Fast algorithms for free-space diffraction patterns calculation

Mas, David; Garcı́a, Javier; Ferreira, Carlos; Bernardo, Luı́s M.; Marinho, Francisco J.

doi:10.1016/s0030-4018(99)00201-1

Cited by 225 publications

(144 citation statements)

References 17 publications

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“…The advantages of using FrFT for cascades of axially centered lenses are well known in the context of visible-light optics (Ozaktas et al, 2001;Ozaktas & Mendlovic, 1995). More recently, its use for simulating free space propagation of X-rays has been presented by Le Bolloc'h et al (Le Bolloc'h et al, 2012;Mas et al, 1999). Performing an FrFT is equivalent to solving the Fresnel diffraction integral, but the FrFT is associated with favorable mathematical properties, such as being additive in index.…”

Section: Introductionmentioning

confidence: 99%

The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

Pedersen

Simons

Detlefs

et al. 2018

J Synchrotron Radiat

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The fractional Fourier transform (FrFT) is introduced as a tool for numerical simulations of X-ray wavefront propagation. By removing the strict sampling requirements encountered in typical Fourier optics, simulations using the FrFT can be carried out with much decreased detail, allowing, for example, on-line simulation during experiments. Moreover, the additive index property of the FrFT allows the propagation through multiple optical components to be simulated in a single step, which is particularly useful for compound refractive lenses (CRLs). It is shown that it is possible to model the attenuation from the entire CRL using one or two effective apertures without loss of accuracy, greatly accelerating simulations involving CRLs. To demonstrate the applicability and accuracy of the FrFT, the imaging resolution of a CRL-based imaging system is estimated, and the FrFT approach is shown to be significantly more precise than comparable approaches using geometrical optics. Secondly, it is shown that extensive FrFT simulations of complex systems involving coherence and/or non-monochromatic sources can be carried out in minutes. Specifically, the chromatic aberrations as a function of source bandwidth are estimated, and it is found that the geometric optics greatly overestimates the aberration for energy bandwidths of around 1%.

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Section: Introductionmentioning

confidence: 99%

The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

Pedersen

Simons

Detlefs

et al. 2018

J Synchrotron Radiat

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“…For better visualization, the longitudinal spacing has been chosen 4 times denser than given by Eq. (22).…”

Section: Discussionmentioning

confidence: 99%

“…We also analyze the evolution of spatial information along the longitudinal direction and show that the spherical reference surfaces should be equally spaced with respect to the fractional Fourier transform order. Our results are relevant to work on both sampling and fast computation of light fields propagating through quadratic-phase systems [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Optimal representation and processing of optical signals in quadratic-phase systems

Arık

Özaktaş

2016

Optics Communications

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a b s t r a c tOptical fields propagating through quadratic-phase systems (QPSs) can be modeled as magnified fractional Fourier transforms (FRTs) of the input field, provided we observe them on suitably defined spherical reference surfaces. Non-redundant representation of the fields with the minimum number of samples becomes possible by appropriate choice of sample points on these surfaces. Longitudinally, these surfaces should not be spaced equally with the distance of propagation, but with respect to the FRT order. The non-uniform sampling grid that emerges mirrors the fundamental structure of propagation through QPSs. By providing a means to effectively handle the sampling of chirp functions, it allows for accurate and efficient computation of optical fields propagating in QPSs.

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“…The direct method of reconstruction [33] can be derived by applying the Fresnel Transform to the sampled signal O(n x ∆ξ, n y ∆η), which denotes the sampled object term in the hologram (CCD) plane to obtain an equation for the continuous reconstructed image recon(x ′ , y ′ ). It is given by…”

Section: Direct and Spectral Methods Of Reconstructionmentioning

confidence: 99%

Speckle reduction of reconstructions of digital holograms using three dimensional filtering

Maycock

McDonald

Hennelly

2013

Optics Communications

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We report on a new digital signal processing technique that reduces speckle in reconstructions of digital holograms. This is achieved by convolving the three dimensional intensity pattern (the intensity of the propagated DH at a series of different distances) with a 3D point spread function in all three dimensions (x,y,z ). It is based on the fact that the addition of different independent speckle images on an intensity basis reduces the speckle content. We provide quantitative results in terms of speckle index and resolution, and show that filtering in the z direction has the added benefit of an increase the depth of focus of the digital hologram reconstruction.

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Fast algorithms for free-space diffraction patterns calculation

Cited by 225 publications

References 17 publications

The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

Optimal representation and processing of optical signals in quadratic-phase systems

Speckle reduction of reconstructions of digital holograms using three dimensional filtering

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