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Dependence of the Knox–Thompson transfer function on the difference of spatial frequencies

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Abstract

The magnitude of the Knox–Thompson phasor (occurring in white-light speckle imagery) is dependent on the separation of the two spatial frequencies, κ, and κ′, for which the phasor is evaluated. Following the general approach laid down by von der Lühe [ J. Opt. Soc. Am. A 5, 721 ( 1988)], we have developed results for the dependence of the magnitude of the phasor on κκ′ and on ½(κ + κ′). Our results show that the (κκ′) -dependence for modest values of ½(κ + κ′) is significantly different from that for large values of ½(κ + κ′) and that the phasor’s magnitude depends on the orientation between κκ′ and ½(κ + κ′). An analytic expression is developed; the expression fairly closely approximates the dependence of the phasor’s magnitude on κκ′ and on ½(κ + κ′) over the range of significant values of these two quantities.

© 1990 Optical Society of America

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