Natural optical design concepts for highly miniaturized

Natural optical design concepts for highly miniaturized camera systemsR. Völkel

Institute of Microtechnology, Université de Neuchâtel(now: Karl Suss KG, Neuchâtel, Switzerland)

ABSTRACT

Microcameras for computers, mobile phones, watches, security systems and credit cards is a very promising future market.Semiconductor industry is now able to integrate light reception, signal amplification and processing in a low-power-consuming microchip of a few mm2 size. Active pixel sensors (APS) supply each pixel in an image sensor with anindividually programmable functionality.[ I ] Beside the electronic receptor chip, a highly miniaturized lens system isrequired. Compared to the progress in microelectronics, optics has not yet made a significant step forward.{2] Today'smicrocamera lenses are usually a downscaled version of a classical lens system and rarely smaller than 3 mm x 3 mm x 3mm. This lagging of optics is quite surprising. Biologists have systematically studied all types of natural eye sensors sincethe eighteenth century.[3J Mother Nature provides a variety of highly effective examples for miniaturized imaging systems.Single-aperture systems are the appropriate solution if the size is a free design parameter. If the budget is tight and opticslimited in size, nature prefers multiple-aperture systems, the so-called compound eyes. As compound eyes are limited inresolution and night view, a cluster of single-aperture eyes, as jumping spiders use, is probably a better solution. The recentdevelopment in micro-optics offers the chance to imitate such natural design concepts. We have investigated miniaturizedimaging systems based on microlens arrays and natural optical design concepts. Practical limitations for system design,packaging and assembling are given. Examples for micro-optical components and imaging systems are presented.

1. OPTICAL DESIGN IN NATURE

Since the Cambrian period about 500 million years ago nature has been exploring and optimizing image-forming lenssystems.[3, 4, 5] For all types of creatures evolution has found appropriate image capturing systems to give them allnecessary visual information about their environment. For relatively large vertebrates, like humans, eyes were optimized toprovide a high resolution, large field of view, focusing ability, color detection and a very large dynamic range to see both inthe bright sunshine and in the dark night. Here, the size or volume of the eye is a free parameter for the design. The opticalperformance is the key issue. A large single-pupil eye seemed to be the best solution. For small invertebrates having anexternal skeleton, the volume, weight and functionality is the figure of merit. The smaller an animal is, the higher is usuallythe percentage ofthe animal's body reserved for the eye. For small animals the eyes are very expensive in weight and meta-bolic energy consume. If the budget is tight, nature prefers to distribute the image capturing to a matrix of some small eyesensors instead of using a single eye. The resolution of such so-called compound or fly's eyes is usually poor compared tothe single-aperture eyes.[4] However, this lack of resolution is often counterbalanced by additional functionality like a largeview angle, polarization or fast movement detection. Natural eyes are a perfect compromise suited to the requirements of thelife-style ofthe animal. In the following, we will briefly explain the optical properties ofnatural eye sensors.

Single-aperture eyesThe human eye is a single-aperture image capturing system similar to photographic or electronic camera systems (see Table1). The eye consists of a flexible lens for focussing, a variable pupil (iris) for fast sensitivity adaptation and the retina, theimage detector. A nice definition of the human eye is given by Hofmann.[6] "The human eye is a special version of a pin-hole camera, where Fresnel diffraction is compensated by the introduction of a focussing system". The diameter of thepinhole or iris is variable from 1.8 mm to 8 mm for bright light and dark viewing. The lens of the human eye is sphericallyovercorrected by graded index effects and aspherical surface profiles. The refractive index ofthe lens is higher in the centralpart of the lens, the curvature becomes weaker towards the margin. This correction offsets the undercorrected sphericalaberration of the outer surface of the cornea. Contraction or relaxation of muscles changes the focal length. The retinacontains nerve fibers, light-sensitive rod and cone cells and a pigment layer. There are about 6 million cones, about 120million rods, and only about 1 million nerve fibers. The cones of the fovea (center of sharp vision) are 1 to 1 .5 tm indiameter and about 2 to 2.5 tm apart. The rods are about 2 tm in diameter. In the outer portions of the retina, the sensitivecells are more widely spaced and are multiply connected to nerve fibers (several hundred to a fiber). The field of vision of

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an eye approximates an ellipse about l50 high by about 2l0 wide. The angular resolution or acuity AP is around 0.6 to I

mm of arc for the fovea.

Compound eyesCompound eyes are multi-aperture optical sensors of insects and crustaceans and generally divided into two main classes.

apposition compound eyes and superposition compound eyes (see lable I). An apposition eye consists of an array otlcnses

and photoreceptors each of the lenses focusing light from a small solid angle of object space onto a single photoreceptor.Each lens-photoreceptor system isreferred to as ommatidia or littleeve'. Apposition eves have somehundreds up to tens of thousandsof these ommatidia packed in non-uniform hexagonal arravs.[7]

The superposition compound evehas primarily evolved on noctur-nal insects and deep-water

J I II 1crustaceans. The light from multi-

flfl :ijT - pIe facets combines on the surface

/ /\ j_- --- of the photoreceptor layer to form

V J ' ]a single erect image of the object.Compared to apposition eves, thesuperposition eye is much morelight sensitive. Nature has evolvedtwo principal optical methods to

create superposition images: gradient refractive index and reflective ommatidia.[4J Some insects use a combination of both

types of compound eyes. Variable pigments switch between apposition (daylight) and superposition (night) or change the

number of recruited facets making up the superpositionimage.[8] A very interesting modification is the neuralsuperposition eye of a housefly. where each ommatidia hasseven detector pixels or rhabdomeres. Signals of differentadjacent ommatidia interact within the neurons of the fly's brainsystem. This allows fast directionally selective motion detection,which enables the housefly to maneuver perfectly in three-dimensional space.[91

Jumping spidersin contrast to insects, jumping spiders have opted for single-lenseyes. but eight of them (see Figure 1). Jumping spiders have twohigh-resolution eyes. two wide-angle eyes and four additionalside eyes. The two antero-median eves provide a magnifiedimage at a high resolution for a rather small visual field.[lO]Jumping spiders use these eyes for detailed inspection of objectsof interest. It is worth to note that these eyes have a moveableretina. The retina can be moved vertically, laterally androtationally. The spider can track a prey without moving itself. The two antero-lateral eyes provide a largevisual field at a

reduced resoiution.[1 1] The small side eves cover the large field lefi and right of the spider. The spider uses different single-

lens eyes tailored for different functions. This trick seems to be the best compromise to combine highresolution and large

observation field within the limited budget of a small animal or microsystem.

Natural optical materialsThe way in which animal eyes form images are either based on refracting lenses, reflecting mirrors orin the simplest case

just on pinholes. Nature has experimented with all types of refractive index-variant materials and aspherical surfaces.

Natural lens systems are e.g. constructed from an optically inhomogeneous gradient of protein and water mixtures. Natural

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PTTable 1. Different types of natural eye sensors and its artificial counterpart. Artificial eyesensors are based on planar components due to manufacturing restrictions.

,'t

Figure 1. SEM picture of the head of a jumping spider.Photograph by Aaron Bell, http.Ilwww.hotistra cdu/weh/docsIS±1


mirrors are made of multiple quarter-wavelength thick layers of materials with alternating high and low refractive indices,e.g. guanine (n = 1 .83) and cytoplasm (n 1 .34).[4]

In image forming systems based on spherical shaped lenses, the most serious potential problem is spherical aberration.Peripheral rays tend to be over-focussed, and uncorrected the image quality is often poor. Most other defects matter less. Forexample, off-axis aberrations and field curvature do not matter much in a human eye, where critical resolution is onlyneeded in the center and the receptors are located on a concave surface.[4] A correction of the spherical aberration in naturaleyes is achieved by using aspherical surfaces profiles and graded refractive index (GRIN). For example, the refractive indexofthe human eye lens varies from 1 .386 in the center to 1.406 at the periphery.[12J

Natural imaging systems are based on refraction and reflection. The optical imaging system is often not perfect, but thecomplete eye sensor including the retina and the computing neural network is optimized and well adapted to needs of theanimal. Nature handles carefully the tightest budgets and never wastes space and metabolic energy. This is the real benefitof studying natural eye sensors for micro-optical system designers. In the following we discuss the influence of scale andphysical dimensions on the optical properties of image forming systems.

2. OPTICAL PROPERTIES OF SMALL-SCALE LENS SYSTEMS

Aberrations and diffraction limitThe stop number ofa lens is given by F =fIØ, where f is the focal length and 0 is the lens diameter. The diffraction limitedresolution of a lens is given by x U 2F, the depth of focus by z E 4XF2. Both values are independent of the lensscale. Adownscaling of both, the diameter 0 and the focal length f does not affect the diffraction-limited resolution, if the stopnumber is not changed. Furthermore, scaling will not change the type of aberrations created by a certain lens profile.However, it will change the magnitude of the wavefront aberrations, as aberrations are expressed in fractions of thewavelength. Small lenses have fewer aberrations than large lenses (for the same F-number and wavelength).[13J It'srelatively simple to achieve diffraction-limited performance for miniaturized lens systems. Aberrations do not have the sameweight in micro-optics as they have for macro-optics. For small-scale lens systems, the diffraction limit itself is theimportant criteria describing and limiting the resolution and image fineness.

Space-bandwidth productIt was mentioned that a downscaling of the physical dimensions of a lens system does not change the size of the diffraction-limited spot or image pixel the system generates. On the other hand, a downscaling reduces the number oftransported imagepixels drastically. We assume a diffraction limited lens system that provides a quadratic image field of I xI 02/2 size. Thediagonal d1 = I is set equal to the lens diameter 0. For such an optical system, the number of transported image pixelsM is given by

j2 1 02 1 04M ()2

=2 (F)2 2 (f)2 (1)

The number of image pixels M, also referred as space-bandwidth product, scales with the square of the lens diameter 0 for aconstant F-number and with the

large lens small lens fourth power in 0 for a constantfocal length f. A miniaturizedimaging system is able to imagefine details of a scene, but not

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) image field

Electronic light receptor chips havetypically a pixel pitch of 3 to 5 imcorresponding to a spatialresolution v of 100 to 166 lines per

(equal F-number and pixel size)mm. According to the samplingtheorem, it does not make sensethat the resolution of an opticalsystem v0 is better than that of theFigure 2. The number of image pixels M scales with the square of the lens diameter.


receptor mosaic. An F-number of 6 to 1 0 is sufficient for most artificial eye sensors. Table 2 gives the number of imagepixels M for F/6 and P/10 diffraction limited systems of different diameters 0. The image fineness is rapidly decreasingbelow 5 mm lens diameter.

We now better understand why the single-lens eye concept does not work for tiny insects. The number of pixels respectivelythe space bandwidth product supplied by a small-scale single-lens eye sensor is not sufficient to recognize the insect's matesand enemies. The nature's design strategy was to further reduce the lens diameter and to distribute the imaging task to somehundreds or thousands of individual eye facets.

Resolution of compound eyesFor a round-shaped apposite compound eye, the observed scene is divided in angular sectors p as shown in Table 1 .The

angle between the optical axes of two adjacent eyes or ommatidia is referred as the inter-ommatidial angle AcI. Eachommatidium usually detects only one pixel. The image detection is performed massively parallel. This is a very effectiveconcept for movement detection and large object field observation. A fly almost achieves observation range of 4z by usingtwo compound eyes on each side of the head.

In general the resolution of

lens diameter 0 5mm 2 mm 1 mm 500 tm 100 tm 50 tm

image pixelsM 1389000 222000 56000 14000 560 140

(f /6) 1180 x1180 283 x283 236 x236 118 x 118 23 x23 12x 12

a compound eye dependson two factors: a) thefineness of the mosaic ofreceptive elements that

_______ sample the image and b)50 the optical quality of the

image, that those elements7 x 7 receive.[14] A sinusoidal

pattern structure isresolved if the spatialfrequency of the detector

image pixels M 500000 80000 20000 5000 200

(f/10) 707x707 283x283 141x141 71x71 14x14

Table 2. Number of image pixels M for a diffraction limited f/6 and f/b-systems providing animage field of I x I= 02/2

mosaic v is equal, orhigher than the pattern frequency v0 of the image. The spatial resolution (v 1/(2.M) of the receptor mosaic and theoptical cut-offlimit of v0 = ø/X leads to the definition ofthe eye parameter p given by

p = 0 . AcI � . (2)

The eye parameter p is a measure how close an eye sensor comes to the diffraction limit and reaches AJ2 for diffractionlimited eyes. For a diffraction-limited round-shaped compound eye the eye parameter Pdl corresponds to

Pdl (Reye)/ = , (3)eye

where 0 is the lens diameter, zW the inter-ommatidial angle and Rye the radius of the compound eye as shown in Table 1.From equation (1) and (3), we now understand the key problem of compound eyes. It is very difficult to increase theresolution of a compound eye as a whole, because the eye becomes too big.[14] The diffraction-limited resolution isinversely related to the lens diameter 0. To achieve a higher resolution we have to increase the diameter of the eye facets.By doubling the lens diameter 0, the radius ofthe eye must increase by factor 4 to keep the eye parameter constant.

In conclusion, compound eyes are inherently low-resolution image sensors. For small animals, a limited number of imagepixels is the only way to avoid a flooding of the animal's neural system with too much information. The low resolution isoften counterbalanced by additional ftmctionality like wide-angle observation, polarization or fast movement detection.

3. MICRO-OPTICSSince the invention of the first integrated circuit (IC) in 1958, optical lithography is a key technology for the rapidlygrowing semiconductor industry. Optical designers and lens manufacturers have used all possible tricks to further improvethe resolution of photolithography. Despite of the enormous success in these large-scale imaging systems, optical designers

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glass substrate by metal ions, b)diffusion polymerization inplastics and c) chemical vapordeposition.[16} GRIN lenses arewell suited for imaging tasks andhave been successfullyimplemented, e.g. for 1:1

imaging in photocopyingmachines.[18, 19] However, thedifficult fabrication processseverely limits the assortment ofcommercially available GRINlenses.

are quite inexperienced in working with small volume budgets of 1 00 mm3 and below. Miniaturization requires differentdesign strategies than perfection does. The severest problems are the availability of miniaturized optical elements. Themicro-optical toolbox is still quite incomplete. In addition, packaging and alignment of optical microsystems is an ambitioustask. Standard mounting using a close-fitting sleeve, lock- or distance rings and grooves are not very practical. Micro-opticsdesigners have to learn how to overcome these restrictions.

Micro-optical designMicro-optics is still closely tied to ideas, concepts and microfabrication technologies developed for semiconductor industry.[15, 16] This includes a general restriction to flat building parts (planar lens and receptor arrays), a matrix-orientedpatterning (Cartesian coordinates) and pure bulk materials (very limited possibility of index modification). Micro-optics isstill a component-oriented discipline aiming on the improvement of efficiency or functionality of single elements. Inaddition, micro-optics' research is often divided in diffractive, refractive and graded index communities. Nature never hadthese problems. Nature did not care if light is diffracted, refracted, reflected or absorbed. Nature always optimized thecomplete eye sensor, considering optics, detection and image processing.

Compared to nature, a micro-optics system designer has not much choice in building parts and optical materials.Commercially available micro-optical components are rare. Very often, a designer has to order individual components as'special request' or even has to manufacture the components himself Classifying units for micro-optics are missing, notstandardized or misleading. For example, a diffraction efficiency of 99% must not mean that a grating diffracts 99% of thelight. This lack of clarity leads to a more fundamental problem, the diversity of micro-optics. For example, a microlens forcollimation might be diffractive, refractive or both (hybrid). All three types of microlenses will collimate the incoming light.Despite their equal optical functionality, their aberrations, tolerances and problems are completely different. It is not trivialto choose the right type of element for a specific optical design. Additionally, the decision is often influenced by thepreferences of the individual optics designer. Most experts for micro-optics prefer either a diffractive or refractive solution,depending to what they know best or have available.

Microlenses for imagingAs previously discussed, most animal eyes are based on a combination of curved lens surfaces and a radial symmetricvariation of the refractive index within the bulk material (GRrN).[l7] Different techniques to fabricate technical GRINlenses have been developed: a)selective exchange of ions in a

= )Figure 3. Refractive microlenses: a) Very small lenses of 5 tm diameter, b) lens profile'(310 pm diameter, f 375 tm).1Courtesy of J.C. Roulet, Institut de Microtechnique, Université de Neuchâtel, Switzerland

Diffractive microlenses are generally not well suited for imaging tasks. Focal length and efficiency depend strongly on thewavelength of the light and limit the lenses to monochromatic applications.[l6] In addition, a finite angular field diameter,low numerical apertures, straylight and ghost images created by spurious diffraction orders will limit their ability forimaging. Nature has never used a diffractive lens for imaging (as far as the author knows).

A very simple fabrication technique for refractive microlens arrays is the reflow or melting resist technique.[20, 21, 22]Photoresist is micro-structured by photolithography and melted at a temperature of 150 to 20011C on a hot plate or in anoven. The melted resist lenses serve as a master element for subsequent transfer processes like reactive ion etching orreplication in plastic. Figure 3 shows different types of piano-convex microlenses fabricated by reflow techniques.[23] Adiffraction-limited optical performance (p-v wave aberrations < ?J9, Strehl 0.98) was demonstrated for a refractive

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microlens of 135 im diameter and a focal length of 370 j.tm. Aspheric lens profiles are obtained by varying the etchparameters during the reactive ion etching transfer.

Aperture arraysApertures, stops, pupils or baffles are essential parts of every optical system. They are used to improve the image contrastby blocking vignetting or aberrant rays, and reducing straylight. For lens array systems, aperture arrays are realized by thinfilm deposition, photolithography and consequent etch or lift-off steps.

Packaging and assembling of micro-opticsPackaging and alignment of miniaturized optical systems orcomponent has to be aligned according to 3 lateral and 3rotational degrees of freedom. For micro-optics, standard"classical" mounting is not practical. One packagingapproach is to reduce these 6 degrees of freedom by using astack of planar optical layers as shown in Figure 4.[24] Theoptical elements are fabricated on one- or both sides of aplanar wafer equipped with alignment marks. A stack ofdifferent optical layers is mechanically aligned in a mask- orbond-aligner. Glass plates, metal wires, optical fibers orplastic sheets are used as spacers. The different optical layersare bond by using UV-curing epoxy, fusion bonding or thick-film solder glass bonding. An accuracy of tm lateral and

tm vertical was achieved using a MA6/BA6 from SussKG Munich. Self-alignment techniques use lenses, balls orwires and grooves or rings as counterparts.

modules is a rather difficult task. Every micro-optical

(1

sc.

4. DESIGN STRATEGY FOR IMAGE CAPTURING MICROCAMERAS

In most applications humans have to inspect the resulting microcamera images. Therefore, the image fineness must besufficient for humans to identify the observed object or scene. In addition, microcameras should have (optional) wide-angleobservation ability. Neither single-lens systems nor fly or bee eye systems are well suited to fulfill these demands. Therestriction to planar lens- and receptor arrays makes it even more difficult to design artificial eye systems. Based on theprior considerations, we get the following design strategy for image capturing microcameras:

1) The resolution of the optical system should not be finer than the receptor mosaic. A detector resolution of 3 to 5 jimrequires a f/6 to ff10 optical system respectively.

2) For a f/6 system, the image distance is about seven times the aperture diameter. The lens diameter is calculated from thedesired overall thickness ofthe microcamera system.

3) If the number of image pixels (or angular field) of one single image channel is not sufficient for the envisagedapplication, multiple channels should be used in parallel. A superposition of the partial images is performed either withinthe signal-processing unit (neural superposition) or by spatial superposition in the image plane. For spatial superposition,erect imaging is required.{25, 26] Only next neighbor images should superimpose to limit off-axis aberrations.

4) The resolution of the imaging system should be higher in the center and lower at the rim to provide both, telephotu andwide-angle characteristics.

If we look for examples in nature, we find that the proposed camera design has very much in common with the eyes ofjumping spiders. Jumping spiders do not have compound eyes. Their resolution would be too poor to identify targets worthto jump on. To have single-lens eyes as vertebrates, spiders are too small. The spider uses a cluster of single-lens eyes, eachpair tailored for a different task. Spiders see almost as sharp as we do and have a good idea what is going on in itssurroundings. The natural design concept to distribute the imaging task to a cluster of different single-lens eyes, is as wellthe most promising approach for very small microcamera systems. Examples for arrays of micro-camera systems are shownin the following.

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alignment marks

Figure 4. Alignment marks and spacers are used for themounting of a micro-optical array imaging system.


rr4

5. MICRO-OPTICAL IMAGING SYSTEMS

Array imaging systems for large object fieldsFigure 5 shows a schenie of a multiple-lens imaging system for 1:1 imaging of extended planar objects (13 -1-1). [he micro-

optical system consists of a stack of three microlens arrays forming an array of microcameras. Two lens arrays are used törimaging. The intermediate array serves as a field lens. Ademagnification of the intermediate image is introduced toavoid crosstalk between adlacent camera channels. Theimaging system takes advantage of the following opticaldesign concepts:

i) MA6IBA6 maskaligner from Karl Suss KG FRG.

Smmetrv. For symmetrical optical systems theantisymmetrical wavefront aberrations (coma, distortion.and lateral color) are minimized. However, symmetricalaberrations (spherical aberration) are doubled and have tobe compensated in another way.

Aspherical surfaces. Spherical aberration is minimized byusing aspherical lenses. A piano-convex hyperboloid hasno spherical aberration for the paraxial region.

Telecentrv. For telecentric systems a small detbcusing b'vchanging the distance of the object or the observing planedoes not affect the image size.

aperture

inter-mediateimage

microlens

Figure 5. Micro-optical array imaging system for 1:1 imagingof an extended planar object as used for microlens projectionlithography (MPL).

Array optics. Each point in the object plane is simultaneously transported by different microcameras. The partial imagesoverlap coincidentally to provide a single. complete image of the object (superposition). The image quality is invariable forthe whole image field. Theimage size is only limited by thesize of the microlens arraysystem. No matter how large thesystem is, it will provideuniform image quality (no fieldcurvature, distortion, or contrastdegradation at the edge of theimage).

object plane

/H

Typical applications for such an image planeoptical system are microlensprojection lithography (MPL),photocopy machines and Figure 6. Micro-optical array imaging system for 1:1 imaging of an extended planar objectscanners. Microlens projection as used for microlens projection lithography (MPL) and microcamera arrays.lithography is a lithographictechnique where a photomask is projected by using an array of microcameras.[26. 27]Figure 5 shows a photograph of a 6-layer imaging system for MPL consisting of a stack of 3 lens and 3 aperture arrays. The planar arrays were aligned in aSUSS-maskaligner' with a precision better than 2 tm. A resolution of 3 to 5 m and a depth of focus of more than 50 im isachieved. Figure 6 shows the scheme of the micro-optical array imaging systems as used for microlens projectionlithography. Figure 7 shows the image plane of the system shown in Figure 5 for a 25:1 demagnification of a photographicslide of the Neuchãtel castle. The image size is about 90 iim diameter, the resolution on the order of 3 iim (diffractionlimited, Strehl 0.83).


If an object consists of a periodic array of identicalpatterns, an observation by a compound eye or

6. CONCLUSIONNature has developed a diversity of optical lens designs that enable animals to recognize their mates, enemies and food.This immense pooi of system designs is a very exciting resource for optical designers who search for new ideas how tominiaturize imaging systems. Unfortunately, the toolbox of a micro-optical designer is still quite incomplete. Today'smicro-optics is closely tied to ideas, concepts and microfabrication technologies developed in semiconductor industry. Thisincludes e.g. a general restriction to flat building parts (planar lens and receptor arrays), a matrix-oriented patterning(Cartesian coordinates) and pure bulk materials (very limited possibility of index modification).

Fundamental problems for small-scale lens systems are diffraction effects and the limited space-bandwidth product, whichdrastically limit resolution and image fineness for lens systems below 1 mm diameter. The natural optical design concept ofcompound or fly's eyes is very useful for wide-angle observation and fast movement detection, e.g. a camera system forpath finding in a micro-robot. However, compound eyes are intrinsically low-resolution systems and not suited for capturingsharp images. Miniaturized single-lens cameras suffer from the low number of image pixels transmitted. A f/6 system of 0.5mm aperture provides an image fineness of less than 120 x 120 pixels. This makes it hard for humans to recognized objectsor persons. The most promising compromise is a camera "cluster", where different single-lens microcameras are locatedside-by-side. Each camera observes only a small part of the object field. The partial images are combined by neuralsuperposition in the signal-processing unit or by spatial superposition on the detector chip. The microcameras within thecluster should have a decreasing resolution and an increasing field of view from the center to the rim. The cluster concept isbased on the eyes ofjumping spiders, which use 4 pairs of different eyes to combine sharp view for a small visual field andwide-angle observation at a moderate resolution.

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Side-looking cameras and GaborsuperlensesA transversal misalignment of one ofthe lens arrays in a stacked arrayimaging system as shown in Figure 6will result in a tilt of the optical axe(s)and will slant the field of view. Thiseffect can be used to scan extendedobjects or scenes without moving themicrocamera.[28] Figure 8 shows amodification of the system shown inFigure 6. A tilt of the optical axes isintroduced by changing the lensdiameter and pitch. Each camera of thecluster may now observe a differentangular field. The image is obtained by

spatial superposition in the image plane or by neural superposition within the data processing system. A more sophisticatedarray imaging system is a so-called Gabor superlens. A Gabor superlens is an array of afocal telescopes, wherein both lensarrays differ slightly in the lens pitch or period.[29, 30] It is worth to note, that the change of the lens array period is alsoachieved by a rotation ofthe lens arrays with respect to each others.[3 1]

Moire effects

Figure 7. Image plane of the array imaging system shown in Figure 4 for a 25xdemagnification. Each camera forms a separate image of the object. Diffractionlimited resolution of3 pm (Strehi ratio 0.83) is observed.

•••••.../'•,.•.r./4microcamera array might lead to moire effects in ______ ______

the image pattern. For certain combinations of theobject and lens period, the individual imagesgenerate a magnified or demagnified image of theobject pattern. A periodic object pattern and a lensarray imaging systems are referred as a 'moiremagnifier'.[32} This phenomenon frequentlyappears if microlens arrays are used in conjunction with arrays of light sources, photo-detectors, liquid crystals displays,CCD-chips, etc..

image plane

Figure 8. Cluster of microcameras consisting of two optical layers.Each microcamera observes a different angular field.


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