Phase retrieval using a modified Shack–Hartmann wavefront sensor with defocus

Abstract

This paper proposes a modified Shack-Hartmann wavefront sensor for phase retrieval. The sensor is revamped by placing a detector at a defocused plane before the focal plane of the lenslet array of the Shack-Hartmann sensor. The algorithm for phase retrieval is an optimization with initial Zernike coefficients calculated by the conventional phase reconstruction of the Shack-Hartmann sensor. Numerical simulations show that the proposed sensor permits sensitive, accurate phase retrieval. Furthermore, experiments tested the feasibility of phase retrieval using the proposed sensor. The surface irregularity for a flat mirror was measured by the proposed method and a Veeco interferometer, respectively. The irregularity for the mirror measured by the proposed method is in very good agreement with that measured using the Veeco interferometer.

Wave-front reconstruction with Hartmann–Shack sensor using a phase-retrieval method

“…A phase-retrieval method is proposed to improve the wavefront estimate for the HSWS [15][16][17]. Wave-front phase is retrieved from the intensity measurement on the detector plane.…”

“…Polo et al presented a phase retrieval algorithm to determine the wave-front aberration using a Hartmann wavefront sensor (HWS) for an extreme ultraviolet lithography (EUVL) projection objective [16]. Li et al used a modified HSWS for phase retrieval with a detector placed at a defocused plane of the microlens array [17]. They all obtained the intensity of the CCD sensor once and chose a minimizing function to retrieve the phase using different convergent algorithms.…”

“…They all obtained the intensity of the CCD sensor once and chose a minimizing function to retrieve the phase using different convergent algorithms. Algorithm-specific parameters were chosen in their algorithms [16,17]. However the accuracy of these convergent algorithms and speed of the convergences are limited mutually by these chosen parameters.…”

Wavefront sensing using a graphical user interface

“…The local tilt of the wavefront across each lens can then be calculated from the position of the focal spot on the sensor. The complete wavefront is then derivated using a reconstruction algorithm based, for instance, on Zernike polynomial decomposition .…”

Phase imaging using shifted wavefront sensor images

“…Hence, many methods have been developed to shape the intensity for phase retrieval, e.g., holography [1][2][3][4][5][6], wavefront sensing with lens arrays [7][8][9][10][11], iterative projections [12,13], transport-of-intensity equation (TIE) methods [14,15], ptychography [16][17][18], and quantitative differential interference contrast (DIC) imaging [19]. Recent lens array imaging papers [9][10][11] adopt iterative algorithms instead of classic centroidbased reconstruction to exploit the additional information contained in the structure of the intensity behind each lenslet. However, they still impose strong restrictions on the field-while centroid-based reconstruction methods assume an extremely smooth phase profile, these iterative methods employ smooth basis functions with large spatial support (i.e., Zernike polynomials and vortex modes).…”