China
Africa
Explore chapters and articles related to this topic
Numerical diffraction calculation
Published in Tomoyoshi Shimobaba, Tomoyoshi Ito, Computer Holography, 2019
Tomoyoshi Shimobaba, Tomoyoshi Ito
The angular spectrum method is also important because it gives a physical interpretation that diffraction calculation can be expressed by the superposition of plane waves. When taking the inverse Fourier transform of the angular spectrum (Eq. (2.12)), it can be written as () u1(x1,y1)=ℱ−1[U(fx,fy)]=∫−∞∞∫−∞∞U(fx,fy)exp(2πi(fxx1+fyy1))dfxdfy.
Light, Waves, and Rays
Published in Vincent Toal, Introduction to Holography, 2011
This restriction can be avoided by the angular spectrum method in which the spatial Fourier transform of the recorded hologram is calculated and spatially filtered in order to extract the angular spectrum of the object wave [3]. If we use a plane reference wave at angle θ to the horizontal axis given by R˜x',y'=expjky'sinθ, Equation 13.7 becomes Hx',y'=1+O˜x',y'2+O˜x',y'exp-jky'sinθ+O˜⋆x',y'expjky'sinθ
Propagating beams carrying orbital angular momentum through simulated optical turbulence generated by Rayleigh–Bénard natural convection
Published in Waves in Random and Complex Media, 2023
S. Avramov-Zamurovic, K. P. Judd, S. Matt, R. A. Handler, A. T. Watnik, J. R. Lindle, J. M. Esposito, W. A. Jarrett
Equation (2) gives finer resolution limit (7598 points in ROI is higher resolution compared to 5071 points), consequently we select the number of grid points N = 213 = 8192 for both the source and observation planes. This selection is driven by the computational speed of Fourier transform used in the angular spectrum method. Since the RB simulations do not have this resolution, we interpolate the screens using a natural interpolation scheme from a commercial software package. Natural neighbor interpolation is used, where the interpolating surface is C1 continuous except at the sample points. The class C1 consists of all differentiable functions whose derivative is continuous. Natural method is an efficient tradeoff between linear and cubic grids. Note that the RB volume resolution in the ROI is (x,y) = (20, 100) pixels and it is extended to (8192, 8192) pixels. We do this in two steps, first going from (20, 100) to (1024, 1024) then to (8192, 8192) pixels.
Solving the twin image problem in in-line holography by using multiple defocused intensity images reconstructed from a single hologram
Published in Journal of Modern Optics, 2022
Marius Ipo Gnetto, Yao Taky Alvarez Kossonou, Yao Koffi, Kenneth A. Kaduki, Jérémie T. Zoueu
We propose a technique in which a single hologram acquired by an in-line holographic device is needed to recover the phase. We start by using the angular spectrum method to reconstruct, from a single in-line hologram and at different focusing distances, a stack (dataset) of intensity images. In this dataset, all reconstructed images are stacked in a column ready for input into a GP-TIE algorithm similar to the one developed by Zhong et al. [17] in optical microscopy to recover the phase of biological samples with a small phase variation. The algorithm uses Gaussian regression to estimate the axial derivative of intensity used to recover the phase. Thus, by using a single hologram to recover the phase, we free ourselves not only from the need to use several holograms and support constraints to recover the phase as in most iterative methods of phase reconstruction in in-line holography. Finally, the use of the GP-TIE method allowed us to solve the linearity problem inherent in the TIE method.