On Fresnel Diffraction by One-dimensional Periodic Objects, with Application to Structure Determination of Phase Objects

Abstract-We define a temporal similarity function for assessing the temporal evolution of short pulses in dispersion media. For first-order dispersion media the temporal similarity function has a simple close expression. We use the sampled values of the temporal similarity function as coefficients, for expressing the output complex amplitude envelope as a finite linear superposition of the input complex amplitude envelope.

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“…For describing Fresnel diffraction, Guigay [7] reported a closed formula for evaluating equation (13):…”

Section: Fractional Talbot Effectmentioning

confidence: 99%

Temporal similarity for optical short pulses

Ojeda‐Castañeda

Gómez-Sarabia

2010

Photon. Lett. Poland

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“…It is easy to see that each individual projection datum Θ(ρ, θ) can also be relabeled in terms of the Radon distance ρ and angle θ by the following nonlinear coordinate transform: (8) This transform introduces an extra Jacobian factor: (9) (10) where the functions L(x, y; t) and U(x, y; t) is given by (11) Qi and Chen Page 4 (12) Therefore, the equation (7) can now be written as (13) where the filtered function F[t, U(x, y)] is given by (14) In this equation, the pre-weighted projection data Θ(t, u) is defined as: (15) Equations (13,14,15) provide a direct image reconstruction from the measured projection data Θ(t, u). The algorithm is summarized in the following steps:…”

Section: Fan-beam Reconstruction Formula For Full Scan Casementioning

confidence: 99%

An FBP image reconstruction algorithm for x-ray differential phase contrast CT

Chen

2008

SPIE Proceedings

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Most recently, a novel data acquisition method has been proposed and experimentally implemented for x-ray differential phase contrast computed tomography (DPC-CT), in which a conventional x-ray tube and a Talbot-Lau type interferometer were utilized in data acquisition. The divergent nature of the data acquisition system requires a divergent-beam image reconstruction algorithm for DPC-CT. This paper focuses on addressing this image reconstruction issue. We developed a filtered backprojection algorithm to directly reconstruct the DPC-CT images from acquired projection data. The developed algorithm allows one to directly reconstruct the decrement of the real part of the refractive index from the measured data. In order to accurately reconstruct an image, the data need to be acquired over an angular range of at least 180° plus the fan-angle. Different from the parallel beam data acquisition and reconstruction methods, a 180° rotation angle for data acquisition system does not provide sufficient data for an accurate reconstruction of the entire filed of view. Numerical simulations have been conducted to validate the image reconstruction algorithm.

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“…It was shown by Guigay [21] and later found independently [22][23][24], that the Fresnel images of binary phase gratings, at multiples of certain fractions of the Talbot distance, exhibit binary intensity distributions, whose visibility depends on the phase step height. This property of Fresnel images has found numerous applications in various areas of physics [24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Phase calibration of spatial light modulators by means of Fresnel images

Martínez-León¹,

Jaroszewicz²,

Kołodziejczyk³

et al. 2009

J. Opt. A: Pure Appl. Opt.

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Reliable application of spatial light modulators (SLMs) as programmable diffractive optical elements requires a thorough calibration. In this paper, we propose a method for calibrating SLMs based on the evaluation of Fresnel images. Fresnel images generated by a binary phase diffraction grating consist of binary irradiance distributions whose visibility depends on the phase modulation. By displaying on our device a diffraction grating with a binary phase step along one direction and a linearly increasing phase along the orthogonal direction, we perform a complete phase calibration. In this way, the phase modulation for every pixel and for every value of the entrance signal can be determined experimentally.Additionally, data acquisition can be significantly simplified with this scheme.

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On Fresnel Diffraction by One-dimensional Periodic Objects, with Application to Structure Determination of Phase Objects

Cited by 94 publications

References 5 publications

Temporal similarity for optical short pulses

Temporal similarity for optical short pulses

An FBP image reconstruction algorithm for x-ray differential phase contrast CT

Phase calibration of spatial light modulators by means of Fresnel images

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