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 half-maximum) 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 half-maximum 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.

In this work, efficient amplitude-apodization pupils have been presented for tailoring the point spread function (PSF), which results in a decreased full-width at half-maximum (FWHM) and suppressed sidelobes. Comparison of PSF intensity profiles for both the unapodized and apodized cases have been reported. By analysing the resulting PSFs, the well-known effects induced by monochromatic aberrations such as defocussing effect, and the primary spherical aberration have been controlled for various degrees of apodization parameter $\beta$. It is shown that the two-point resolution of the apodized optical system significantly increased in the presence of aberrations. The proposed pupil apodizer is very effective in enhancing the resolution of the optical systems applicable in imaging and focussing applications.