2007
DOI: 10.1364/josaa.25.000108
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Noninterferometric phase retrieval using a fractional Fourier system

Abstract: The signal extraction method based on intensity measurements in two close fractional Fourier domains is examined by using the phase space formalism. The fractional order separation has a lower bound and an upper bound that depend on the signal at hand and the noise in the optical system used for measurement. On the basis of a theoretical analysis, it is shown that for a given optical system a judicious choice of fractional order separation requires some a priori knowledge of the signal bandwidth. We also prese… Show more

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Cited by 30 publications
(13 citation statements)
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“…The continuous LCT has been used in a number of applications, e.g., in optical systems to measure tilt and translation [10][11][12], to provide additional keys in doublerandom phase encoding optical encryption schemes [13,14], in analysis of speckle size [15], and in noninterferometric phase extraction schemes [16,17]. However, there are many situations where it is desirable to numerically approximate the transform.…”
Section: Introductionmentioning
confidence: 99%
“…The continuous LCT has been used in a number of applications, e.g., in optical systems to measure tilt and translation [10][11][12], to provide additional keys in doublerandom phase encoding optical encryption schemes [13,14], in analysis of speckle size [15], and in noninterferometric phase extraction schemes [16,17]. However, there are many situations where it is desirable to numerically approximate the transform.…”
Section: Introductionmentioning
confidence: 99%
“…Most of them, either iterative or non-iterative ones, involve digital post processing. In particular, the phase information can be recovered using non-iterative approaches based on so-called transport of intensity equation [21]− [24]. Nevertheless, it is often mathematically complex (e.g.…”
Section: Phase Retrieval Approach Based On Measurement Of Wd Projectionsmentioning
confidence: 99%
“…One such insight is that the phase of a signal can be retrieved without the use of interferometric techniques by capturing projections (marginals) of the same signals' WDF in different domains. To do this in [3] the Fractional Fourier transform, (FRT), distributions (intensities) for different FRT orders were imaged. Thus the FRT, which is a special case of the LCT, was used and the signal phase extracted experimentally.…”
Section: Measurement: Phase Motion and Specklementioning
confidence: 99%