Modified Shack-Hartmann wavefront sensor using an array of superresolution pupil filters

COACH-based Shack-Hartmann wavefront sensor with an array of phase coded masks

Shack-Hartmann wavefront sensors (SHWS) are generally used to measure the wavefront shape of light beams. Measurement accuracy and the sensitivity of these sensors are important factors for better wavefront sensing. In this paper, we demonstrate a new type of SHWS with better measurement accuracy than the regular SHWS. The lenslet array in the regular SHWS is replaced with an array of coded phase masks, and the principle of coded aperture correlation holography (COACH) is used for wavefront reconstruction. Sharper correlation peaks achieved by COACH improve the accuracy of the estimated local slopes of the measured wavefront and consequently improve the reconstruction accuracy of the overall wavefront. Experimental results confirm that the proposed method provides a lower mean square wavefront error by one order of magnitude in comparison to the regular SHWS.

Measuring two-dimensional profiles of beam spots in a high-density spot array for a maskless lithography system

We measure two-dimensional (2D) profiles of beam spots in a high-density spot array for a maskless lithography system. Since the size of each spot is comparable to that of a pixel in a charge-coupled device (CCD), we detect image frame data, which are the distribution of the intensity of the spot overlapped on the active area of the pixel in the CCD, by scanning with a nano-stage. Using the image frame data of the scanning CCD we determine reconstructed images of the beam spot array. We calculate the 2D profile of each spot by taking the deconvolution of the reconstructed image of the spot with the active area of the CCD pixel. We theoretically analyze the uncertainty in the measurement of profiles in terms of spot size for the variation of the scanning step of the nano-stage and determine the step size to achieve uncertainty of less than 100 nm. We experimentally demonstrate the measurement of profiles of an 11×11 spot array for the proof of concept. Also, we analyze various parameters of the spot array, such as ellipticity, rotation of the spot profile, spot size, intensity distribution, and position.

Extension of the modal wave-front reconstruction algorithm to non-uniform illumination

Attempts are made to eliminate the effects of non-uniform illumination on the precision of wave-front measurement. To achieve this, the relationship between the wave-front slope at a single sub-aperture and the distributions of the phase and light intensity of the wave-front were first analyzed to obtain the relevant theoretical formulae. Then, based on the principle of modal wave-front reconstruction, the influence of the light intensity distribution on the wave-front slope is introduced into the calculation of the reconstruction matrix. Experiments were conducted to prove that the corrected modal wave-front reconstruction algorithm improved the accuracy of wave-front reconstruction. Moreover, the correction is conducive to high-precision wave-front measurement using a Hartmann wave-front sensor in the presence of non-uniform illumination.

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

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.

Reconfigurable wavefront sensor for ultrashort pulses

A highly flexible Shack-Hartmann wavefront sensor for ultrashort pulse diagnostics is presented. The temporal system performance is studied in detail. Reflective operation is enabled by programming tilt-tolerant microaxicons into a liquid-crystal-on-silicon spatial light modulator. Nearly undistorted pulse transfer is obtained by generating nondiffracting needle beams as subbeams. Reproducible wavefront analysis and spatially resolved second-order autocorrelation are demonstrated at incident angles up to 50° and pulse durations down to 6 fs.

Optimization of scanning strategy of digital Shack-Hartmann wavefront sensing

In the traditional Shack-Hartmann wavefront sensing (SHWS) system, a lenslet array with a bigger configuration is desired to achieve a higher lateral resolution. However, practical implementation limits the configuration and this parameter is contradicted with the measurement range. We have proposed a digital scanning technique by making use of the high flexibility of a spatial light modulator to sample the reflected wavefront [X. Li, L. P. Zhao, Z. P. Fang, and C. S. Tan, "Improve lateral resolution in wavefront sensing with digital scanning technique," in Asia-Pacific Conference of Transducers and Micro-Nano Technology (2006)]. The lenslet array pattern is programmed to laterally scan the whole aperture. In this paper, the methodology to optimize the scanning step for the purpose of form measurement is proposed. The correctness and effectiveness are demonstrated in numerical simulation and experimental investigation.

Interferometric Shack-Hartmann wavefront sensor with an array of four-hole apertures

A modified Hartmann test based on the interference produced by a four-hole mask can be used to measure an unknown wavefront. To scan the wavefront, the interference pattern is measured for different positions of the mask. The position of the central fringe of the diamond-shaped interference pattern gives a measure of the local wavefront slopes. Using a set of four-hole apertures located behind an array of lenslets in such a way that each four-hole window is inside one lenslet area, a set of four-hole interference patterns can be obtained in the back focal plane of the lenslets without having to scan the wavefront. The central fringe area of each interference pattern is narrower than the area of the central maximum of the diffraction pattern of the lenslet, increasing the accuracy in the estimate of the lobe position as compared with the Shack-Hartmann wavefront sensor.