Microoptical Arti¯cial Compound Eyes Dissertation zur Erlangung des akademischen Grades doctor rerum naturalium (Dr. rer. nat.) vorgelegt dem Rat der Physikalisch-Astronomischen FakultÄat der Friedrich-Schiller-UniversitÄat Jena von Diplomphysiker Jacques Duparr¶e geboren am 23. MÄarz 1977 in Zwickau Gutachter 1. Prof. Dr. rer. nat. habil. Andreas Tunnermann,Ä Friedrich-Schiller-UniversitÄat Jena 2. Prof. Dr. rer. nat. habil. Stefan Sinzinger, Technische UniversitÄat Ilmenau 3. Prof. Sadik Esener, Ph.D., University of California San Diego Tag der letzten Rigorosumsprufung:Ä 07.06.05 Tag der Äo®entlichen Verteidigung: 23.06.05 Contents 1 Introduction 1 2 Fundamentals 4 2.1 Natural Vision . 4 2.1.1 Single Aperture Eye . 4 2.1.2 Apposition Compound Eye . 5 2.1.3 Superposition Compound Eye . 10 2.1.4 Vision System of the Jumping Spider . 11 2.2 State of the Art of Man-Made Vision Systems . 12 2.3 Scaling Laws of Imaging Systems . 19 2.3.1 Resolution and Space Bandwidth Product . 19 2.3.2 Sensitivity . 23 2.4 3x3 Matrices for Paraxial Representation of MLAs . 25 3 Anamorphic Microlenses for Aberration Correction under Oblique Incidence 28 3.1 Gullstrand's Equations of the Oblique Focal Length . 29 3.2 Ellipsoidal Microlenses by Melting of Photo Resist . 31 3.3 Spot Size Determination Under Oblique Incidence . 32 4 Arti¯cial Apposition Compound Eye Objective (APCO) 35 4.1 Principle { MLA with Assigned Array of Photo Receptors . 35 4.2 Design and Simulation of APCO . 37 4.2.1 Angular Sensitivity Function . 37 4.2.2 Characteristic Parameters of the APCO . 40 4.2.3 Interrelationship of Optical Properties under Scaling . 42 4.3 Fabrication of APCO . 44 4.3.1 Imaging System without Opaque Walls Between Adjacent Channels . 44 4.3.2 Imaging System with Opaque Walls Between Channels . 49 4.4 Experimental Characterization of APCO . 50 4.4.1 Resolution and Sensitivity . 50 4.4.2 Ghost and Flare Analysis { Test of the Opaque Walls . 55 I Contents 4.4.3 Extension of the FOV by an Additional Diverging (Fresnel-) Lens . 59 4.5 Summary and Outlook on APCO . 60 5 Cluster Eye (CLEY) 65 5.1 Principle { Array of Telescopes with Tilted Optical Axes . 65 5.2 Design and Simulation of CLEY . 66 5.2.1 Paraxial Description . 66 5.2.2 Sets of Equations Determining the Performance of the CLEY . 68 5.2.3 Determination of the Paraxial Geometrical Parameters . 70 5.2.4 Paraxial System, Examples . 70 5.2.5 Considerations to Sensitivity and Equivalent F/# of the CLEY . 71 5.2.6 Transfer of Paraxial Lens Array Parameters to Chirped Real MLAs . 75 5.2.7 Simulation of Imaging Systems with Real Microlenses . 75 5.3 Fabrication of CLEY with 21x3 Channels . 78 5.4 Experimental Characterization of CLEY . 82 5.5 Summary and Conclusions on CLEY . 85 6 Conclusions and Outlook 88 Bibliography 91 Appendix 101 A Anamorphic Microlenses by Reflow on an Ellipsoidal Base . 101 B Further Simulation Methods of APCO . 107 C Elements of the CLEY Paraxial Transfer Matrix . 111 D Further Conditions Determining the CLEY Performance . 111 E Paraxial Conditional Equations of CLEY . 113 F Paraxial Optical Input and Geometrical Output Parameters of Analyzed CLEYs 115 G Concentrator- or Integrator Array . 115 H Non-Sequential Raytracing Analysis of CLEY . 117 I Future Working Tasks . 118 Symbols and Abbreviations 125 Acknowledgements 131 Kurzfassung 133 EhrenwÄortliche ErklÄarung 138 Lebenslauf 139 II 1 Introduction Natural vision, in particular natural compound eyes, have always fascinated mankind [1]. Com- pound eyes combine small eye volumes with a large ¯eld of view, at the cost of comparatively low spatial resolution. For small invertebrates as for instance flies or moths the compound eyes are the perfectly adapted solution to obtain su±cient visual information about their environ- ment without overloading their brain with the necessary image processing [2]. The compound eye design is highly specialized for the natural living habitat, ambient illumination, required sensing tasks and available processing time, eye size and energy for processing. However, up to date little e®ort has been made to technically adopt this principle in optics. Classical imaging always had its archetype in natural single aperture eyes as, for example, human vision is based on. But not always a high resolution image is required. Often the main aim is on a very compact, robust and cheap vision system. Miniaturized digital cameras and optical sensors are important features for next generation customer products. Key speci¯cations are resolution, sensitivity, power consumption, manu- facturing and packaging costs and, maybe most important of all, overall thickness. Digital microcameras which are based on miniaturized classical lens designs used today are rarely smaller than 5x5x5mm3. The magni¯cation is related to the system length. Recent improve- ments of CMOS image sensors would allow further miniaturization. Nevertheless, as a result of di®raction e®ects, a simple miniaturization of known classical imaging optics would drastically reduce the resolution [3] and potentially also the sensitivity. A simple scaling of the imaging system to the desired size does not seem to be the clever way. How then to overcome these limitations of optics? A fascinating approach is to look how nature has successfully solved similar problems in the case of very small creatures [4]. During the last century, the optical performance of natural compound eyes was analyzed exhaustively with respect to resolution and sensitivity [2]. Several technical realizations or concepts of imaging optical sensors based on the principle of image transfer through separated channels were presented in the last decade. A detailed list is provided in Chapter 2, Section 2.2. However, since the major challenge for a technical adoption of natural compound eyes consists in the required fabrication and assembly accuracy, all those attempts have not lead to a breakthrough because classical, macroscopic technologies were exploited to manufacture microscopic structures. Sometimes only schematic macroscopic devices were fabricated. A statement of one of the scientists working on arti¯cial compound eyes in the nineties was: "... Nature has to operate under certain material constraints for its optical designs, and arti¯cial compound eyes will be able to take advantage of a wider assortment of optical materials and elements. ... On the other hand, it is unlikely that arti¯cial compound eyes will be able to have the huge numbers of ommatidia present in their biological counterparts, due to manufacturing and connectivity limitations." [5]. For the early, rather macroscopic arti¯cial compound eyes [6{8], this may be true. 1 1 Introduction It is the aim of this thesis to show that these limitations can be overcome by using state of the art microoptics technology. This enables the generation of highly precise and uniform microlens arrays and their accurate alignment to the subsequent optics-, spacing- and optoelec- tronics structures. The result are thin, simple and monolithic imaging devices with the high accuracy of microoptics photo lithography. Many imaging applications could bene¯t from this bioinspired microoptics, where classical objectives will never ¯nd their way in. Compound eye cameras should for instance ¯t into tight spaces in automotive engineering, credit cards, stick- ers, sheets or displays, security and surveillance, medical technology and shall not be recognized as cameras. In contrast to other attempts, here the imaging optics itself is considered as the key com- ponent to achieve this goal. (Opto-) Electronics and information processing will only take a minor part of this work. The main focus of this thesis is therefore on the fundamental analysis of imaging properties of compound eyes, the adaption of the optical design to the capabilities of microoptics technology, the formulation of new design strategies which match to the scal- ing laws of compound eye imaging systems, and the experimental characterization of realized demonstrators. It will be investigated how far technology can follow nature in the speci¯c case of compound eye vision. In general, arti¯cial compound eye concepts ¯t perfectly with microoptical fabrication technologies on wafer scale. However, for the current state of the art of technology, they are limited to planar arrangements while the natural archetypes are curved. The explicit microoptics technology was carried out by cooperating groups of the Fraunhofer Institute Applied Optics and Precision Engineering, the Institute of Applied Physics in Jena, and the Institute of Microtechnology and SUSS MicroOptics SA in Neuch^atel, Switzerland. Chapter 2 provides an introduction into natural compound eye vision, which is necessary to understand and classify the presented work on arti¯cial compound eyes. The state of the art of microoptical imaging systems which have their archetypes in natural vision is subsequently discussed. Furthermore, an introduction into microoptics principles and scaling laws of imaging systems is given. At this point it can already be understood that microlenses o®er good imaging quality because aberrations scale with the lens size. On the other hand, di®raction limitation seems to prevent microoptical imaging systems ever to stand in competition to classical imaging systems with some "megapixel" resolution. Nevertheless, it will be examined in this work whether bioinspired microoptics is able to establish new imaging functionalities and to open up new ¯elds of applications to electronic imaging. A paraxial model