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The effect of broadband illumination on the imaging characteristics of a birefringent lens suffering from primary spherical aberration
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This report forms a part of the systematic investigation on the imaging behaviour of an optical system consisting of a lens made of a uniaxial birefringent crystal sandwiched between two linear polarizers into which primary spherical aberration is introduced. The optic axis of the birefringent crystal is perpendicular to the lens axis. The proposed system is illuminated with a polychromatic beam of light, the spectral profile of which is considered to be uniform for all wavelengths. The axial irradiance distribution function and the intensity point spread function are used as the image assessment parameters. Some specific cases are computed and illustrated graphically. The study reveals that if the variation of the birefringent parameters of the device with wavelength is less, a larger bandwidth may be used without considerably deviating from the imaging characteristics under strictly monochromatic illumination suffering from similar primary spherical aberration.
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This paper reports the imaging behavior of an optical system consisting of a uniaxial birefringent lens sandwiched between two linear polarizers suffering from primary spherical aberration. The optic axis of the birefringent crystal is perpendicular to the lens axis. The said system is illuminated with a polychromatic beam of light having flat-top spectral profile and the quality of image formed by the system is evaluated by means of the intensity point spread function (IPSF) and optical transfer function (OTF). The proposed system has high tolerance to primary spherical aberration under broadband illumination.
Polychromatic or white-light optical transfer function (OTF) is put forward as a criterion to evaluate the performance of a uniaxial birefringent lens sandwiched between two linear polarizers. The optic axis of the birefringent crystal is perpendicular to the lens axis. The results show that the same system may be adapted for both enhanced resolution and apodization just by rotating any of the polarizers included in the system even under broadband illumination. The proposed system may also be exploited for image processing applications under polychromatic input illumination. (C)2013 Elsevier GmbH. Allrights reserved.
The degree of polarization of a polarized polychromatic beam decreases during the passage of the beam through an optically active medium. In a previous paper [B. Chakraborty and A. K. Chakraborty, J. Phys. D 18, 145 (1985)], this depolarizing effect in the case of a linearly polarized polychromatic beam having a flat-topped spectral profile was studied. In the present paper the effect of propagation of an elliptically polarized polychromatic beam having a Gaussian spectral profile through an optically active medium is studied. The results of the previous paper can be obtained as a particular case of this generalized study.
We propose a method for designing apodizers that increase the depth of focus and reduce the influence of spherical aberration. These two properties are explicitly manifested in computer-generated pictures and values of the Strehl ratio for variable spherical aberration.
The influence of primary astigmatism on the performance of optimum apodizers has been investigated theoretically. The analytical method used in.this study is quite general in the sense that it can be extened to make similar studies regarding the influence of other aberrations, such as spherical aberration and coma, on the performance of any of a general class of optimum apodizers. The aberration function used in this study is that given by the ZERNIKE-NIJBOER theory of wave aberrations. Analytical expressions have been obtained for various quantities, for example the intensity distribution, the fractional encircled energy distribution, the Strehl ratio etc., in order to make a thorough study of the diffraction pattern. Numerical results have been computed for two chosen apodizers and for certain amounts of primary astigmatism. These results have been illustrated graphically and discussed. Isophote diagrams for a few cases have also been presented.
The imaging characteristics of a birefringent lens sandwiched between two polarizers is studied analytically. If the optic axis of the birefringent crystal is perpendicular to the lens axis, the system behaves as a bi-focus lens for proper orientations of the polarizers. It is shown that the proposed system can be adapted either for apodization or for superresolution simply by rotating any of the two polarizers. It has larger depth of focus than conventional systems as is evident from the results obtained. Expressions are obtained for the effective pupil function of such a system and the corresponding intensity point spread function. Some specific cases are computed and illustrated graphically.
Publisher Summary This chapter describes the correction of optical images by compensation of aberrations and spatial frequency filtering. Efforts are being made to reduce the disturbing effects of aberrations on image formation in optical systems and its amount in designing and in the production of optical instruments. Techniques by means of which correcting the aberrant image under given conditions of relative aperture, focusing, and so on can be attained are required. The chapter describes two different methods. In the first method, the aberration is compensated by the use of an optical filter at the pupil of the objective. The second method consists of applying double diffraction (Abbe's experiment) to correction of photographic images. The chapter focuses on the application of these two methods in relation to correction of optical images formed by an aberrant objective.
The imaging characteristics of a birefringent lens sandwiched between
two polarizers is studied analytically. If the optic axis of the
birefringent crystal is perpendicular to the lens axis, the system
behaves as a bifocal lens for proper orientations of the polarizers. It
is shown that the proposed system can be adapted either for apodization
or for super-resolution simply by rotating either of the two polarizers.
It has greater depth of focus than conventional systems, as is evident
from the results obtained. Expressions are obtained for the point spread
function of such a system. Some specific cases are illustrated
graphically.
In this paper a study is made of the annular aperture with primary spherical aberration and coma using the Zernike polynomials. The three-dimensional irradiance distributions in meridional sections of diffraction images of the annular aperture with primary spherical aberration have been evaluated for a variety of cases aud illustrated in the diagram of lines of equal light irradiance. The irradiance distributions are briefly discussed. A further increase in the focal depth as compared to the annular aperture without aberration is obtained by introducing spherical aberration in it. An addition of coma in the annular aperture is also treated and the diffraction images in the central plane have been obtained for various amounts of primary coma and central obstruction. The diffraction images are shown in the diagram of lines of equal irradiance and discussed briefly.