In this research paper, in a major departure from conventional 2D micromachining processes, design and fabrication of a 3D compound eye system consisting of a 3D microprism array, an aperture array, and a microlens array were investigated. Specifically, the 3D microprism array on a curved surface was designed to steer the incident light from all three dimensions to a 2D plane for image formation. For each microprism, there is a corresponding microlens to focus the refracted light on the image plane. An aperture array was also implemented between the microprism array and the microlens array to eliminate cross-talk among the neighboring channels. In this system, 601 individual micro-assemblies consisting of microprisms and microlenses were constructed in a 20 mm diameter area. In this configuration, the maximum light deviation angle was determined to be 18.43°. This research demonstrated an innovative and integrated approach to fabricating true 3D micro and meso scale optical structures. This work also validated the feasibility of using ultraprecision machining process for 3D microoptical device fabrication. The technology demonstrated in this research has high potentials in optical sensing, vision research and many other optical and photonic applications.
©2010 Optical Society of America
Compound eyes have been the focus for numerous inspiring research topics for more than a century for their unique mechanisms and highly effective performance. The compound eyes in nature with integrated optical and signal processing units can achieve a very large field-of-view (FOV) with extremely small volume and very short processing time [1–3]. The compound eyes have potential applications in many areas such as optical sensing, machine vision, and robotic systems. Over the years many have tried to develop artificial compound eye systems. Although the functionalities of the artificial devices are still inferior to their biological counterparts in many categories, enormous progresses have already been made, particularly in the last few decades [2–14].
The basic imaging units, which are called ommatidia  in a natural compound eye, are commonly represented by using microlenses, photodetector cells, and the associated relay optics in an artificial compound eye system. The artificial compound eyes often combine individual units into different structures depending on the fabrication methods used. In terms of the basic geometry of a compound eye system, generally speaking there are two types of structures for most of the artificial compound eyes, namely, two dimensional (2D) flat and three dimensional (3D) curved structure.
The 2D flat compound eye structure is more often adopted because the fabrication process is readily available and less complicated. The 2D structure is also compatible to commercially available photodetectors such as charge-coupled device (CCD) and complementary metal–oxide–semiconductor (CMOS) cameras. A 2D structure based device usually consists of three components: a microlens array, an aperture, and a photodetector array [3–5]. In addition to this basic configuration, other optical components may be added to enlarge the FOV such as a plano-concave lens  or a Gabor-superlens array . The development of the 2D flat artificial compound eye design owns its success to the recent development in microelectronics and MEMS or microelectromechanical systems technology. However the 2D devices have at least one major limitation due to the structural differences from the natural compound eyes, i.e., lack of 3D curved surface where microoptics reside.
A 3D curved structure with microoptics more closely resembles a natural compound eye. However the development of the 3D compound eyes has been limited by fabrication methods and available 3D image sensors. Because of the limitation of the fabrication methods, some 3D compound eyes only have a very small number of units [8–10] and are most likely fabricated by assembling individual parts together thus resulting in devices with relatively large size. In addition, assembly errors can also be an issue. Because there are no commercially available curved photodetector arrays, planar photodetector arrays in a CCD or CMOS camera are still exclusively used even though they are not compatible with the 3D compound eye structure. Therefore a relay optic is needed for proper image formation. For example, some systems utilized optical fibers for signal relay [9,11,12]. These systems thus have complicated structures and higher fabrication cost. Recently, more 3D artificial compound eye developments have been reported [13,14]. Because of the limitation of the imaging methods, these two compound eye designs used auxiliary devices such as a C-mount objective  or a confocal microscope  to read out the signal.
On a different front, ultraprecision diamond turning process has been developed for more than fifty years. In recent years, several new processes based on ultraprecision diamond turning technique have become available and these new processes allow the fabrication of special optical surfaces and devices [15–18]. In this paper, the design and fabrication of a 3D artificial compound eye was introduced. This 3D compound eye was based on a 3D microprism array and a microlens array. The microprism array and microlens array were precisely fabricated on a curved and a flat surface respectively using ultraprecision diamond machining process thus allowing the incident light from different directions to project to a flat image plane. Specifically, the efforts of this study will be focused on achieving a true 3D compound eye which has a wide FOV, high position sensitivity, compact size, and simple structure thus can be manufactured easily using low cost replicating techniques such as microinjection molding process [19,20].
2. Design of the Compound Eye System
The basic requirements for the compound eye system in this paper include a wide FOV and a flat image plane. To achieve a wide FOV, 3D microlens array structure of the compound eye in nature is an excellent example to emulate. However in order to combine optics on a curved surface with a flat image plane, a beam steering/refracting component is required. The operating principle of the proposed 3D compound eye system is shown on the left in Fig. 1 . The front end of the proposed compound eye design is on a curved surface thus the system can have a very large field angle but the image plane of the system is on a flat surface so a commercial photoelectric sensor such as a conventional CCD camera can be used. Compared with the commonly used artificial 2D compound eye structure (Fig. 1, right), evidently this 3D system will have a much larger field angle but still maintain a compact size.
There are several optical components that can be used for beam steering. These include waveguides or optical fibers, mirrors, decentered lenses or Gabor-superlens, and prisms. Considering cost, difficulty of machining, and size, a 3D microprism design was chosen as the beam steering devices to work with a secondary microlens array.
Figure 2 shows the principal section and the optical path of a microprism. In this configuration, O 1 is the apex of the microprism, and the refracting angle of the microprism is A. To simplify the machining process, the top surface of the prism was set to be parallel to X axis. An incident light at angle I 1 (at the top surface) enters the microprism and exits at angle (at the bottom surface). is the refractive angle at the top surface and I 2 is the incident angle to the bottom surface. The deviation angle of the incident light δ is given by the Eq. (1) :
Inside the prism and I 2 are related by Eq. (2):
The microprism was designed to steer the incident light, which is in the direction KK with the Z axis, to the direction parallel with Z axis. Therefore we have I 1 = KK,, and δ = KK.
The refractive index of the microprism material is defined as n. The microprism is operated in air and the refractive index of air is assumed to be n 0 = 1.0. Applying the Snell's law and substituting I 1 = KK, into Eq. (2):
From Eq. (3) the value of A can be calculated for the selected incident direction KK. In this design the maximum incident angle KK can reach 90° without total internal refraction (TIR) occurring inside the microprism for the material which was going to be used (n = 1.491). This means that theoretically the FOV can be as large as 180° for the entire device.
Considering the 3D compound eye system in Fig. 1, if the top curved surface of that system is consisted of thousands of microprisms as shown in Fig. 2 the incident light in a 3D spherical space can be steered to a 2D flat plane. All the microprisms have the same size with different refracting angle based on their location. There were 12 layers of microprisms on the sphere cap. Figure 3 shows the cross section of the entire 12 layers of microprisms. The microprisms on the same layer are symmetric to the sphere cap apex with identical refracting angle but are facing different azimuth directions. The number of microprisms in each layer depends on the size of the microprisms. In this design, the width of the microprism (normal to the paper plane in Fig. 3) is 0.6 mm and the length of the microprism (in the paper plane in Fig. 3) is 0.85 mm. The prism at the vertex is just a flat circular plate of radius of 0.9 mm and will not cause light deviation. This gave a total of 596 microprisms on the sphere cap. Combined with the flat prism at the vertex and the plano microlens array below resulted in total of 601 microchannels.
Figure 3 shows half of the cross section of the microprism array design. In this design, the bottom surface of each layer is connected without gap and the top surface of each layer is arranged in a way that there is a step between the neighboring layers. The dashed lines depict the center line of each layer. The 3D plots of the microprism array are shown in Fig. 4 , which is plotted in Matlab using calculated surface profile. Figure 4(a) is the top surface and Fig. 4(b) the bottom surface (the cap shown in Fig. 4(b) is located inside the cap shown in Fig. 4(a) for the actual device). The cross sectional plot in Fig. 3 is from X = 0 to X = 10 and along the Y = 0 direction in Fig. 4. Figure 4(c) and 4(d) shows the enlarged details around the center of the microprism array.
The 3D microprism array is used for light steering. For image formation a 2D microlens array is also needed to focus the deviated light to the image plane. The location (in X-Y plane) and size of the microlenses is decided by the location of the microprisms. Each microprism channel had one corresponding microlens to form an image while the center flat microprism works with six microlenses (one in the center and five others around in a circular pattern) due to the large size of the microprism at the vertex. The radius of curvature of each microlens was 4 mm and the aperture was 0.58 mm. The optical design can be performed using software programs such as Zemax (Zemax Development Corporation, Bellevue, WA).
As discussed in details, the 3D compound eye system is composed of three components: the prescribed 3D microprism array, the microlens array, and an aperture array, which is located between the microprism array and the microlens array to prevent signal cross-talk. These three components formed the 601 individual channels and each channel was aimed to view a specific direction in the 3D space.
3. Fabrication of the Compound Eye System
As described earlier, fabrication of 3D micro optical components is still a challenging work today. Although several methods have been developed [13,14,22,23], most of these methods are restricted to simple base curves (sphere or cylinder) and simple optical features (spherical microlenses). On the other hand, ultraprecision diamond machining process utilizing multiple axis real time servo control with nanometer resolution is becoming a viable approach to creating complex true 3D micro and meso scale features with optical surface finish on a wide range of machinable materials. The capability of ultraprecision machining process has been demonstrated in creating diffractive lenses, microlens arrays and even 3D microstructures [16–18].
The compound eye system in this research has three major components and the fabrication utilized the combination of regular diamond turning, diamond broaching , slow tool servo [17,18] and micromilling [19,20] processes. All three components were machined on the ultraprecision machine (350FG, Moore Nanotechnology Systems, Keene, New Hampshire). The optical materials used for the microprisms and microlenses are polymethylmethacrylate (PMMA) and the opaque material used for the aperture array is white ThermoPlastic Olefin (TPO). The latter material was selected for convenience.
The machining process for the 3D microprism array is schematically illustrated in Fig. 5 . A piece of round PMMA substrate was first machined to rough dimensions [Fig. 5(a)]. Both the top and bottom surfaces were diamond turned to establish the flatness and parallelism of these surfaces. The outside circular surface was also diamond turned and can be used as a reference to center the part. The part was then mounted on the vacuum chuck and the best fit convex surface C1 of the top surface was machined right at the middle of the part by diamond turning [Fig. 5(b)]. After the best fit surface used as the 3D base surface was completed, the top flat steps of the microprism array were diamond turned by using a diamond tool with radius of 0.381 mm [Fig. 5(c)]. As described in the previous section, the top surfaces with the prisms were designed to be flat and the conventional diamond turning was used. The top surface was finished after the flat steps were machined and the process continued for the bottom side. Since the designed part is hollow and the thickness of the part is small, it cannot be mounted on the vacuum chuck due to deformation. To support the thin PMMA part, an aluminum mandrel [as shown in Fig. 4(d)] was machined to match the top shape of the PMMA part machined in the last step. The PMMA part was bounded to the aluminum mandrel using optical wax [Fig. 5(e)] and the mandrel was then mounted on the vacuum chuck of the diamond machine. The center of the PMMA part was aligned with the machine spindle using the outside circular surface as reference with a precision dial indicator with nanometer resolution (Federal gage, model EHE-2056). The bottom side of PMMA part was first machined by diamond turning to the best fit concave surface C2 [Fig. 5(f)]. Then the bottom surface of the prisms was fabricated by broaching process using the 0.381 mm tool nose radius diamond cutter [now the top surface in Fig. 5(g)]. In this step the diamond tool was cutting vertically along the microprism's width direction (circumferentially to the machine spindle axis) and the microprisms were machined sequentially using slow tool servo broaching process. The details of the broaching process can be found elsewhere . Finally, the aluminum mandrel and wax were removed to complete the construction of the 3D microprism array [Fig. 5(h)].
The microlens array was machined using slow tool servo process as well [17,18]. The aperture array was machined by high speed micromilling. The process details for the aperture array can be found in . The diameter of each micro aperture is 0.5 mm. For part alignment, fiducial marks were machined in the same operation when the parts were being fabricated. The tolerance of these fiducial marks is derived directly from the precision of the ultraprecision machine which is less than a micron. The fabricated microprism array, microlens array, and the assembled compound eye system are shown in Fig. 6 .
4. Results and Discussion
The performance of the 3D microprism array was measured first. Figure 7(a) shows the setup for measuring the steering angle of the microprisms. A collimated He-Ne laser was used as the incident light. After passing the aperture array and the microprism array, the incident light wave was divided into 601 sub waves and each traveled along a specific direction. A CCD camera (PL-B957F, pixeLINK) was used to record the position of each light spot at a plane vertical to the incident laser beam [as shown in Fig. 7(b)]. By moving the microprism array along the Z direction and measuring the displacement of the light spots along the X direction, the steering angle of each beam can be calculated. Figure 8 shows the measured steering angles and the design values. The prisms from the center to the edge along the radius were measured. In Fig. 7(b), the center spot and the five spots next to the center were passed through the flat plate at the center, which is microprism 1. All six plates at the center have zero degree steering angle. The measured steering angle of each microprism agreed with the design value. The maximum steering is 18.43° for the microprism at the most outside layer (microprism 12 in Fig. 8). The steering angle measurement results indicate that if light incident from the microprism's top surface along the measured steering directions then the output light will be along the Z direction.
We used the assembled compound eye and the CCD camera to form a 3D compound eye camera. Due to the size limit of the CCD camera’s image sensor, a zoom lens (VZMTM 450i, Edmund Optics) was added to include more channels [Fig. 9(a) ]. The magnification of the zoom lenses is 0.75x. A computer screen was placed at L = 780 mm away from the compound eye system as an object [as shown in Fig. 9(b)] and the fish in Fig. 9(b) were numbered to illustrate the performance of the compound eye camera system.
Figure 10 shows the image obtained using the 3D compound eye system. As mentioned earlier, due to the limited size of the CCD image sensor, not every microchannel was visible, but the entire computer screen has been sampled (the edges of the screen are clearly visible in the circled areas). Figure 11 shows the flipped and enlarged images of the six layers around the vertex of the 3D compound eye and these images convey the most important information of the object. Compared to the object [as shown in Fig. 9(b)], all of the seven fish can be seen with each fish numbered in the same layout. In Fig. 11 the relative position of each individual fish on the object plane can be clearly distinguished. Compared to the image obtained using a 2D compound eye system (same setup shown in Fig. 9(a) but without the 3D microprism array and the aperture array) as shown in Fig. 12 . It is obvious that the FOV of the 2D system is very narrow as indicated in Fig. 13 .
According to the setup and the object dimensions in Fig. 9, the approximate half field angles of the 3D compound eye system and the 2D compound eye were 10.8 degree and 2.9 degree for the center 8 layer channels. For the eight layer microchannels at the center, the FOV of the 3D compound eye system is about four times of that of the 2D system. The approximate half field angle of the 3D compound eye system of 10.8° for the center 8 layer channels also agree with the measured steering angle 10.35° for microprism 7 (the microprisms in the 2 layer at the center are all corresponding to microprism 1).
By comparing the performance of the 3D compound eye system (Fig. 10, 11) and the 2D compound eye system (Fig. 12), it is clear that the 3D system has a much wider FOV and is more sensitive to the position (direction) of the target. It will be much easier to locate the position of the object by using the 3D system than the 2D system. However due to the wider FOV, the 3D system sampled less data per area than the 2D system because the average number of channel per spatial angle is less. The 2D system can sample abundant information to reconstruct a clearer object image and this will be difficult for the 3D system. Increasing the number of channels for the 3D system can help sampling more information but it will also increase the cost of fabrication. Future work would include optimization of the 3D microprism design and image reconstruction using the 3D compound eye.
In this research paper, a 3D compound eye system which consists of a 3D microprism array, an aperture array, and a microlens array was developed. The 3D microprism array was fabricated on a curved spherical surface and was designed to steer the incident light to a 2D image plane. For each microprism, there was a corresponding microlens to focus the deviated light to the image plane. An aperture array was placed between the microprism array and the microlens array to prevent cross-talk among the neighboring channels. Altogether 601 individual units were designed in the 20 mm diameter area and the measured maximum light deviation angle is 18.43°.
All three parts were machined on an ultraprecision machine by using ultraprecision diamond machining processes including diamond turning, slow tool servo process, broaching, and micromilling. Compared to other possible machining process, the ultraprecision diamond machining process is capable of producing more complex structures with larger and small feature size coverage, better surface finish, and most importantly true 3D micro and meso scale structures. Another important feature which is fundamentally different from most other micromachining processes is that the entire optical structures were created in a single setup without re-chucking therefore allows extremely accurate devices to be created with minimum or no assembly required. In case assembly is needed, fiducial marks and fitting features can be created during the fabrication of microoptical components therefore allows easy assembly with high repeatability [19,20]. This approach is critical in microoptical fabrication as it provides an integrated approach to seamlessly bridging the microoptical features and the macro size supporting structures.
Moreover, the steering angles of the machined 3D microprism array were measured and were determined to match the design values. In addition, the 3D compound eye system has also undergone an imaging test. The results of the imaging test confirmed that the 3D compound eye has a much larger FOV than the 2D compound eye therefore can simultaneously acquire more information than a 2D design.
In the 3D compound eye system developed in this research, only a very small portion of the base curve was used to demonstrate a much larger FOV on the 3D compound eye than the 2D compound eye of the same size. The theoretical maximum FOV of this type of 3D compound eye can be as large as 180° if we can use the entire semispherical surface as the front optical surface. The process for a full 180° design is currently being investigated.
This material is partially based on work supported by National Science Foundation under Grant Numbers CMMI-0928521 and EEC-0914790. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors would also like to acknowledge Nanotechnology Systems in Keene, New Hampshire for their continuous support.
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