Errors Correction Analysis of Wavefront Testing in Quadriwave Lateral Shearing Interferometry

Quadriwave lateral shearing interferometry (QWLSI) is based on double birefringent crystals of a beam displacer (DBCs-BD), which can generate the lateral shearing interference wavefront of four beams of overlapped replicas in the DBCs-BD orthogonal directions. When the replica waves are overlapped incident to the analyzer and the direction of the transmission axis is set as 45° or 135°, the QWLSI's polarization interferogram can be obtained. This paper deduces the principle of QWLSI based on the DBCs-BD and presents the analysis of orthogonal error influence based on the DBCs-BD and the phase retrieval error of QWLSI when shear displacement by tilted incident on the DBCs-BD. In our investigation, we have established the correction range of the PBD's orthogonal angle error is within -0.5∘-0.5∘, the maximum error in PV is 0.0012λ, and the maximum error in RMS is 1.3789×10-4 λ in wavefront reconstruction. Moreover, when the testing light tilts to incident on the PBD in the range of -0.4∘-0.4∘, correction of the shear distance is used for wavefront reconstruction to achieve a high-precision wavefront testing result. Finally, the experiment shows that QWLSI based on the DBCs-BD exhibits feasibility and high precision.

A quadriwave lateral shearing interferometry (QWLSI) is proposed based on double birefringent crystals of a beam displacer (DBCs-BD). The DBCs-BD is formed by adopting two birefringent crystals of a polarization beam displacer (PBD), which can generate the lateral shearing interference waves of four beams of overlapped replicas in the DBCs-BD orthogonal directions. When the replica waves are overlapped incident to the analyzer, and the direction of the transmission axis is set as 45° or 135°, the QWLSI's polarization interferogram can be obtained. The high-precision phase can be obtained by simple spectrum denoising and performing the Fourier transform of the resulting interferogram. We deduce the principle of QWLSI in detail, and the wavefront distribution can be achieved by the phase calculation. The experiment shows that the DBCs-BD-QWLSI exhibits feasibility and high precision.

Quantitative phase imaging (QPI) has emerged as a powerful tool in label-free bioimaging, in situ microstructure characterization for advanced manufacturing, and high-speed imaging of material property changes. Among various QPI methods, quadri-wave lateral shearing interferometry (QWLSI) stands out for its unique advantages in compactness, robustness, and high temporal resolution, making it an ideal choice for a wide range of applications. The compact design of QWLSI allows for easy integration with existing microscopy systems, while its robustness is manifested in the ability to maintain precise interferometric sensitivity even in high-vibration environments. Moreover, QWLSI also enables single-shot measurements that facilitate the capture of fast dynamic processes. This paper provides an in-depth exploration of the technical aspects of QWLSI, focusing on the evolution of its optical system and the primary algorithms used in wavefront reconstruction. The review also showcases significant applications of QWLSI, with a particular emphasis on its contributions to biomedical imaging. By discussing the advantages, limitations, and potential future developments of QWLSI, this paper aims to provide a comprehensive overview of this powerful QPI technique and its impact on various research fields.

Algorithms to eliminate the influence of non-uniform intensity distributions on wavefront reconstruction by quadri-wave lateral shearing interferometers

Quadriwave lateral shearing interferometry (QLSI) is a powerful quantitative phase imaging technique, offering compactness, robustness, high resolution, and single-shot measurement. However, since QLSI phase retrieval relies primarily on phase gradient integration, it may struggle with speckle beams containing phase singularities, where phase discontinuities lead to non-conservative gradients and reduce integration accuracy. Here, we propose a convolutional neural network (CNN)-assisted QLSI sensing method for speckle beam reconstruction. The CNN is trained to directly retrieve the complex amplitude information of speckle beams from their QLSI interferograms. Experimental results demonstrate that the proposed method can accurately reconstruct both amplitude and phase profiles of speckle beams with various complexities, achieving a Pearson correlation coefficient exceeding 0.9 compared to the ground truth. This method is expected to enhance the sensing capability of traditional QLSI wavefront sensors and enable broader applications, such as free-space laser communication and advanced optical imaging in strong turbulence scenarios.

Quadriwave lateral shearing interferometry (QWLSI) is a wave front sensing technology based on the analysis of an interferogram created by waves diffracted by an optical grating set in front of a camera sensor. Since QWLSI is a single-arm interferometry modality is has the advantage of being very compact, robust and easy to implement. It enables to achieve a phase resolution of 5nm. In this paper, we will describe the QWLSI system and apply it to metasurface shape and laser-induced refractive index variation measurements like waveguides and LIDT.

Lateral Shearing Interferometer (LSI), as a kind of self-interference technology, can achieve high-precision wavefront sensing and phase imaging. Quadriwave Lateral Shearing Interferometry (QWLSI) divides the wavefront into four transverse dislocated beams by a checkerboard phase grating. The lateral-shearing interferogram of the four waves occurs on the image plane, and then the test wavefront is reconstructed. The reconstruction precision is determined by the shear ratio, thus the variable shear ratio can meet the requirement of the different measurement accuracy. Here we proposed variable-ratio lateral-shearing interferometry with a vortex-splitting grating. Different from the checkerboard grating, topological charge is first encoded into grating and is then optimized to obtain two shear ratios in the same interference setup. The proposed variable-ratio lateral-shearing setup including of only an axial motion device is robust, effective and variable precision for wavefront sensing.

The effective focal length is a critical determinant of optical performance and imaging quality, serving as a fundamental parameter for components ranging from ophthalmic lenses to precision microlens arrays. With the rapid advancement of complex optical systems in microscopy and smart manufacturing, there is an increasing demand for high-precision measurement techniques that can characterize these parameters with low uncertainty. In this paper, a quadri-wave lateral shearing interferometry (QWLSI) measurement system was developed. A novel precision focal length measurement method of optical lenses based on the principle of QWLSI is presented. A theoretical model for solving the focal length of the measured lens from the curvature radius of the wavefront was derived. We also proposed a novel algorithm and subsequently developed a dedicated hardware platform and a corresponding software package for its real-time implementation. Different sets of repeated measurement experiments were carried out for two convex lenses with symmetrical and asymmetrical structures, a large-scale concave lens, and a microlens array, to verify the measurement uncertainty and robustness of the QWLSI measurement system. The expanded uncertainty was also analyzed and determined as 0.31 mm (k = 1.96, normal distribution). The results show that the proposed QWLSI measuring system possesses good performance in measuring the focal lengths of different kinds of lenses and can be widely used in fields such as advanced optics manufacturing.

This paper introduces a procedure aimed to quantitatively measure the optical properties of nanoparticles, namely the complex polarizability and the extinction, scattering, and absorption cross sections, simultaneously. The method is based on the processing of intensity and wavefront images of a light beam illuminating the nanoparticle of interest. Intensity and wavefront measurements are carried out using quadriwave lateral shearing interferometry, a quantitative phase imaging technique with high spatial resolution and sensitivity. The method does not require any preknowledge on the particle and involves a single interferogram image acquisition. The full determination of the actual optical properties of nanoparticles is of particular interest in plasmonics and nanophotonics for the active search and characterization of new materials, e.g., aimed to replace noble metals in future applications of nanoplasmonics with less-lossy or refractory materials.

Meeting the nanometre resolution promised by super-resolution microscopy techniques (pointillist: PALM, STORM, scanning: STED) requires stabilizing the sample drifts in real time during the whole acquisition process. Metal nanoparticles are excellent probes to track the lateral drifts as they provide crisp and photostable information. However, achieving nanometre axial super-localization is still a major challenge, as diffraction imposes large depths-of-fields. Here we demonstrate fast full three-dimensional nanometre super-localization of gold nanoparticles through simultaneous intensity and phase imaging with a wavefront-sensing camera based on quadriwave lateral shearing interferometry. We show how to combine the intensity and phase information to provide the key to the third axial dimension. Presently, we demonstrate even in the occurrence of large three-dimensional fluctuations of several microns, unprecedented sub-nanometre localization accuracies down to 0.7 nm in lateral and 2.7 nm in axial directions at 50 frames per second. We demonstrate that nanoscale stabilization greatly enhances the image quality and resolution in direct stochastic optical reconstruction microscopy imaging.

We present the application of Quadri-Wave Lateral Shearing Interferometry (QWLSI), a wave front sensing technique, to characterize optical beams at infrared wavelengths from 2 to 16μm with a single instrument. This technique can be used to quantify the quality of optical systems (like thermal infrared lenses) by measuring their aberrations. It can also evaluate laser sources in the infrared range like some gas lasers (HeNe laser or CO2 laser), infrared Optical Parametric Oscillator laser sources or Quantum Cascade Laser sources. In all cases, QWLSI offers the crucial advantage that it yields an analyzed wave front without the use of a reference arm and consequent time consuming alignment. In this paper, we first present the single interferometer which can be used with wavelength within 2 and 16μm, covering this way the MWIR (λ within 3 and 5μm) and LWIR (λ within 8 and 14μm) ranges. We then present the characterization of two gas lasers: an infrared HeNe lasers (λ=3.39μm) and a CO2 laser (λ=10.6μm) with this instrument. We finally show the experimental analysis of an infrared lens at two different wavelengths, one in the MWIR range (λ=3.39μm) and the other in the LWIR range (λ=10.6μm). λ

With the continuous development of the semiconductor industry, advanced chip manufacturing technology has reached the node of 5 nm and below, and wafer defects will inevitably occur in the manufacturing process. These tiny defects will lead to chip failure and significantly affect product yield. Semiconductor wafer manufacturing involves multiple stages, each of which introduces surface defects that affect the quality of lithography and cause device characteristics to fail. Therefore, it is very important to detect the surface defects of bare wafers. In this paper, a high-precision detection method based on quadriwave lateral shear interferometry (QLSI) is proposed, which can detect nanoscale height changes with high sensitivity and provide wafer surface topology measurement. The non-contact technology avoids the damage caused by probe contact, realizes efficient and real-time detection, reduces production costs and improves product quality.

Wavefront reconstruction for multi-lateral shearing interferometry using difference Zernike polynomials fitting

A novel simultaneous two-step phase-shifting lateral shearing interferometry for aspherical surface based on an orthogonal shear displacer (OSD) is proposed, it is an effective technological measure of aspherical surface measurement, to effectively solve the non-uniformity of light intensity and limited transmission order caused by the beam displacer device. The OSD system is formed by the adoption of two-crystal polarization parallel beam displacers (PBDs), which makes it achieve the orthogonal shearing in the x- and y-directions simultaneously. A quarter-wave plate (QWP) is used to generate the desired phase-shifting, and four beam lateral shearing interference waves are simply generated in OSD orthogonal directions without any bulky and complicated optical components. The phase maps of the aspherical surface can be instantly obtained using the spatial phase-shifting technique with a polarization pixelated mask (or called micro-polarization array: MPA) integrated into CCD. In this study, the proposed method was theoretically described and simulation results were analyzed. The simultaneous two-step phase-shifting lateral shearing interference fringes can be extracted in real-time with the MPA. The experiment results compared with the ZYGO interferometer were performed, and proved that the measurement error is not more than 2%. This interferometry has made it possible to improve the stability and feasibility of aspherical surface testing experiments.

Lateral shearing interferometry is widely applied in wavefront sensing, optical components testing, and defect inspection. The procedure of reconstructing the wavefront is the most specific difference between lateral shearing interferometry and other classical methods such as the Fizeau and Twyman interferometers. The speed and accuracy are two main features to evaluate the performance of one wavefront reconstruction method. In this work, optimized procedures for three typical wavefront reconstruction methods-the iterative FFT wavefront reconstruction method (FFT method), the partial differential least-squares method (LSQ method), and the difference Zernike polynomial fitting method (DZF method)-are designed. The calculation speeds of the three wavefront reconstruction methods are evaluated with different GPUs and CPUs. According to the test results, the DZF method is the fastest method both in the GPUs and CPUs. The shortest processing times of the DZF, FFT, and LSQ methods are 100, 449, and 494 ms, respectively, with the wavefront size of 1024×1024pixels. The calculation speeds of the FFT method and the LSQ method are similar in the CPUs, and the FFT method is faster in the GPUs. The relationship between the consumed time and the wavefront size is an exponential function in the CPUs and a power function in the GPUs. Generally speaking, GPUs' processing speeds are faster than CPUs'. But CPUs can be faster than GPUs when the test wavefront sizes are smaller than 64×64pixels. Besides, the differences between the consumed times of different CPUs are relatively smaller than those of the GPUs.