The measurement accuracy of a point diffraction interferometer is influenced by the quality of the diffraction wavefront generated by a nanometer-scale pinhole. This paper analyzes the diffraction process of a pinhole illuminated by deep ultraviolet converging light with a large numerical aperture (NA) based on vector diffraction theory. Key metrics, including the diffraction NA and the wavefront aberrations relative to an ideal spherical wavefront, are examined in relation to the polarization state, pinhole diameter, and Cr thickness. Additionally, the impact of alignment errors is investigated. The results indicate that for a converging beam with and , the optimal polarization state is linear polarization, and the diffraction wavefront most closely approximates an ideal spherical wavefront when the pinhole diameter is 200nm and the Cr thickness is 100nm. Alignment errors alter the magnitude of the original central-symmetric aberration components and introduce asymmetric components such as coma.

In the construction of the pinhole point diffraction interferometer, the alignment error between the convergent spot of the microscopic objective lens and the diffraction hole in the front end of the pinhole diffraction will lead to problems such as diffraction wavefront error, diffraction intensity reduction, and interference fringe contrast reduction, which will affect the actual measurement accuracy. In order to solve the problem of inaccurate alignment between the convergent spot of the microscopic objective lens and the diffraction hole, a diffraction hole visual alignment method based on the auxiliary optical path is proposed in this work. An auxiliary alignment optical path is built at the front end of the pinhole diffraction, and the beam reflected by the pinhole diffraction plate is mainly reflected by the beam splitter prism, and then received by a charge coupled device (CCD). By collecting and processing the spot image reflected by the small hole diffraction plate, the alignment state of the small hole is monitored and the alignment error is calculated. In this work, a visual-precision optical path alignment scheme is designed, and the visual performance of the alignment image under three typical alignment deviations of translation, tilt and defocus is simulated and analyzed. The mathematical model of the object-image relationship between the alignment image and the alignment error is constructed, and the alignment image error measurement and processing algorithm is studied. The experimental results show that the auxiliary optical path alignment method and the alignment image processing algorithm proposed in this work are feasible, and the alignment accuracy can reach 0.05 μm. The research results are helpful in improving the alignment efficiency and accuracy of point diffraction interferometer, and can lay a certain technical foundation for the development of practical point diffraction interferometer.

This work describes the development and testing of a diagnostic technique, based on a robust setup named Point Diffraction Interferometer, to characterize the wavefronts generated by metalenses. The presented optical setup is simple, cheap and insensitive to mechanical disturbances, nevertheless precisely capable to reconstruct the radiation wavefront produced by a metalens. The obtained interference patterns exhibit suitable contrast ratio of the fringes and high spatial resolution, thus allowing the detection of even highly distorted wavefronts, and providing a measurable information about the metalens properties.

In the pinhole point diffraction interferometer (PPDI), proper alignment between the reflection spot of the tested component and the pinhole is critical to obtain accurate interferograms. At present, adjusting for tilt error requires manual manipulation, and defocus error cannot be corrected. These limitations impede the instrumentation process of PPDI. To address this issue, the proposed tested mirror alignment system utilizes diffraction theory to analyze the mathematical error caused by the misalignment of the tested mirror's reflected beam and pinhole. An alignment system based on machine vision was designed according to specific requirements. This system incorporates a CCD camera with a zoom lens, the classic PPDI with a pinhole substrate containing a lithography-made mark, and a 3-DOF stepper motor adjusting frame to mount the tested mirror. Additionally, image processing algorithms and step motor driving programs were applied to achieve precise alignment. The system implementation and experimental results indicated that the tilt errors are well-controlled, achieving the defocus error modification, making the interferogram acquisition process more convenient. From the results, this system offers desirable precision and efficiency for PPDI's tested mirror alignment.

The pinhole plate is a key component of the point diffraction interferometer (PDI). The reasonable improvement and simulation of this device would enhance the application of point diffraction interferometry technology during the measurement of wavefronts. The traditional point diffraction interferometry measurement method is easily disturbed by environmental noise, making it difficult to obtain high-precision dynamic measurements. This paper introduces a four-step phase-shift PDI that can be employed in a common optical path. By using the principle of the finite-difference time-domain method (FDTD), a simulation model of the orthogonal polarization point diffraction pinhole plate (OP-PDPP) structure is established. The results show that when Cr is used as the film material in the pinhole plate, the parameters include a film thickness of 150 nm, a pinhole diameter of 2 μm, a wire grid period of 150 nm, and a wire grid width of 100 nm; in addition, the comprehensive extinction ratio of the pinhole plate is the greatest and the diffraction wavefront error is the smallest. Finally, the constructed experimental system is used to test the wavefront of a flat sample with a 25.4 mm aperture, and the test results are compared with those of the ZYGO interferometer. The difference in the peak-to-valley (PV) value between the OP-PDI and the ZYGO interferometer measurement is 0.0028λ, with an RMS value difference of 0.0011λ; this verifies the feasibility of the scheme proposed in this paper. The experimental results show that the proposed OP-PDPP is an effective tool for high-precision dynamic measurement.

A single shot point-diffraction interferometer (PDI) is proposed in this paper, in which the object beam is split into two copies by means of a beamsplitting module consisting of one plate beamsplitter and one mirror. One of the reflected beams is spatially filtered as a reference beam by one pinhole array in the spectral plane. The split two beams share almost the same path, and by adjusting the inclined angle of the plate beamsplitter, the carrier frequency and legibility of the interferogram can be modulated easily. Moreover, the contrast of the interferogram can be adjusted by changing different plate beamsplitters. Compared to conventional common path off-axis interferometers, this PDI has a simple optical setup, easy optical implementation and outstanding measurement ability with high precision, measurement efficiency and stability. Several experimental results will be provided to demonstrate the effectiveness of the proposed system.

The assessment of painting surfaces at the microscale has been historically impeded by challenges related to limited resolution and accuracy in traditional methodologies. This study pioneers the utilization of non-contact 3D optical scanning technology, meticulously calibrated for nanoscale precision, to unravel the intricate features residing on painting surfaces. The initial phase employs the Point Diffraction Interferometer (PDI) for 3D optical scanning, incorporating meticulously optimized parameters tailored to nanoscale analysis. Subsequent phases involve the application of Phase Shifting Interferometry (PSI) and Holographic Interferometry (HI). PSI is employed to discern morphological alterations, while HI captures the nuanced color and optical characteristics embedded in the painting surfaces. To enhance the continuity of phase information, the Goldstein algorithm is introduced during phase stitching, fortifying the method’s robustness against discontinuities. Further refinement is achieved through the Iterative Closest Point (ICP) algorithm, orchestrating precise 3D data reconstruction. This process encompasses multi-view stereo matching and surface fitting, ensuring a meticulous representation of the painting surface geometry. The study meticulously presents detailed 3D optical scanning results, probing into the painting surface’s performance concerning nanoscale resolution, measurement accuracy, and color consistency. The unveiled findings showcase a remarkable minimum feature capture capability of 1.8 at nanoscale resolution. The quantitative assessment, encapsulated by a Root Mean Square Error (RMSE) ranging from 0.001 to 0.012 for 100 scanned data points, and a Standard Deviation (STD) oscillating between 0.0008 to 0.0018, attests to the method’s efficacy. This effectiveness is underscored by its capacity to deliver a thorough and intricate analysis of painting surface performance at the nanoscale.

The direct imaging of extrasolar planets requires extreme adaptive optics (ExAO) in the near-infrared wavelengths. The ExAO needs a high-efficient wavefront sensor (WFS) to measure the phase aberration accurately with a small number of photons. In addition, the WFS in the ExAO is required to run at high sampling rates of 1 − 7 kHz. To meet these requirements, we developed the birefringent point-diffraction interferometer (b-PDI) presented in our earlier paper. We tested the b-PDI in the laboratory with a polychromatic light source with wavelengths of 800 ± 100 nm. The b-PDI showed a relatively high efficiency, comparable to that of a fixed pyramid WFS. The b-PDI has a low calculation cost and a small readout region, which are suitable for high-speed sampling at 6.5 kHz.

In this paper, a simultaneous phase-shifting point-diffraction interferometer (SPS-PDI) at632.8nm is designed with the assistance of an off-axis parabolic mirror (OAPM), through which the dynamic wavefront with 400mm aperture can be detected. In the system, a polarization point-diffraction plate (P-PDP) is developed to modulate the polarization states of the reference light and the test light through a simultaneous phase-shifting system based on a chessboard phase grating and a retarder array, and four phase-shifting interferograms can be acquired to realize dynamic detection. Furthermore, the circular carrier squeezing interferometry (CCSI) is proposed to suppress the phase errors generated by position mismatch, intensity distortion, and phase-shift error. The detection result of the SPS-PDI is consistent with the 4D PhaseCam6000 dynamic interferometer. The difference of the peak-to-valley (PV) and root-mean-square (RMS) values are only 0.04λ and 0.008λ. Additionally, the capacity to detect dynamic wavefront is good.

为了提高现有的三维坐标定位技术的测量精度、稳定性和测量效率，提出了基于深度学习的点衍射干涉三维坐标定位方法。该方法设计了一个深度神经网络用于点衍射干涉场的坐标重构，将相位差矩阵作为输入，构建训练数据集，将点衍射源坐标作为输出，训练神经网络模型。利用训练有素的神经网络对测量到的相位分布进行初步处理，将相位信息转换为点衍射源坐标，根据得到的点衍射源坐标进一步修改粒子群算法的初始粒子，进而重构出高精度的三维坐标值。该神经网络为建立干涉场相位分布与点衍射源坐标之间的非线性关系提供了一种可行的方法，显著提高了三维坐标定位的精度、稳定性和测量效率。为验证所提方法的可行性，进行了数值仿真和实验验证，采用不同的方法进行反复对比与分析。结果表明：所提方法的单次测量时间均在0.05 s左右，其实验精度能够达到亚微米量级，重复性实验的均值和RMS值分别为0.05 μm和0.05 μm，充分证明了该方法的可行性，并证明了其良好的测量精度和可重复性，为三维坐标定位提供了一种有效可行的方法。

Analysis of stagger effects on Busemann supersonic biplane airfoil in shock tube tests by point diffraction interferometer method

We report a phase-shifting method based on a pinhole point diffraction interferometer. Using the random two-frame phase-shifting algorithm, the piezo electric transducer (PZT) drives the pinhole moving a certain step length along the axis of the tested aspheric mirror. In each step, the CCD collects an interferogram. Then two interferograms are processed by the phase-shifting algorithm. After that, we can acquire the phase map of the interferograms. This technique has great potential for increasing the measuring aperture of the aspheric mirror in the pinhole point diffraction interferometer (PPDI) under the premise of keeping the advantages of PPDI of which the optic devices, as well as error sources, are few behind the substrate.

A point diffraction interferometer based on silicon nitride waveguide (WG-PDI), adopting a silicon nitride waveguide spherical wave source (WG-SWS) with Si substrate and SiO2 cladding, is proposed for spherical surface testing. The WG-SWS is used to overcome the drawbacks of the existing spherical wave sources, which can generate high accuracy and high numerical aperture spherical reference wave. In this paper, the theory of the WG-PDI is described, and the possible errors introduced by the device are analyzed. In addition, the lateral deviation between the curvature center of the test wave and the curvature center of the reference wave cannot be eliminated in the reflected configuration of the pinhole diffraction interferometer. After analyzing the influence of the systematic error introduced by the lateral deviation, the semi-reflective film was coated on the output facet of the waveguide spherical wave source to realize point diffraction interference without lateral deviation. Finally, the surface error of a spherical surface was measured by WG-PDI. The experimental results agree well with those measured by the ZYGO interferometer.

Abstract In this work, a Gaussian laser beam is propagated through a thermally turbulent region before passing through a point diffraction interferometer to produce a circular interferogram. This was done to ascertain how turbulent windstreams of various wind speeds and temperatures affect a laser beam when directed at different angles to the beam axis. The interferometric results portray a clear dependence on the angle of application. That is, deviations away from 90° result in increased wavefront fluctuations. The refractive index structure constant, Rytov variance, and Fried’s parameter were computed to quantify each turbulent model. The attributed strength regimes of these atmospheric parameters were in varying degrees of agreement with the interferometric data. These contradictions and resulting conclusions were discussed in full.

The direct detection and imaging of exoplanets requires the use of high-contrast adaptive optics (AO). In these systems quasi-static aberrations need to be highly corrected and calibrated. To achieve this, the pupil-modulated point-diffraction interferometer (m-PDI) was presented in an earlier paper. This present paper focuses on m-PDI concept validation through three experiments. First, the instrument's accuracy and dynamic range are characterized by measuring the spatial transfer function at all spatial frequencies and at different amplitudes. Then, using visible monochromatic light, an AO control loop is closed on the system's systematic bias to test for precision and completeness. In a central section of the pupil with 72% of the total radius, the residual error is 7.7 nm rms. Finally, the control loop is run using polychromatic light with a spectral FWHM of 77 nm around the R-band. The control loop shows no drop in performance with respect to the monochromatic case, reaching a final Strehl ratio larger than 0.7.

Proton acceleration obtained by focusing an ultraintense ultrafast laser beam presents the technological and metrological challenge of correctly placing diffuse metallic target at the focus of the laser beam. In this work we present the use of the Point diffractive interferometer for solving this problem. We studied the accuracy and precision of the system at repositioning the metallic target after displacing and horizontally tilting the target out of its reference position. We achieved an accuracy at repositioning the target at its reference position of 1.50 µm and 6 arcmin with a precision of 1.40 µm and 5.7 arcmin. Our work shows the high accuracy provided by a system as simple as the Point Diffraction interferometer even at positioning surfaces with diffuse reflection.

Magnification and distortion are two important parameters for high-precision imaging systems. Point diffraction interferometers (PDIs) can measure the magnification, distortion, and wavefront aberration of imaging systems with high precision. However, determining the precise pinhole alignment of the classical PDI is difficult. A new method for measurement of the magnification and distortion based on a dual-fiber point diffraction interferometer (DFPDI) is proposed. The end faces of two fibers are placed on the object plane of the optics under test and imaged to the image plane. The distance between the image points in the x and y directions are proportional to the Z2 and Z3 Zernike coefficients of the wavefront measurement result, respectively. The measurements of the image placement shift and precise alignment of the point diffraction pinhole are realized rapidly with high accuracy. The feasibility of the method is verified experimentally. The wavefront aberration, magnification, and distortion of a 5 × reduction lens with numerical aperture (NA) of 0.3 is measured jointly. The measurement uncertainties (3σ) of the magnification in the x and y directions and distortion are 756 ppm, 793 ppm, and 0.233 μm, respectively. Error analysis shows that the position error of the object- and image-plane stages is the main error source. An improved measurement scheme with a pinhole–pinhole pairs array in the object plane and a pinhole–window pairs array in the image plane is proposed. The influence of the position errors of the stages is eliminated with optimized measurement procedure. The DFPDI’s measurement repeatability (3σ) of the Z2 and Z3 coefficients is 0.65 and 0.33 nm, respectively, corresponding measurement uncertainties (3σ) of the magnification (in the x and y directions) and distortion can reach 1.88 ppm, 1.69 ppm, and 0.812 nm, respectively.

In this study, we proposed a point diffraction interferometer based on birefringence polarization beam splitting (BPBS-PDI) for transmission wavefront measurements. Using the polarization beam splitting property of birefringent crystals and a specially designed calcite crystal as a polarization beam splitter, two beams of linearly polarized light with orthogonal polarization directions and a small angular separation can be obtained to produce the reference and test beams with perpendicular polarization directions through a pinhole point diffraction plate. By introducing spatial synchronization phase-shifting technology, influencing factors such as environmental vibrations on the measurement results, are reduced. Subsequently, the birefringent crystal and system error calibration methods were studied. Finally, a BPBS-PDI experimental device was set up to obtain the wavefront distribution of the lens to be tested. The experimental results are consistent with those of the ZYGO interferometer, indicating that the BPBS-PDI wavefront measurement method can be used to measure a lens transmission wavefront with high accuracy.

To avoid exhaustive calibration of the shifter device in point diffraction interferometers, we present a dimension-reduction-based method to reconstruct the phase map from more phase-shifting fringe patterns with three or more frames. The proposed method assumes that the intensity space can be described adequately by the sine and cosine of multiple phase shifts introduced, which are the basis of the intensity space. Then, low-dimensional approximations of high-dimensional intensity spaces are determined by the newly developed reduced basis decomposition technique. Finally, the phase is reconstructed using the low-dimensional surrogates of the intensity spaces without the knowledge of accurate phase steps. Numerical and experimental studies demonstrated that the proposed method outperforms the existing popular phase reconstruction techniques in terms of accuracy and efficiency. Moreover, the performance of the proposed method is not limited by variations in the background and modulation, unlike the existing phase-shifting-algorithm-based approaches.

This Letter introduces a technique for performing binary adaptive optics, which is carried out by optical components only, without the help of any electronic or optoelectronic device. In this technique, the interferogram produced by a point diffraction interferometer modulates a light-driven crystal. The modulated light-driven crystal may produce pupil-plane only-phase or only-amplitude binary masks to mitigate phase aberrations. The capability of working unsupported makes it suitable for application in hard-to-reach or hazardous locations such as satellites, underwater, or contaminated places. The Letter includes an experimental validation where the ability of the technique to produce pupil amplitude masking is confirmed.