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To better meet the wavefront measurement requirements for large-aperture segmented mirrors after in-orbit deployment, this paper designs a measurement system based on an optical camera and targets. This system utilizes photogrammetry principles to measure target positions, fit the wavefront of the segmented mirror, and form a closed-loop control with the calibration mechanism. Based on the wavefront measurement range and accuracy requirements during the coarse calibration phase of the segmented mirror, the optical system was first designed. The measurement camera features a 16° × 12° rectangular field of view with a 100 mm focal length, achieving near-diffraction-limited imaging quality. The structural fundamental frequency of the measurement camera exceeds 400 Hz. Under a 4 °C temperature rise environment, the surface error of the optical lens remains better than 1/80λ. Based on error theory, a quantitative analysis of error sources and their impact on target position measurement accuracy was conducted, yielding theoretical measurement errors of ±0.0853 mm in the Z-direction and ±0.1525 mm in the X-direction. Through focal length calibration and imaging tests of the prototype, the measurement camera achieved a modulation transfer function greater than 0.11 with excellent imaging quality. With a focal length of 101.356 mm and a measurement range exceeding ±4 mm, it meets design requirements. Finite element simulation and Monte Carlo methods analyzed wavefront fitting accuracy under different operating conditions, yielding peak-to-valley values of 0.397 mm and root mean square values of 0.073 mm. The wavefront measurement system designed in this paper meets the structural rigidity and temperature adaptability requirements for in-orbit measurement systems. The prototype’s field of view satisfies the wavefront measurement range requirements, the camera’s focal length meets design specifications with good imaging quality, and the wavefront measurement deviation meets the accuracy requirements for the coarse calibration phase. Compared to current wavefront measurement systems, the proposed system significantly expands the measurement range, offering a novel wavefront measurement method for coarse calibration of tiled mirrors.

Presented is a novel way to combine snapshot compressive imaging and lateral shearing interferometry in order to capture the spatio-spectral phase of an ultrashort laser pulse in a single shot. A deep unrolling algorithm is utilized for snapshot compressive imaging reconstruction due to its parameter efficiency and superior speed relative to other methods, potentially allowing for online reconstruction. The algorithm’s regularization term is represented using a neural network with 3D convolutional layers to exploit the spatio-spectral correlations that exist in laser wavefronts. Compressed sensing is not typically applied to modulated signals, but we demonstrate its success here. Furthermore, we train a neural network to predict the wavefronts from a lateral shearing interferogram in terms of Zernike polynomials, which again increases the speed of our technique without sacrificing fidelity. This method is supported with simulation-based results. While applied to the example of lateral shearing interferometry, the methods presented here are generally applicable to a wide range of signals, including Shack–Hartmann-type sensors. The results may be of interest beyond the context of laser wavefront characterization, including within quantitative phase imaging.

Digital image correlation (DIC) technology is widely employed in speckle-based measurement techniques, including X-ray speckle tracking. By enhancing DIC’s measurement capability to the subpixel scale through subpixel registration technology, the accuracy of such tracking methods is significantly improved. Consequently, selecting an appropriate subpixel registration algorithm becomes crucial for advancing the precision of both DIC and its application in tracking methods. Nevertheless, current evaluation approaches for these algorithms overlook spatial resolution—an essential metric not only for X-ray speckle tracking but also for other comparable methodologies. Inspired by the modulation transfer function, this study proposes a novel evaluation method that uses the root mean square error of displacement measurement at different spatial frequencies to assess spatial resolution. Two widely used subpixel registration algorithms—the peak-finding algorithm and the iterative spatial domain cross-correlation algorithm—are evaluated and compared. The result strongly contrasts with traditional evaluations based on ideal translational conditions, and underscores the necessity of incorporating spatial resolution and speckle size into algorithm selection criteria for practical applications.

In this paper, a turbulent wavefront measurement model based on the Hartmann system structure is proposed. The maximum recognizable mode number of different lens units is discussed, and the influence of different lens array arrangements on the accuracy of turbulent wavefront reconstruction is analyzed. The results indicate that the increase in the aberration order of the turbulent wavefront has a certain influence on the reconstruction ability of the system. Different lens arrangements and number of lens units will lead to the effective reconstruction of different final mode orders. When using a 5 × 5 lens array arrangement and a hexagonal arrangement of 19 lenses, the maximum order of turbulent wavefront aberrations allowing for effective reconstruction was 25. When the sparse arrangement of 25 lenses or the sparse arrangement of 31 lenses was used, the maximum order allowing for effective reconstruction was 36. If the aberration composition of the turbulent wavefront contained higher-order aberrations, the system could not accurately measure the turbulent wavefront. When the order of the aberrations of the turbulent wavefront was low, the turbulent wavefront could be measured by the lens arrangement with fewer lens units, and the wavefront reconstruction accuracy was close to the measurement results obtained when more lens units were used.

As with the decreasing feature size prompted by Moore’s law and the continuous technological advancements in the semiconductor industry, the distortion of the projection lens is an important factor that affects the overlay. In this paper, we propose a wavefront-measurement-based method to detect the projection lens distortion in the lithographic system. By normalizing the coordinates of the Shack–Hartmann system with the image displacements represented in the Z2 and Z3 terms of Zernike coefficients, the offsets between the actual image points and the ideal image points can be determined. By offset collection at an array of 7 × 7 field points to establish an overdetermined system of equations, the proposed method can simultaneously detect the distortions of translation, magnification, rotation, decentering distortion, thin prism distortion, and third-order radial distortion. This distortion measurement method is highly flexible for distortion measurement with portable and compactly integrated sensors, enabling the real-time and cost-efficient measurement of wave aberration and distortion. For proof-of-concept experiments, a projection lens with a numerical aperture (NA) of 0.58 for i-line (365 nm) is used for experimental testing. The results reveal that the repeatability accuracy of distortion detection is 51 nm and the 72 h long-term reproducibility is 143 nm.

The projection objective lens holds a pivotal role in lithography, directly influencing imaging system quality and, consequently, the lithography machine’s feature dimensions. Optical inspection methods for this lens require advancements in calibrating systematic error and enhancing alignment precision of auxiliary devices, given their impact on calibration accuracy. In the random averaging method, random ball can give rise to additional wavefront aberrations due to misalignment and numerical aperture mismatch. To mitigate these aberrations and enhance the accuracy of systematic error calibration, this paper introduces a random ball residual compensation (RBRC) model. Additionally, when combined with the random averaging technique, it elevates the calibration accuracy of the measured lens’s wavefront aberrations. The experimental results underscore the method’s effectiveness, accurately determining optical component eccentricities and numerical aperture errors. After eliminating these errors, more accurate values of lens wavefront aberrations are achieved. This research significantly contributes to enhancing error calibration of lithography objective lens systems.

Measurement of trapping force with Shack Hartmann sensor, which is done in this paper, offers many advantages. It opens a way for phase and force measurement at the same time. In line alignment, correcting optical beam aberration, OPD and nonlinear refractive index measurement of the trapped particle is easily achievable with phase measurement. The new method is as accurate as old methods and has high precision since it can be evaluated by a single measurement of Shack Hartmann sensor in millisecond. Also mapping laser beam spot in trapping site may lead to further discovery in the potential well studies.

To overcome the limitations of phase sampling points in testing aspherical surface wavefronts using traditional interferometers, we propose a high-spatial-resolution method based on multi-directional orthogonal lateral shearing interferometry. In this study, we provide a detailed description of the methodology, which includes the theoretical foundations and experimental setup, along with the results from simulations and experiments. By establishing a relational model between the multi-directional differential wavefront and differential Zernike polynomials, we demonstrate high-spatial-resolution wavefront reconstruction using multi-directional orthogonal lateral shearing interferometry. Theoretical calculations and simulations of aspherical surface wavefront testing are followed by experimental verification on an aspherical surface with a known asphericity. Comparing the measurement results with those from the LuphoScan profilometer, we achieve a relative measurement error with an RMS precision better than λ/100.

Terahertz quantum-cascade lasers (QCLs) are very promising radiation sources for many scientific and commercial applications. Shaping and characterizing the beam profile of a QCL is crucial for any of these applications. Usually the beam profile should be as close as possible to a fundamental Gaussian TEM 00 mode. In order to completely characterize the laser beam the power and the wavefront have to be measured. We describe methods for characterizing the beam properties of QCLs. Several QCLs with single-plasmon waveguide and emission frequencies between 2 and 5 THz are investigated. The beam profiles of these lasers are shaped into almost fundamental Gaussian modes using dedicated lenses. The beam propagation factor M 2 is as low as 1.2. The wavefront is measured along the axis of propagation with a THz Hartmann sensor. Its curvature behaves as expected for a Gaussian beam. The applied methods can be transferred to any other THz beam.

Radiation damage is often an issue during high-resolution imaging, making low-dose focusing and stigmation essential, in particular when no part of the sample can be “sacrificed” for this. An example is serial block-face electron microscopy, where the imaging resolution must be kept optimal during automated acquisition that can last months. Here, we present an algorithm, which we call “Maximum-A-Posteriori Focusing and Stigmation (MAPFoSt),” that was designed to make optimal use of the available signal. We show that MAPFoSt outperforms the built-in focusing algorithm of a commercial scanning electron microscope even at a tenfold reduced total dose. MAPFoSt estimates multiple aberration modes (focus and the two astigmatism coefficients) using just two test images taken at different focus settings. Using an incident electron dose density of 2,500 electrons/pixel and a signal-to-noise ratio of about one, all three coefficients could be estimated to within <7% of the depth of focus, using 19 detected secondary electrons per pixel. A generalization to higher-order aberrations and to other forms of imaging in both two and three dimensions appears possible.