Quadriwave Lateral Shearing Interferometer Research Articles

Fast reconstruction technology of a laser beam spatial transmission characteristic curve.

The traditional multiposition method of the M2 factor measurement system is a good method, but it is relatively time consuming, so it cannot meet the requirements of the transient test of a Gaussian beam. To solve this problem, a quadriwave lateral shearing interferometer and a wavefront construction method based on a difference Zernike polynomial are analyzed. This interferometer uses a special grating to select four replicas of the wavefront, and the interferogram generated by four replicas includes difference wavefront information. Then the difference Zernike polynomial method is used to analyze quadriwave lateral shearing interferograms. The characteristic parameters are obtained after finding the optimal terms of the Zernike polynomials. As a result, the errors of F-number, beam radius, and radius of curvature are 3.7%, 3.8%, and 0.6%, respectively, which verifies this method to calculate parameters of Gaussian beam. In addition, we also find that the shear amount has influence on the reconstructed wavefront. It is showed that as the amount of shear increases from 20 pixels to 90 pixels, the peak-to-valley (P-V) values and RMS values both gradually decrease with a nonlinear relationship, which could be used to decrease the error of wavefront reconstruction further.

Non-null testing of the aspheric surface using a quadriwave lateral shearing interferometer

A non-null aspheric surface testing system using a quadriwave lateral shearing interferometer (QWLSI) based on the randomly encoded hybrid grating is proposed. The system uses a non-null lens to partially compensate for the longitude aberration of the aspheric surface, which is more versatile than the null configuration. QWLSI is a common-path and self-reference system and requires no reference surface. Compared with the conventional Twyman–Green interferometer (TGI), QWLSI has higher dynamic range, better antivibration ability, and higher stability. For a non-null testing system based on the QWLSI and TGI, the compensation ranges of different aspheric surfaces and the allowable range of aspheric axial positions are analyzed under the condition that the interference fringe satisfies the Nyquist sampling theorem. The iterative reverse optimization retrace error-correction algorithm based on the exact system modeling and the localization algorithm of aspheric axial position are discussed. Simulation results show that the root mean square value of the aspheric surface reconstruction residual is less than 1 / 200 λ , which indicates that the system has extremely high theoretical testing accuracy. In the experiment, the QWLSI non-null system and the autocollimation null method with a ZYGO interferometer agree with the testing results of the same aspheric surface, which demonstrates the feasibility and accuracy of the QWLSI aspheric non-null testing method.

Analysis of laser M2 determination in a quadriwave lateral shearing interferometer with CCD vertical blooming

Abstract Charge-coupled device (CCD) vertical blooming is inevitable in silicon-based cameras when near-infrared lasers are measured. In this study, we analyze the mechanism responsible for the influence of CCD vertical blooming on the beam quality factor (M2) measurement with a quadriwave lateral shearing interferometer (QWLSI). Based on a CCD vertical blooming model, we reconstruct the bloomed interferogram, which is used to retrieve the intensity and phase distributions of the laser. Then, the relationship between the M2 and degree of CCD vertical blooming is revealed. In addition, the M2 of single- and multi-mode lasers is measured with the QWLSI under different degrees of vertical blooming streaks. The results from the experiment are reasonably consistent with the simulation results. Meanwhile, the method of improving the exposure time of CCD camera for suppressing the blooming is also analyzed, indicating that the method can effectively suppress the influence of the blooming on the M2 measurement in a QWLSI.

High-precision calibration method for shear ratio based on the shearing wavefront feature extraction of a phase plate.

A new method based on the shearing wavefront feature extraction (SWFE) of a phase plate is proposed to accurately estimate the shear ratio of the system. The relationship between the shear ratio of a quadriwave lateral shearing interferometer based on a randomly encoded hybrid grating (REHG) and the measurement sensitivity, dynamic range, and wavefront retrieval accuracy is analyzed to provide a theoretical guidance for practical application. The simulation result of the SWFE method shows that the relative error of the shear ratio value is about 1.8×10-3, within the acceptable range of the system. In the experiment, two fused quartz phase plates etched with step change edge grooves were introduced to calibrate the shear ratio of the REHG wavefront diagnosis system. Then, the etching depths of these two phase plates and the figure error of a spherical surface were characterized by the REHG. A comparison with a ZYGO GPI interferometer exhibits that the testing results by the REHG are highly precise, which further confirms the effectiveness of the SWFE method in the shear ratio calibration. This shear ratio calibration method is available for similar kind of shearing interferometric wavefront sensor.

Quantitative retardance imaging by means of quadri-wave lateral shearing interferometry for label-free fiber imaging in tissues

We describe the use of quantitative retardance imaging, previously introduced in Aknoun et al. (2015), as a label-free method for in situ tissue imaging and extra-cellular matrix fiber organization study. A technical improvement of this quantitative retardance imaging technique, based on the use of a high-resolution quadri-wave lateral shearing interferometer, is implemented to perform fast quantitative linear retardance and retardance measurements on biological tissues. The technique combines a stack of quantitative phase images with varying polarization excitation to create retardance and orientation images at 1 Hz. This technique gives information about local retardance and structure of anisotropic components. In addition to bringing morphological information on unstained biopsies, it can reveal tumors development grades thanks to specific fiber organization imaging. In this present study, we demonstrate how this information can be used as tumor associated signature. We show the capability of our approach on mouse skin and human breast tissues.

Measurement of high-dynamic temperature field using high-speed quadriwave lateral shearing interferometer

An approach to measure a high-dynamic two-dimensional (2D) temperature field using a high-speed quadriwave lateral shearing interferometer (QWLSI) is proposed. The detailed theoretical derivation to express the wavefront reconstruct principle of the proposed method is presented. The comparison experiment with thermocouples shows that the temperature field measurement using QWLSI has a precision of ±0.5 °C. An experiment for measuring the highdynamic temperature field generated by an electrical heater is carried out. A 200 frame rate temperature field video with 512 × 512 resolution is obtained finally. Experimental results show that the temperature field measurement system using a QWLSI has the advantage of high sensitivity and high resolution.

Calibration of Wavefront Phase Image Using Phase-Shifting Iteration Algorithm in Quadriwave Lateral Shearing Interferometry

A phase-shifting iterative algorithm is proposed to calibrate the wavefront phase image demodulated from an interferogram generated by quadriwave lateral shearing interferometer. It reduces the error of the residual slope to RMS < 1.5×10 −4λ after calibration. A favorable result was obtained in the present experiment. We measured a certain wavefront provided by a deformable mirror using the quadriwave lateral shearing interferometer after calibration. The deviation between the wavefront graph of the deformable mirror and the wavefront constructed by quadriwave later shearing interferometer was 2.63%. Our method increases the accuracy and reliability of the reconstructed wavefront data and has a high practical value, all of which meets the requirement of high-precision wavefront sensing.

Determination of the laser beam quality factor (M2) by stitching quadriwave lateral shearing interferograms with different exposures.

A complete complex amplitude reconstruction method for the determination of the laser beam quality factor M2 based on the multiple exposure of a quadriwave lateral shearing interferometer (QWLSI) is presented. The theoretical analysis and simulation of the influence of the information in the small signal area on the calculation of the M2 factor is provided. The experimental results demonstrate that the new method can be an accurate means to measure the M2 factor. The proposed method can avoid the influence of phase inaccuracy in the small signal area of the interferogram, during the measurement of the M2 factor.

Systematic error analysis and correction in quadriwave lateral shearing interferometer

To obtain high-precision and high-resolution measurement of dynamic wavefront, the systematic error of the quadriwave lateral shearing interferometer (QWLSI) is analyzed and corrected. The interferometer combines a chessboard grating with an order selection mask to select four replicas of the wavefront under test. A collimating lens is introduced to collimate the replicas, which not only eliminates the coma induced by the shear between each two replicas, but also avoids the astigmatism and defocus caused by CCD tilt. Besides, this configuration permits the shear amount to vary from zero, which benefits calibrating the systematic errors. A practical transmitted wavefront was measured by the QWLSI with different shear amounts. The systematic errors of reconstructed wavefronts are well suppressed. The standard deviation of root mean square is 0.8 nm, which verifies the stability and reliability of QWLSI for dynamic wavefront measurement.

Quantitative retardance imaging of biological samples using quadriwave lateral shearing interferometry.

We describe a new technique based on the use of a high-resolution quadri-wave lateral shearing interferometer to perform quantitative linear retardance and birefringence measurements on biological samples. The system combines quantitative phase images with varying polarization excitation to create retardance images. This technique is compatible with living samples and gives information about the local retardance and structure of their anisotropic components. We applied our approach to collagen fibers leading to a birefringence value of (3.4 ± 0.3) · 10(-3) and to living cells, showing that cytoskeleton can be imaged label-free.

Quadriwave lateral shearing interferometer based on a randomly encoded hybrid grating.

A compact quadriwave lateral shearing interferometer (QWLSI) with strong adaptability and high precision is proposed based on a novel randomly encoded hybrid grating (REHG). By performing the inverse Fourier transform of the desired ±1 Fraunhofer diffraction orders, the amplitude and phase distributions of the ideally calculated quadriwave grating can be obtained. Then a phase chessboard is introduced to generate the same phase distribution, while the amplitude distribution can be achieved using the randomly encoding method by quantizing the radiant flux on the ideal quadriwave grating. As the Faunhofer diffraction of the REHG only contains the ±1 orders, no order selection mask is ever needed for the REHG-LSI. The simulations and the experiments show that the REHG-LSI exhibits strong adaptability, nice repeatability, and high precision.

Enhanced 3D spatial resolution in quantitative phase microscopy using spatially incoherent illumination

We describe the use of spatially incoherent illumination to make quantitative phase imaging of a semi-transparent sample, even out of the paraxial approximation. The image volume electromagnetic field is collected by scanning the image planes with a quadriwave lateral shearing interferometer, while the sample is spatially incoherently illuminated. In comparison to coherent quantitative phase measurements, incoherent illumination enriches the 3D collected spatial frequencies leading to 3D resolution increase (up to a factor 2). The image contrast loss introduced by the incoherent illumination is simulated and used to compensate the measurements. This restores the quantitative value of phase and intensity. Experimental contrast loss compensation and 3D resolution increase is presented using polystyrene and TiO(2) micro-beads. Our approach will be useful to make diffraction tomography reconstruction with a simplified setup.

Wide-field vibrational phase imaging in an extremely folded box-CARS geometry

We present a method that allows one to measure the real and imaginary parts of the third-order susceptibility in a wide-field coherent anti-Stokes Raman scattering setup using a quadriwave lateral shearing interferometer. This permits the retrieval of the undistorted Raman spectrum and the removal of a nonresonant signal from the surrounding solvent, which otherwise may overwhelm weak resonances.

Optical detection and measurement of living cell morphometric features with single-shot quantitative phase microscopy

We present a quadriwave lateral shearing interferometer used as a wavefront sensor and mounted on a commercial non-modified transmission white-light microscope as a quantitative phase imaging technique. The setup is designed to simultaneously make measurements with both quantitative transmission phase and fluorescence modes: phase enables enhanced contrasted visualization of the cell structure including intracellular organelles, while fluorescence allows a complete and precise identification of each component. After the characterization of the phase measurement reliability and sensitivity on calibrated samples, we use these two imaging modes to measure the characteristic optical path difference between subcellular elements (mitochondria, actin fibers, and vesicles) and cell medium, and demonstrate that phase-only information should be sufficient to identify some organelles without any labeling, like lysosomes. Proof of principle results show that the technique could be used either as a qualitative tool for the control of cells before an experiment, or for quantitative studies on morphology, behavior, and dynamics of cells or cellular components.

Modeling quantitative phase image formation under tilted illuminations

A generalized product-of-convolution model for simulation of quantitative phase microscopy of thick heterogeneous specimen under tilted plane-wave illumination is presented. Actual simulations are checked against a much more time-consuming commercial finite-difference time-domain method. Then modeled data are compared with experimental measurements that were made with a quadriwave lateral shearing interferometer.

Quadriwave lateral shearing interferometry in an achromatic and continuously self-imaging regime for future x-ray phase imaging

We present in this Letter a type of quadriwave lateral shearing interferometer for x-ray phase imaging. This device is based on a phase chessboard, and we take advantage of the large spectrum of the source to produce interferograms with a propagation-invariant contrast. Such a grating has been created for hard x-ray interferometry and experimentally tested on a synchrotron beamline at Soleil.

Collective phase measurement of an array of fiber lasers by quadriwave lateral shearing interferometry for coherent beam combining

We present a new configuration of quadriwave lateral shearing interferometer dedicated to phase detection for beam-combining purposes. Assuming that the fibers are disposed in a matrix arrangement, our scheme gives direct access to the phase step between adjacent fibers in two dimensions. Experimentally recorded interferograms are made only of two-wave interference fringes that scroll as the phase evolves in the fibers. This simplicity allows fast treatment by the spatial demodulation process, and the phase map from the fibers can be estimated in real time. No external reference is required, and the technique is fully compatible with a high number of fibers.

Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells

Phase imaging with a high-resolution wavefront sensor is considered. This is based on a quadriwave lateral shearing interferometer mounted on a non-modified transmission white-light microscope. The measurement technology is explained both in the scope of wave optics and geometrical optics in order to discuss its implementation on a conventional microscope. In particular we consider the effect of a non spatially coherent source on the phase-image signal-to-noise ratio. Precise measurements of the phase-shift introduced by microscopic beads or giant unilamellar vesicles validate the principle and show the accuracy of the methods. Diffraction limited images of living COS-7 cells are then presented, with a particular focus on the membrane and organelle dynamics.

In situoptical testing of infrared lenses for high-performance cameras

We propose to evaluate infrared lenses with a dedicated analyzer having the same mechanical interface as the usual cameras. The proposed analysis is based on a wavefront measurement and allows a diagnostic of possible internal defects of the analyzed lens. The infrared lens analyzer described is constituted with a quadriwave lateral shearing interferometer and works with a blackbody light. We describe the response of this interferometer and an innovative method to obtain the wavefront under test. We finally present the experimental analysis of long-wavelength infrared lenses and the particular case of a modified lens that generates a large spherical aberration.

Two-color multi-wave lateral shearing interferometry for segmented wave-front measurements

The possibility to measure segmented wave-front thanks to lateral shearing interferometry using diffraction grating is presented and analyzed. Aside from the response of such technique, the dynamic range is evaluated and shown to be limited. To greatly extend this one, a new method based on the use of two colors, not necessarily monochromatic, combined with an innovative Fourier treatment, is proposed. The two-color proposed in this paper is a high dynamic and low sensitivity technique; it can be completed by a one-color analysis, with low dynamics and high sensitivity, to reach high precision measurements. The ability of this method to measure Keck-like wave-front is demonstrated thanks to a computational analysis. Finally, a first experimental measurement of an etched substrate by using a quadri-wave lateral shearing interferometer is detailed.