Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula

Shen, Fengyu; Wang, Anbo

doi:10.1364/ao.45.001102

Cited by 272 publications

(160 citation statements)

References 18 publications

(28 reference statements)

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“…The Nyquist sampling criterion states that if f max is the maximum (spatial) frequency with which the field changes in the sampling space, the aliasing is avoided when the sampling step d in the sampling window satisfies the condition 2d f À1 max . However, since the aperture is finite in its extent, the Fourier transform of the field at the aperture has infinite extent in the spatial-frequency domain [33]. Therefore, the Nyquist criterion for sampling the U 0 x 0 ; y 0 ð Þ, given in Eq.…”

Section: Samplingmentioning

confidence: 99%

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Optical aperture area determination for accurate illuminance and luminous efficacy measurements of LED lamps

Dönsberg

Mäntynen

Ikonen

2016

Opt Rev

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The measurement uncertainty of illuminance and, consequently, luminous flux and luminous efficacy of LED lamps can be reduced with a recently introduced method based on the predictable quantum efficient detector (PQED). One of the most critical factors affecting the measurement uncertainty with the PQED method is the determination of the aperture area. This paper describes an upgrade to an optical method for direct determination of aperture area where superposition of equally spaced Gaussian laser beams is used to form a uniform irradiance distribution. In practice, this is accomplished by scanning the aperture in front of an intensity-stabilized laser beam. In the upgraded method, the aperture is attached to the PQED and the whole package is transversely scanned relative to the laser beam. This has the benefit of having identical geometry in the laser scanning of the aperture area and in the actual photometric measurement. Further, the aperture and detector assembly does not have to be dismantled for the aperture calibration. However, due to small acceptance angle of the PQED, differences between the diffraction effects of an overfilling plane wave and of a combination of Gaussian laser beams at the circular aperture need to be taken into account. A numerical calculation method for studying these effects is discussed in this paper. The calculation utilizes the Rayleigh-Sommerfeld diffraction integral, which is applied to the geometry of the PQED and the aperture. Calculation results for various aperture diameters and two different aperture-to-detector distances are presented.

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Section: Samplingmentioning

confidence: 99%

“…The Rayleigh-Sommerfeld integral has an analytical solution for the former and the analytical solution for the latter can be derived using Fresnel approximation. When a circular aperture with radius a is illuminated with a plane wave, the diffracted field on the z axis given by the Rayleigh-Sommerfeld diffraction integral is [33].…”

Section: Appendix Amentioning

confidence: 99%

Optical aperture area determination for accurate illuminance and luminous efficacy measurements of LED lamps

Dönsberg

Mäntynen

Ikonen

2016

Opt Rev

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“…(4) but we can use also a numerical approach. We have used a fast Fourier Transform based direct-integration method, [18], which uses the Rayleigh-Sommerfeld approach to determine the intensity distribution at the observation plane placed at a distance z 2 from the grating. Using this numerical approach, the optical intensity after the mask is shown, Fig.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Lissajous figure-based single-frame collimation technique

Torcal-Milla

Sanchez‐Brea

Herrera-Fernandez

2015

Sensors and Actuators A: Physical

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“…Remind that these sort of double size calculations are typical for accurate convolutional techniques (e.g. [7]). Second, the extra area of images appeared due to zero padding is essential for the recursive inverse performed in the frequency domain [1].…”

Section: Observation Modelsmentioning

confidence: 99%

Multiple Plane Phase Retrieval Based On Inverse Regularized Imaging and Discrete Diffraction Transform

Migukin¹,

Katkovnik²,

Astola³

et al. 2010

AIP Conference Proceedings

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Abstract. The phase retrieval is formulated as an inverse problem, where the forward propagation is defined by Discrete Diffraction Transform (DDT) [1], [2]. This propagation model is precise and aliasing free for pixelwise invariant (pixelated) wave field distributions in the sensor and object planes. Because of finite size of sensors DDT can be illconditioned and the regularization is an important component of the inverse. The proposed algorithm is designed for multiple plane observations and can be treated as a generalization of the Gerchberg-Saxton iterative algorithm. The proposed algorithm is studied by numerical experiments produced for phase and amplitude modulated object distributions. Comparison versus the conventional forward propagation models such as the angular spectrum decomposition and the convolutional model used in the algorithm of the same structure shows a clear advantage of DDT enabling better accuracy and better imaging.

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Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula

Cited by 272 publications

References 18 publications

Optical aperture area determination for accurate illuminance and luminous efficacy measurements of LED lamps

Optical aperture area determination for accurate illuminance and luminous efficacy measurements of LED lamps

Lissajous figure-based single-frame collimation technique

Multiple Plane Phase Retrieval Based On Inverse Regularized Imaging and Discrete Diffraction Transform

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