Abstract
The measurement of continuous wave fields by a digital (pixellated) screen of sensors can be used to assess the quality of a beam by finding its formant modes. A generic continuous field sampled at an Cartesian grid of point sensors on a plane yields a matrix of values , where are integer coordinates. When the approximate rotational symmetry of the input field is important, one may use the sampled Laguerre–Gauss functions, with radial and angular modes , to analyze them into their corresponding coefficients of energy and angular momentum (E-AM). The sampled E-AM modes span an -dimensional space, but are not orthogonal—except for parity. In this paper, we propose the properly orthonormal “Laguerre–Kravchuk” discrete functions as a convenient basis to analyze the sampled beams into their E-AM polar modes, and with them synthesize the input image exactly.
© 2011 Optical Society of America
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