Self-imaging with nonparabolic approximation of spherical wave fronts

Patorski, Krzysztof; Kozak, Sylwester

doi:10.1364/josaa.5.001322

Cited by 11 publications

(4 citation statements)

References 15 publications

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“…The simple equation Eq. (1), which assumes the ideal case of zero divergence, is corrected for the spherical-wave beam with a non-zero divergence in the following formula: zT=md2λz0z0−md2λ(m=1,2,3…),where z0 represents the distance between the x-ray source and slits 28 . It follows that the optimal distance z for a spherical wave is larger than that derived with Eq.…”

Section: Resultsmentioning

confidence: 99%

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Multi-image x-ray interferometer module: I. Design concept and proof-of-concept experiments with fine-pitch slits

Asakura

Hayashida

Kawabata³

et al. 2023

J. Astron. Telesc. Instrum. Syst.

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.We propose an x-ray imaging system, multi-image x-ray interferometer module (MIXIM), with which a very high angular resolution can be achieved even with a small system size. MIXIM is composed of equally spaced multiple slits and an x-ray detector, and its angular resolution is inversely proportional to the distance between them. Here, we report our evaluation experiments of MIXIM with a newly adopted CMOS sensor with a high spatial resolution of 2.5 μm. Our previous experiments with a prototype MIXIM were limited to one-dimensional imaging, and more importantly, the achieved angular resolution was only ∼1 ″ , severely constrained due to the spatial resolution of the adopted sensor with a pixel size of 4.25 μm. By contrast, one-dimensional images obtained in this experiment had a higher angular resolution of 0.5″ when a configured system size was only ∼1 m, which demonstrates that MIXIM can simultaneously realize a high angular resolution and compact size. We also successfully obtained a two-dimensional profile of an x-ray beam for the first time for MIXIM by introducing a periodic pinhole mask. The highest angular resolution achieved in our experiments is smaller than 0.1″ with a mask-sensor distance of 866.5 cm, which shows the high scalability of MIXIM.

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Section: Resultsmentioning

confidence: 99%

“…where z 0 represents the distance between the x-ray source and slits. 28 It follows that the optimal distance z for a spherical wave is larger than that derived with Eq. ( 1).…”

Section: One-dimensional Imagingmentioning

confidence: 87%

Multi-image x-ray interferometer module: I. Design concept and proof-of-concept experiments with fine-pitch slits

Asakura

Hayashida

Kawabata³

et al. 2023

J. Astron. Telesc. Instrum. Syst.

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“…where A 0 and A 1 are constant amplitudes. The intensity of the diffraction pattern in the Fresnel zone at illumination with a point source located at distance d in front of the SAG is given by [42]…”

Section: B Comparison With a Sinusoidal Amplitude Gratingmentioning

confidence: 99%

Fringe projection with a sinusoidal phase grating

2009

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Phase-shifting profilometry requires projection of sinusoidal fringes on a 3D object. We analyze the visibility and frequency content of fringes created by a sinusoidal phase grating at coherent illumination. We derive an expression for the intensity of fringes in the Fresnel zone and measure their visibility and frequency content for a grating that has been interferometrically recorded on a holographic plate. Both evaluation of the systematic errors due to the presence of higher harmonics by simulation of a profilometric measurement and measurement of 3D coordinates of test objects confirm the good performance of the sinusoidal phase grating as a projective element. In addition, we prove theoretically that in comparison with a sinusoidal amplitude grating this grating produces better quality of fringes in the near-infrared region. Sinusoidal phase gratings are fabricated easily, and their implementation in fringe projection profilometry facilitates construction of portable, small size, and low-cost devices.

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“…Figure 4 gives the intensity distribution behind the grating with L = 0.025 cm along the xand z-axes depending on the distance (s) between the point source and the grating. The diffraction pattern is calculated for illumination with a spherical wave at paraxial approximation [29] for λ = 790 nm. As can be seen, at s = 7 cm there is no Talbot plane, at s = 12 cm the plane is only one, whereas at s = 30 cm the Talbot planes are three.…”

Section: Frequency Content Of Diffraction Pattern From a Sinusoidal Pmentioning

confidence: 99%

Pattern Projection with a Sinusoidal Phase Grating

Stoykova

Harizanova

Sainov

2008

EURASIP J. Adv. Signal Process.

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The aim of this work is to study the diffractive properties of a sinusoidal phase grating for incorporation as a pattern projection element in a multisource and multicamera phase-shifting profilometric system. Two challenges should be overcome for successful operation of such a system, which are connected to inherent limitations of the phase-shifting algorithm-requirements for a sinusoidal fringe profile and for equal background and contrast of fringes in the recorded patterns. As a first task, we analyze the frequency content of the projected fringes in the Fresnel diffraction zone for parallel and divergent light illumination at different grating parameters and wavelengths. As a second task, we evaluate the systematical errors due to higher harmonics and multiwavelength illumination. Finally, operation of the four-wavelength profilometric system is simulated, and the error of the profilometric measurement evaluated. The results of test measurements are also presented.

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Self-imaging with nonparabolic approximation of spherical wave fronts

Cited by 11 publications

References 15 publications

Multi-image x-ray interferometer module: I. Design concept and proof-of-concept experiments with fine-pitch slits

Multi-image x-ray interferometer module: I. Design concept and proof-of-concept experiments with fine-pitch slits

Fringe projection with a sinusoidal phase grating

Pattern Projection with a Sinusoidal Phase Grating

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