1 January 1986 Image Quality Of Optical Systems For Truncated Gaussian Laser Beams
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In general the Gaussian intensity distribution of a laser beam is truncated at the pupil of the image-forming system. The more pronounced the truncation effect, the less the energy portion used, and it deteriorates toward zero for a very pronounced beam expansion with 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, for example, in optical data storage technology and in infrared laser applications. The smallest point image is obtained for homogeneous illumination of the pupil, but the beam expansion needed utilizes only a small portion of the total incident energy. The more pronounced the apodization effect in the truncated Gaussian beam, the wider the central core becomes. The encircled energy functions for less pronounced apodizations are similar in the central region to those without apodization. Outside a diameter corresponding to the first dark Airy ring an increase of the apodization effect (which means less pronounced truncation) reduces 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% is encircled for homogeneous illumination. A nontruncated Gaussian beam results in a reduction up to about 0.25 in the MTF values in the higher spatial frequency range. With a nontruncated Gaussian beam a depth of focus some 50% larger is obtained, compared with that for homogeneous illumination.
Paul Kuttner, Paul Kuttner, } "Image Quality Of Optical Systems For Truncated Gaussian Laser Beams," Optical Engineering 25(1), 251180 (1 January 1986). https://doi.org/10.1117/12.7973797 . Submission:

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