Accuracy Of Wavefront Reconstruction Research Articles

Neural network assisted high flexibility and high resolution Shack-Hartmann wavefront sensing for astronomical observation in darker sky areas

Shack-Hartmann (SH) wavefront sensing is widely applied to astronomical observations with its fast and accurate measurement. However, due to the computational nature of SH that the input beam is segmented to provide local wavefront slopes, the sampling density of the sub-apertures and the calculation accuracy of each sub-focal spot’s centroid have great influence on the wavefront reconstruction accuracy. Therefore, it is usually difficult to achieve high resolution wavefront reconstruction for dark stars in the astronomical observations with insufficient light intensity. We present a neural-network assisted high resolution SH wavefront sensing method to overcome the shortages and obtain results with enhanced resolution from the separated information inside each sub-aperture. With this method, high resolution wavefront sensing in darker sky area could be realized.

Pitch‐Switchable Metalens Array for Wavefront Profiling at Multiwavelength

AbstractThe wavefront sensor is a crucial component in the adaptive optics system (AOS), responsible for detecting aberrated wavefronts. However, The Shack–Hartmann wavefront sensor with single‐pitch microlens array is limited in its adaptability to different observing conditions, affecting wavefront reconstruction accuracy. And conventional microlens arrays are wavelength‐specific. Here, a polarization‐dependent pitch‐switchable metalens array based on non‐interleaved silicon metasurfaces is proposed, capable of working at multiple wavelengths. By controlling the incident and outgoing light polarization, three metalens arrays with customized pitches can be switched at will. Furthermore, achromatic performance is achieved in the 950 nm and 1030 nm wavelengths through structural dispersion engineering. Finally, wavefront detection experiments are finally conducted to demonstrate the phase reconstruction with variable spatial resolution. The metalens array with high flexibility in wavefront sensor can further enhance the adaptability of AOS and has great potential for applications in light‐field imaging, and machine vision, etc.

Method for testing freeform surfaces based on a Shack-Hartmann sensor with plane wavefront scanning and stitching.

Currently, the surface error measurement technology for freeform faces a significant contradiction between measurement accuracy and dynamic range. The study proposes a non-null testing method for measuring freeform surfaces by utilizing a Shack-Hartmann wavefront sensor to emit a small aperture parallel beam and scan along the normal direction at the center of subapertures for stitching (SHPSS). A mathematical model based on ray tracing and the reflection theorem is established to calculate the sampling points on an ideal freeform surface, the reference spot array on CCD, and the corresponding relationship between microlens array and spots. An algorithm is proposed to iteratively calculate the wavefront aberration and gradually approach the actual sampling points using the established model. Theoretical analysis and numerical simulation results indicate that SHPSS can increase the dynamic range and improve the accuracy of wavefront reconstruction. The error analysis of the SHPSS method is carried out, the measurement accuracy of full aperture freeform surface is 11.45 nm. A testing system is set up and experiments are conducted on a 100 mm aperture freeform reflective mirror. The RMS of the SHPSS test results is less than λ/30 (λ=635 nm) compared to the interferometric test results. By analyzing five groups of repeated measurement experiments, the repeatability accuracy of SHPSS method is less than 1/80 λ (RMS). This demonstrates the feasibility and measurement capabilities of the method for freeform surface testing.

Influence of Image Processing Method on Wavefront Reconstruction Accuracy of Large-Aperture Laser

In order to improve the wavefront reconstruction accuracy of a large-aperture laser, this paper proposed an adaptive window preprocessing algorithm based on the threshold center of gravity method (AW-TCoG). The effects of median filtering and mean filtering on spot image processing and wavefront reconstruction accuracy are simulated and analyzed. The results show that the mean filtering method has a better effect on noise elimination and can further improve the accuracy of wavefront reconstruction. In addition, the centroid detection errors of large-aperture laser wavefront reconstruction through the center of gravity (CoG), the threshold center of gravity (T-CoG), and the Windowing method were studied. The analysis shows that, due to the influence of noise, the wavefront reconstruction accuracy is poor when the CoG and Windowing methods are used to calculate centroid parameters, while the wavefront reconstruction accuracy of the threshold centroid method is better and can reach 0.2λ. When using the AW-TCoG proposed in this paper, the wavefront reconstruction accuracy can be maintained within 0.1λ for different incident wavefront RMS values and spot images with different signal-to-noise ratio (SNR) levels. Compared with the traditional threshold centroid method, the wavefront reconstruction accuracy of this method is significantly improved.

Optimization of wavefront reconstruction accuracy for conjugate shift differential absolute testing

The conjugate shift differential method, based on Fourier transforms, is critical for surface error testing of high-precision optical elements. However, this common approach is also prone to periodic spectrum loss. As such, this paper proposes conjugate double shift differential (CDSD) absolute testing, which can effectively compensate for spectrum loss and achieve accurate wavefront reconstructions. Spectrum loss in the single shift differential method is analyzed through a study of the Fourier reconstruction process. A calculation model for the proposed CDSD method is then established and constraint conditions for shift quantities are provided by analyzing double shear effects observed in transverse shear interference. Finally, the reconstruction accuracies of various spectrum compensation methods are compared. Results showed that spectrum loss became more evident with increasing shift amounts. However, the CDSD method produced the smallest measurement error compared with conventional direct zero filling and adjacent point averaging, suggesting our approach could effectively improve absolute shape measurement accuracy for planar optical elements.

Space-variant Shack-Hartmann wavefront sensing based on affine transformation estimation.

The space-variant wavefront reconstruction problem inherently exists in deep tissue imaging. In this paper, we propose a framework of Shack-Hartmann wavefront space-variant sensing with extended source illumination. The space-variant wavefront is modeled as a four-dimensional function where two dimensions are in the spatial domain and two are in the Fourier domain with priors that both gently vary. Here, the affine transformation is used to characterize the wavefront space-variant function. Correspondingly, the zonal and modal methods are both escalated to adapt to four-dimensional representation and reconstruction. Experiments and simulations show double to quadruple improvements in space-variant wavefront reconstruction accuracy compared to the conventional space-invariant correlation method.

Reliable wavefront reconstruction from a single lateral shearing interferogram using Bayesian convolutional neural network

The reconstruction of the original wavefront from its sheared information is an ill-posed inverse problem in the sense of Hadamard. In this paper, we present a new technique for reconstructing the wavefront from a single lateral shearing interferogram using a Bayesian convolutional neural network. With the synthesized data, the trained network can robustly invert the physical model, recover the spectral leakage problem caused by the shear operation, and reconstruct the desired phase distribution. In addition, a quantitative pixel-level uncertainty measure of the reconstruction results is provided simultaneously, which can be used as an indicator to judge the validity of reconstruction accuracy in the absence of ground truth. Numerical experiments are carried out to investigate the robustness and accuracy of the method, in which the effects of different noise levels and shear distances on reconstruction accuracy are evaluated. We further show that the uncertainty maps are highly indicative of the true error and properly calibrated. Finally, optical tests on reconstructing the topology of object deformation have confirmed that our method can considerably increase the accuracy of wavefront reconstruction as compared with the two baseline methods.

Study of a Shack-Hartmann wavefront sensor with adjustable spatial sampling based on spherical reference wave

For the astronomical adaptive optics systems, the observation condition is constantly changing or in a regime of low photon flux. Besides, for various brightness seeing conditions, the Shack-Hartmann wavefront sensor has a matching spatial sampling that avoids extra wavefront reconstruction error. To integrate advantageous spatial samplings, we propose a novel Shack-Hartmann wavefront sensor with adjustable spatial sampling (ASS-WFS) based on spherical reference wave. In principle, only a simple movement of the microlens array (MLA) and the CCD detector in the direction of the optical axis is required to achieve variable spatial sampling. This is also obviously advantageous in the adaptive optics performance as it allows the wavefront sensor to dynamically match brightness of the observation. To demonstrate the performance of the ASS-WFS, we present the sensor in terms of the principles, the simulation, and the experiment. Results show that the ASS-WFS is able to precisely measure and reconstruct the wavefront, and also demonstrate that advantages resulting from adjusting the spatial samplings can efficiently reduce the disadvantages of low signal-to-noise ratio to boost wavefront reconstruction accuracy.

Multi-surface Phase-shifting Interferometry Using Harmonic Frequency Solution Based on the Total Least Squares

Wavelength-tuning phase-shifting interferometry plays a significant role in the measurements of transparent parallel plates. The difficulty of multi-surface measurements is that the harmonics with different frequencies and phases make the captured interference signal mixed. In multi-surface measurements, the demodulation of phases builds on the determination of the frequency of each signal, which is traditionally estimated from the prior information including the cavity length and the optical thickness of the measured plate. However, the estimation accuracy of this method is not satisfactory. In order to accurately obtain the signal frequencies and demodulate the initial phases of the measured surfaces simultaneously, this paper proposes a total least squares wavelength-tuning phase-shifting algorithm (TLSWPA). The developed TLSWPA includes two steps: Firstly, considering the influence of the Gaussian noise on the captured interferograms, the signal frequencies are obtained based on the total least squares principle with high accuracy; Secondly, introducing the Householder transformation, the least squares error based on the 2-Norm is used to demodulate the initial phase distribution for each signal. Comparison of the obtained results of the frequency solution and the accuracy of wavefront reconstruction shows that the developed TLSWPA allows obtaining results with an accuracy 2 orders of magnitude higher than the algorithm based on the fast Fourier transform and 1 order of magnitude higher than the advanced iterative algorithm. Experimental study on a borosilicate crown glass using a Fizeau wavelength-tuning interferometer further verifies its effectiveness.

Cross-iteration multi-step optimization strategy for three-dimensional intensity position correction in phase diverse phase retrieval.

Parameters mismatching between the real optical system and phase retrieval model undermines wavefront reconstruction accuracy. The three-dimensional intensity position is corrected in phase retrieval, which is traditionally separated from lateral position correction and axial position correction. In this paper, we propose a three-dimensional intensity position correction method for phase diverse phase retrieval with the cross-iteration nonlinear optimization strategy. The intensity position is optimized via the coarse optimization method at first, then the intensity position is cross-optimized in the iterative wavefront reconstruction process with the exact optimization method. The analytic gradients about the three-dimensional intensity position are derived. The cross-iteration optimization strategy avoids the interference between the incomplete position correction and wavefront reconstruction during the iterative process. The accuracy and robustness of the proposed method are verified both numerically and experimentally. The proposed method achieves robust and accurate intensity position correction and wavefront reconstruction, which is available for wavefront measurement and phase imaging.

Experimental investigation of aero-optics induced by supersonic film based on near-field background-oriented schlieren.

The effective acquisition of a distorted wavefront is the foundation of studying how to suppress and correct aero-optical effects. The background-oriented schlieren (BOS) technique, as a commonly quantitative measurement method of flow field, has great application potential in aero-optical effect measurement. With consideration of the thickness change of the refractive index field, introduction of near-field correction and construction of the double telecentric configuration, wavefront measurement accuracy was improved. A standard plano-convex lens was utilized to quantitatively evaluate the improved results, and the effectiveness of the improvement was verified. Determination methods of spatial resolution, sensitivity, and dynamic measurement range of wavefront measurement based on BOS were studied. The influences of cross-correlation interrogation window size and step length on the wavefront reconstruction accuracy were investigated. The step length should be less than the size of the interrogation window to make the reconstructed results have a satisfactory accuracy. Wavefront results of supersonic film at different positions and cases were obtained. The fitting results show that there is a good linear relationship between the root mean square of the optical path difference (OPDrms) and ρ1/ρ∞ at different locations. Under different experimental cases, the aero-optical distortion tends to become stronger first and then weaker along the flow direction, and the aero-optical distortion around Position 3 is relatively strong. The large aperture approximation can be used to predict Strehl ratio values effectively in a considerable range by OPDrms.

Accurate reconstruction in digital holographic microscopy using antialiasing shift-invariant contourlet transform

The measurement of microstructured components is a challenging task in optical engineering. Digital holographic microscopy has attracted intensive attention due to its remarkable capability of measuring complex surfaces. However, speckles arise in the recorded interferometric holograms, and they will degrade the reconstructed wavefronts. Existing speckle removal methods suffer from the problems of frequency aliasing and phase distortions. A reconstruction method based on the antialiasing shift-invariant contourlet transform (ASCT) is developed. Salient edges and corners have sparse representations in the transform domain of ASCT, and speckles can be recognized and removed effectively. As subsampling in the scale and directional filtering schemes is avoided, the problems of frequency aliasing and phase distortions occurring in the conventional multiscale transforms can be effectively overcome, thereby improving the accuracy of wavefront reconstruction. As a result, the proposed method is promising for the digital holographic measurement of complex structures.

Hartmann-Shack wavefront sensing method and experiment of dual-wedge micro-scanning

For large aperture complex optical wavefront sensing, the lenticule array of Hartmann-Shack wavefront sensor limits the sampling of the wavefront. Thus the accuracy of wavefront reconstruction is affected. In order to improve the sampling rate of wavefront, the detection method of micro-scanning technology which added in Hartmann-Shack wavefront sensing method is proposed. Based on the results of simulation analysis, the dual-wedge micro-scanning Hartmann sensor is designed. The experiment which 2×2 mode dual-wedge micro-scanning Hartmann-Shack sensor detects the wavefront of telescope optical system is set up. The experimental results are compared with the ZYGO interferometer. The results of dual-wedge micro-scanning Hartmann-Shack sensor are better than that of the traditional sensor. Conclusions show that the micro-scanning technology has a certain effect on the improvement of the wavefront reconstruction accuracy of Hartmann-Shack sensor.

Research on encoding multi-gray-scale phase hologram and wavefront reconstruction.

Application of computer-generated holography for wavefront generation is beneficial for optical interferometry and 3D image display. However, there is a noticeable encoding error in computer-generated holograms, which is encoded by using the object's wavefront function in a computer. The encoding error will be transmitted and amplified during fabrication of a hologram, which can cause a reconstructed error in the generated wavefront. A correction method of encoding errors based on the least-squares fitting is proposed. A validating experiment is completed by using a liquid crystal spatial light modulator to reconstruct a group of paraboloid wavefronts. The results show that encoding errors increase the reconstructed error of a wavefront less than optical system errors, and the root-mean-square value drops 0.022λ after the correction of the encoding error, but it falls 0.092λ after the correction of optical system errors. The total error has been reduced by 0.114λ. This research is helpful for prediction of encoding errors and improvement of wavefront reconstruction accuracy.

Hartmann–Shack sensor based micro-scanning image detection

A single optical wedge micro-scanning system was designed and added to a Hartmann sensor by analyzing Hartmann–Shack sensor wave-front theory and micro-scanning technology. Micro-scanning overcame the lack of detection accuracy caused by small numbers of pixels in the detector, which gave the Hartmann–Shack sensor high-precision detection with a low number of pixels. Combined with a wave-front reconstructed algorithm and micro-scanning reconstructed high-resolution algorithm, the results were achieved using Lighttools and Zemax software. The wave-front reconstruction accuracy of three CCD detectors which are added to micro-scanning device can raise 72.55%, 32.47%, 0.48%.

Zernike modal wavefront reconstruction algorithm based on model selection

In Zernike modal wavefront reconstruction algorithm, because of a certain number of the low Zernike modes is selected subjective for making up the reconstruction model, the modes confusion and modes coupling will produced, the accuracy reduction of wavefront reconstruction is deduced. According to the minimal description length principal, a principle can balance the model error against model size so as to prevent the model from overfitting. The reconstruction model is selected by top-down method, and Levenberg-Marquardt nonlinear optimization algorithm is applied to the solution of reconstruction coefficients, then the wavefronts reconstruction is realized. Under different noise conditions, the reconstruction algorithm is validated with the numerical simulation of the wavefront reconstruction of uniform amplitude incidence beam, the results indicate: Zernike modal wavefront reconstruction algorithm based on the model selection can improve the wavefront reconstruction accuracy, and algorithm possesses the property of resistance to noise.

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

We apply a phase retrieval algorithm to the intensity patterns acquired from a Hartmann–Shack wave-front sensor to measure the wave-front aberration of a deep ultraviolet lithography system. The intensity patterns are obtained with and without the micro-lens array. Thus, we avoid selecting algorithm-specific parameters such as step-size and trust-region. Simulation results show that the phase-retrieval method enhances the accuracy of wave-front reconstruction compared with the conventional wave-front slope method. The relationships between the number of iterations of the phase retrieval algorithm, the calculating time and the wave-front reconstruction error are studied. This study demonstrates that the phase-retrieval method provides more accurate estimates of aberrations in near-flat wave-fronts relative to the wave-front slope method.

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.

Improving wavefront reconstruction accuracy by using integration equations with higher-order truncation errors in the Southwell geometry

Least-squares (LS)-based integration computes the function values by solving a set of integration equations (IEs) in LS sense, and is widely used in wavefront reconstruction and other fields where the measured data forms a slope. It is considered that the applications of IEs with smaller truncation errors (TEs) will improve the reconstruction accuracy. This paper proposes a general method based on the Taylor theorem to derive all kinds of IEs, and finds that an IE with a smaller TE has a higher-order TE. Three specific IEs with higher-order TEs in the Southwell geometry are deduced using this method, and three LS-based integration algorithms corresponding to these three IEs are formulated. A series of simulations demonstrate the validity of applying IEs with higher-order TEs in improving reconstruction accuracy. In addition, the IEs with higher-order TEs in the Hudgin and Fried geometries are also deduced using the proposed method, and the performances of these IEs in wavefront reconstruction are presented.

Myopic aberrations: impact of centroiding noise inHartmannShack wavefront sensing

The presence of photon noise and readout noise can lead to centroiding errors in a Hartmann Shack wavefront sensor (HS) and hence limit the accuracy of wavefront reconstruction. The aim of this paper is to compare, via Monte Carlo simulations, the accuracy of various centroiding methods in detecting noisy focal spot patterns of the HS while sensing ocular aberrations of myopic eyes. Myopic ocular aberrations were randomly simulated by using the modal statistics obtained from the measurements of 41 myopic subjects. HS spot patterns were simulated using a fast Fourier method where photon noise and readout noise were added using appropriate statistics. Adopting five different centroiding techniques: (1) centre of gravity, (2) weighted centre of gravity, (3) intensity weighted centroiding, (4) iteratively weighted centre of gravity and (5) matched filter based centroiding along with a zonal based wavefront sensing approach; the wavefronts were estimated and compared, by calculating the root mean square (RMS) wavefront error, with the initially simulated wavefront. The magnitude of readout noise was varied in terms of the maximum number of photons and electrons per subaperture per frame. The RMS error was calculated for each of the centroiding algorithms. For higher magnitude of readout noise and lesser number of photons per subaperture per frame (n), matched filter, iteratively weighted centre of gravity and intensity weighted centroiding outperform centre of gravity and weighted centre of gravity methods, for an appropriately chosen focal length and subaperture pitch. The plots of RMS error as a function of 'n' show that for lower amplitude of readout noise, computationally efficient centre of gravity and intensity weighted centroiding methods can be safely adopted to obtain high enough reconstruction accuracy. Also, even at greater readout noise levels, for a large enough 'n', intensity weighted centroiding is enough to sense the aberrations with high accuracy. It is shown that the wavefront sensing accuracy depends on the size of the spots and bit resolution of the camera. Five different centroid detection methods used in a HS in the presence of photon noise and readout noise were analysed in the context of sensing ocular aberrations of myopic subjects and identify cases under which each of these methods is appropriate.