scholarly journals Is Aberrometric Analysis Based on Zernike Modes That May Not be Correct?

2021 ◽  
Vol In Press (In Press) ◽  
Author(s):  
Mehrdad Sadeghi ◽  
Jalil Omidian
Keyword(s):  
Treatment Plan ◽  
Crystalline Lens ◽  
Optical Systems ◽  
Reference Level ◽  
Reference Surface ◽  
Light Rays ◽  
Seventh Order ◽  
Pass Through ◽  
Fifth Order ◽  
Zernike Modes

Context: Aberrometric analysis of the wavefront in patients with refractive disorders is performed using the Zernike pyramid mode and based on that, a treatment plan is determined however, it is not clear what Zernike modes are derived from mathematical analysis, exactly how much they correspond to the clinical facts this article discusses ways to study this issue. Evidence Acquisition: One of the methods for studying optical systems is the aberrometry of wavefront. the wavefront is a two-dimensional surface perpendicular to a bunch of parallel light rays, that all these rays have the same phase on this surface (because light emits sinusoidally and therefore has multiple identical phases) whenever these rays pass through a refractive surface, it is also called the reference level this refractive index will be ideal if the homogeneity of these rays is maintained and the rays of this bunch of light will be able to focus at one point, but if the by passing light through the refractive surface the wavefront will be disturbed and the lights on this surface have different phases than the reference surface then it is said there is a discrepancy or deviation between the reference surface and the wavefront. Therefore, aberration is the creation of the distance of the wavefront in a certain phase from the refractive surface or reference surface. When we say refractive surface, we do not mean a specific place like the cornea because other than the cornea other factors such as crystalline lens, vitreous, retin even tear layer they are involved in creating aberrations, but usually the pupil range is considered as the reference surface. Results: Modes z-13 and z13 of the fourth order and modes z04 and z-24, z24 from the fifth order and modes z-15, z15 of six order and modes z06, z-26, z26 of seventh order they are not pure and mathematically they have some lower order which may cause in analysis aberrometry disruption as a result, the relevant orders have a little more or less value. Conclusions: There are no strong clinical reasons for Zernike modes to be a fully accurate description of aberromerty, so clinicians should consider other clinical data and findings in their interpretation. Some modes of high-order Zernike have sentences of low-order This can cause abnormal analysis.

Cataract

2020 ◽  
Vol 02 (03) ◽  
pp. 13-16
Author(s):  
Sayali Yolchu Ibrahimova ◽  
◽  
Gulara Rufat Sadikhova ◽  
Keyword(s):  
Key Words ◽  
Elderly People ◽  
Crystalline Lens ◽  
Eye Diseases ◽  
Key Words Trauma ◽  
Human Eye ◽  
Light Rays

Cataract iz one of the most common eye diseases among elderly people. The crystalline lens of the human eye is like a “natural lens which skips and refractors light rays. The crystalline lens is located inside the eyeball between the iris and vitreous parts of the eye. In youth the eye’s lens is transparent, elastic, can change its shape, almost instantly directing and managing its focus, this is why an eye sees the far and near objects equally good. In case of the cataract there is partial or absolute clouding of the lens, which may lead to the loss of its transparency and the eye gets only the small amount of light rays, thus it causes the complication of vision, and the eyesight becomes unclear and blurry. Over the years, the disease progresses: the degraded part increases and eyesight completely weakens. If the disease will not be treated in time cataract may even lead to the complete blindness. Key words: trauma, blindness, hyperopic, turbidity in eyes

Fifth-order Aberration Coefficients for Plane-symmetric Optical Systems

2021 ◽  
Author(s):  
Yuxuan Liu ◽  
Jessica Steidle ◽  
Jannick P. Rolland
Keyword(s):  
Optical Systems ◽  
Plane Symmetric ◽  
Fifth Order

Spatial optical solitons in fifth order and seventh order weakly nonlocal nonlinear media

Optik ◽  
2013 ◽  
Vol 124 (22) ◽  
pp. 5683-5686 ◽  
Author(s):  
Qin Zhou ◽  
Duanzheng Yao ◽  
Sijing Ding ◽  
Yafang Zhang ◽  
Feng Chen ◽  
...  
Keyword(s):  
Optical Solitons ◽  
Nonlinear Media ◽  
Spatial Optical Solitons ◽  
Seventh Order ◽  
Nonlocal Nonlinear Media ◽  
Fifth Order ◽  
Nonlocal Nonlinear

scholarly journals Achieving Seventh-Order Amplitude Accuracy in Leapfrog Integrations

2013 ◽  
Vol 141 (9) ◽  
pp. 3037-3051 ◽  
Author(s):  
Paul D. Williams
Keyword(s):  
Nonlinear System ◽  
Third Order ◽  
First Order ◽  
Time Stepping ◽  
The Third ◽  
Numerical Integrations ◽  
Seventh Order ◽  
Ocean Models ◽  
Stability And Accuracy ◽  
Fifth Order

Abstract The leapfrog time-stepping scheme makes no amplitude errors when integrating linear oscillations. Unfortunately, the Robert–Asselin filter, which is used to damp the computational mode, introduces first-order amplitude errors. The Robert–Asselin–Williams (RAW) filter, which was recently proposed as an improvement, eliminates the first-order amplitude errors and yields third-order amplitude accuracy. However, it has not previously been shown how to further improve the accuracy by eliminating the third- and higher-order amplitude errors. Here, it is shown that leapfrogging over a suitably weighted blend of the filtered and unfiltered tendencies eliminates the third-order amplitude errors and yields fifth-order amplitude accuracy. It is further shown that the use of a more discriminating (1, −4, 6, −4, 1) filter instead of a (1, −2, 1) filter eliminates the fifth-order amplitude errors and yields seventh-order amplitude accuracy. Other related schemes are obtained by varying the values of the filter parameters, and it is found that several combinations offer an appealing compromise of stability and accuracy. The proposed new schemes are tested in numerical integrations of a simple nonlinear system. They appear to be attractive alternatives to the filtered leapfrog schemes currently used in many atmosphere and ocean models.

scholarly journals Comparative Study of Three High Order Schemes for LES of Temporally Evolving Mixing Layers

2012 ◽  
Vol 12 (5) ◽  
pp. 1603-1622 ◽  
Author(s):  
Helen C. Yee ◽  
Bjorn Sjögreen ◽  
Abdellah Hadjadj
Keyword(s):  
High Order ◽  
Mixing Layers ◽  
Compressible Turbulence ◽  
Filter Method ◽  
Eighth Order ◽  
Base Scheme ◽  
High Order Schemes ◽  
Supersonic Regime ◽  
Seventh Order ◽  
Fifth Order

AbstractThree high order shock-capturing schemes are compared for large eddy simulations (LES) of temporally evolving mixing layers for different convective Mach numbers ranging from the quasi-incompressible regime to highly compressible supersonic regime. The considered high order schemes are fifth-order WENO (WENO5), seventh-order WENO (WENO7) and the associated eighth-order central spatial base scheme with the dissipative portion of WENO7 as a nonlinear post-processing filter step (WENO7fi). This high order nonlinear filter method of Yee & Sjögreen is designed for accurate and efficient simulations of shock-free compressible turbulence, turbulence with shocklets and turbulence with strong shocks with minimum tuning of scheme parameters. The LES results by WENO7fi using the same scheme parameter agree well with experimental results compiled by Barone et al., and published direct numerical simulations (DNS) work of Rogers & Moser and Pantano & Sarkar, whereas results by WENO5 and WENO7 compare poorly with experimental data and DNS computations.

The geometrical aberrations of general electron optical systems II. The primary (third order) aberrations of orthogonal systems, and the secondary (fifth order) aberrations of round systems

1965 ◽  
Vol 257 (1086) ◽  
pp. 523-552 ◽  
Keyword(s):  
Second Order ◽  
Order Perturbation ◽  
Optical Systems ◽  
Characteristic Functions ◽  
Electron Optics ◽  
Third Order ◽  
Variation Of Parameters ◽  
General Kind ◽  
Fifth Order ◽  
Orthogonal Systems

The theory of characteristic functions, developed by Sturrock for electron optics, is used to calculate the primary aberrations of rectilinear orthogonal systems of the most general kind. In the second part, the secondary aberrations of round systems are calculated with the aid of Sturrock’s second-order perturbation characteristic functions. A proof of the equivalence of the aberration formulae obtained by Melkich, using the variation of parameters method, and those obtained below is offered in an appendix.

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