In general the Gaussian intensity distribution of a laser beam is truncated at the pupil of the image forming system. The more the truncation effect is pronounced the less is the energy portion used and it deteriorates towards zero for a very pronounced beam expansion with an almost homogeneous illumination. For an image forming system the Gaussian intensity distribution of the incident beam may be interpreted as an apodization with a Gaussian amplitude in the pupil. Point image, encircled energy, MTF and depth of focus can be calculated from the pupil function that is defined in this way. For diffraction limited lenses it is shown how different pronounced truncations of the incident Gaussian beam will affect these image quality criteria. Applications of this effect occur e.g. in the optical data storage technology and in infrared laser applications. The smallest point image is obtained for homogeneous illumination of the pupil but the needed beam expansion utilizes only a small portion of the total incident energy. The central core is becoming wider the more the apodization effect is pronounced in the truncated Gaussian beam. The encircled energy functionsfor less pronounced apodi-zations are similar in the central region to those without apodization. Off a diameter corresponding to the first dark Airy ring an increase of the apodization effect that means a less pronounced truncation is reducing the fraction of the total energy contained in the outer region of the point image. For a 3x Airy disk diameter almost the total energy is encircled for a Gaussian distribution whereas only some 90% are encircled for homogeneous illumination. A non truncated Gaussian beam results with a reduction up to some 0.25 in the MTF values in the higher spatial frequency range. With a non-truncated Gaussian beam some 50% larger depth of focus is obtained compared with that for a homogeneous illumination.
Paul Kuttner, Paul Kuttner,
"Image Quality Of Optical Systems For Truncated Gaussian Laser Beams.", Proc. SPIE 0518, Optical Systems Engineering IV, (29 January 1985); doi: 10.1117/12.945174; https://doi.org/10.1117/12.945174