• # [Special Report] Wave front Reconstruction Using Small Lenses I

In a previous article, I have briefly mentioned about a wavefront sensor that uses small lenses. In this article, we are going to take a closer look at howwavefront can be reconstructed using collected data. I think it would help to first review the definition ofwavefront.

Light emitted from the point source generally propagates in the form of spherical waves. However, to a distant observer, the profile of the light beam appears closer to a plane wave. Wavefront is defined as a plane made up of points that are in the same phase at a given time. When all points upon wavefronthave a fixed amplitude, wave function will yield a certain value on thewavefront. However, as the amplitude is a distance function,it is not consistent in all spaces.

In order to reconstruct wavefront based on the gradient information obtained from Shack-Hartmann wavefront sensor, a mathematical algorithm is needed to reconstruct the phase of wavefront from the phase difference of eachimage point. Using the center point extraction algorithm of each image pointfn the digital image sent from a CCD camera, horizontal and vertical gradients and phase can be calculated. Based on the traditional theory onwavefrontreconstruction, each case was generalized usingmatrix computation. And I would like to discuss the interpretation errors of wavefront reconstruction andcorrection.

Figure 1.Wavefront reconstruction model based on phase point and gradientlocation.

In order to analyze the aberrationand distorted information of wavefront, the phase ofwavefront needs to be found. In general, wavefrontreconstructioncan be divided into zonal sensing that divides the wavefront into areas (zones) and modal sensing that analyzes the coefficients of modes of the polynomial function. Here, we have analyzed the reconstruction matrix using the zonal sensing method ofHudgin, Fried, Southwell and their proposed relational expression of phase point and gradient location. As for modal sensing, we performed wavefront reconstruction by computing the coefficient of each mode of Zernike polynomial equation.

WavefrontReconstructionUsing Zonal Sensing

In order to calculate the phase of wavefrontgradient information, we obtained a precise solution of wavefront distortion by generalizing the zonal sensing model using least square estimation bymatrix computation. <Figure 1> a), b) and c) show simplifiedHudgin, Fried, Southwellmodel for precise definition of the phase point and gradient location required for wavefrontreconstruction. Each number in the <Figure 1>indicate the order of calculation used in wavefrontreconstruction.

As the array lens of Shack-Hartmann wavefront sensor of adaptive optics are 12×12, the wavefront was reconstructed based on the gradient location andimage point of each model when N=12 to discuss the error in phaseandwavefront. <Figure 2> shows computer simulation of wavefrontreconstruction of each model’s wavefront with gradient aberration.

Figure 2.wavefront reconstruction of gradient aberration through zonal sensing.a) Hudgin b) Fried c) Southwell d) Wavefront reconstruction usingzonal sensing.

-To be continued-