We report a systematic investigation of the imaging behavior of an optical system consisting of a lens from a uniaxial birefringent crystal sandwiched between two linear polarizers into which primary spherical aberration has been introduced. The proposed system has higher tolerance to primary spherical aberration and has a larger depth of focus than an imaging system found with an isotropic lens. Some specific cases are computed and illustrated graphically. © 2002 Optical Society of America.

S SANYAL

A GHOSH

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

High tolerance to spherical aberrations and defects of focus with a birefringent lens

Applied Optics

We study the intensity point spread function (IPSF) of a uniaxial birefringent lens sandwiched between two linear polarizers under broadband illumination having flat-top spectral profile. The optic axis of the birefringent crystal is perpendicular to the lens axis. For monochromatic input illumination, a low-power birefringent lens offers enhanced resolution under parallel-polarizers configuration and apodization under crossed-polarizers configuration with a single focus as well. At a relatively high value of birefringence parameter, the proposed system behaves as a double-focus lens. The present communication uses a novel technique to study the effect of polychromatic illumination on the imaging characteristics of birefringent lenses. The studies reveal that the imaging characteristics of the low-power birefrigent lens does not deteriorate considerably under polychromatic illumination. However, for a polychromatic beam with large bandwidth, the imaging behavior of the system having high birefringence parameter deviates appreciably from that under strictly monochromatic illumination. The said system even loses its inherent bi-focal nature due to depolarization of polarized polychromatic light upon passage through the birefringent crystal. © 2011 Elsevier GmbH.

Optik

Polychromatic intensity point spread function of a birefringent lens

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. © Optical Society of India 2011.

Journal of Optics (India)

The effect of broadband illumination on the imaging characteristics of a birefringent lens suffering from primary spherical aberration

We report the frequency response characteristics of an optical system consisting of a lens made of uniaxial birefringent crystal sandwiched between two linear polarizers; the lens has prespecified off-axis aberrations such as primary astigmatism and primary coma. An analytical expression is obtained for the optical transfer function of the proposed system by use of the autocorrelation of the pupil function over the lens aperture. Some specific cases are computed and illustrated graphically. It has been shown that the proposed system has imaging characteristics distinctly different from those of an ordinary glass lens, and these may be advantageous for better balancing of aberrations in conventional imaging systems. © 2004 Optical Society of America.

Frequency response characteristics of a birefringent lens with off-axis aberrations

The factor of encircled energy (FEE) in the diffraction pattern formed by an optical system consisting of an aberration-free birefringent lens sandwiched between two linear polarizers is computed directly from the optical transfer function (OTF) of the system. FEE curves are given showing the variation of image quality of the proposed system at the Gaussian Image plane and other observation planes with the birefringent lens parameters and the azimuthal settings of the transmission axes of the polarizers. The performance is compared to that of an ideal conventional glass lens. © 2003 Society of Photo-Optical Instrumentation Engineers.

Optical Engineering

Image assessment of a birefringent lens based on the factor of encircled energy

The diffraction-based optical frequency response characteristic of a birefringent crystal lens sandwiched between two linear polarizers has been studied analytically using the autocorrelation of the pupil function over the lens aperture. The optical transfer function (OTF) of this proposed system depends on the material as well as design parameters of the crystal lens, along with the orientations of the transmission axes of the two polarizers relative to each other and to the optic axis of the birefringent lens. Naturally, the OTF of such a system can be varied at the lens fabrication stage like other lenses. An online variation of the OTF is also possible just by rotating any of the two polarizers included in the system. It has been shown that the proposed system can be adapted either for apodization or for super-resolution simply by rotating any of the two polarizers. This system may be designed for obtaining high depth of focus without significant image degradation, as well as for image processing operations like high frequency enhancement. The response of the system is studied at the Gaussian image plane as a function of the line frequencies in the object for different values of the birefringent lens parameters, and also for two different settings of the analyzer. The results are compared with the response of an ideal lens. © 2002 Society of Photo-Optical Instrumentation Engineers.

Frequency response characteristics of a birefringent lens

The Strehl definition along the axis of a birefringent lens sandwiched between two polarizers is studied analytically. The optic axis of the birefringent lens made of a uniaxial crystal is perpendicular to the lens axis, and the system behaves like a bifocus lens for proper orientation of the polarizers. The Sparrow criterion is employed for designing an imaging system with high depth of focus. It is shown that, when the two foci are separated by the Sparrow limit of resolution, the focal depth is maximum and the intensity point-spread function remains almost identical within this limit. The resolution according to the Rayleigh criterion in this zone is more than that of an ideal lens. © 2000 Optical Society of America.

High focal depth with a quasi-bifocus birefringent lens

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. © 1998 Society of Photo-Optical Instrumentation Engineers.

Vector wave imagery using a birefringent lens

In the present paper we discuss the imaging qualities of a biréfringent lens. The transmittance of such a lens, sandwiched between two polarizers varies radially. The fact that the nature of this radial variation of transmittance can be controlled by changing the orientations of the two polarizers relative to the optic axis of the biréfringent lens, may be utilised for continuously modifying the imaging characteristics of the lens. The study of the point spread functions (PSF) of such a polarizer-birefringent lens-polarizer combination reveals that this can be utilised both for achieving apodisation and superresolution. © 1990 SPIE.

Journal	Applied Optics
Publisher	OPTICAL SOC AMER
ISSN	1559-128X