Lateral Shearing Interferometry Research Articles

Calibration Method to Eliminate Zeroth Order Effect in Lateral Shearing Interferometry

In this paper, a calibration method is proposed which eliminates the zeroth order effect in lateral shearing interferometry. An analytical expression of the calibration error function is deduced, and the relationship between the phase-restoration error and calibration error is established. The analytical results show that the phase-restoration error introduced by the calibration error is proportional to the phase shifting error and zeroth order effect. The calibration method is verified using simulations and experiments. The simulation results show that the phase-restoration error is approximately proportional to the phase shift error and zeroth order effect, when the phase shifting error is less than 2° and the zeroth order effect is less than 0.2. The experimental result shows that compared with the conventional method with 9-frame interferograms, the calibration method with 5-frame interferograms achieves nearly the same restoration accuracy.

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.

Two dimensional wavefront retrieval using lateral shearing interferometry

A new zonal two-dimensional method for wavefront retrieval from a surface under test using lateral shearing interferometry is presented. A modified Saunders method and phase shifting techniques are combined to generate a method for wavefront reconstruction. The result is a wavefront with an error below 0.7λ and without any global high frequency filtering. A zonal analysis over square cells along the surfaces is made, obtaining a polynomial expression for the wavefront deformations over each cell. The main advantage of this method over previously published methods is that a global filtering of high spatial frequencies is not present. Thus, a global smoothing of the wavefront deformations is avoided, allowing the detection of deformations with relatively small extensions, that is, with high spatial frequencies. Additionally, local curvature and low order aberration coefficients are obtained in each cell.

Thermal residual stress evaluation based on phase-shift lateral shearing interferometry

An interesting phase-shift lateral shearing interferometry system was proposed to evaluate the thermal residual stress distribution in transparent specimen. The phase-shift interferograms was generated by moving a parallel plane plate. Based on analyzing the fringes deflected by deformation and refractive index change, the stress distribution can be obtained. To verify the validity of the proposed method, a typical experiment was elaborately designed to determine thermal residual stresses of a transparent PMMA plate subjected to the flame of a lighter. The sum of in-plane stress distribution was demonstrated. The experimental data were compared with values measured by digital gradient sensing method. Comparison of the results reveals the effectiveness and feasibility of the proposed method.

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 binary gas diffusion coefficients using large lateral shearing interferometry

A measurement system consisting of a large lateral shearing interferometry and an experimental setup which can be used under high pressures (pressure ≤ 10 MPa) has been built up to measure the binary gas diffusion coefficients. Fringe pattern in the large lateral shearing interferometry can be as simple as the holographic interferometry. The preliminary experimental results of the diffusion coefficients of CO2 and CH4 in O2 near room temperature and atmospheric pressure have been obtained. Comparison of the experimental results with the data calculated by the Fuller correction and the formulas of Landolt-Börnstein database shows that our measured results are accurate and credible. The experimental system used in this study is suitable for the measurement of the gas diffusion coefficients under high pressures which have not been thoroughly experimental studied.

Optical Imaging and Characterization of Graphene and Other 2D Materials Using Quantitative Phase Microscopy

This article introduces an optical microscopy technique for the characterization of two-dimensional (2D) materials. The technique is based on the use of quadriwave lateral shearing interferometry (QLSI), a quantitative phase imaging technique that allows the imaging of both the intensity and the phase of an incoming light beam. The article shows how QLSI can be used to (i) image 2D materials with high contrast on transparent substrates, (ii) detect the presence of residues coming from the fabrication process, and (iii) map the 2D complex optical conductivity and complex refractive index by processing the intensity and phase images of a light beam crossing the 2D material of interest. To illustrate the versatility of this approach for 2D material imaging and characterization, measurements have been performed on graphene and MoS2.

Post-blink tear film dynamics in healthy and dry eyes during spontaneous blinking

PurposeThe aim was to investigate the dynamics of post-blink tear film leveling in natural blinking conditions (NBC) for healthy subjects and those diagnosed with dry eye syndrome (DES) and to relate this phase to the tear film surface quality (TFSQ) before the following blink. MethodsThe study included 19 healthy persons and 10 with dry eye, grouped according to symptoms and signs observed during examination. Lateral shearing interferometry was used to examine TFSQ. Post-blink tear film dynamics was modeled by an exponential function, characterized by the decay parameter b, and a constant, describing the level of the stabilized TFSQ. Pre-next-natural-blink TFSQ dynamics was modeled with a linear trend, described by a parameter A. ResultsThe post-blink tear film dynamics reached its plateau at a significantly (P = 0.006) lower level in the normal tear film group than in the dry eye group. The median exponential decay parameter b was statistically significantly higher for the control group than for the DES group, P = 0.026. The parameter b calculated for each interblink interval was significantly correlated with the corresponding parameter A (Spearman's R = 0.35; P < 0.001). Correlation between the median b and tear film fluorescein break-up time for each subject was also found (R = 0.41, P = 0.029). ConclusionsSignificantly faster leveling of post-natural-blink tear film was observed in the group with DES than in healthy eyes. This dynamic was correlated with the pre-next-natural-blink TFSQ and tear film stability. The results of this pilot study support previous works that advocate the importance of polar lipids in the mechanism of tear film lipid spreading.

Shape measurement with modified phase-shift lateral shearing interferometry illumination and radial basis function.

Three-dimensional shapes of objects were evaluated with modified phase-shift lateral shearing interferometry illumination and radial basis function. A simple optical system was developed to create the fringe pattern based on the Murty interferometer. The phase shift was generated only by moving a plane-parallel plate along an in-plane parallel direction. A novel moving radial basis function method was presented to improve the quality of fringe patterns. And the proper calculation window size was given based on numerical simulation. Three-dimensional shapes of two kinds of objects were determined to verify the feasibility and effectiveness of the proposed method, and the reconstructed height distributions were in good accordance with the referenced data.

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

In quadri-wave lateral shearing interferometry (QWLSI), when the intensity distribution of the incident light wave is non-uniform, part of the information of the intensity distribution will couple with the wavefront derivatives to cause wavefront reconstruction errors. In this paper, we propose two algorithms to reduce the influence of a non-uniform intensity distribution on wavefront reconstruction. Our simulation results demonstrate that the reconstructed amplitude distribution (RAD) algorithm can effectively reduce the influence of the intensity distribution on the wavefront reconstruction and that the collected amplitude distribution (CAD) algorithm can almost eliminate it.

Review of self-referenced measurement algorithms: Bridging lateral shearing interferometry and multi-probe error separation

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.

Method for improving measurement efficiency of lateral shearing interferometry

The computation time of wavefront reconstruction is decreased by sampling the difference fronts in the present study. The wavefront can be reconstructed with high accuracy up to 64 Zernike terms with only 32×32 sampled pixels. Furthermore, the computational efficiency can be improved by a factor of more than 1000, and the measurement efficiency of lateral shearing interferometry is improved. The influence of the terms used to reconstruct the wavefront, the grid size of the test wavefront, the shear ratio, and the random noise on the reconstruction accuracy is analyzed and compared, when the difference fronts are sampled with different grid sizes. Numerical simulations and experiments show that the relative reconstruction error is <5% if the grid size of the sampled difference fronts is more than four times the radial order of difference Zernike polynomials with a reasonable noise level and shear ratio.

Experimental investigation on gas-phase temperature of axisymmetric ethylene flames by large lateral shearing interferometry

The gas temperature fields of axisymmetric co-annular laminar diffusion ethylene flame jets in air and oxygen-enriched atmospheres were measured and visualized using large lateral shearing interferometry technique. Seven cases of reconstructed temperature fields were investigated using various compositions of fuel/oxidant with an average correction factor. The phase difference field were obtained using a fringe trace algorithm. A discrete Abel inversion process was adopted to resolve the refractive index distribution from the line-of-sight integrated data. The peak temperatures of the flame varied between 1980 K and 2050 K using air as the oxidant and increased to more than 2150 K when oxygen was added. Two separate high temperature zones, one located at the side edge of the flame, the other in the upper part of the flame around the centerline of the burner were observed in four of the seven instances of high mixture stoichiometry. The proposed methodology was verified to be suitable for the reconstruction of temperature distributions from the experimental measurement results.

Modal wavefront reconstruction based on Zernike polynomials for lateral shearing interferometry

The Zernike-polynomials-based modal reconstruction method is an important wavefront reconstruction method for lateral shearing interferometry. There are four typical Zernike-polynomial-based modal reconstruction methods: the Rimmer-Wyant method, the elliptical orthogonal transformation method, the numerical orthogonal transformation method (NOT), and the difference Zernike polynomial fitting method (DZF). In a previous paper [Appl. Opt. 51, 5028 (2012)], the overall performances of these four methods were comprehensively compared with each other. The conclusions showed that NOT and DZF have the highest reconstruction accuracies among these four methods. In addition, it was shown that the performance of NOT is identical to that of DZF; however, the reason behind this was not known until now, to our knowledge. In the present paper, we present a strictly mathematical proof for this highly significant result. (C) 2016 Optical Society of America

Single-shot 3 × 3 beam grating interferometry for self-imaging free extended range wave front sensing.

Crossed grating 3×3 beam lateral shear interferometry for extended range wave front sensing is presented. A Fresnel diffraction pattern of two multiplicatively superimposed linear diffraction gratings each generating three diffraction orders is recorded. A simple solution employs a common crossed binary amplitude Ronchi grating with spatial filtering. Digital processing of a single-shot pattern includes separating multidirectional pairs of orthogonal lateral shear interferograms, retrieving second harmonics of their intensity distribution, and calculating shearing phases. Single-frame automatic fringe pattern processing based on the Hilbert-Huang transform is used for this purpose. Using second harmonics extends the aberration measurement range since they encode self-imaging free two-beam interferograms without contrast modulations. Experimental works corroborate the principle and capabilities of the proposed approach.

Dual-wavelength common-path digital holographic microscopy for quantitative phase imaging based on lateral shearing interferometry.

A dual-wavelength common-path digital holographic microscopy based on a single parallel glass plate is presented to achieve quantitative phase imaging, which combines the dual-wavelength technique with lateral shearing interferometry. Two illumination laser beams with different wavelengths (λ1=532 nm and λ2=632.8 nm) are reflected by the front and back surfaces of the parallel glass plate to create the lateral shear and form the digital hologram, and then the hologram is reconstructed to obtain the phase distribution with a synthetic wavelength Λ=3339.8 nm. The experimental configuration is very compact, with the advantages of vibration resistance and measurement range extension. The experimental results of the laser-ablated pit, groove, and staircase specimens show the feasibility of the proposed configuration.

Zernike polynomials as a basis for modal fitting in lateral shearing interferometry: a discrete domain matrix transformation method.

A Zernike-polynomials-based wavefront reconstruction method for lateral shearing interferometry is proposed. Shear matrices are calculated using matrix transformation instead of mathematical derivation. Simulation results show that the shear matrices calculated using the proposed method are the same as those obtained from mathematical derivation. The advantage of the proposed method is that high order shear matrices can be obtained easily; thus, wavefront reconstruction can be extended to higher order Zernike terms, and reconstruction accuracy can be improved.

One-shot and aberration-tolerable homodyne detection for holographic storage readout through double-frequency grating-based lateral shearing interferometry.

A simple method to decode the stored phase signal of volume holographic data storage with adequate wave aberration tolerance is highly demanded. We proposed and demonstrated a one-shot scheme to decode a binary-phase encoding signal through double-frequency-grating based shearing interferometry (DFGSI). The lateral shearing amount is dependent on the focal length of the collimated lens and the frequency difference between the gratings. Diffracted waves with phase encoding were successfully decoded through experimentation. An optical model for the DFGSI was built to analyze phase-error induction and phase-difference control by shifting the double-frequency grating longitudinally and laterally, respectively. The optical model was demonstrated experimentally. Finally, a high aberration tolerance of the DFGSI was demonstrated using the optical model.

White-light quantitative phase imaging unit

We introduce the white-light quantitative phase imaging unit (WQPIU) as a practical realization of quantitative phase imaging (QPI) on standard microscope platforms. The WQPIU is a compact stand-alone unit which measures sample induced phase delay under white-light illumination. It does not require any modification of the microscope or additional accessories for its use. The principle of the WQPIU based on lateral shearing interferometry and phase shifting interferometry provides a cost-effective and user-friendly use of QPI. The validity and capacity of the presented method are demonstrated by measuring quantitative phase images of polystyrene beads, human red blood cells, HeLa cells and mouse white blood cells. With speckle-free imaging capability due to the use of white-light illumination, the WQPIU is expected to expand the scope of QPI in biological sciences as a powerful but simple imaging tool.

Exact two-dimensional zonal wavefront reconstruction with high spatial resolution in lateral shearing interferometry

A novel zonal method is proposed for exact discrete reconstruction of a two-dimensional wavefront with high spatial resolution for lateral shearing interferometry. Four difference wavefronts measured in the x and y shear directions are required. Each of the two shear directions is measured twice with different shear amounts. The shear amounts of the second measurements of the x and y directions are Sx+1 pixels and Sy+1 pixels, where Sx pixels and Sy pixels are the shear amounts of the first measurements in the x and y directions, respectively. The shear amount in each direction can be chosen freely, provided that it is below a maximum value determined by the pupil shape and the number of samples N in that direction; thus, the choices are not limited by the more stringent condition required by previous methods, namely, that the shear amounts must be divisors of N. This method can exactly reconstruct any wavefront at evaluation points up to an arbitrary constant if the data is noiseless, and high spatial resolution can be achieved even with large shear amounts. The method is applicable not only to square pupils, but also to general pupil shapes if a sufficient number of Gerchberg iterations are employed. In this study, the validity and capability of the method were confirmed by numerical experiments. In addition, the experiments demonstrated that the method is stable with respect to noise in the difference wavefronts.