluate the tests, but we used the visual observation of light beams incident on a cardboard screen in the concentration plane, which is a common technique. More sophisticated masks and techniques would have been used if more time were available.

In order to appreciate the performance of the optic and the assembly and alignment procedures, it is necessary to estimate the light concentration for a non-ideal MCO. In this case, the reflectance of the stainless steel mirrors is far from ideal, perhaps as low as 60%. This is particularly important for the double reflection contributions from the two rows. The mirror reflectance was measured using an optical power meter and a light source on a lab bench. These measurements supported our ability to account for all of the incident light on the MCO.

Most of the testing was done indoors using a lab bench and an electric light source. This effort was rushed because so much time was devoted to the design and fabrication phases of this project, but generally an adequate effort was made and additional learn by doing objectives were fulfilled by this activity. The lab set-up has a great deal of room for improvement. One of the important lessons learned from indoor testing is the importance of a uniform light source, particularly for subaperture testing and for reflectance measurements. The second lesson is to be careful to maintain a constant source to sensor distance to avoid complications related to the inverse square intensity law. The third lesson is to try to mount the sensor on an adjustable stage so that its position in translation and focus can be optimized. It is also desirable to be able to switch between a cardboard screen and the sensor repeatedly without having to realign the sensor repeatedly. Another lesson is to be careful to match the sensor to the test optic, particularly with wide field of view optics like the MCO. Finally it is important to minimize the amount of stray light incident on the sensor.

Two other methods were used to evaluate the MCO. One was to place your eye where the sensor goes and look at a small light source (not the sun!). Observing the multiple lights as you scan the optic can provide a subjective feel for how many channels are contributing to the light concentration. In our case, it made it clear that the double reflections from the two rows were participating even if the beams did not overlap sufficiently in the concentration plane to raise the peak as high as expected. The other method is to place the MCO in a plane perpendicular to the rays of the sun and observe the concentration on a screen or on a light meter. The sun uniformly illuminates the MCO and provides an intense beam. This test produced very encouraging results, better than the indoor tests. It is hard to align the MCO to the sun, it is hard to do outdoor experiments, and there are no guarantees that the sun is not too low in the sky or blocked by clouds or other objects when you are ready to do some tests. Given enough time, it would be possible to construct a crude azimuth-elevation mount to position the MCO and to manually follow the sun as it moves. It would be possible to construct a reliable mount for the sensor as well. Given our constraints, no alignment procedures were attempted using sunlight.

Another common industry tactic for evaluating novel optical systems is to build subscale models or mockups. In our case, several mockups were made out of highly reflecting poster board. One represented a row of individual channels on a portion of a spherical curved surface. A second one represented intersecting planes that were sections of a spherical surface. The third was a series of flat sheets mounted at varying angles in a foam board frame. None of the mockups were very effective due to fabrication tolerances, but they did exhibit some light concentration capability and provide insight into light concentrating phenomena and fabrication issues for the real demonstration test article.

Another tool that was used in fabrication was drawing a full size template of the pieces that would be assembled into the Plexiglas frame. The template included extended color-coded dashed lines to help establish the angles for cutting the slots that hold the mirrors. Ultimately, these templates were mounted on the Plexiglas and used as cutting guides with great success. The 0.25 inch thick Plexiglas sheets were slotted in pairs and the orientation marked so that the assembled frame would have matching slots on both sides of each mirror sheet despite any fabrication errors.

Nilsson's drawing of a superposition compound eye

template and Plexiglas

assembled Plexiglas frame

frame holding 36 stainless steel mirrors

view of 289 channels formed by 36 mirrors

cross bar and central peak and non-reflected light pattern in lab bench test

"a hundred points of light" seen through MCO

cross bar pattern of MCO observed with sunlight

first poster board mock-up with channels concentrating sunlight

Mathcad chart showing half of the mirrors in one row (red) with upper (blue) and lower (black) light ray paths converging in concentration plane (green)