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Showing 1 to 12 of 12 for “"Zernike polynomials"”.
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Orthogonality and convergence of discrete Zernike polynomials
The Zernike polynomials are an infinite set of orthogonal polynomials over the unit disk, which are rotationally invariant. They are frequently utilized in optics, opthal- mology, and image recognition, among many other applications, to describe spherical aberrations and image features. …
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Modal Analysis of Axisymmetric Structures using Zernike Polynomials and Machine Learning
… manual and labor-intensive process. Leveraging Zernike Annular Moment Descriptors (ZAMD) as feature maps, supervised learning models, such as decision trees, random forests, and XGBoost, achieve a high classification accuracy, thus eliminating the need for manual intervention. Furthermore, …
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Algorithms for the application of Hartmann-Shack wavefront sensors in ophthalmology
… In addition to a modal approach with Zernike Polynomials, alternative possibilities of representation of the wavefront with non-modal and heterogeneous procedures are presented. Within the framework of this thesis, extensive measuring software was developed. An additional program that …
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Fine surface control of flexible space mirrors using adaptive optics and robust control
… this, a new technique for model reduction using Zernike polynomials was developed. The H[infinity] controller was able to achieve a minimum 15 Hz control bandwidth. The previous integral controller was unable to meet the 10 Hz bandwidth requirement. The H[infinity] design process used was …
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Tomographic Reconstruction of Wavefront Aberrations using Multiple Laser Guide Stars
… Modal decomposition of wavefront phase using Zernike polynomials is a widely used technique in adaptive optics (AO) research. However, this approach breaks down with the large number of degrees of freedom required by ELTs.This research proposes the use of an alternative basis, the disk …
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Coherence-Gated Wave-Front Sensing in Strongly Scattering Samples
… measured wave-front with a linear combination of Zernike polynomials up to the fifth radial degree. The principle of CGWS is tested by measuring two wave-front aberrations, defocus and astigmatism, for a mirror as a sample and a strongly scattering sample. The results are compared to theoretical …
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Fabrication of extremely smooth blazed diffraction gratings
… wavefront aberration functions known as the Zernike polynomials. The thin film stress is proved to be linearly related to the change of the Z₂₁ Zernike coefficient. The anisotropic material properties of silicon are taken into account in the derivation, and a prediction of lattice dependent …
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On The Use Of Gaussian Filter Functions For Adaptive Optics
… filter functions calculated using various Zernike modes can be useful in removing lower-order aberrations caused by atmospheric turbulence. Traditionally, these filter functions are calculated using the step function depicting a hard aperture that introduces integrals that are sometimes …
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Performance analysis of functional expansion tallies on 2D PWR pin cell
… applications, the performance of FETs using a Zernike polynomial series has never been thoroughly tested. This work performs an analysis of Zernike-based FETs on a 2D PWR pin-cell geometry and compares the simulation time and accuracy with conventional histogram tallies for reaction rate …
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Low-Cost Spatial Light Modulator for Applications in Free-Space Optical Communication
… algorithm optimizes x-tilt, y-tilt, and defocus Zernike polynomials, improving the quality metric function by 13% under phase-limited conditions in simulation. Similarly, the SPGD algorithm is employed again for a propagation path 2.85 [m], where the system achieved a 406% increase in quality …
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Modeling and Control of SPIDER Satellite Components
… aberrations. The new basis, coined the clamped Zernike polynomials, provides a mapping for distributed spatial actuation of a membrane mirror that is amiable to the clamped boundary conditions of the mechanical lens. Consequently, based on the work presented here and being carried out in …
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Stability, Range and Statistical Aspects of non-Abelian X-ray tomography
… is a Sobolev type space, defined in terms of Zernike polynomials. The estimate is based on a related isomorphism property, established by Monard–Nickl–Paternain (2021b). We then go on to show that with high probability, and restricted to suitable D-dimensional function spaces, the Bayesian …