Quadriwave Lateral Shearing Interferometry Research Articles

Linear and nonlinear optical properties of femtosecond laser inscribed waveguides into GLS glass

Gallium lanthanum sulfide (GLS) glass is a promising material for mid-infrared photonics due to its wide transmission window and its high nonlinear refractive index that is almost three orders of magnitude higher than that of fused silica. In this paper, we present the results of a detailed study into the linear and nonlinear optical properties of waveguides fabricated in GLS glass via ultrafast laser direct-inscription using three different techniques: cumulative heating in the thermal regime as well as multi-scan and half-scan in the athermal regime. Using quadriwave lateral shearing interferometry, we fully characterized the refractive index profiles of such inscribed waveguides and found no difference between half-scan and multi-scan writing which indicates the absence of laser-induced stress in this soft glass in stark contrast to fused silica. In terms of nonlinearity, we utilized self-phase modulation (SPM)-induced spectral broadening experiments at mid-IR wavelengths to demonstrate that waveguides fabricated in the athermal regime preserve the high intrinsic nonlinearity of the GLS bulk material, outperforming those written in the thermal regime based. These findings pave the way for the fabrication of fiber-coupled optical waveguide chips for nonlinear mid-infrared photonics.

High-definition quadriwave lateral shearing interferometry

We present an evolution of quadriwave lateral shearing interferometry that improves the definition of quantitative phase images. It is now possible to produce images with as many pixels as the camera that records the interferogram. This is done by moving a diffraction grating in front of the camera and linearly combining at least nine acquisitions. In this paper, we present the principle of this technique and illustrate it by several examples acquired on a microscope with both calibrated and biological samples. We demonstrate the possibility of producing quantitative phase images with 5.5 million pixels, which are to our knowledge the largest images ever produced by a wavefront sensor.

Fast and direct calibration for high numerical aperture quadriwave lateral shearing interferometry using geometry model with higher-order Taylor expansion

The current research on quadriwave lateral shearing interferometry (LSI) is primarily focused on the measurements of plane wave or quasiplane wave. When directly measuring spherical waves with high numerical apertures (NA>0.35), it will generate additional systematic errors, which affect measurement accuracy. To make the quadriwave LSI applicable to the measurements of a high-NA spherical wave, this paper proposes a fast and direct calibration method by establishing the geometry model of the quadriwave LSI with high-NA spherical wave incidence. The expression for the optical path difference represented systematic errors introduced by high-NA spherical waves in the shearing wavefronts are derived, which utilize a ninth-order Taylor expansion and Zernike polynomials fitting to achieve the high accuracy required by the high-NA spherical wave incidence. Then, the systematic errors are directly calibrated in the shearing wavefronts of four directions. This paper presents the theoretical analysis and verifies the feasibility and reliability of the proposed method through simulations and experiments, achieving a good measurement accuracy.

Error 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 1.3789×10−4λ 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.

In situ calibration of shear ratio for quadriwave lateral shearing interferometry using double-slit interference.

A new method, to the best of our knowledge, based on double-slit (DS) interference is proposed to accurately estimate the shear ratio of the system, with plane wave or spherical wave incidence. Existing shear ratio calibration methods, designed primarily for lateral shearing interferometry (LSI) with plane wave incidence, are not applicable to LSIs directly testing divergent or convergent spherical waves. Equations for calculating the shear ratio using the fringe spacing of the DS interferogram and the NA of the incident spherical wave are derived in this paper. The simulation result shows that the relative error of the shear ratio value is about 0.3%, when the shear ratio is 0.1. In the experiment, the quadriwave LSI is designed with a plug-in feature. The shear ratio at integer multiples of 1/6 Talbot distance from the modified Hartmann mask was calibrated using a DS, and the results were in good agreement with theoretical values, confirming the accuracy of the method. Subsequently, with the assistance of an inductance micrometer, the shear ratio was calibrated at intervals of 0.5mm, and the results closely matched the theoretical variation of the shear ratio caused by displacement, confirming the high precision of the method.

High-Precision Correction for Spatial Light Modulator Based on Quadriwave Lateral Shearing Interferometry

High-Precision Correction for Spatial Light Modulator Based on Quadriwave Lateral Shearing Interferometry

Absolute measurement of focusing properties of a large-aperture diffractive lens.

Diffractive lenses are popular in large optical systems owing to their lightweight and multifunctional design. However, they are difficult to calibrate accurately due to the cross talk between the first-order diffraction and the background light. Here, a quadriwave lateral shearing interferometry (QWLSI) with spherical wave illumination was proposed to absolutely measure the focusing properties of diffractive lenses by means of the reference background light, in which the corresponding theoretical modeling was first derived, and then the single-shot experiment on a 210 mm-diameter beam was carried out. The results showed that the measurement error of the focal length was 0.59%, and the consistency error was 0.008%.

Wavefront Microscopy Using Quadriwave Lateral Shearing Interferometry: From Bioimaging to Nanophotonics

Common cameras are only sensitive to the intensity of light, discarding an essential feature of a light wave: its phase profile or, equivalently, its wavefront profile. This Review focuses on a rising wavefront imaging technique called quadriwave lateral shearing interferometry (QLSI), based on the simple use of a 2-dimensional diffraction grating, aka a cross-grating, in front of a regular camera. We detail the working principle of QLSI and its implementation on an optical microscope. We highlight its microscopy applications in bioimaging and nanophotonics, in particular for the characterization of living cells, nanoparticles, 2D materials, metasurfaces, microscale temperature gradients, and surface topography. Finally, we draw a critical comparison of QLSI with current quantitative phase microscopy techniques, namely, digital holography microscopy (DHM), spatial light interference microscopy (SLIM), and diffraction phase microscopy (DPM).

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.

High-precision gaseous flame temperature field measurement based on quadriwave-lateral shearing interferometry

Quadriwave-lateral shearing interferometry (QLSI) has a broad utilization in quantitative phase imaging (QPI) for refraction-type objects due to its compact structure and stable performance against external disturbance. Here we propose to use the QLSI technique to image and measure the gaseous flame temperature field distribution in high precision. The quantitative phase image of an axisymmetric candle flame is firstly reconstructed from the wire-mesh-like QLSI interferogram, and then the three-dimensional temperature field distribution is calculated with the axisymmetric projection transform algorithm. Compared to the conventional digital holographic interferometry (DHI) based on Mach-Zehnder architecture, the proposed method possesses a high-precision measurement and better stability in disturbed environment, benefiting from the compact common-path structure of QLSI. The temperature measurement errors of the proposed QLSI method are ±5.0 K and ±5.3 K in the presence of airflow disturbance and mechanical vibration, respectively, while those of the DHI method are ±7.6 K and ±12.9 K, respectively.

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.

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.

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

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’.

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.

Printing polarization and phase at the optical diffraction limit: near- and far-field optical encryption

AbstractSecuring optical information to avoid counterfeiting and manipulation by unauthorized persons and agencies requires innovation and enhancement of security beyond basic intensity encryption. In this paper, we present a new method for polarization-dependent optical encryption that relies on extremely high-resolution near-field phase encoding at metasurfaces, down to the diffraction limit. Unlike previous intensity or color printing methods, which are detectable by the human eye, analog phase decoding requires specific decryption setup to achieve a higher security level. In this work, quadriwave lateral shearing interferometry is used as a phase decryption method, decrypting binary quick response (QR) phase codes and thus forming phase-contrast images, with phase values as low as 15°. Combining near-field phase imaging and far-field holographic imaging under orthogonal polarization illumination, we enhanced the security level for potential applications in the area of biometric recognition, secure ID cards, secure optical data storage, steganography, and communications.

Quantitative phase imaging to study transmembrane water fluxes regulated by CFTR and AQP3 in living human airway epithelial CFBE cells and CHO cells.

In epithelial cells, the cystic fibrosis transmembrane conductance regulator (CFTR), a cAMP-regulated Cl- channel, plays a key role in water and electrolytes secretion. A dysfunctional CFTR leads to the dehydration of the external environment of the cells and to the production of viscous mucus in the airways of cystic fibrosis patients. Here, we applied the quadriwave lateral shearing interferometry (QWLSI), a quantitative phase imaging technique based on the measurement of the light wave shift when passing through a living sample, to study water transport regulation in human airway epithelial CFBE and CHO cells expressing wild-type, G551D- and F508del-CFTR. We were able to detect phase variations during osmotic challenges and confirmed that cellular volume changes reflecting water fluxes can be detected with QWLSI. Forskolin stimulation activated a phase increase in all CFBE and CHO cell types. This phase variation was due to cellular volume decrease and intracellular refractive index increase and was completely blocked by mercury, suggesting an activation of a cAMP-dependent water efflux mediated by an endogenous aquaporin (AQP). AQP3 mRNAs, not AQP1, AQP4 and AQP5 mRNAs, were detected by RT-PCR in CFBE cells. Readdressing the F508del-CFTR protein to the cell surface with VX-809 increased the detected water efflux in CHO but not in CFBE cells. However, VX-770, a potentiator of CFTR function, failed to further increase the water flux in either G551D-CFTR or VX-809-corrected F508del-CFTR expressing cells. Our results show that QWLSI could be a suitable technique to study water transport in living cells. We identified a CFTR and cAMP-dependent, mercury-sensitive water transport in airway epithelial and CHO cells that might be due to AQP3. This water transport appears to be affected when CFTR is mutated and independent of the chloride channel function of CFTR.

Full optical characterization of single nanoparticles using quantitative phase imaging

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.

Circular-aperture Modified Hartmann Mask for quadriwave lateral shearing interferometry

A circular-aperture Modified Hartmann Mask (cMHM) for quadriwave lateral shearing interferometry is proposed. The cMHM features in the hybrid structure consisting of a phase chessboard and a circular-aperture array, which is easy to manufacture. The diffraction properties of cMHM are numerically analyzed. By choosing the radius of the circular aperture to be the first positive root of Bessel function, the intensities of parasitic diffraction orders are largely diminished. In the simulations, the parasitic errors are evaluated from the perspectives of both extraction error and reconstruction error. The parasitic error of cMHM is about only half of the parasitic error of MHM. In the experiments, a compact cMHM-based lateral shearing interferometer has been built. Wavefront measurement results obtained by cMHM-LSI are compared with those obtained by commercial wavefront sensor, and the results correspond with each other well. The adaptability and accuracy of the proposed cMHM are validated.

Quantitative model of the image of a radiating dipole through a microscope

In this paper, we introduce a formalism to determine the relationship between the full vectorial electric field existing at the object plane of a microscope and that existing at the image plane. The model is then used to quantitatively simulate, in both phase and intensity, the image of a radiating electric dipole placed either in a homogeneous medium or in the vicinity of a substrate. These simulations are compared with experimental measurements on single gold nanoparticles carried out by quadriwave lateral shearing interferometry.