Biswajit Pathak

Improved wavefront reconstruction algorithm for Shack–Hartmann type wavefront sensors

In the present work, we propose an improved wavefront reconstruction algorithm for zonal wavefront estimation using Shack–Hartmann type wavefront sensors. We start with the well known W H Southwell reconstruction algorithm, where phase at a central point is described in terms of horizontal and vertical slope values. We develop the mathematical expressions to show that by incorporating the diagonal slope values in addition to the horizontal and vertical slope values, accuracy in phase estimation can be increased. We present here experimental results that demonstrate significant improvement in the wavefronts, estimated using the proposed algorithm, in comparison to the Southwell algorithm.

Analysis of error propagation in an improved zonal phase-gradient model

Wavefront sensing and reconstruction finds numerous applications in the field of optical technology. Zonal estimation from the wavefront difference or slope data is an important wavefront reconstruction approach. In this reconstruction method, the wavefront is estimated at specific grid points directly from the wavefront differences by using the least-square method. One of the important sources of error in wavefront estimation process is the detector or CCD centroiding error which may propagate in a basic wavefront estimation process, thereby degrading the performance of the wavefront sensor. Hence, quantification of this error is important as this may be considered as one of the selection parameter of a particular estimation geometry. In the present work, we compute the wavefront difference based (WFDB) error propagation coefficient due to this centroiding error for an improved zonal phase-gradient model which is formally applicable for a Shack-Hartmann (S-H) type sensor and show that the improved model offers a substantial reduction of error propagation. The theoretical error propagation coefficient is shown to have a strong correlation with the experimentally obtained RMS errors for the same model.

High-speed zonal wavefront sensing

High speed wavefront sensing is important in real time profile analysis, analysis of fluid dynamics, ophthalmology and so on. Conventional Shack-Hartmann wavefront sensor uses an array of tiny lenses and a digital camera to record the focal spot array. Thus the frame rate of the sensor depends on the camera. In this paper we present a zonal wavefront sensor where the array of lenses is replaced by an array of gratings followed by a focusing lens. The gratings can be configured to generate just one array of focal spots. This reduction in row of the focal spot array leads to increase in the frame rate of the proposed wavefront sensor.

Improvement in error propagation in the Shack–Hartmann-type zonal wavefront sensors

Estimation of the wavefront from measured slope values is an essential step in a Shack-Hartmann-type wavefront sensor. Using an appropriate estimation algorithm, these measured slopes are converted into wavefront phase values. Hence, accuracy in wavefront estimation lies in proper interpretation of these measured slope values using the chosen estimation algorithm. There are two important sources of errors associated with the wavefront estimation process, namely, the slope measurement error and the algorithm discretization error. The former type is due to the noise in the slope measurements or to the detector centroiding error, and the latter is a consequence of solving equations of a basic estimation algorithm adopted onto a discrete geometry. These errors deserve particular attention, because they decide the preference of a specific estimation algorithm for wavefront estimation. In this paper, we investigate these two important sources of errors associated with the wavefront estimation algorithms of Shack-Hartmann-type wavefront sensors. We consider the widely used Southwell algorithm and the recently proposed Pathak-Boruah algorithm [J. Opt.16, 055403 (2014)JOOPDB0150-536X10.1088/2040-8978/16/5/055403] and perform a comparative study between the two. We find that the latter algorithm is inherently superior to the Southwell algorithm in terms of the error propagation performance. We also conduct experiments that further establish the correctness of the comparative study between the said two estimation algorithms.

Investigation of algorithm discretization error in a zonal wavefront estimation process

Wavefront estimation from measured slope value is an integral part in Shack Hartmann type zonal wavefront sensors that are widely used to analyze the optical aberrations in numerous application areas. Using a specific estimation algorithm, these measured slopes are converted into wavefront phase values. Hence, accuracy in wavefront estimation lies in proper interpretation of these measured slope values using an appropriate estimation algorithm. One of the important sources of error in a basic wavefront estimation process is the algorithm discretization error that primarily depends on the estimation scheme adopted. Basically, this type of error is a result of the finite sampling of the slope geometry. Algorithm discretization error plays an important role and is needed to be considered while choosing a particular estimation geometry as it determines how well the estimation process reconstructs a phase profile. In this paper, we investigate the algorithm discretization error in a recently proposed improved zonal phase-gradient algorithm18 which is a modified form of the popular Southwell geometry. The error is calculated theoretically to ascertain the causes of error and also find ways to reduce it. Both the estimation algorithms are modeled using Taylor series expansion to show the order of discretization error and eventually make a comparison of the improved geometry with the standard Southwell geometry.

Binary hologram based high speed zonal wavefront sensing with reduced estimation time

Reduced wavefront estimation time in a Shack-Hartmann type wavefront sensor plays an important role in any high speed application of the sensor. Exploiting computer generated holography technique, one can generate an array of binary diffraction grating pattern to produce an array of focal spots, similar to that in a Shack Hartmann wavefront sensor (SHWS). The transmittance functions of each of such a grating pattern can be configured to produce a one dimensional (1D) array of focal spots of a desired order. In this paper, we show that the formation of 1D array, further facilitates in the process of single indexed wavefront estimation in its true sense that considerably reduces the wavefront estimation time.

Zonal wavefront sensing with enhanced spatial resolution

In this Letter, we introduce a scheme to enhance the spatial resolution of a zonal wavefront sensor. The zonal wavefront sensor comprises an array of binary gratings implemented by a ferroelectric spatial light modulator (FLCSLM) followed by a lens, in lieu of the array of lenses in the Shack-Hartmann wavefront sensor. We show that the fast response of the FLCSLM device facilitates quick display of several laterally shifted binary grating patterns, and the programmability of the device enables simultaneous capturing of each focal spot array. This eventually leads to a wavefront estimation with an enhanced spatial resolution without much sacrifice on the sensor frame rate, thus making the scheme suitable for high spatial resolution measurement of transient wavefronts. We present experimental and numerical simulation results to demonstrate the importance of the proposed wavefront sensing scheme.

Zonal wavefront sensing using a grating array printed on a polyester film

In this paper, we describe the development of a zonal wavefront sensor that comprises an array of binary diffraction gratings realized on a transparent sheet (i.e., polyester film) followed by a focusing lens and a camera. The sensor works in a manner similar to that of a Shack-Hartmann wavefront sensor. The fabrication of the array of gratings is immune to certain issues associated with the fabrication of the lenslet array which is commonly used in zonal wavefront sensing. Besides the sensing method offers several important advantages such as flexible dynamic range, easy configurability, and option to enhance the sensing frame rate. Here, we have demonstrated the working of the proposed sensor using a proof-of-principle experimental arrangement.

Reduction in the amount of crosstalk with reduced number of focal spot rows in a grating array based zonal wavefront sensor

The Shack Hartmann wavefront sensor (SHWS), named after Johannes Franz Hartmann and Roland Shack, is one of the most well-known and popularly used optical wavefront sensor that finds numerous applications in various optical technologies. SHWS samples the incident wavefront by means of a lenslet array to produce an array of regular 2D array of focal spots on the detector plane of a digital camera, in the case of an unaberrated plane wavefront. If the incident wavefront is aberrated or deviates from a plane wavefront, the respective focal spots get shifted from its reference positions corresponding to the regular grid. If the incident wavefront aberration increases or has a very large curvature, the focal spot of one lenslet may enter the detector sub-aperture of the nearby lenslet. Thus, the SHWS has a limited dynamic range that is restricted to aberrations which do not allow the sub-images to be displaced out from their own detector sub-array. It makes the SHWS sensitive to cross-talk when higher order aberrations are present thereby unavoidably a ecting the wavefront estimation process. The array of tiny lenses of the SHWS can be replaced by an array of gratings followed by a focusing lens, generating an array of focal spots which is similar to that as in the case of a SHWS. In this paper, the spatial frequency of such a grating array based zonal wavefront sensor is configured to produce lesser number of rows of focal spots. The reduction in the number of focal spot rows reduces the amount of cross talk in the vertical direction. In this paper we present preliminary experimental results to demonstrate the above stated reduction in crosstalk.

Zonal wavefront estimation using an array of hexagonal grating patterns

Accuracy of Shack-Hartmann type wavefront sensors depends on the shape and layout of the lenslet array that samples the incoming wavefront. It has been shown that an array of gratings followed by a focusing lens provide a substitution for the lensslet array. Taking advantage of the computer generated holography technique, any arbitrary diffraction grating aperture shape, size or pattern can be designed with little penalty for complexity. In the present work, such a holographic technique is implemented to design regular hexagonal grating array to have zero dead space between grating patterns, eliminating the possibility of leakage of wavefront during the estimation of the wavefront. Tessellation of regular hexagonal shape, unlike other commonly used shapes, also reduces the estimation error by incorporating more number of neighboring slope values at an equal separation.