Implementing a cross-talk-less novel wavefront reconstruction algorithm to be used with a Shack-Hartmann sensor

Abstract

For wavefront reconstruction, often the combination of a Shack-Hartmann sensor and a reconstruction method utilizing the Cartesian derivatives of Zernike polynomials (the least-squares method) is used, which is known to introduce cross-talk. In Janssen (2014) a new wavefront reconstruction algorithm is introduced to be used with the Shack-Hartmann sensor that does not present cross-talk. To our knowledge, this method has never been demonstrated. In the current research, Janssen's method and the conventional least-squares method are compared on a modified Michelson interferometer setup with a spatial light modulator to first remove the aberrations of the complete system, and subsequently introduce specific aberrations for which the Zernike coefficients are reconstructed using both reconstruction methods. It is found that both methods work equally well with optimal fitting powers. When fitting fewer than the optimal amount of fitting powers, it was found that Janssen's method accurately recovered Zernike coeficient amn when n + 1 powers are fit, while the conventional method achieves the same accuracy only at n + 2 fitting powers, especially when aberrations introducing cross-talk are present. When more than the optimal amount Zernike powers are used, it is seen that Janssen's method presents aliasing at lower fitting powers. At the optimal fitting power, the RMS landscape for both methods is shown to be similar, and therefore they are equally susceptible to errors due to mis- estimation of the center position and radius of the beam on the ShackHartmann
sensor. Lastly, it is shown that theoretically, Janssen's method is at least 3.5 times slower than the conventional least-squares method due to the use of complex valued Zernike polynomials.