Lateral Shearing Interferometer Research Articles

Distortion measurement of a lithography projection lens based on multichannel grating lateral shearing interferometry.

The optical distortion of the lithographic projection lens can reduce imaging quality and cause overlay errors in lithography, thus preventing the miniaturization of printed patterns. In this paper, we propose a technique to measure the optical distortion of a lithographic projection lens by sensing the wavefront aberrations of the lens. A multichannel dual-grating lateral shearing interferometer is used to measure the wavefront aberrations at several field points in the pupil plane simultaneously. Then, the distortion at these field points is derived according to the proportional relationship between the Z 2 and Z 3 Zernike terms (the tilt terms) and the image position shifts. Without the need for additional devices, our approach can simultaneously retrieve both the wavefront aberrations and the image distortion information. Consequently, it improves not only measurement speed and accuracy but also enables accounting for displacement stage positioning error. Experiments were conducted on a lithographic projection lens with a numerical aperture of 0.57 to verify the feasibility of the proposed method.

Polarization singularity index determination using wedge plate lateral shear interferometry

Polarization singularity is a point in an inhomogeneous polarization distribution at which the azimuth of the polarization ellipse is indeterminate. The azimuth gradient is solenoidal around the polarization singular point. In metrology, shear interferometry enables the visualization of phase gradients in optical beams. Since the polarization azimuth gradient is related to the Stokes phase gradient, we adopt the shear interferometry technique to visualize these phase gradients for the detection of polarization singularity. We use a wedge plate lateral shear interferometer (LSI) in our experiments for the detection of the ellipse and vector field singularities. Being a self-referencing and intensity-based technique, this method is convenient for practical use. Unlike the traditional Stokes polarimetry method, where the polarization distribution at every spatial point is evaluated, this technique can distinguish degenerate states of polarization singularities simply by visual observation of intensity fringes. Index and helicity measurement of these polarization singularities without using polarization measurement methods are novel aspects of this scheme. Both theoretical and experimental results are presented to support our claim.

Wavefront restoration from lateral shearing data using spectral interpolation.

Although a lateral-shear interferometer is robust against optical component vibrations, its interferogram provides information about differential wavefronts rather than the wavefronts themselves, resulting in the loss of specific frequency components. Previous studies have addressed this limitation by measuring four interferograms with different shear amounts to accurately restore the two-dimensional wavefront. This study proposes a technique that employs spectral interpolation to reduce the number of required interferograms. The proposed approach introduces an origin-shift technique for accurate spectral interpolation, which in turn is implemented by combining two methods: natural extension and least-squares determination of ambiguities in uniform biases. Numerical simulations confirmed that the proposed method accurately restored a two-dimensional wavefront from just two interferograms, thereby indicating its potential to address the limitations of the lateral-shear interferometer.

Polarizing white light interferometry for phase measurements using two simultaneous interferograms.

Our research introduces a design for a polarization phase-shifting white light interferometric system (PPS-WLIS) that operates in a transmissive mode for measuring the slope phase of transparent objects. It comprises a cyclic path interferometer (lateral shear interferometer) coupled with a multiplexing Michelson interferometer. The system uses polarization to produce two parallel interferograms with polarization modulated with relative shifts simultaneously. To determine the optical phase, we used a two-step algorithm for phase demodulation that does not necessitate precise phase shifts, making the system more straightforward to operate. As a result, we could observe variations in the object associated with optical phase changes. Furthermore, our method simplifies the phase-shift interferometry process by requiring only one capture, making it an effective way to examine objects at dynamic events. As an illustration, we demonstrated the temperature measurement generated by a section of a candle flame.

The efficacy of ocular surface assessment approaches in evaluating dry eye treatment with artificial tears

This study evaluates the effectiveness of objective techniques in assessing dry eye disease (DED) treatment compared with the subjective assessment commonly used in clinical practice. Thirty subjects were recruited for two visits separated by 28(± 3) days of treatment with artificial tears. A buttery of common subjective assessment methods were accompanied by a set of objective techniques including measurement of noninvasive tear film break-up time (NIBUT), lipid layer thickness (LLT), and quantitative evaluation of tear film surface quality and dynamics (TFD). Additionally, meibography was performed. Two commercially available videokeratoscopes and a prototype of a lateral shearing interferometer were used for the measurements. Both subjective and objective techniques showed a positive effect of artificial tears in DED treatment. Statistically significant improvements were observed in subjective symptoms (from P < 0.001 for Ocular Surface Disease Index, OSDI to p = 0.019 for tearing), conjunctival redness (P = 0.022), ocular staining (P = 0.012), fluorescein tear film break-up time (P = 0.015), NIBUT (P = 0.037), LLT (P < 0.001), and TFD (P = 0.048). In general, weak or statistically insignificant correlations were observed between subjective and objective assessment methods. The apparent lack of correlation between these methods might indicate the complementary character of objective techniques that likely assess other characteristics of ocular surface health than those assessed subjectively.

Generation of Stokes singularities using polarization lateral shear interferometer.

Lateral shear interferometer, being a self-referenced interferometer, has proven to be an important tool in scalar optics. Here we employ a vectorial counterpart - polarization lateral shear interferometer, in which the two interfering beams apart from being derived from the test wavefront, are in orthogonal states of polarization. Therefore when the test wavefront has spatially varying phase gradient across the beam cross-section, the resulting shearogram produces polarization fringes instead of intensity fringes. Further, the shearogram becomes inhomogeneously polarized. This polarization lateral shear interferometer may have potential uses in metrology, but in this article we demonstrate the ability of the interferometer in the generation of all Stokes singularities in the single beam by launching a phase singular beam into it. It is found that a vortex dipole is formed along with other generic Stokes singularities. Experimental observations support the results and they are discussed in the article.

파면 분석을 위한 편광 격자 기반 층밀림 간섭계

In this investigation, we propose a simple and effective lateral shearing interferometer based on a polarization grating. In the lateral shearing device, an incident beam is split into two beams by a polarization grating, and the returning beams can be laterally shifted after reflecting off a flat mirror and passing through the polarization grating again. These two beams are not only laterally shifted, but also their polarization states are orthogonal to each other as circular polarizations. With a single image obtained by a pixelated polarization CMOS camera, the proposed LSI can obtain the phase map corresponding to the x-sheared interferogram, and the other phase map can be calculated from another single image obtained by 90° rotation of the shearing device. Then, the original wavefront corresponding to the surface figure of the specimen can be reconstructed by wavefront reconstruction algorithms. In the experiments, various wavefronts generated by concave mirrors and a deformable mirror were measured and compared with those of a commercial Shack-Hartmann sensor.

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.

Generation and evolution of vortex array with variable-ratio lateral-shearing interferometry

Different from the method by plane-wave interference, here an efficient approach is proposed to generate optical vortex array (VA) based on lateral-shearing interferometer, in which the evolution from light spot array to VA can be observed by continuously variable shear ratio in a certain range. VAs with topological charge 2 and 1 are simulated by software GLAD and proved to be effectiveness through optical experiment. Theoretical analysis and experimental results show that when the shear ratio approaches to zero, we can stably obtain a VA with high density and variable topological charge.

Surface form error measurement for rough surfaces using an infrared lateral shearing interferometry

The fabrication of a large monolithic mirror or a segmented mirror requires a high throughput that satisfies the time-cost requirement. Particularly, the rough surface properties of grinding pose a challenge for accurate measurement of the surface figure error (SFE). If the SFE during grinding is as small as possible, the material removal volume in the figuring process gets reduced, and the total required time of the fabrication is greatly minimized. In this paper, we propose a new metrology tool called intermediate surface figure error measurement (ISFEM) that can be applied to measurement of SFE for rough surfaces. It consists of a CO2 laser of wavelength 10.6 µm as a light source, a lateral shearing interferometer as a wavefront sensor, and several optical components for beam shaping and imaging. The ISFEM demonstrated its ability to measure the microns to sub-micron rms SFE of the ground surface by testing the samples with a 0.59 µm -1.56 µm rms of surface roughness and a large SFE of about 3 µm rms. The system was applied to the fabrication of an off-axis parabolic mirror of diameter 1.1 m, where it successfully performed as an intermediate metrology between laser tracker measurement for the rough surface and interferometric measurement for the polished surface. The ISFEM obtained measurements from 3.88 µm rms SFE during the fine grinding process and down to 0.38 µm rms during the polishing process. Therefore, we confirmed that the ISFEM provides a unique solution for high throughput for the fabrication of large or multiple segmented mirrors.

Ultraestable spatiotemporal characterization of optical vortices in the visible and near infrared

We show the versatility of the bulk lateral shearing interferometer characterizing complex spatiotemporal structures in different spectral ranges. Specifically, we have characterized constant and timevarying optical vortices in the visible and near infrared spectral ranges respectively. The high stability of the system combined with its spectral versatility will ease the spatiotemporal characterization of ultrafast phenomena.

5D-fusion sensing via interference illumination and polarization imaging.

This study proposes a polychromatic interferometric illumination and polarimetric sensor-based imaging method for spectrum, polarization, and 3D shape, which are significant physical parameters of feature analysis for target detection. 5D-fusion sensing refers to the joint detection and fusion of the above 5D information, which is currently a great challenge. The method generates a polychromatic interference pattern using a Sagnac lateral shearing interferometer and projects it to the target. Then, interferograms modulated by the target are acquired during scanning. Fast Fourier transform (FFT) is performed on the interferograms to obtain their frequency spectra. The spectral and polarization information is extracted from the moduli of the frequency spectra. The 3D shape is recovered from the phase of the frequency spectra using the calibration data. The theory of 5D-fusion sensing is investigated, and verification experiments are then performed. The experiments indicate that the proposed method can fulfill 5D-fusion sensing in one scanning and with FFT using only one device compared with other separate methods. Consequently, the proposed method can improve the sensing and recognition ability of optical imaging technology, which provides great application potential in biomedicine, food safety, material analysis, criminal investigation, archeology, and other fields.

Retrieval of Phase and Temperature Distributions in Axisymmetric Flames From Phase-Modulated Large Lateral Shearing Interferogram

A precise phase modulation and demodulation method was proposed to retrieve temperature distributions in axisymmetric flames by using a single-wavelength large lateral shearing interferometer. A spatial light modulator (SLM) was employed to vary the phases in each pixel continuously in the flame-phase measurement. The uniqueness of the phase extraction was mathematically proved for the first time, and a least square method was applied to recover the profile of flame phase in the interferometer. The ambiguity of the phases at different cycles of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\pi $ </tex-math></inline-formula> was eliminated. The phase shift at each pixel was uniquely determined and verified by using simulated data. Further, precise-phase distributions were utilized to retrieve the temperature distribution in a laminar flame. In actual experiments, four axisymmetric laminar flames from diffused to premixed flames were generated by using a Bunsen burner. Profiles of temperature distribution in the flames were extracted and agreed well with the results scanned by using a thermocouple. With the increase of airflow rate, the position of high-temperature zone was observed moving down, and the thermal structure of the premixed flame became more and more obvious. The preheating zone, reaction front, and reaction zone inside the flames were clearly captured.

Collimation testing of laser beams having different diameters using compact holographic lateral shearing interferometer (Erratum)

A quick and accurate way for testing collimation of laser beams is desired to achieve correct results in many optical instruments. Laser beam collimation is generally performed using glass wedge plates. For better accuracy, a set of wedge plates of different thicknesses and wedge angles are required to acquire first-hand visual information about collimation of laser beams having a wide range of diameters. Use of a compact holographic lateral shearing interferometer (HLSI) is demonstrated for collimation testing of laser beams having different beam diameters. The interferometer uses two holographic optical elements (HOEs) with provision of variable tilt in one of the HOEs to maintain a constant number of fringes in the interferograms for different diameters of input test beams. An angle of rotation of interference fringes from a reference position is measured to be 0.9 deg for a test beam of diameter 2 mm and 16 deg for the test beam of diameter 35 mm. We experimentally demonstrated range of optimum number of interference fringes in the interferogram for visual inspection of the collimation state of the test beam. Thus the proposed interferometer could replace a set of wedge plates generally required for collimation testing of beams having different diameters. The functioning of the interferometer for collimation testing of beams having different diameters is discussed and experimentally demonstrated.

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.

Optimal modified lateral shearing interferometer with axial range extension by using a dual optical plate.

We present a method to extend the axial range of digital holographic microscopy based on the optimal modified lateral shearing interferometer (MLSI). The proposed system can extend the axial range by using a dual optical plate. The interference pattern with two spatial wavelengths is generated by the plate with different thicknesses. These spatial wavelengths transfer a dual spatial frequency into the Fourier plane by using FFT. Two phases are extracted by a dual spatial frequency and combined to create a synthetic wavelength, which is applied to measure the micrometer-scale object without phase unwrapping. Also, the noise-reducing algorithm is used to reduce phase noise caused by the amplified noise of the synthetic wavelength. The experimental result confirms the feasibility of the optimal MLSI by using a dual optical plate.

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.

Snapshot phase-shifting lateral shearing interferometer

We propose a novel, low-cost snapshot phase-shifting lateral shearing interferometer (SPLSI) with full-range continuously adjustable lateral shear ratio. A tunable shear plate, consisting of a polarizing beam splitter (PBS) plate and a reflective mirror, separates the orthogonally polarization states of the test wavefront into original and sheared wavefronts. The lateral shear ratio can be tuned by adjusting the spacing between PBS plate and the mirror. A pixelated polarization camera simultaneously captures four π/2 phase-shifted interferograms for phase-shifting interferometric measurement. In addition to tunable shear ratio and snapshot capture of phase-shifted interferograms, one more key feature is that SPLSI can measure the wavefront of low-coherence light. The feasibility of the proposed system is demonstrated experimentally. The proposed system provides a simple, compact, and fast way to achieve the instantaneous phase-shifting lateral shearing interferometric testing of wavefronts with minimal impact from environmental disturbance.

平行平板横向剪切干涉仪装调误差的矫正方法研究

平行平板横向剪切干涉仪装调误差的矫正方法研究

Double-wedge Sagnac lateral shearing interferometer for measuring the upper atmospheric wind field

The double-wedge Sagnac lateral shearing interferometer was put forward as a novel device for the upper atmospheric wind field measurement, and its shearing principle was presented. Using the geometrical optics, the exact expression of the optical path difference (OPD) within the range of the whole field was calculated when the incident ray with arbitrary directions arrived at the incoming plane. In order to analyze and discuss the influences of different parameters on the OPD, the computer simulations were performed for two moveable directions (the hypotenuse and right angle side) of the moving wedge prism. The OPD of the double-wedge Sagnac lateral shearing interferometer was changed by the moving wedge prism, which could enlarge the field of view be as much as possible for a specific OPD. These works provided an important theoretical guidance for improving the detecting precision of the upper atmospheric wind field, and had great practical value for the development of the double-wedge Sagnac lateral shearing interferometer apparatus.