Optics

4.1 Definition of a Thin Lens A thin lens is a theoretical lens whose thickness is assumed to be zero and, therefore, negligible during thin-lens calculations. The thin lens is a design tool used to simulate a real lens during the preliminary stages of optical system design and analysis. The concept is particularly valuable because it enables the optical engineer to quickly establish many basic characteristics of a lens or optical system design. By assuming a lens form where the thickness is zero, the formulas used to calculate object and image relationships are greatly simplified. The drawback to the thin-lens approach is that it is not possible to determine image quality without including actual lens thickness (and other lens data) in the calculations. As a result, while it is possible to establish many valuable facts about an optical system by the application of thin-lens theory and formulas, the ultimate quality of the final image can, at best, only be estimated. 4.2 Properties of a Thin Lens Figure 4.1 is an illustration of a positive thin lens. Any lens system analysis must start with several known factors that will generally be provided by the end user, i.e., the customer. From these given starting factors it will be possible, using thin-lens theory and formulas, to generate the missing information required to completely describe the final lens system. In the case shown in Fig. 4.1, for example, it is given that the system detector (image size) will be 25 mm in diameter and that the full field of view of the lens will be 10 deg. Other system considerations dealing with detector sensitivity - thus required image brightness - dictate that a lens speed (f/#) of f/2.0 will be required. Since we know the image size and the field of view, applying the formulas shown in Fig. 4.1, we can calculate the effective focal length (EFL) of the lens. The image size dimension used for this calculation is measured from the optical axis and is designated as y1. In this case, the maximum value for y1 is 12.5 mm.

: Excellent agreement has been shown between element patterns of circumferential and radial slots on a cone, computed with the normal mode series computer programs, and patterns measured with an experimental model with both types of slots. When the modal series is used for the computation of exact patterns, the number of modes required for convergence of the series increases as the distance of the slot location from the tip of the cone increases. Computational difficulties from accumulated round-off errors also affect the accuracy and limit the applicability of the modal series program to element positions not too far from the cone tip. The approximate asymptotic approach, on the other hand, allows the separation of the diffracted field and the geometrical optics field. More specifically, the asymptotic approach resulted in complete expressions for the E sub theta and E sub phi radiation fields in terms of optical, transition, and diffraction fields. The complete expressions for each of the two field components, in a form suitable for numerical computation, were included in the Final Report on Contract No. N00019-74-C-0127. An examination of these expressions indicates that the diffraction coefficients of both field components are only a function of the angular coordinates and not of the location of the radiating element.

Effect of chromatic aberration on Gaussian beams: non-dispersive laser resonators

This study presents an 8x four-group inner-focus zoom lens with one-moving group for a compact camera by use of a focus tunable lens (FTL). In the initial design stage, we obtained the powers of lens groups by paraxial design based on thin lens theory, and then set up the zoom system composed of four lens modules. Instead of numerically analytic analysis for the zoom locus, we suggest simple analysis for that using lens modules optimized. After replacing four groups with equivalent thick lens modules, the power of the fourth group, which includes a focus tunable lens, is designed to be changed to fix the image plane at all positions. From this design process, we can realize an 8x four-group zoom system having one moving group by employing a focus tunable lens. The final designed zoom lens has focal lengths of 4 mm to 32 mm and apertures of F/3.5 to F/4.5 at wide and tele positions, respectively.

A novel class of special functions for electromagnetics is presented. Formed by the incomplete Hankel and modified Bessel functions, this class allows solving electromagnetics problems concerning truncated cylindrical structures. The differential and recurrence equations of these functions feature additional terms with respect to the classical theory of the Hankel and Bessel functions. The general properties, the most important analytical characteristics, and the large argument asymptotic approximations of the incomplete functions are derived using the steepest descent path (SDP) technique, showing that each special function splits into two terms. The first one has a discontinuous character and is linked to the saddle-point(s) contribution(s), while the second one, arising from the integral end-point contribution(s), compensates exactly the said discontinuity. In the solution of electromagnetic problems, the first term describes the geometrical optics (GO) field, the diffracted field being described by the second one. The general theory is employed to find the closed form analytical solution of the field radiated from a uniform line current source. Using the properties of the incomplete Hankel functions, it is demonstrated that this source excites cylindrical fields having optical character. Finally, the shape of the spatial regions where the GO solution cannot be applied is determined and discussed in details.

Polarization changes in vector Gaussian-Schell-model beams propagating through a thin lens

Diffraction, Fourier Optics and Imaging

For pt.I see ibid., vol.37, no.2, p.212-18 (1989). In Part I a rigorous integral representation for the field scattered at a finite distance from the edge of an impedance wedge when it is illuminated by a line source was derived. It was shown that the total field can be expressed as the sum of the geometrical optics (GO) field, the field diffracted by the edge, and terms related to the excitation of surface waves. The double spectral integral representation for the diffracted field was asymptotically evaluated there, in the case in which no surface wave can be supported by the two faces of the wedge. In particular, the high-frequency solution was expressed in the special format of the uniform geometrical theory of diffraction (UTD). Here, field contributions related to the surface wave excitation mechanism are examined. By a convenient asymptotic approximation of the integrals, a high-frequency solution which is uniform with respect to aspects of both incidence and observation is obtained. Moreover, this solution has useful symmetry properties so that it explicitly exhibits reciprocity. Numerical results are presented to show the relevance of the surface wave terms in the evaluation of the field. >

An approach is presented by which synthesis of offset dual-reflector antennas is reduced to solving nondifferential equations. This is made possible by approximating a known solution for the geometrical optics (GO) field reflected from a surface, and using local parabolic expansions of the reflector surfaces. The advantages of this approach are that the calculation is easy to carry out, the condition of low cross-polarization is included, and the question of existence clearly can be answered. The synthesis method can also readily be extended to the synthesis of multireflector antennas. >

The formalism of generalized diffraction integral for paraxial misaligned optical systems is used to investigate the propagation of the Modified Bessel-Gaussian (MBG) beam through a misaligned thin lens. The properties of the propagation of MBG beam traveling through this misaligned ABCD optical system are discussed. A special case of misaligned circular thin lens is illustrated analytically and numerically. The shape of the MBG beam at the exit of the misaligned optical system is unchanged; however the center of the beam is shifted from the propagation axis in correlated manner with the design parameters of the optical system.

Essence of this work is formulation of nonlinear dependencies, which allow to determine parameters of an optical system. Previous methods of the aberration correction have commonly used algebraic methods in a simple form for primary aberrations and thin lenses. Efficiency of those methods should be appreciated critically because they usually need a further aberration correction. Nowadays, progress in development professional mathematical software commercially available encourages to taking out works concerning algebraic correction methods. In this work aberration dependencies are investigated in their full complexity without simplification and approximation. Dependencies containing angles and ratios of dimensions have form of very complex trigonometric expressions. An optical system may be corrected by controlling these dependencies in the entire optical systems. Solution of the problem require the selection of number of unknowns, and expression of all residual relations as a function of these unknowns. Problem of the algebraic correction relies on solving of a non- linear equation system with separately described auxiliary functions which are nested up to certain depth. Radii of curvatures and eventual distances between surfaces are determined in the second final stage after solving the nonlinear equation system and taking account of the scale. Two simple numerical examples are presented.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Scattering of plane waves by a rational half-plane between DNG media

The scattering of plane waves by an impedance half-plane located at the interface of two isorefractive media is investigated. The scattered field, in addition to the diffracted and geometrical optics fields, is analyzed numerically and compared to the scattered field of perfectly conducting half-plane. The effect of the isorefractive media on the scattered field is also examined.

This paper is about a theoretical framework on perceptual reproduction quality assessment. — Visual perception is the main theme for two approaches on image metrics, visual performance and image quality. Visual performance looks at the perception of standard elementary images, such as gratings, by different observers or by a single observer in different visual conditions; image quality looks at the perception of variations of the same complex scene by a standard observer. — Visual performance, for which Barten proposed a model in 1999, is studying threshold responses in visual perception. For image quality, on the other hand, indexes are built which must evaluate responses to a variety of suprathreshold visual characteristics, attempting to give results as close as possible to human visual perception. — In audiovisual field, all the configurations approved by the creative team must be reproduced in the final viewing. This cannot be measured by visual performance or image quality indexes. A third approach is needed. This may be called perceptual reproduction quality assessment. Visual perception assessment is not measuring defects, per se; it is built to evaluate the perceptual effectiveness of a given scene coding through a given reproduction technology. — It is only dependent on the number of configurations being reproduced by a given theater system relatively to the various configurations reproduced and approved in the review room. As such, it is a statistical measure. It is in fact similar to the definition of relative entropy. One important fact is that this evaluation must include a model of visual perception. — This paper shows how relative entropy, and entropy loss, can be estimated while taking into account the coding transform, the projector performances, maximum light and the characteristics of human visual system. — This scheme is carried easily for monochromatic content. Color, trichromacy, is quite challenging. The size of configurations goes from 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sup> to 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">36</sup> , around 6 billion configurations. Calculation and memory requirements are huge. Non-linearities are adding complexity leading to calculation of an upper limit only of entropy loss. — Presentation of results is also a challenge. One way to solve this is to process separately lightness and chromatic information. — In summary the main arguments in this paper are: — • Besides image quality and visual performance there is a need for perceptual reproduction quality assessment — • Entropy is the proper statistical estimator to evaluate the perceptual reproduction quality — • Color reproduction quality estimation requires processing lightness and chromatic attributes separately

It was about 125 years ago that the light bulb was commercialized by Thomas Edison. No doubt a brilliant invention at the time, today its low power conversion efficiency is one of the reasons why lighting in the western world has such high energy consumption. Thus, the potential for saving energy is enormous in this area. The introduction of halogen, discharge and fluorescent lamps has lead to certain efficiency improvements, however more than half of the energy is still lost as heat. Light-emitting diodes (LEDs) are very promising candidates for high efficiency light sources, with modern devices showing internal quantum efficiencies of virtually 100 %. However, due to the high refractive index of the commonly used semiconductor materials it is very difficult to have a large extraction efficiency; in a standard cubic geometry most of the internally emitted light is trapped inside the device due to total internal reflection. Several methods have been developed in order to circumvent this problem, either by optimizing the device geometry in order to increase the escape cone or by incorporating a resonant structure in order to force the internal emission into the existing escape cone. The latter approach is called microcavity LED (MCLED) or resonant cavity LED (RCLED). In a MCLED the spontaneous internal emission is controlled by placing the emitter inside an optical cavity with a thickness of the order of its emitting wavelength. The resulting interference effects increase the part of the emission that can be extracted. Contrary to the other approaches this is possible without changing the device geometry and thus without additional costly back-end processing steps. The control of the farfield radiation pattern makes these devices particularly interesting for high brightness applications, which demand highly directional emitters, such as for printing, bar code reading, large area displays and optical communication. The extraction efficiency of a MCLED is inversely proportional to the effective cavity length. An ideal cavity, allowing an extraction efficiency close to unity, consists of a low refractive index material and has an optical length of λ/2. In contrast to this, to obtain high internal quantum efficiencies it is necessary to use high index cavities with an optical length of at least λ. It should be noted, that the large penetration depth of the optical field in the semiconductor-based distributed Bragg reflectors (DBRs) leads to a significant increase of the effective cavity length and thus further reduces the achievable extraction efficiencies. In this thesis novel concepts to reduce effective cavity lengths and therefore increase extraction efficiencies are implemented into standard MCLED structures. The phaseshift cavity principle whilst maintaining the electrical properties of a standard A cavity achieves optical properties approaching that of a λ/2 cavity. The use of AlOx instead of AlAs as the, low refractive index component in the DBRs leads to smaller penetration depths and a concomitant reduction of the effective cavity length. A similar effect can be obtained by combining a resonant cavity with a thin-film structure. Thanks to these design improvements, the external quantum efficiency of different types of MCLEDs was increased. Near infrared emitting InGaAs/GaAs MCLEDs including a phase-shift cavity were realized, as both bottom and top emitting structures. The external quantum efficiencies achieved for emission into air were 18 and 19 %, respectively. With the additional incorporation of an oxide based bottom DBR, the efficiency of top emitting near infrared MCLEDs was further increased to 28 %. Red emitting AlGaInP-based structures are not compatible with the phase-shift cavity principle. However the beneficial effect of the implementation of an oxide DBR is greater at their wavelength rather than in the near infrared. Thus with preliminary red emitting GaInP/AlGaInP MCLEDs containing a bottom oxide DBR external quantum efficiencies of 12% could be achieved. Unfortunately, the incorporation of an oxide DBR significantly complicates the device design and the device fabrication. These problems can be avoided by combining the resonant cavity with a thin-film structure instead. Initial non-optimized red emitting thin-film MCLEDs were realized by OSRAM Opto Semiconductors and characterized in this work. They show external quantum efficiencies of 23 % and 18 % with and without encapsulation, respectively. It is assumed that a significant fraction of the high external quantum efficiency is due to a strong photon recycling effect in these devices. Simulations presented in this thesis show that the theoretical limits for the MCLEDs discussed above are slightly higher than the values obtained, encouraging further device optimization. The thin-film MCLEDs seem to hold the biggest potential for high efficiency emission from MCLEDs, independent of the wavelength range of emission.