Zernike polynomials and their applications

Niu, Kuo; Tian, Chao

doi:10.1088/2040-8986/ac9e08

Cited by 38 publications

(16 citation statements)

References 172 publications

(322 reference statements)

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“…Therefore, our first challenge was to convert two-dimensional morphology to a one-dimensional vector. To solve this issue, we used Zernike polynomials on the cellular mask [36] [37]. TI tools can only work properly when we have a well-behaved normalized matrix [33] [34].…”

Section: Resultsmentioning

confidence: 99%

Cell-TIMP: Cellular Trajectory Inference based on Morphological Parameter

Raj,

Gupta,

Anantha

et al. 2024

Preprint

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Cellular morphology, shaped by various genetic and environmental influences, is pivotal to studying experimental cell biology, necessitating precise measurement and analysis techniques. Traditional approaches, which rely on geometric metrics derived from stained images, encounter obstacles stemming from both the imaging and analytical domains. Staining processes can disrupt the cell's natural state and diminish accuracy due to photobleaching, while conventional analysis techniques, which categorize cells based on shape to discern pathophysiological conditions, often fail to capture the continuous and asynchronous nature of biological processes such as cell differentiation, immune responses, and cancer progression. In this work, we propose the use of quantitative phase imaging for morphological assessment due to its label-free nature. For analysis, we repurposed the genomic analysis toolbox to perform trajectory inference analysis purely based on morphology information. We applied the developed framework to study the progression of leukemia and breast cancer metastasis. Our approach revealed a clear pattern of morphological evolution tied to the diseases' advancement, highlighting the efficacy of our method in identifying functionally significant shape changes where conventional techniques falter. This advancement offers a fresh perspective on analyzing cellular morphology and holds significant potential for the broader research community, enabling a deeper understanding of complex biological dynamics.

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Section: Resultsmentioning

confidence: 99%

Cell-TIMP: Cellular Trajectory Inference based on Morphological Parameter

Raj,

Gupta,

Anantha

et al. 2024

Preprint

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“…(i) The wavefront data W(x, y) is multiplied by the wavelength λ to express it in length units. (ii) From a Zernike fit [23] of W(x, y) • λ the defocus term D is obtained. (iii) The curvature radius of a Gaussian beam can be related to D via:…”

Section: Appendix a Finding The Beam Parametersmentioning

confidence: 99%

High-accuracy determination of the beam divergence error in free-fall absolute gravimeters

Rothleitner,

Andreas

2024

Metrologia

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We investigate the bias due to the beam divergence of the collimator in a free-fall absolute gravimeter of type FG5X. First, we measure the beam parameters with a Shack-Hartmann sensor. Then, we use the parameters to simulate the relative gravitational acceleration error of an FG5X gravimeter, which employs an unbalanced Mach-Zehnder laser interferometer. This investigation we do with four diff erent commercial collimators, providing diff erent divergence angles. We compare the results to real gravity measurements using the same collimators. The larger the divergence angle, and the bigger the relative length error, the bigger is the bias in the gravity measurements. A good agreement between theory and experiment is found, resulting in a relative bias of −2.77(24) · 10^{−9} (−2.72(24) µGal) for our standard collimator of type Thorlabs TC25APC, which is usually used for free-fall acceleration determinations. The outcome is also important for the realisation of the SI unit kilogram via Kibble balance experiments that, on one side, employ laser interferometers for velocity measurements, and, on the other side, require accurate values of the gravitational acceleration. For example, if this divergence error is not corrected in the Kibble balance, then the mass determination would be biased by 2.77(24) µg kg^{−1} (numbers are valid only for our gravimeter with our collimator and fiber).

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“…We generated circular surfaces with a diameter of 50 mm by choosing a random set of expansion coefficients that weight the first 21 orthonormal Zernike polynomials [11], following Noll's numbering scheme [12]. We ignore the three polynomials corresponding to rigid-body displacements (Z 0 , 'piston') and rotations (Z 1 and Z 2 , 'tilts') since they do not correspond to surface deformations.…”

Section: Generalizing With Simulationsmentioning

confidence: 99%

Autocollimators: plane angle measurand ambiguities and the impact of surface form

Eves,

Leroux

2023

Metrologia

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A phase shifting interferometer and a deformable mirror were used to study the impact of surface form on autocollimators, which detect the orientation of a plane reflecting surface. As real surfaces are not strictly planar, autocollimators must reduce a distribution of local surface orientations to a single reported angle, implicitly defining a measurand. Plausible choices of the summary statistic used to collapse an angle distribution to a single number can disagree by \SI{4}{\arcsecond} for a surface with a \SI{35}{mm} diameter and \SI{130}{nm} standard deviation from the best-fit plane. Combining a general framework for specifying autocollimator measurand definitions with Monte-Carlo simulation of random test surfaces yields estimates of the plausible differences between autocollimator measurands as a function of surface deformation amplitude, and shows the existence of three separate classes of measurands according to their sensitivity to subsets of the Zernike polynomials. Uncertainties due to surface form and measurand ambiguity can be eliminated by explicitly specifying a plane angle measurand for imperfect surfaces, such as a least-squares plane fit realized using an interferometer.

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Zernike polynomials and their applications

Cited by 38 publications

References 172 publications

Cell-TIMP: Cellular Trajectory Inference based on Morphological Parameter

Cell-TIMP: Cellular Trajectory Inference based on Morphological Parameter

High-accuracy determination of the beam divergence error in free-fall absolute gravimeters

Autocollimators: plane angle measurand ambiguities and the impact of surface form

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