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 F(x,y) sampled at an N×N Cartesian grid of point sensors on a plane yields a matrix of values F(qx,qy), where (qx,qy) 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 (n,m), to analyze them into their corresponding coefficients Fn,m of energy and angular momentum (E-AM). The sampled E-AM modes span an N2-dimensional space, but are not orthogonal—except for parity. In this paper, we propose the properly orthonormal “Laguerre–Kravchuk” discrete functions Λn,m(qx,qy) 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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