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Optical fiber devices
Published in John P. Dakin, Robert G. W. Brown, Handbook of Optoelectronics, 2017
Suzanne Lacroix, Xavier Daxhelet
Apodization: For most applications, side lobes seen in the spectral response are undesirable. They originate from the multiple reflections that take place between the grating ends as in a Fabry–Perot resonator. One can also understand this effect by remembering that, in a first approximation (i.e., when the perturbation is weak), the spectral response of a grating is the Fourier transform of the amplitude c of the refractive index modulation. The Fourier transform of a rectangular function is a sinc function. The larger the rectangular function, the narrower the sinc function. Similar observations are valid for the grating: the longer the grating, the narrower the spectral width and its side lobes.
High compressive ghost imaging method based on discrete cosine transform using weight coefficient matching
Published in Journal of Modern Optics, 2019
Huazheng Wu, Xiangfeng Meng, Yurong Wang, Yongkai Yin, Xiulun Yang, Wenqi He, Guoyan Dong, Hongyi Chen
We can see that their extreme values in their spectrum always appear in the similar positions on the coordinate axes in the DCT spectrum. According to the characteristic of DCT, the larger the absolute value of the coefficient in the DCT spectrum, the more significance the contribution to the reconstruction result, and the coefficient close to zero, has no special contribution to the result. Therefore, if we want to accelerate the convergence and improve the SNR in the case of low sampling (21,22), we only need to obtain DCT coefficients with the larger absolute values. In other words, we only need to sample the frequency signals near to the peak coefficient of the one-dimensional DCT spectrum. To obtain the peak value of the corresponding DCT frequency domain, a weight coefficient matching (WCM) filter system is designed with variable neighbourhood length. It can effectively elect the frequency domain neighbourhood corresponding to the peak coefficient F(u0), and as the value of domain u0 increases, the length of the filter domain becomes shorter. Finally, the cosine structure light corresponding to each frequency is calculated for measurement. If the structured light with a pixel size of N × N is used, the one-dimensional filtering system can be expressed as: where, the symbol ‘rect’ represents a rectangular function, λ represents the attenuation coefficient of the sampling interval width, and the symbol ‘[ ]’ represents the rounding symbol. The final sampling spectrum of the proposed method can be written as: where the symbol ‘.*’ represents a hadamard product. The reconstruction result of the proposed method can be expressed as (14,15): Finally, the notation η (25,26) is designed as the compression ratio denoting the relationship between M and λ: