In optics, Zernike polynomials are widely used in testing, wavefront sensing, and aberration theory. This unique set of radial polynomials is orthogonal over the unit circle and finite on its boundary. This Letter presents a recursive formula to compute Zernike radial polynomials using a relationship between radial polynomials and Chebyshev polynomials of the second kind. Unlike the previous algorithms, the derived recurrence relation depends neither on the degree nor on the azimuthal order of the radial polynomials. This leads to a reduction in the computational complexity.
In this paper, we propose the use of geometric moments to the field of nonblind image deblurring. Using the developed relationship of geometric moments for original and blurred images, a mathematical formulation based on the Euler-Lagrange identity and variational techniques is proposed. It uses an iterative procedure to deblur the image in moment domain. The theoretical framework is validated by a set of experiments. A comparative analysis of the results obtained using the spatial and moment domains are evaluated using a quality assessment method known as the Blind/Reference-less Image Spatial Quality Evaluator (BRISQUE). The results show that the proposed method yields a higher quality score when compared with the spatial domain method for the same number of iterations.
We present two designs of all-solid photonic bandgap fiber for higher order bandgap suppression to realize a unique transmission window for optical filtering purpose. These two approaches are based on either applying a low refractive index core or a high refractive index background. This work describes direct calculations of different modes in high-index rods in the all-solid photonic bandgap fiber using the ARROW model for a double cladded step index fiber. The flat-top single-band bandpass filter obtained with potential center wavelength over UV, visible and IR region. We achieve the single-band bandpass filter with minimum pass band to rejection band ratio of 20 dB in core power. From the calculated performance, both analytical and simulation results are in good agreement with confinement loss calculation.
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