Zonal Wavefront Research Articles

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.

Improved method for rapid shape recovery of large specular surfaces based on phase measuring deflectometry.

Incorporating the modal and zonal estimation approaches into a unifying scheme, we introduce an improved three-dimensional shape reconstruction version of specular surfaces based on phase measuring deflectometry in this paper. The modal estimation is first implemented to derive the coarse height information of the measured surface as initial iteration values. Then the real shape can be recovered utilizing a modified zonal wavefront reconstruction algorithm to simultaneously achieve consistently high accuracy and dramatically rapid convergence. Moreover, the iterative process based on an advanced successive over-relaxation technique shows a consistent rejection of measurement errors, guaranteeing the stability and robustness in practical applications. The reconstruction results of numerical examples of the sphere, hyperbolic, and arbitrary surfaces, as well as an experimentally measured sphere mirror demonstrate the validity and efficiency of the proposed improved method. In the simulations, the proposed method increases the rate of convergence by fourfold compared with the existing zonal approach and realizes three orders of magnitude improvement in reconstruction accuracy compared with the modal technique when handling the sample points of 401×401 pixels of a sphere surface. Furthermore, the computation time decreases approximately 74.92% in contrast to the zonal estimation, and the surface error is about 6.68μm with reconstruction points of 391×529 pixels of an experimentally measured sphere mirror. In general, this new method can be conducted with fast convergence speed and high accuracy, providing an efficient, stable, and real-time approach for shape reconstruction in practical situations.

Exact two-dimensional zonal wavefront reconstruction with high spatial resolution in lateral shearing interferometry

A novel zonal method is proposed for exact discrete reconstruction of a two-dimensional wavefront with high spatial resolution for lateral shearing interferometry. Four difference wavefronts measured in the x and y shear directions are required. Each of the two shear directions is measured twice with different shear amounts. The shear amounts of the second measurements of the x and y directions are Sx+1 pixels and Sy+1 pixels, where Sx pixels and Sy pixels are the shear amounts of the first measurements in the x and y directions, respectively. The shear amount in each direction can be chosen freely, provided that it is below a maximum value determined by the pupil shape and the number of samples N in that direction; thus, the choices are not limited by the more stringent condition required by previous methods, namely, that the shear amounts must be divisors of N. This method can exactly reconstruct any wavefront at evaluation points up to an arbitrary constant if the data is noiseless, and high spatial resolution can be achieved even with large shear amounts. The method is applicable not only to square pupils, but also to general pupil shapes if a sufficient number of Gerchberg iterations are employed. In this study, the validity and capability of the method were confirmed by numerical experiments. In addition, the experiments demonstrated that the method is stable with respect to noise in the difference wavefronts.

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.

Wide dynamic range wavefront sensor using sub-wavelength grating array

We propose a new zonal wavefront sensor with a very wide dynamic range. The proposed sensor uses a sub-wavelength grating array to subdivide the input wavefront and produce transmitted light spots on CCD. The wavefront tilts are calculated from the transmissions of a sub-wavelength grating array. The dynamic range and resolution of the proposed sensor are respectively decided by the grating parameters and the sub-unit size of the array. So these two performances of the sensor are independent of one another, which enables the realization of wide dynamic range and high resolution simultaneously. We introduce the principle of the sensor by both Rigorous Coupled Wave Analysis and Finite-Difference Time-Domain methods. A simulation is designed to validate our proposed method, and the measurement errors are analyzed. The sensor performs good sensitivity for wide incident angles, which is particularly suitable for spherical input wavefront.

Non-common path aberration correction in an adaptive optics scanning ophthalmoscope.

The correction of non-common path aberrations (NCPAs) between the imaging and wavefront sensing channel in a confocal scanning adaptive optics ophthalmoscope is demonstrated. NCPA correction is achieved by maximizing an image sharpness metric while the confocal detection aperture is temporarily removed, effectively minimizing the monochromatic aberrations in the illumination path of the imaging channel. Comparison of NCPA estimated using zonal and modal orthogonal wavefront corrector bases provided wavefronts that differ by ~λ/20 in root-mean-squared (~λ/30 standard deviation). Sequential insertion of a cylindrical lens in the illumination and light collection paths of the imaging channel was used to compare image resolution after changing the wavefront correction to maximize image sharpness and intensity metrics. Finally, the NCPA correction was incorporated into the closed-loop adaptive optics control by biasing the wavefront sensor signals without reducing its bandwidth.

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.

Direct phase measurement in zonal wavefront reconstruction using multidither coherent optical adaptive technique

In traditional zonal wavefront sensing for adaptive optics, after local wavefront gradients are obtained, the entire wavefront can be calculated by assuming that the wavefront is a continuous surface. Such an approach will lead to sub-optimal performance in reconstructing wavefronts which are either discontinuous or undersampled by the zonal wavefront sensor. Here, we report a new method to reconstruct the wavefront by directly measuring local wavefront phases in parallel using multidither coherent optical adaptive technique. This method determines the relative phases of each pupil segment independently, and thus produces an accurate wavefront for even discontinuous wavefronts. We implemented this method in an adaptive optical two-photon fluorescence microscopy and demonstrated its superior performance in correcting large or discontinuous aberrations.

High spatial resolution zonal wavefront reconstruction with improved initial value determination scheme for lateral shearing interferometry

In a recent paper [J. Opt. Soc. Am. A 29, 2038 (2012)], we proposed a generalized high spatial resolution zonal wavefront reconstruction method for lateral shearing interferometry. The test wavefront can be reconstructed with high spatial resolution by using linear interpolation on a subgrid for initial values estimation. In the current paper, we utilize the difference between the Zernike polynomial fitting method and linear interpolation in determining the subgrid initial values. The validity of the proposed method is investigated through comparison with the previous high spatial resolution zonal method. Simulation results show that the proposed method is more accurate and more stable to shear ratios compared with the previous method. A comprehensive comparison of the properties of the proposed method, the previous high spatial resolution zonal method, and the modal method is performed.

Wavefront reconstruction in adaptive optics systems using nonlinear multivariate splines

This paper presents a new method for zonal wavefront reconstruction (WFR) with application to adaptive optics systems. This new method, indicated as Spline based ABerration REconstruction (SABRE), uses bivariate simplex B-spline basis functions to reconstruct the wavefront using local wavefront slope measurements. The SABRE enables WFR on nonrectangular and partly obscured sensor grids and is not subject to the waffle mode. The performance of SABRE is compared to that of the finite difference (FD) method in numerical experiments using data from a simulated Shack-Hartmann lenslet array. The results show that SABRE offers superior reconstruction accuracy and noise rejection capabilities compared to the FD method.

3D shape reconstruction of large specular surface

A novel three-dimensional (3D) reconstruction method based on fringe reflection technique for shape measurement of large specular surfaces is presented in this paper, which effectively integrates path integration technique with zonal wavefront reconstruction algorithm. The height information of specular surface obtained from cross-path integration can then be used as the initial value in a zonal wavefront reconstruction algorithm. This method not only has the advantages of global integration, but also enables user-friendly, high-speed operation. A specific iterative algorithm is adopted to improve the antinoise capability of the measuring system, which accelerates the rate of convergence significantly and even improves the accuracy of the reconstructed 3D surface. Moreover, the proper use of boundary contour extraction of the acquired images reduces the computational load of 3D reconstruction dramatically and hence achieves high reconstruction accuracy and enhances the surface integrity at the boundary. An ultraprecision, diamond-turned planar mirror with diameter of 150 mm has been employed to implement the system calibration. The reconstruction results of simulated and actual hyperbolic surfaces and the gauge blocks identify the validity of this new method. It is demonstrated that the measurement error is about 50 μm with reconstruction points of 150×560 pixels of gauge blocks.

Generalized zonal wavefront reconstruction for high spatial resolution in lateral shearing interferometry

A new zonal wavefront reconstruction method for lateral shearing interferometry was presented. The proposed algorithm allows shear amounts equal to arbitrary integral multiple of the sample intervals. High spatial resolution reconstruction is achieved with only two difference wavefronts measured in orthogonal shear directions. The presented algorithm was generalized to be applicable for general aperture shape by using zero padding and Gerchberg-type iterative methods. The capability of the presented algorithm was demonstrated by some numerical examples. Also, the reconstruction error was analyzed theoretically and numerically.

Zonal wavefront sensor with reduced number of rows in the detector array

In this paper, we describe a zonal wavefront sensor in which the photodetector array can have a smaller number of rows. The test wavefront is incident on a two-dimensional array of diffraction gratings followed by a single focusing lens. The periodicity and the orientation of the grating rulings of each grating can be chosen such that the +1 order beam from the gratings forms an array of focal spots in the detector plane. We show that by using a square array of zones, it is possible to generate an array of +1 order focal spots having a smaller number of rows, thus reducing the height of the required detector array. The phase profile of the test wavefront can be estimated by measuring the displacements of the +1 order focal spots for the test wavefront relative to the +1 order focal spots for a plane reference wavefront. The narrower width of the photodetector array can offer several advantages, such as a faster frame rate of the wavefront sensor, a reduced amount of cross talk between the nearby detector zones, and a decrease in the maximum thermal noise. We also present experimental results of a proof-of-concept experimental arrangement using the proposed wavefront sensing scheme.

Long-distance propagation of ionospheric disturbance generated by the 2011 off the Pacific coast of Tohoku Earthquake

Propagation of the initial ionospheric total electron content (TEC) disturbances generated by the 2011 off the Pacific coast of Tohoku Earthquake at 05:46:23 UT on March 11, 2011, was investigated with ground-based Global Positioning System (GPS) receivers in the east-Asian region. It was found that the initial ionospheric disturbance formed a zonal wave front after the earthquake occurrence. Four zonal wave fronts of this initial ionospheric disturbance were observed to travel southward from Japan to Taiwan with a velocity of about 1,000– 1,700 m/s. This study further found that the direction of the wave vector rotated from the south-southwest to the south-southeast as it traveled from Japan to Taiwan. The meridional propagation of the coseismic ionospheric disturbances is consistent with those observed after previous intense earthquakes. The temporal evolutions of initial ionospheric disturbances, after the earthquake, near the epicenter was observed in two-dimensions. The directivity of the disturbances was caused by a geomagnetic field effect.

Phasor averaging for wavefront correction with liquid crystal spatial light modulators

We describe strategies for zonal wavefront correction and generation using liquid crystal spatial light modulators (LC-SLM) with 2π radians phase dynamic range and limited spatial resolution. Computer simulations using realistic wavefront aberrations and the specification of a commercially available LC-SLM device are shown. In spite of the general modest improvement in the correction of large aberrations, the best performance after compensation is attained with a phasor averaging strategy for driving the LC-SLM. Experimental results for wavefront generation are shown as well.

Systems of equations fo zonal wavefront recovery in adaptive optics

The basic results obtained in the present work may be stated as follows: 1) a method of obtaining the analytical solution of the systems of difference equations arising in problems of zonal wavefront recovery is described; the expressions obtained may be used for a noniterative algorithm of solution of the given systems; 2) the possibility of choosing an optimal recovery algorithm in accordance with the system characteristics of the adaptive instrument and the phase fluctuations of the detectable field is shown; 3) analytical expressions are obtained for the recovery error due to measurement noise, depending on the dimension of the mass of recovered phase values; the agreement between Eqs. (24), (26), and (28) and the results of numerical solution of the given systems in [10, 11] is complete.