Vibrating membrane mirror concept for adaptive optics

Hadipour, Mousa; Tahtalı, Murat; Lambert, Andrew

doi:10.1117/12.2231835

Cited by 5 publications

(1 citation statement)

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“…where J m (r) are the Bessel functions of the first kind, and k m,n some constants depending on the boundary conditions. It's interesting to note that this set of functions, referred as the Bessel circular functions or the membrane vibration modes, has already popped up recently in the literature 8,17 as being more suitable than Zernike polynomials for some applications, but, to our knowledge, was not yet considered as optimal for wavefront sensor-less methods.…”

Section: Derivation Of An Aliasing-free Basis For Any Aperturementioning

confidence: 99%

Alias-Free Basis for Modal Sensorless Adaptive Optics Using the Second Moment of Intensity

Soloviev

2017

Preprint

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In theory of optical aberrations, an aberrated wavefront is represented by its coefficients in some orthogonal basis, for instance by Zernike polynomials. However, many wavefront measurement techniques implicitly approximate the gradient of the wavefront by the gradients of the basis functions. For a finite number of approximation terms, the transition from a basis to its gradient might introduce an aliasing error. To simplify the measurements, another set of functions, an "optimal basis" with orthogonal gradients, is often introduced, for instance Lukosz-Braat polynomials. The article first shows that such bases do not necessarily eliminate the aliasing error and secondly considers the problem of finding an alias-free basis on example of second-moment based indirect wavefront sensing methods. It demonstrates that for these methods any aliasfree basis should be formed by functions simultaneously orthogonal in two dot-products and be composed of the eigenfunctions of the Laplace operator. The fitness of such alias-free basis for optical applications is analysed by means of numerical simulations on typical aberrations occurring in microscopy and astronomy.

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Section: Derivation Of An Aliasing-free Basis For Any Aperturementioning

confidence: 99%