Sucharita Sanyal

High focal depth with a quasi-bifocus 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.

Vector wave imagery using a 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 superresolution 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.

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

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.

Performance of a polarization-masked lens aperture in the presence of spherical aberration

This paper suggests the possibility of partial compensation of spherical aberration with a polarization-masked lens aperture. The principle is based on the fact that any pre-specified phase step can be introduced between two zones of a lens aperture masked by suitably oriented linear polarizers and employing an elliptically polarized imaging beam. By comparison of the point-spread function of such a polarization-masked imaging system with that of an ideal lens, it has been shown that the effect of spherical aberration can be appreciably compensated by making an appropriate choice of the polarization parameters involved.

Frequency response characteristics of a birefringent lens

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.

The factor of encircled energy from the optical transfer function

This paper proposes a generalized technique for computing the factor of encircled energy (FEE) in a diffraction image from the optical transfer function (OTF) of the imaging system. This technique is applicable to diffraction-limited optical systems as well as to systems suffering from any aberrations, provided the transfer function of the same is known. It is also applicable to any kind of rotationally symmetric or asymmetric apertures. The accuracy of the results depends on the precision with which the OTF of the system can be determined. The FEE values are obtained using this technique for an aberration-free spherical lens as well as for the same having primary spherical aberration. The results are computed for the Gaussian image plane and other observation planes and are compared with the previously reported results. A numerical technique for computing the FEE in a diffraction pattern formed by a conventional lens suffering from off-axis aberrations and that formed by rotationally asymmetric apertures is also depicted.

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

We report the frequency response characteristics of an optical system consisting of a lens made of a 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.

Imaging Behaviour of a Birefringent Lens Suffering from Primary Coma

The imaging characteristics of an optical system consisting of a lens made of a birefringent material sandwiched between two polarizers are studied analytically. The birefringent lens has some pre-specified primary coma present in it. Expressions are obtained for the effective pupil function and the intensity point spread function of this system. Some specific cases are computed and illustrated graphically. The performance of the proposed system has been compared with that of an identical clear aperture lens.

Light Throughput of a Birefringent Lens a: Comparative Study

This report forms a part of the systematic investigation on the imaging behaviour of a birefringent lens sandwiched between two linear polarizers. Since an appreciable amount of light energy is absorbed in the polarizers, an analytical formula for the light throughput of the proposed system has been developed. A comparative study of the performance of the said system with an isotropic lens of reduced size which give equal light levels at the output side has been performed.

High efficiency laser beam shapers using phase -only filters at fractional Fourier transform plane

The output profile of the most of the conventional laser resonators is gaussian in natur e. In the recent past, a number of beam shaping techniques has been reported for converting the gaussian profile to any profile useful for some specific applications. The simplest technique for getting a uniform flat-top profile is to truncate the beam by an aperture. A neutral density filter having suitable transmittance profile may also be used for the same purpose. A laser beam with flat-top profile has many applications in optical processing, laser micro -fabrication and laser surgery. Unfortunately, most of these techniques suffer from a serious limitation of having very low energy efficiency. Binary diffraction gratings may also be used to get a desired beam profile. However, this technique is also associated with limited diffraction efficiency. Aspheric reflective mirrors or aspheric lenses redistributes energy of a gaussian beam and are highl y energy efficient. But the fabrication of these elements is very difficult and related applications are limited to only circular beam shaping geometry. A phase -only filter in this respect seems to be highly effective since its theoretical energy efficienc y may approach 100%. The present communication reports our study on the design of a phase -only laser beam shaper. Such filters when placed at the fractional Fourier transform plane of a two lens Fourier transform setup, produces a new profile at the Fourie r transform plane.