Extension of the Fresnel transform to ABCD systems

Palma, C.; Bagini, V.

doi:10.1364/josaa.14.001774

Cited by 66 publications

(34 citation statements)

References 14 publications

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“…From a theoretical point of view, the field emitted by a point Dirac emitter , whose transverse position in the plane of the scattering particle is ( , ), can be evaluated in the plane of the CCD sensor by generalized Huygens Fresnel integrals [12][13][14][15]. Their coefficients depend on the coefficients of optical transfer matrices describing the optical elements encountered between the particle and the sensor.…”

Section: Simulation Of Speckle-like Interferometric Out-of-focus Pattmentioning

confidence: 99%

Determination of the Size of Irregular Particles Using Interferometric Out-of-Focus Imaging

Brunel

Shen

Coëtmellec

et al. 2014

International Journal of Optics

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We present a mathematical formalism to predict speckle-like interferometric out-of-focus patterns created by irregular scattering objects. We describe the objects by an ensemble of Dirac emitters. We show that it is not necessary to describe rigorously the scattering properties of an elliptical irregular object to predict some physical properties of the interferometric out-of-focus pattern. The fit of the central peak of the 2D autocorrelation of the pattern allows the prediction of the size of the scattering element. The method can be applied to particles in a size range from a tenth of micrometers to the millimeter.

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Section: Simulation Of Speckle-like Interferometric Out-of-focus Pattmentioning

confidence: 99%

Determination of the Size of Irregular Particles Using Interferometric Out-of-Focus Imaging

Brunel

Shen

Coëtmellec

et al. 2014

International Journal of Optics

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“…The ABCD matrix can be decomposed in different ways as the product of three simpler matrices, each one accounting for an elementary transformation: propagation through free space, magnification, and refraction by a lens [33]. It has also been shown that the wave propagation between the input and output planes in an ABCD system can be accounted for by an integral transform with an ABCDdependent quadratic kernel, as a generalization of the usual Fresnel transform associated with diffraction in a homogeneous medium [32,33]. There is a wide class of optical systems whose behavior can satisfactorily be modeled by an ABCD matrix within the paraxial domain.…”

Section: Centroid Propagation In Abcd Systemsmentioning

confidence: 99%

“…where the integration is extended to the whole input plane; d 2 r ¼ dxdy is the differential area element at that plane; and Kðr o ; rÞ is the quadratic diffraction kernel given by [33]:…”

Section: Centroid Propagation In Abcd Systemsmentioning

confidence: 99%

Centroid propagation through optical systems with ABCD kernels and non-uniform or finite apertures

et al. 2011

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If the propagation of a light field can be satisfactorily described by a diffraction integral with an ABCD kernel, the propagation of its irradiance centroid is completely determined by the corresponding ABCD ray-transfer matrix in exactly the same way as if the centroid path were a conventional geometrical ray. However, potentially significant deviations from this geometrical propagation rule may arise in the presence of finite or nonuniform apertures truncating or otherwise modifying the input beam irradiance distribution.

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“…These systems belong to the class of quadratic-phase systems, which are also known as ABCD systems or lossless first-order optical systems [18][19][20][21][22][23][24][25][26][27]. LCTs have also been referred to as generalized Huygens integrals [28], generalized Fresnel transforms [29,30], special affine Fourier transforms [31,32], extended fractional Fourier transforms [33], and Moshinsky-Quesne transforms [18], among other things, and have found use in image filtering [34]. In this paper we show that LCT domains are essentially equivalent to fractional Fourier domains.…”

Section: Introductionmentioning

confidence: 99%

Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space–bandwidth product

Oktem

Özaktaş

2010

J. Opt. Soc. Am. A

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Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.

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Extension of the Fresnel transform to ABCD systems

Cited by 66 publications

References 14 publications

Determination of the Size of Irregular Particles Using Interferometric Out-of-Focus Imaging

Determination of the Size of Irregular Particles Using Interferometric Out-of-Focus Imaging

Centroid propagation through optical systems with ABCD kernels and non-uniform or finite apertures

Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space–bandwidth product

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