Test Wavefront Research Articles

Wafer focusing measurement of optical lithography system based on Hartmann–Shack wavefront testing

To improve the focusing measurement precision of wafer in optical lithography instrument (OLI), a method based on Hartmann–Shack (HS) testing principle is introduced. Defocus of wafer is immediately detected by measuring the image change between plane and spherical wavefront. As defocus is measured by every sub-lens of microlens array (MLA), serials of defocus position are calculated at single shot of CCD sensor. Choose the average in this measurement the outstanding advantage of this technology is the high accuracy and efficiency. With an experiment to validate the feasibility, the accuracy of focusing measurement is indicated as 20nm.

Analysis and demonstration of multiplexed phase computer-generated hologram for modal wavefront sensing

We propose to implement a modal wavefront sensor (MWS) using a multiplexed phase computer-generated hologram (MPCGH). Based on general orthogonal aberration modes, the theoretical treatments of the MWS employing a MPCGH are presented with scalar diffraction approximations and Fourier analysis. Under the small aberration approximations, we give the analytical formula for characterizing the relationship between the sensor signal and the amplitude of the aberration mode. We design several MPCGHs with an effective method of modified off-axis reference beam holograms superposition, and code some common orthogonal Zernike aberration modes into the MPCGH. The numerical simulation is carried out to investigate the performance of MWS to detect particular aberration mode(s). The results exhibit the expected responses of the corresponding symmetric spot pair, and indicate that the wavefront distorted by a special Zernike aberration mode, after modulated by the MPCGH, can be transformed into beams with an intensity-normalized differential signal, which can reflect the change trend of the aberration coefficients in the test wavefront. The experimental demonstration with designed MPCGHs in conjunction with two phase-only spatial light modulators was carried out to test the performance of the MWS.

哈特曼夏克波前传感器的高精度质心探测方法

In order to improve spots centroid detection accuracy of Hartmann-Shack wavefront sensor (HS-WFS) to achieve high-precision of wavefront test of optical system, a centroid detecting method is proposed. The nonlinear filtering and the windowing spot image in global processing are used, combining with median filtering, cubic spline interpolation and adaptive Otsu thresholding for a single spot in local processing. The regulation of centriod error and calculation time with different interpolation points is discussed. For a spot image with noise, the centroid detection error is only 0.0442 pixel. Compared with the traditional methods of nonlinear filtering, the Otsu thresholding method and the detection windowing, the accuracies are increased by 91.86%, 87.97% and 31.79%. The known wavefront aberration of an optical system is simulation tested. The wavefront testing accuracy is 0.0098 in peak-valley (PV) value, and is 0.0027 in root-mean-square (RMS) value. The results show that this method enhances the accuracy of centroid detection, and is suitable for high-precision optical systems.

高精度瑞奇康芒检测法研究及测试距离精度影响分析

In order to realize high precision Ritchey-Common test for large flat mirrors, the relationship between the system pupil coordinate and test flat mirror surface coordinate is utilized to dispose the test wavefront, and then combine with the least square method to detach the alignment errors which are caused by the adjustments of optical system, after this an exact flat surface can be obtained. It analyzes the effects of the test distance on the relationship between the two coordinates and the value of Ritchey angle, and makes the test program according to analysis. In the test process, two measurements in different angles have been taken and the wavefront is found, after detaching the power errors, the peak-valley (PV) and root mean square (RMS) of the final results are 0.182 and 0.0101, compared with the results of Zygo which are 0.229 and 0.013 for PV and RMS, the test accuracies of PV and RMS can reach /20 and /100, respectively. The experimental results prove that this method is effective to calculate the test flat surface and the theory of accuracy analysis is correct, it also realizes the high accuracy of Ritchey-Common test.

可用于小口径光束波前检测的横向剪切干涉仪

可用于小口径光束波前检测的横向剪切干涉仪

差分五棱镜扫描法在波前检测中的应用

In order to realize the high precise wavefront test of large-aperture collimator and evaluate its wavefront quality,the method of differential pentaprism scanning wavefront detection is proposed in this paper.This method is the optimization of pentaprism scanning detection. Firstly,the information of wavefront curvature is obtained by measuring wavefront slope change to reconstruct the wavefront. The title and defocus error instructed by inaccurate calibration of center of mass are eliminated. Secondly,the differential pentaprism scanning wavefront detection system is established to verify the feasibility of this method. Lastly,the error analysis is given. The error analysis shows that the testing precise of this method is 10. 54 nm. The experimental results show that the repeatability precisions of wave peak and valley value( PV) and root mean square( RMS) are increased by 74. 41% and 125. 81% compared with pentaprism scanning method. This method basically meets the requirements of high accuracy and good stability for collimator wavefront detection,which can be used to evaluate the quality of collimator wavefront.

Practical and accurate method for aspheric misalignment aberrations calibration in non-null interferometric testing

Calibration for misalignment aberrations is one of the challenges in non-null interferometric aspheric testing. The high-order misalignment aberrations are especially difficult to distinguish from the rest of the testing system. The traditional calibration method removing the first four terms from the Zernike coefficients of the test wavefront is obviously inaccurate. Computer-aided alignment is considered to be an effective method; however, it is less practical due to its dependency on mechanical or manual adjustment, as are other common methods. A practical and accurate calibration method based on system modeling is proposed in this paper for misalignment aberrations' removal. In this work, actual misalignments, which are calculated from five selected low-order aberrations of the test wavefront in the experiment, are simulated in the model to predict all misalignment aberrations by ray tracing. These aberrations then are removed by a simple wavefront data subtraction. The method depends on neither a precise adjusting mechanism nor a troublesome manual adjustment. Experimental results showing feasibility and repeatability of the proposed method are presented.

Evaluation of a global algorithm for wavefront reconstruction for Shack–Hartmann wave‐front sensors and thick fundus reflectors

Conventional aberration analysis by a Shack-Hartmann aberrometer is based on the implicit assumption that an injected probe beam reflects from a single fundus layer. In fact, the biological fundus is a thick reflector and therefore conventional analysis may produce errors of unknown magnitude. We developed a novel computational method to investigate this potential failure of conventional analysis. The Shack-Hartmann wavefront sensor was simulated by computer software and used to recover by two methods the known wavefront aberrations expected from a population of normally-aberrated human eyes and bi-layer fundus reflection. The conventional method determines the centroid of each spot in the SH data image, from which wavefront slopes are computed for least-squares fitting with derivatives of Zernike polynomials. The novel 'global' method iteratively adjusted the aberration coefficients derived from conventional centroid analysis until the SH image, when treated as a unitary picture, optimally matched the original data image. Both methods recovered higher order aberrations accurately and precisely, but only the global algorithm correctly recovered the defocus coefficients associated with each layer of fundus reflection. The global algorithm accurately recovered Zernike coefficients for mean defocus and bi-layer separation with maximum error <0.1%. The global algorithm was robust for bi-layer separation up to 2 dioptres for a typical SH wavefront sensor design. For 100 randomly generated test wavefronts with 0.7 D axial separation, the retrieved mean axial separation was 0.70 D with standard deviations (S.D.) of 0.002 D. Sufficient information is contained in SH data images to measure the dioptric thickness of dual-layer fundus reflection. The global algorithm is superior since it successfully recovered the focus value associated with both fundus layers even when their separation was too small to produce clearly separated spots, while the conventional analysis misrepresents the defocus component of the wavefront aberration as the mean defocus for the two reflectors. Our novel global algorithm is a promising method for SH data image analysis in clinical and visual optics research for human and animal eyes.

Synthetic phase-shifting for optical testing: Point-diffraction interferometry without null optics or phase shifters

An innovative iterative search method called the synthetic phase-shifting (SPS) algorithm is proposed. This search algorithm is used for maximum-likelihood (ML) estimation of a wavefront that is described by a finite set of Zernike Fringe polynomials. In this paper, we estimate the coefficient, or parameter, values of the wavefront using a single interferogram obtained from a point-diffraction interferometer (PDI). In order to find the estimates, we first calculate the squared-difference between the measured and simulated interferograms. Under certain assumptions, this squared-difference image can be treated as an interferogram showing the phase difference between the true wavefront deviation and simulated wavefront deviation. The wavefront deviation is the difference between the reference and the test wavefronts. We calculate the phase difference using a traditional phase-shifting technique without physical phase-shifters. We present a detailed forward model for the PDI interferogram, including the effect of the finite size of a detector pixel. The algorithm was validated with computational studies and its performance and constraints are discussed. A prototype PDI was built and the algorithm was also experimentally validated. A large wavefront deviation was successfully estimated without using null optics or physical phase-shifters. The experimental result shows that the proposed algorithm has great potential to provide an accurate tool for non-null testing.

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.

Focal length and radius of curvature measurement using coherent gradient sensing and Fourier fringe analysis

A procedure for the measurement of focal length and radius of curvature of a lens using coherent gradient sensing system and Fourier transform fringe analysis technique has been demonstrated. Light from the laser illuminates the specimen and the wavefront emerging from the specimen is tested using coherent gradient sensing interferometer. The fringe pattern corresponding to the test wavefront is stored, and analyzed using Fourier fringe analysis technique. The slope of the wavefront in the direction of shear has been evaluated. It provides the information regarding exact location of points corresponding to the focus/center of curvature of the lens. High accuracy and precision has been achieved.

Wave-front analysis of personal eye protection

Shack-Hartmann wave-front sensing has been successfully applied to many fields of optical testing including the human eye itself. We propose wave-front measurement for testing protective eye wear for production control and investigation of aberrations. Refractive power data is derived from the wave-front data and compared to a subjective measurement technique based on a focimeter. Additional image quality classification was performed with a multivariate model using objective parameters to resample a subjectively determined visual quality. Wave-front measurement advances optical testing of protective eye wear and may be used for objective quality control.

Phase-shifting Jamin double-shearing interferometer based on polarization beam splitting film

To improve the performance of existing Jamin double-shearing interferometer for wavefront testing, a phase-shifting Jamin double-shearing interferometer based on polarization beam splitting (PBS) film is proposed. It is composed of a polarization Jamin double-shearing interferometer and a polarization phase shifter. The polarization Jamin double-shearing interferometer keeps up the optical configuration of the existing Jamin double-shearing interferometer by coating PBS film on its first Jamin plate. The polarization phase shifter analyzes the interference beams emitted from the rear surface of the second Jamin plate. The interferometer has no additional wavefront distortion and its fringe visibility is improved. In experiments, phase-shifting double-shearing interferograms with straight interference fringes and high fringe visibility are obtained. The availability of the interferometer is verified.

Enhanced deterministic phase retrieval using a partially developed speckle field

A technique for enhanced deterministic phase retrieval using a partially developed speckle field (PDSF) and a spatial light modulator (SLM) is demonstrated experimentally. A smooth test wavefront impinges on a phase diffuser, forming a PDSF that is directed to a 4f setup. Two defocused speckle intensity measurements are recorded at the output plane corresponding to axially-propagated representations of the PDSF in the input plane. The speckle intensity measurements are then used in a conventional transport of intensity equation (TIE) to reconstruct directly the test wavefront. The PDSF in our technique increases the dynamic range of the axial intensity derivative for smooth phase objects, resulting in a more robust solution to the TIE. The SLM setup enables a fast and accurate recording of speckle intensity. Experimental results are in good agreement with those obtained using the iterative phase retrieval and digital holographic methods of wavefront reconstruction.

Absolutely Testing of Off-Axis Aspherical Mirror Using Dichotomy Computer-Generated Holograms

A method for absolutely testing off-axis aspherical mirror is presented. A dichotomy CGH including two zones on one substrate is designed. One sub aperture generates the spherical wave front that is used for calibrating the pattern errors of the hologram; the other sub aperture reconstructs the aspherical wave front to test the off-axis aspherical mirror. By means of known absolute interferometric methods, the aberrations of the calibration wave front can be obtained. These aberrations can be transferred to the null testing wave front. The testing method is explained and the dichotomy CGH is designed. Finally, a simulation result supports this absolutely testing method.

利用Offner光学系统进行图像恢复和光学检测

Based on phase diversity technology,this paper designs an Offner optical system for image restoration and optical test of wavefront errors.The Offner optical system uses an on-axis parabolic mirror as Offner mirror,and a high speed CCD camera and a Shack-Hartmann wavefront sensor as the receivers to eliminate the chromatic aberration brought by the polychrome light source of the refractive system during image restoration.The system has a simple configuration with the wavefront error(RMS) less than λ/50(λ=632.8 nm).By using the system to perform image restoration experiment for a resolution plate and a fiber source,the resolution of restorated image is improved by 19%.In addition,wavefront error test are performed with the Offner optical system using the phase diversity algorithm,and the result demonstrates that the wavefront sensor difference between phase diversity and Shack-Hartmann is 5%,which proves that it is able to perform optical wavefront test with this Offner optical system.

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.

Measurement of surface profile of a long-radius optical surface with wedge phase shifting lateral shear interferometer

A new technique for the measurement of the surface profile of optical surfaces of long radius of curvature is presented. A phase shifting lateral shearing interferometer is used. Laterally sheared wavefronts are generated due to Fresnel reflections of the test wavefront at oblique inci- dence from the (plane parallel and separated) inner surfaces of a pair of glass wedge plates. A pair of matched wedge plates, which together form a parallel plate, whose thickness can be varied by translating one of the wedges, is used to introduce phase shifts between the laterally sheared components.Surfaceslopesandprofilearedeterminedbyapplyingphase shifting interferometry. An optical setup for measurement of surface profile of beam line mirrors of synchrotron radiation sources is proposed. C 2010

Error-free demodulation of pixelated carrier frequency interferograms

Recently, pixelated spatial carrier interferograms have been used in optical metrology and are an industry standard nowadays. The main feature of these interferometers is that each pixel over the video camera may be phase-modulated by any (however fixed) desired angle within [0,2pi] radians. The phase at each pixel is shifted without cross-talking from their immediate neighborhoods. This has opened new possibilities for experimental spatial wavefront modulation not dreamed before, because we are no longer constrained to introduce a spatial-carrier using a tilted plane. Any useful mathematical model to phase-modulate the testing wavefront in a pixel-wise basis can be used. However we are nowadays faced with the problem that these pixelated interferograms have not been correctly demodulated to obtain an error-free (exact) wavefront estimation. The purpose of this paper is to offer the general theory that allows one to demodulate, in an exact way, pixelated spatial-carrier interferograms modulated by any thinkable two-dimensional phase carrier.

Fast and precise registration of quasi-planar free-form wavefronts

Quasi-planar free-form wavefronts are featured with vertical fluctuations of small amplitude and high frequency. They can be considered a plane superposed with waviness at the scale of a wavelength, which is the key to enabling control of the optical performance. This paper presents a method for fast and precise registration of quasi-planar free-form wavefronts to obtain the true difference between the test wavefront and the nominal one. We first adapt the planar subaperture stitching algorithm to the registration of two wavefronts with almost 100% overlap. This will usually fail because the registration result is very sensitive to lateral misalignment. Hence a fast and precise method is proposed to directly register two point sets in three-dimensional (3D) space. It is based on a novel procedure to calculate the closest distances of 3D points to another 3D point set. Then registration of a 320 mmx320 mm wavefront with the method is simulated and compared with the subaperture stitching method. Finally a corrective machining case is given to demonstrate the validity of the method to achieve high precision.