Variable-ratio lateral-shearing interferometry with a vortex-splitting grating

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.

The quadriwave lateral shearing interferometry (QWLSI) based on double birefringent crystals of 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 of overlapped incident to the analyzer, and it’s the direction of transmission axis is set as 45° or 135°, the QWLSI’s polarization interferogram can be obtained. This paper deduced the principle of QWLSI in detail, and showed the phase retrieval by the Fourier analysis of the QWLSI’s interferogram, then the wavefront can be reconstructed by using the differential Zernike polynomial fitting. In our investigation, the correction range of PBD’s orthogonal angle error is within –0.5° ~ 0.5°, the maximum error in PV: 0.0012λ and the maximum error in RMS: 1.3789×10-4λ in wavefront reconstruction. Moreover, when the testing light tilts to incident on the PBD in the range of –0.4° ~ 0.4°, by correcting the shear distance be used for wavefront reconstruction to achieve high-precision wavefront testing result. Finally, the experiment shows that the DBCs-BD-QWLSI exhibits feasibility, and high precision.

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.

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.

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

The need for segmented wave front measurements has been rocketing for several years. The applications are various: thickness of metallic masks, diffracting elements, phasing of the primary segmented mirrors of telescopes, such as the Keck telescope, laser beam coherent recombination... Lateral shearing interferometers are common wave front sensors, used with success to test classical optical components. This technique does not require a reference wave, which is a major advantage. The lateral shearing interferometry has also proved successful to analyze segmented wave front; results of such a measurement by a diffraction-grating based interferometer are presented and analyzed. We dwell upon quadri-wave lateral shearing interferometers (QWLSI), which offer the possibility to characterize two-dimensionally the wave front, in a single measurement. This technique combines accuracy and qualities such as compactness and simplicity. Moreover, a chromatic regime of lateral shearing interferometers based on diffraction grating can be pointed out; this allows a two-color analysis to greatly extend the dynamic range. In the first parts we will present general considerations on QWLSI and segmented surface; then a technique to increase the dynamic range is investigated both theoretically and experimentally.

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.

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.

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.

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

Behaviour of short columns subjected to cyclic shear displacements: Experimental results

With the development of new materials and ultra-precision processing technology, the sizes of measured objects increase, and the requirements for machining accuracy and surface quality become more exacting. The traditional measurement method based on reference datum is inadequate for measuring a high-precision object when the quality of the reference datum is approximately within the same order as that of the object. Self-referenced measurement techniques provide an effective means when the direct reference-based method cannot satisfy the required measurement or calibration accuracy. This paper discusses the reconstruction algorithms for self-referenced measurement and connects lateral shearing interferometry and multi-probe error separation. In lateral shearing interferometry, the reconstruction algorithms are generally categorized into modal or zonal methods. The multi-probe error separation techniques for straightness measurement are broadly divided into two-point and three-point methods. The common features of the lateral shearing interferometry method and the multi-probe error separation method are identified. We conclude that the reconstruction principle in lateral shearing interferometry is similar to the two-point method in error separation on the condition that no yaw error exists. This similarity may provide a basis or inspiration for the development of both classes of methods.

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.

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