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Diffraction II
Published in Ajawad I. Haija, M. Z. Numan, W. Larry Freeman, Concise Optics, 2018
Ajawad I. Haija, M. Z. Numan, W. Larry Freeman
This means that light from the secondary sources at the aperture is traveling forward beyond the obstacle and backward in areas in front of the obstacle. As this is not what is observed in real situations, Fresnel supplemented Huygens’ theory with what is called an obliquity factor F(θ), shown by Kirchhoff to be of the form Fθ=121+cosθthat affects the direction of propagation of the wavelets emitted by the secondary sources. In Equation 9.1, θ is the angle between a horizontal line through the secondary source and the line connecting the latter with the observation point. The factor F(θ), multiplied by the amplitude of a spherical secondary wavelet at the aperture, reduces it by a factor ranging between 1 and 0; the angle θ = 0° is for the forward direction, and θ = 180° is for the backward direction. As noticed, F(θ) = 1/2 for θ = π/2. This shows that all wavelets directed between θ = −π/2 and θ = π/2 contribute to the disturbance at point P. The obliquity factor F(θ), though lacking in physical reasoning, helped supplement Huygens’ theory in explaining Fresnel diffraction.
Greyscale image encoding and watermarking based on optical asymmetric cryptography and variational image decomposition
Published in Journal of Modern Optics, 2019
Yonggang Su, Chen Tang, Biyuan Li, Yue Qiu, Tingyue Zheng, Zhenkun Lei
In this section, the feasibility, robustness and security of the proposed scheme have been assessed by extensive experiments. Additionally, the proposed scheme is also compared with other relevant greyscale image encoding and watermarking schemes. To conduct these experiments, the greyscale image Boat with 256×256 pixels shown in Figure 3(a), is chosen as the watermark. Three standard greyscale images Baboon, Sailboat and Cameraman with 256 × 256 pixels shown in Figure 3(b–d), are selected as the host images. These four greyscale images are all selected from CVG-UGR image database (http://decsai.ugr.es/cvg/dbimagenes/g256.php). For the proposed scheme, the two RPMs are, respectively, generated by a random generator. The Fresnel diffraction distance and wavelength are, respectively, set as and . The parameters of model are, respectively, set as and . For other relevant image encoding and watermarking schemes, the parameters are left default as set by the authors.
Fresnel and Fraunhofer diffraction of (l,n)th-mode Laguerre–Gaussian laser beam by a fork-shaped grating
Published in Journal of Modern Optics, 2019
Furthermore, the analytical results are specialized for the following two particular cases: (a) when the incident LG beam has a zeroth radial mode number and azimuthal mode number l and (b) for incident LG beam with zeroth azimuthal mode number and radial mode number n. For the first specialized case, we arrive at results same as those presented in (26, 27) for Fresnel diffraction, i.e. as those given in (25) for Fraunhofer diffraction of (l,n = 0)th-mode LG beam by the FG. However, by the specialization in the second particular case, new results are obtained.
Applying multi-focus filtering plane in double-step Fresnel diffraction method for enhanced holographic projection region
Published in Journal of Information Display, 2023
Before the comparison using quantitative data, we can also directly observe the differences k image qualities. Due to the random phase multiplication in the Fresnel diffraction method, Figure 5(a) shows significant speckle noise and unclear boundaries in the reconstructed image compared to other figures. In addition, if we compare Figure 5(b)–(d), although the small amount of degradation in reconstructed image quality exists as the number of foci increases, it still maintained sufficiently high image uniformity and low speckle noise compared to the SSF case.