Resolution for the modified point spread function (PSF) of asymmetrically apodized optical systems has been analysed by a new parameter half-width at half-maximum (HWHM) in addition to the well-defined parameter full-width at half-maximum (FWHM). The distribution of half-maximum energy in the centroid of modified PSF has been investigated in terms of HWHM on good side and HWHM on bad side. We observed that as the asymmetry in PSF increases, FWHM of the main peak increases and then decreases and is being aided by the degree of amplitude apodization in the central region of slit functions. In the present study, HWHM (half-width at halfmaximum) of the resultant PSF has been defined to characterize the resolution of the detection system. It is essentially a line of projection, which measures the width of the main lobe at its halfmaximum position from the diffraction centre and has been computed for various amplitudes and antiphase apodizations of the slit aperture. We have noticed that HWHM on the good side decreases at the cost of the increased HWHM on the bad side in the presence of asymmetric apodization.

ABSTRACT:Effect of asymmetric apodization applied to two dimensional complex pupil filters on resolution of object points in the image plane of apodized optical systems has been investigated. The required pupil function and its transmittance is formulated and studied. These sparrow limits have been discussed as functions of the degree of spatial coherence of the illumination, intensity ratio of two object points and asymmetric apodization parameter ( ). The sparrow resolution limit increases as the degree of coherence increases, irrespective of the intensity ratio of two point objects. With respect to intensity ratio of two points it is clearly found that for all cases of illumination, employing complex pupil filters in the presence of asymmetric apodization leads to an improvement in resolution of two object points.

The simultaneous suppression of sidelobes and the sharpening of the central peak in the process of diffraction pattern detection based on asymmetric apodization have been investigated. Asymmetric apodization is applied to a semicircular array of two-dimensional (2D) aperture functions, which is a series of 'coded-phase arrays of semicircular rings randomly distributed over the central circular region of a pupil function' and is similar to that used in the field of diffractive optics. The point spread function (PSF) of an imaging system with asymmetric apodization of the discrete type has been found to possess a good side with suppressed sidelobes, whereas its bad side contains enhanced sidelobes. Further, the diffracted field characteristics are obtained in the presence of these aperture functions. Asymmetric apodization is helpful in improving the performance of the optical gratings or 2D arrays used in real-time imaging techniques.

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