The set of orthogonal Walsh filters consists of groups, members of which are self-similar. The corresponding axial and
transverse intensity distributions in the farfield diffraction patterns of these filters possess self-similarity. Results of our
investigations on the same are presented.
Optical system analysis and design constitute one of the core activities in optical engineering. This activity is currently carried out with readily available software. Notwithstanding the significant roles played by the latter in bringing about a paradigm shift in the field, proper appreciation and efficient use of software call for knowledge and understanding of the physical principles involved in optical system analysis and design. A large number of excellent books and publications by experts deal with different aspects of the problem. However, newcomers in the field, and practicing analysts and designers with no formal training in the subject feel bewildered by the plethora of information. The course on ‘Foundations of Optical System Analysis and Design’ is contemplated to alleviate the problem.
Calibration of phase in spatial light modulators is a prerequisite for applications where a prespecified phase distribution needs to be implemented over the surface of the modulator. The present work proposes a full-field polarization phase shifting interferometric technique, based on the Twyman-Green interferometer, for the purpose.
This paper reports our investigations on the design of globally or quasi-globally optimal structures for three-component and four-component mechanically compensated zoom lenses. This is accomplished by implementation of a global optimization technique based on evolutionary programming. The technique searches optimal structures in the configuration space formed by the specific design variables: powers of individual components and the intercomponent separations. Any requirements for system length and Petzval curvature of the zoom lens can be incorporated in the search for optimal solutions. Illustrative numerical results of our investigations on four regular types of zoom systems, as classified by Tanaka, are presented.
Pupil plane filtering provides a convenient technique for modifying the point spread function. Such modifications are
used in many practical applications that require enhancement of selective frequency band in images. Also, in many new
imaging paradigms, acquisition of 3D image information calls for tailoring of the 3D point spread function. This can be
achieved by suitable pupil plane filtering, preferably by phase filters. By using a pupil plane filter with an array of
concentric annuli, the point spread function can be tailored in a fashion such that a narrow central lobe is surrounded by
neighboring lobes of low amplitude, with one or more lobes of high amplitude spaced far away from the center. In our
study we intend to explore the use of phase annuli as pupil filters in tailoring of both transverse and axial resolution.
Determination of such phase filters in accordance with a set of prespecified requirements for amplitude/intensity
distribution around the focus constitutes a problem of nonlinear optimization. This paper reports some results of our
preliminary investigations on an application of evolutionary programming in solving this problem to obtain globally or
quasi-globally optimum solutions.
A new approach for 'ab initio' synthesis of thin lens structure of zoom lenses is reported. This is accomplished by an
implementation of evolutionary programming, based on Genetic Algorithm, which explores the available configuration
space formed by powers of individual components and inter-component separations. Normalization of the variables is
carried out to get an insight on the optimum structures. The method has been successfully used to get thin lens structures
of mechanically compensated, optically compensated, and linearly compensated zoom lens systems by suitable
formulation of merit function of optimization. Investigations have been carried out on three component and four
component zoom lens structures. Illustrative numerical results are presented.
A new approach for structural synthesis of optically compensated zoom lenses is reported. An implementation of
evolutionary programming facilitates the procedure by carrying out a global search over the available degrees of
freedom, namely, powers of the components and the inter-component separations. Practical success of the method
depends on suitable formulation of the fitness function. Normalization of the variables is carried out to get an insight on
the optimum structures. Illustrative numerical results are presented.
In a recent paper we have reported on the feasibility of reducing the problem of structural design of a multicomponent
lens system in accordance with a prespecified set of Gaussian characteristics and primary aberration targets to the
relatively simpler problem of determining optimum structures for the component lenses with central aberration targets.
The structural design of the individual components can be suitably tackled by evolutionary algorithm so that one can
obtain globally or quasiglobally optimum solutions for the purpose. Details of the latter part of the approach are
presented in this paper.
Contrary to the usual practice of heuristic selection of glass types for the lens elements of the component, the glass types
for individual lens elements are treated as discrete independent variables to be selected from a set of prespecified list of
actual glasses. We have dealt with the global or quasiglobal synthesis of the individual lens components with the help of
structures of increasing complexity, e.g. singlets, cemented doublets, broken contact doublets, cemented triplets,
photovisual objectives etc. as necessary for the purpose. The total configuration space consists of continuous variables
like shape variable and power distributions, and discrete variables like available glass types. This approach reduces
significantly the chance of overlooking promising and better solutions by carrying out searches in the total configuration
space simultaneously. Some illustrative examples will be presented.
This paper is in tune with our efforts to develop a systematic method for multicomponent lens design. Our aim is to find a suitable starting point in the final configuration space, so that popular local search methods like damped least squares (DLS) may directly lead to a useful solution. For 'ab initio' design problems, a thin lens layout specifying the powers of the individual components and the intercomponent separations are worked out analytically. Requirements of central aberration targets for the individual components in order to satisfy the prespecified primary aberration targets for the overall system are then determined by nonlinear optimization. The next step involves structural design of the individual components by optimization techniques. This general method may be adapted for the design of triplets and their derivatives. However, for the thin lens design of a Cooke triplet composed of three airspaced singlets, the two steps of optimization mentioned above may be combined into a single optimization procedure. The optimum configuration for each of the single set, catering to the required Gaussian specification and primary aberration targets for the Cooke triplet, are determined by an application of genetic algorithm (GA). Our implementation of this algorithm is based on simulations of some complex tools of natural evolution, like selection, crossover and mutation. Our version of GA may or may not converge to a unique optimum, depending on some of the algorithm specific parameter values. With our algorithm, practically useful solutions are always available, although convergence to a global optimum can not be guaranteed. This is perfectly in keeping with our need to allow 'floating' of aberration targets in the subproblem level. Some numerical results dealing with our preliminary investigations on this problem are presented.
Diffractive optical elements are rapidly finding their way into many practical optical systems, and this has given rise to a spurt of research and developmental activities in this area. IN this paper, the history of these elements is first traced to get a perspective on their current state-of-the- art. The important features of this rapidly advancing field are then identified so that one does not get lost and can easily stick to one's guns while browsing through the maze of publications. Finally a glimpse of the fascinating future trends is given to stimulate further interest in the area.
'Ab initio' design of a Cooke triplet usually necessitates a heuristic preselection of optical glasses for the three lens elements. Though some rules of thumb are available for specific cases in general, this is a tricky problem, and often one has to take recourse to a trial and error approach. We propose to tackle the complex problem of design of a Cooke triplet lens with prespecified aberration targets by reducing it to relatively simpler problems of design of individual components with required amounts of primary spherical aberration, central coma and longitudinal chromatic aberration. This reduction is implemented by a global optimization technique. Our method of global optimization is developed along the lines of the well-known method of simulated annealing. Some new features like constrained random walk have been incorporated for facilitating the solution of our problem. A followup procedure also based on global optimization seeks singlet lenses for the individual components. In case of nonavailability of suitable singlet for a component, one seeks to satisfy requirements of that particular component by using a suitable doublet lens. Indeed, the approach provides a systematic method for the development of triplet derivatives as and when required.
Method of generalized simulated annealing with constrained random walk is used for global optimization of the structural design of cemented/broken contact doublet lenses in accordance with prespecified paraxial characteristics and primary aberration targets.
The phenomenon of total internal reflection sets practical limits for blazing in the case of transmission gratings. Similar effects can be observed in the case of kinoform lenses. The effects manifest themselves in limiting the object distance, the image distance, or the semidiameter of the kinoform lens. These limits are set by the refractive index of the kinoform material and the imaging geometry. This paper presents the results of our investigations on various aspects of these geometric optical limits in the case of planar kinoform lenses for stigmatic imaging between any two prespecified points on the axis.
The Levenberg-Marquardt version of least squares, namely the damped least-squares method, is widely used in lens design optimization. Several modifications of the approach have been proposed to accelerate convergence of the optimization procedure. Recent developments in nonlinear optimization theory indicate that the basic Gauss-Newton method of least squares can play a useful role for this purpose in many practical applications. Giving a brief outline of the pertinent developments, the paper reports on the feasibility of using the basic Gauss-Newton method of least squares in practical lens design optimization when, at each iteration, a line search procedure follows the least-squares solution to determine the optimum change vector for that particular iteration stage. It is observed that incorporation of the line search procedure provides good convergence even without any damping of the least-squares procedure. Some illustrative numerical results are presented.