Lateral Shearing Interferometry Research Articles

Quadriwave lateral shearing interferometry based on double birefringent crystals of beam displacer.

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.

Hyperspectral compressive wavefront sensing

Abstract Presented is a novel way to combine snapshot compressive imaging and lateral shearing interferometry in order to capture the spatio-spectral phase of an ultrashort laser pulse in a single shot. A deep unrolling algorithm is utilized for snapshot compressive imaging reconstruction due to its parameter efficiency and superior speed relative to other methods, potentially allowing for online reconstruction. The algorithm’s regularization term is represented using a neural network with 3D convolutional layers to exploit the spatio-spectral correlations that exist in laser wavefronts. Compressed sensing is not typically applied to modulated signals, but we demonstrate its success here. Furthermore, we train a neural network to predict the wavefronts from a lateral shearing interferogram in terms of Zernike polynomials, which again increases the speed of our technique without sacrificing fidelity. This method is supported with simulation-based results. While applied to the example of lateral shearing interferometry, the methods presented here are generally applicable to a wide range of signals, including Shack–Hartmann-type sensors. The results may be of interest beyond the context of laser wavefront characterization, including within quantitative phase imaging.

Measurement Method for Numerical Aperture of Projection Lens Based on Ronchi Lateral Shearing Interferometry

Measurement Method for Numerical Aperture of Projection Lens Based on Ronchi Lateral Shearing Interferometry

Parameter Fitting-Based Fast Imaging of Axisymmetric Flame Temperature Field Using Wavelength-Modulated Lateral Shearing Interferometry

Parameter Fitting-Based Fast Imaging of Axisymmetric Flame Temperature Field Using Wavelength-Modulated Lateral Shearing Interferometry

Thermally stable high numerical aperture integrated waveguides and couplers for the 3 μm wavelength range

The femtosecond laser direct write technique was used to fabricate mid-infrared compatible waveguide couplers into Suprasil 3001, a fused silica glass with an OH content of as low as ≤1 ppm. Smooth positive step-index change multi-scan waveguides were produced with a high index contrast of 1 × 10−2, measured directly using quadriwave lateral shearing interferometry. Waveguides were annealed at 400 °C for 15 h and found to be highly stable, with only <5% reduction in positive index change. Brillouin microscopy and cathodoluminescence are introduced as novel tools that complement Raman mapping and electron microscopy for the investigation of the laser-induced structural changes within the glass matrix, and it was found that although a uniform step index profile is observed across the entire guiding region, different physical mechanisms underpin the index change in the upper and lower sections of the waveguide cross-section, respectively. Waveguides were optimized for mode-matching with optical fibers for the 3.2 μm wavelength range, and evanescent four-port directional couplers with coupling ratios ranging from 5:95 to 50:50 were designed and fabricated. This demonstration opens the door to the development of fully integrated and temperature-stable hybrid chip/fiber systems for the important mid-infrared spectral range.

Online monitoring and active control of alignment errors in a tiled grating assembly using single wedge plate

With reference to application in chirped pulse amplification (CPA) based high-energy, ultra-short laser systems, online monitoring of alignment errors and active coherent locking of gratings in a tiled grating assembly (TGA) consisting of two gratings, each of size 140 mm x 120 mm and groove density 1740 grooves/mm, is presented. All the tiling alignment errors present in the TGA have been monitored simultaneously using a single wedge plate based lateral shearing interferometry and corrected using piezo motor driven 6-axis aligner stage. As a novelty, to have further advantages in the wedge plate based method for TGA alignment, the He-Ne laser beam diffracted/ reflected from the TGA has been folded back towards the source, which facilitated measurement sensitivity enhancement by a factor of two, and also generation and simultaneously capturing of both reflected and diffracted beam's interferograms using comparatively smaller dimension single wedge plate and CCD camera. The angular and translational alignment errors of the TGA have been actively locked in the range of ± 0.5 µrad and ± 50 nm respectively.

Improving the phase reconstruction accuracy of simultaneous phase-shifted lateral shearing interferometry using a polarization redundant sub-region interpolation method.

In a simultaneous phase-shifted lateral shearing interferometry, a division of focal plane polarization camera is generally used as the phase-shifting device. However, acquiring simultaneous phase-shift interferograms in a single frame suffers from a lack of spatial resolution, significantly affecting the phase reconstruction accuracy. A polarization redundant sub-region interpolation (PRSI) method is proposed to solve this problem. This interpolation method distinguishes smooth regions from stripe fringe regions by calculating the polarization redundancy error of the synchronous phase shift interferogram. After sub-regional processing, resolution reconstruction is performed in the smoothed area using a fast convolutional bilinear interpolation method. In the streak detail region, the resolution reconstruction is performed based on the strength of the correlation between the orthogonal and non-orthogonal polarization channels crossing the streak region. The PRSI method can quickly reconstruct the lost pixels and accurately recover the stripe detail information. Experiment results show that the proposed interpolation method outperforms the existing dominant methods in terms of visual reconstruction effect and quantitative index of phase reconstruction.

In-situ measurement and compensation of complex spatio-temporal couplings in ultra-intense lasers

Diffraction wavefront errors of large-scale Treacy compressors may induce complex spatio-temporal couplings (CSTCs) in chirped pulse amplification and degrade the quality of the pulsed beam in both near and far fields. This problem is particularly pronounced in petawatt laser facilities that require tiled compressor gratings. Here, to the best of our knowledge, we present the first in-situ measurement method named pseudo lateral shearing interferometry (PLSI) for the CSTC wavefront error and manufacture a continuous phase plate (CPP) according to the measurement to reduce the distortion. A Shark-Hartmann wavefront sensor is used to characterize wavefronts of the entire system at two different wavelengths, and the CSTC wavefront error can be reconstructed similarly to lateral shearing interferometry (LSI). Our approach strongly reduces systematic errors and the impact of other optics. The root-mean-square (RMS) value of the resulting error is 40 nm in a single measurement, and the day-to-day repeatability is 55 nm. The employed CPP reduces the peak-to-valley (PV) value of the CSTC wavefront error from 675 to 312 nm, and the focused peak intensity is improved by 51%.

Simultaneous two-step phase-shifting lateral shearing interferometry for aspherical surface based on an orthogonal shear displacer

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.

(3N+1)-frame phase retrieval for double-grating Ronchi lateral shearing interferometry

Accurate wavefront measurement using double-grating Ronchi lateral shearing interferometry significantly relies on the accuracy of shear-phase retrieval. Traditional methods cannot effectively suppress the interferences of unwanted diffractions generated by the Ronchi grating at the image plane. In this paper, we propose a method that uses 3N+1 shear interferograms to retrieve the shear phase, where N is a positive integer. The selection of N depends on the number of the diffraction orders existing in the shearogram. According to the numerical aperture of the optical system under test and the period of image grating, the interferograms corresponding to the specific 3N+1 phase shifts are obtained, from which the shear phase is calculated. For validation, the frequency response of the proposed algorithm is characterized, and the improved accuracy of wavefront measurement is demonstrated by comparisons with the existing 8-frame, 10-frame and 13-frame methods.

Triple-wavelength quantitative phase imaging with refractive index measurement

A method to quantitatively measure the refractive index (RI) and the topography of transparent samples is proposed. Three quantitative phase images at different wavelengths are firstly obtained by using a quadriwave lateral shearing interferometry (QLSI) technique, and then the RIs at the three wavelengths and the physical thickness distribution of the sample are independently calculated with the help of Cauchy's dispersion formula. Neither the highly dispersive medium nor the manual operation of changing the surrounding medium is required. From the measured RIs, the composition of the sample can be identified besides the topography of the sample. Both simulation and experimental results verified the effectiveness and feasibility of the proposed method.

Fast and Calibration-Free Temperature Imaging of Dynamic Flames via Wavelength Modulated Lateral Shearing Interferometry

Temperature distributions of dynamical flames were measured by using a proposed calibration-free wavelength modulated lateral shearing interferometry. A distributed feedback (DFB) laser was modulated in the wavelength as a sawtooth profile. The wrapped flame phase in the images was obtained pixel by pixel by calculating the phase shift between the interference light intensity profiles before and after flame ignition. Phase unwrapping and recovery were adopted to solve the flame phase distribution. The refractive index distribution was reconstructed with the help of Inverse Abel transform. The temperature imaging was further achieved by the ideal gas law and Gladstone-Dale model. Numerical simulations were conducted for performance evaluations. The flame phase, refractive index and temperature distributions were reconstructed with errors of 0.0094, 0.0154 and 0.0958, respectively. Standard deviations were in the magnitude of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> at the presence of Gaussian random noises and showed the noise immunity of the proposed method. In actual experiments, reconstructed temperature distribution of a steady flame generated on a Bunsen burner agreed well with the thermocouple measurements. A dynamical process of flame extinguishment was portrayed at one kilo frames per second. Temporal variation of the flame temperature distribution well reflected the extinguishing process. The entire measurement process did not require prior calibration of the modulated wavelength, and the imaging speed was more than ten times faster than the existing phase modulated interferometer. The proposed method can be used for on-line evaluation of dynamic flames.

Quadriwave Lateral Shearing Interferometry Quantitative Phase Imaging Based on 2D Ronchi Phase Grating

Quadriwave Lateral Shearing Interferometry Quantitative Phase Imaging Based on 2D Ronchi Phase Grating

Echelle gratings tiling method based on lateral shearing interferometry

A method for echelle gratings tiling based on lateral shearing interferometry is proposed. Fringe patterns of the grating assembly are generated by a wedge plate. Mosaic errors can be calculated and corrected by observing the working order and its adjacent order. An experimental mosaic of two 50mm×50mm,79grooves/mm echelles is aligned to verify the theory. The rms wavefront is better than 0.04 wavelength. Angular and translation sensitivities of less than 1 arcsec and 10 nm are achieved respectively.

Quantitative phase microscopy using quadriwave lateral shearing interferometry (QLSI): principle, terminology, algorithm and grating shadow description

Quadriwave lateral shearing interferometry (QLSI) is a quantitative phase imaging technique based on the use of a diffraction grating placed in front of a camera. This grating creates a wire-mesh-like image, called an interferogram, that is postprocessed to retrieve both the intensity and phase profiles of an incoming light beam. Invented in the 90s, QLSI has been used in numerous applications, e.g. laser beam characterization, lens metrology, topography measurements, adaptive optics, and gas jet metrology. More recently, the technique has been implemented in optical microscopes to characterize micro and nano-objects for bioimaging and nanophotonics applications. However, not much effort has been placed on disseminating this powerful technology so far, while it is yet a particularly simple technique. In this article, we intend to popularize this technique by describing all its facets in the framework of optical microscopy, namely the working principle, its implementation on a microscope and the theory of image formation, using simple pictures. We also provide and comment on an algorithm for interferogram processing, written in Matlab. Then, following the new extension of the technique for microscopy and nanophotonics applications, and the deviation from what the technique was initially invented for, we propose to revisit the description of the technique, in particular, by discussing the terminology, insisting more on a grating-shadow description rather than a quadriwave process, and proposing an alternative appellation, namely ‘grating shadow phase microscopy’ or ‘grating-assisted phase microscopy’.

Real-time measurement method for the skin temperature of the human arm via large lateral shearing interferometry.

This paper presents a real-time measurement method for the skin temperature of the human arm. In this method, the air temperature close to the arm skin is measured via large lateral shearing interferometry, thus avoiding the possible influences of the different physical characteristics of different people, while maintaining the advantages of optical measurement, including its noncontact, noninvasive, and rapid features. The method captures the real-time fringe patterns generated using a parallel-sided plate when a collimated laser light beam transfers through the air surrounding the arm to be measured. Additionally, the phase difference distribution caused by the temperature difference is calculated in combination with the background fringe patterns. The phase difference in the light close to the arm skin is then estimated via a linear fitting method. Accordingly, based on the size parameters of the arm cross section and the ambient temperature monitored in real time, the air temperature close to the arm skin, which is considered equal to the arm skin temperature, is determined while considering the heat conduction effect. Experimental measurements of the temperature of human arm skin were conducted using the proposed method, and the axillary temperatures of the same person before and after the experiments were also measured using an electronic thermometer and a mercury thermometer. Good agreements were found, verifying the reliability of the proposed method. Moreover, based on this method, the possibility for the construction of a real-time body temperature measurement system is also discussed.

Metasurface Optical Characterization Using Quadriwave Lateral Shearing Interferometry

An optical metasurface consists of a dense and usually nonuniform layer of scattering nanostructures behaving as a continuous and extremely thin optical component with predefined phase, transmission and reflection profiles. To date, various sorts of metasurfaces (metallic, dielectric, Huygens-like, Pancharatman-Berry, etc.) have been introduced to design ultrathin lenses, beam deflectors, holograms, or polarizing interfaces. Their actual efficiencies depend on the ability to predict their optical properties and to fabricate nonuniform assemblies of billions of nanoscale structures on macroscopic surfaces. To further help improve the design of metasurfaces, precise and versatile postcharacterization techniques need to be developed. Today, most of the techniques used to characterize metasurfaces rely on light intensity measurements. Here, we demonstrate how quadriwave lateral shearing interferometry (QLSI), a quantitative phase microscopy technique, can achieve full optical characterization of metasurfaces of any kind, as it can probe the local phase imparted by a metasurface with high sensitivity and a spatial resolution that reaches the diffraction limit. As a means to illustrate the versatility of this technique, we present measurements on two types of metasurfaces, namely, Pancharatnam-Berry and effective-refractive-index metasurfaces, and present results on uniform metasurfaces, metalenses, and deflectors.

Comparison of processing speed of typical wavefront reconstruction methods for lateral shearing interferometry.

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.

In Situ Stress Measurement of Ni Electrodeposition Using Lateral Shearing Interferometry

In-situ stress measurement has a significant benefit in revealing the deformation and failure mechanism during the deposition process. However, it is difficult to detect an ultrathin deposit and measure deposits of different scales simultaneously. Here, lateral shearing interferometry was used for in situ stress measurement of Ni deposits. we demonstrated that this method showed great stability and sensitivity during in situ process. Additionally, the accuracy of measurement was also been improved in terms of the measurement error (2.96%) and fluctuation (0.00035) of curvature radius. The system was capable of the measuring radius of curvature as large as 250 m. Theoretical calculation and experimental results coherently suggested that the thickness of measurable deposits can be diminished by decreasing the elastic modulus and thickness of the substrate. PMMA substrates can be used to measure the stress evolution of deposits with a thickness of more than 10 nm. Moreover, suitable substrate material and thickness for stress measurement of deposits with different scales can be selected by theoretical calculation before the experiment. This novel method provides valuable insights into the in situ stress towards the ultrathin deposit and paves the way to further understanding on the mechanism of deformation and failure of the deposition process in different states.

Natural convection heat transfer from two horizontal cylinders using a large lateral shearing interferometer

AbstractNatural convection heat transfer from two horizontal cylinders in the air was investigated experimentally and numerically. Two cylinders were spaced at 1.3, 1.8, and 2.7 cylinder diameters horizontally. The experiments were carried out by large lateral shear interferometry (LSI) for various Rayleigh numbers in the range of 103 to 104. Large LSI is common path interferometry with the advantages of simple structure, strong antivibration, and fewer required optical components. It is not necessary for LSI to perform a complex algorithm to restore wavefront with a large shear amount. Simple and infinite fringe interferograms of the cylinders heated from ambient temperature 282.15 to 723.15 K were obtained. A numerical simulation was carried out with ANSYS‐Fluent 18.0. The influence of two factors, the distance between the cylinders, and the Rayleigh number, on the heat transfer of two horizontal cylinders was examined. The average Nusselt number and local Nusselt number were determined from the experimental results and numerical results, respectively, and the two results were in good agreement. The rising direction for the plume flow pattern of each horizontal cylinder was no longer simply vertically upward but was inclined toward the central symmetry axis of the two cylinders. In addition, the heat transfer from a cylinder increased with the cylinder spacing at any Rayleigh number.