Lakshminarayan Hazra - Academia.edu (original) (raw)
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Papers by Lakshminarayan Hazra
Reports on aberrational characteristics of diffractive lens usually assume the lens to be thin, w... more Reports on aberrational characteristics of diffractive lens usually assume the lens to be thin, with zero substrate thickness placed in air. Under these assumptions, the curvature and distortion becomes zero for both plane and curved diffractive lenses, with astigmatism given by H2K, where H is the paraxial invariant and K the lens power. However in real diffractive lenses on finite substrates, large variations in these aberrations take place from the ideal model. This paper presents analytical expressions for these aberrations with numerical results highlighting these variations for diffractive lenses.
Resolution capability of an optical imaging system can be enhanced by reducing width of central l... more Resolution capability of an optical imaging system can be enhanced by reducing width of central lobe of the point spread function (PSF) of the transverse intensity distribution on the far field plane. Attempts to achieve the same by pupil plane filtering, is usually accompanied by concomitant increase in side lobe intensity. The mutual exclusivity between these two objectives may be cast as a multi objective optimization problem that does not have a unique solution; rather a class of trade off solutions called Pareto optimal solutions may be generated. To achieve super resolution, lossless phase only filters with pre-specified lower limits for Strehl ratio are synthesized by using Particle Swarm Optimization technique. Practical validation of the theoretical results is also undertaken by realizing the phase filters on reflective, phase only liquid crystal on silicon spatial light modulator.
Advances in Optics, 2014
In a recent communication we reported the self-similarity in radial Walsh filters. The set of rad... more In a recent communication we reported the self-similarity in radial Walsh filters. The set of radial Walsh filters have been classified into distinct self-similar groups, where members of each group possess self-similar structures or phase sequences. It has been observed that, the axial intensity distributions in the farfield diffraction pattern of these self-similar radial Walsh filters are also self-similar. In this paper we report the self-similarity in the intensity distributions on a transverse plane in the farfield diffraction patterns of the self-similar radial Walsh filters.
Journal of Optics (India), 1977
Foundations of Optical System Analysis and Design, 2022
Foundations of Optical System Analysis and Design, 2022
Foundations of Optical System Analysis and Design, 2022
Foundations of Optical System Analysis and Design, 2022
Walsh functions, Walsh filters and their self-similarity are discussed in this chapter. One and t... more Walsh functions, Walsh filters and their self-similarity are discussed in this chapter. One and two-dimensional Walsh functions in rectangular and polar co-ordinates are defined. The concepts of radial and azimuthal Walsh functions are introduced. The method of generation of azimuthal Walsh functions of different orders has been demonstrated. Azimuthal Walsh functions have been studied for finding out self-similar groups and sub-groups between different orders to examine self-similarity existing within them. Radial and azimuthal Walsh filters have been defined from corresponding Walsh functions.
A structure which can be divided into smaller and smaller pieces, each piece being an exact repli... more A structure which can be divided into smaller and smaller pieces, each piece being an exact replica of the entire structure is called self-similar. The set of Walsh functions can be classified into distinct self-similar groups and subgroups where members of each subgroup exhibit self-similarity. After a brief discussion on the generation of higher order Walsh functions from lower order Walsh functions by an alternating process, a scheme for classification of Walsh functions into self-similar groups and subgroups is presented. Self-similarity in radial and annular Walsh functions and the correspondence between Walsh filters and Walsh functions are also discussed.
Foundations of Optical System Analysis and Design, 2022
Foundations of Optical System Analysis and Design, 2022
Foundations of Optical System Analysis and Design, 2022
Foundations of Optical System Analysis and Design, 2022
Foundations of Optical System Analysis and Design, 2022
Reports on aberrational characteristics of diffractive lens usually assume the lens to be thin, w... more Reports on aberrational characteristics of diffractive lens usually assume the lens to be thin, with zero substrate thickness placed in air. Under these assumptions, the curvature and distortion becomes zero for both plane and curved diffractive lenses, with astigmatism given by H2K, where H is the paraxial invariant and K the lens power. However in real diffractive lenses on finite substrates, large variations in these aberrations take place from the ideal model. This paper presents analytical expressions for these aberrations with numerical results highlighting these variations for diffractive lenses.
Resolution capability of an optical imaging system can be enhanced by reducing width of central l... more Resolution capability of an optical imaging system can be enhanced by reducing width of central lobe of the point spread function (PSF) of the transverse intensity distribution on the far field plane. Attempts to achieve the same by pupil plane filtering, is usually accompanied by concomitant increase in side lobe intensity. The mutual exclusivity between these two objectives may be cast as a multi objective optimization problem that does not have a unique solution; rather a class of trade off solutions called Pareto optimal solutions may be generated. To achieve super resolution, lossless phase only filters with pre-specified lower limits for Strehl ratio are synthesized by using Particle Swarm Optimization technique. Practical validation of the theoretical results is also undertaken by realizing the phase filters on reflective, phase only liquid crystal on silicon spatial light modulator.
Advances in Optics, 2014
In a recent communication we reported the self-similarity in radial Walsh filters. The set of rad... more In a recent communication we reported the self-similarity in radial Walsh filters. The set of radial Walsh filters have been classified into distinct self-similar groups, where members of each group possess self-similar structures or phase sequences. It has been observed that, the axial intensity distributions in the farfield diffraction pattern of these self-similar radial Walsh filters are also self-similar. In this paper we report the self-similarity in the intensity distributions on a transverse plane in the farfield diffraction patterns of the self-similar radial Walsh filters.
Journal of Optics (India), 1977
Foundations of Optical System Analysis and Design, 2022
Foundations of Optical System Analysis and Design, 2022
Foundations of Optical System Analysis and Design, 2022
Foundations of Optical System Analysis and Design, 2022
Walsh functions, Walsh filters and their self-similarity are discussed in this chapter. One and t... more Walsh functions, Walsh filters and their self-similarity are discussed in this chapter. One and two-dimensional Walsh functions in rectangular and polar co-ordinates are defined. The concepts of radial and azimuthal Walsh functions are introduced. The method of generation of azimuthal Walsh functions of different orders has been demonstrated. Azimuthal Walsh functions have been studied for finding out self-similar groups and sub-groups between different orders to examine self-similarity existing within them. Radial and azimuthal Walsh filters have been defined from corresponding Walsh functions.
A structure which can be divided into smaller and smaller pieces, each piece being an exact repli... more A structure which can be divided into smaller and smaller pieces, each piece being an exact replica of the entire structure is called self-similar. The set of Walsh functions can be classified into distinct self-similar groups and subgroups where members of each subgroup exhibit self-similarity. After a brief discussion on the generation of higher order Walsh functions from lower order Walsh functions by an alternating process, a scheme for classification of Walsh functions into self-similar groups and subgroups is presented. Self-similarity in radial and annular Walsh functions and the correspondence between Walsh filters and Walsh functions are also discussed.
Foundations of Optical System Analysis and Design, 2022
Foundations of Optical System Analysis and Design, 2022
Foundations of Optical System Analysis and Design, 2022
Foundations of Optical System Analysis and Design, 2022
Foundations of Optical System Analysis and Design, 2022