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Piezoelectric Thin Films for MEMS Applications
Published in Vikas Choudhary, Krzysztof Iniewski, MEMS, 2017
To evaluate the applicability of piezoelectric MEMS DMs to the AO system, deformation of the mirror corresponding to Zernike mode was produced. The Zernike polynomials are commonly used to express the deformation of a circular plane by a complete set of orthogonal polynomials [49]. If the optical wavefront is represented by the Zernike polynomials, aberration can be corrected by producing deformation of the Zernike mode by the DMs. Figure 3.29 shows both the ideal and reproduced Zernike modes of Z3, Z4, Z6, and Z7. The Zernike modes of Z3, Z4, and Z7 are known as the aberrations of astigmatism, defocus, and coma-aberration, respectively. Although some deviations still remain between ideal and observed deformations, it was confirmed that the piezoelectric MEMS DMs can reproduce low-order Zernike modes by low-voltage operation. For the practical use of the piezoelectric MEMS DMs to AO, it is necessary to increase the number of individual electrodes to correct the higher-order aberration. However, piezoelectric MEMS DMs composed of PZT films are promising devices for the low-voltage wavefront generator in AO.
Advanced Widefield Microscopy
Published in John Girkin, A Practical Guide to Optical Microscopy, 2019
Phase contrast microscopy was invented in the 1930s by Frits Zernike, a Dutch theoretical physicist specializing in optics. He was examining the way light travelled through objects and in particular how the wavefront was distorted due to local changes in the refractive index. This work led to his development of Zernike polynomials, which were discussed in Chapter 2 in relation to optical aberrations. Zernike then considered a practical optical method by which the changes in phase of the wavefront, caused by refractive index changes, could be visualized. Cameras and the human eye cannot directly detect the phase of light, only its intensity. For this work Zernike was awarded the 1953 Nobel Prize for Physics.
Structural Analysis of Optics
Published in Anees Ahmad, Handbook of Optomechanical Engineering, 2017
Zernike polynomials are a common method to represent optical surface deformations that offers several benefits including data interpretation, transfer of data to optical design tools, and evaluation of residual errors after alignment and/or focus correction. The Zernike polynomials are the most commonly used; however, other useful polynomial forms include annular Zernikes, X-Y, Legendre–Fourier, and aspheric polynomials.
Detection of Hermite-Gaussian modes in vortex beams affected by convective turbulence
Published in Waves in Random and Complex Media, 2022
Benjamin Salgado, Eduardo Peters, Gustavo Funes
Zernike polynomials are a set of polynomials defined on a unit circle. They can be decomposed into a product of an angular function and radial polynomials in polar coordinates. They conform an orthonormal set and for that reason they can be used as basis functions for representing two dimensional surfaces [23–25]. They are widely used in adaptive optics to reconstruct and correct distorted wavefront phases [26]. The decomposition of a turbulence phase mask into Zernike polynomials is used here as a tool to identify the characteristics of the turbulences that generated the necessary perturbation over the beam for the appearance of HG modes. We will apply the decomposition in the usual way: where Θ represents the turbulence phase mask, is the nth Zernike polinomial using the order presented in the appendix and represents the coefficients of the series.
A high-resolution wavefront sensing method to investigate the annular Zernike polynomials behaviour in the indoor convective air turbulence in the presence of a 2D temperature gradient
Published in Journal of Modern Optics, 2021
E. Mohammadi Razi, Saifollah Rasouli, M. Dashti, J. J. Niemela
Atmospheric turbulence can have a significant impact in many areas, including earth-based astronomical observations, air travel, pollution dispersal, etc. Its study can be enhanced using laser-based methods and the evaluation of wavefront distortion, which can be determined through use of Zernike polynomials. In the case of atmospheric turbulence, conventional and Zernike annular polynomials were used by many authors, e.g. Noll [1] and Fried [2], who were the pioneers in this application. The conventional Zernike polynomials are orthogonal in a circle with a unit radius. For annular pupils, e.g. in a conventional Cassegrain telescope in which the central hole in the primary mirror allows a reflected light from the secondary, annular Zernike polynomials are used to determine the wavefront aberrations. Related efforts can be found in the work by Mahajan [3–8] and Roddier [9], who describe an algorithm that simulates atmospherically distorted wavefronts using a Zernike expansion of randomly weighted Karhunen-Loeve functions. Canan [10] and Hu and coworkers [11] expanded further the use of Zernike polynomials for studying atmospheric turbulence. In this paper, we investigate wavefront aberrations of a plane wave laser beam with an annular cross-section having a diameter of 20 cm, when it passes through a convective air turbulence with different strengths generated with various 2D temperature gradients (TGs). The wavefront aberrations were determined by measuring the annular Zernike polynomials of the wavefront over the annular area having a diameter 18 cm with a spatial resolution of 3.1 mm in real space.
Super-resolution pupil filtering for visual performance enhancement using adaptive optics
Published in Journal of Modern Optics, 2018
Lina Zhao, Yun Dai, Junlei Zhao, Xiaojun Zhou
where ρ is the normalized radius over the circular pupil. The filter is characterized by the amplitude transmittance A(ρ) and the phase function φ(ρ). Super-resolution techniques differ in the way the functions A(ρ) and φ(ρ) are defined and optimized. Our strategy is based on the control of continuous phase function φ(ρ) so that they can be reproduced by a deformable mirror. The general modification procedure is to expand the pupil function in some complete set of functions and adjust the coefficients to approximate the pre-specified point spread functions (PSF). Because Zernike polynomials are orthogonal over a unit circle, they are usually used as a representation of wave-front phase. The phase function φ(ρ) can be mathematically described as the weighted sum of Zernike basis functions: