Three-degree-of-freedom autocollimator based on a combined target reflector.

As an angle measuring instrument, the traditional autocollimator has the ability to measure the two-degree-of-freedom angles, namely, pitch and yaw, but fails to measure the roll angle. In this study, we propose a novel autocollimator that can simultaneously measure the three-degree-of-freedom (3-DOF) angles. As a key component, a combined target reflector (CTR) is meticulously designed to split the collimated laser beam into two beams. The 3-DOF angle measurement is achieved by sensing the displacements of the two beam spots reflected from the CTR. The measurement principle and simulation analysis are presented in detail. Experiments are conducted to assess the performance of the proposed autocollimator, and the results indicate that it has an accuracy of better than 0.74 arcsec over a range of ${ \pm 200}\,\,{\rm arcsec}$±200arcsec, and it can be used for 3-DOF angular motion error measurement of a precision displacement stage.

Sparse aperture arrangement for periodic LED array sampling in a Fourier ptychography microscopy system.

In a traditional Fourier ptychography microscopy (FPM) system, multiple low-resolution (LR) intensity images have to be sequentially captured under variable illumination angles and then stitched together in the Fourier domain, which is time-consuming. This paper proposes a sparse aperture arrangement method in which the relationship between the spatial spectrum distribution and the light-emitting diodes array sampling pattern is investigated. Mathematical models of the proposed method are developed, and numerical simulations and optical experiments are demonstrated to verify its feasibility. The results show that the number of LR images could be decreased significantly without sacrificing image reconstruction quality. To the best of our knowledge, this is the first time that the sparse aperture arrangement has been exploited for FPM. The proposed method may provide new insights for improving the efficiency of the FPM platform and discovering more applications in digital pathology.

Reconstruction method based on the Hilbert fractal curve recovery sequence in a Fourier ptychography microscope.

Many Fourier ptychography microscopy techniques have been proposed to achieve higher recovery accuracy in the past few years, yet it is little known that their reconstructed quality is also dependent on the choice of recovery sequence, which is important for fast solution convergence during the Fourier ptychography reconstruction process. In this paper, we propose to use the Hilbert fractal curve, which is one of the most representative of classic space-filling curves, as a new kind of recovery sequence of mesh LED arrays and validate its effectiveness and robustness with both simulated and real experiments. Results show that the Hilbert fractal curve as the recovery sequence is a better choice for periodic LED arrays, compared with raster line, spiral line, and wave-shaped-curve three-recovery sequences.

Coherent noise reduction of phase images in digital holographic microscopy based on the adaptive anisotropic diffusion.

The suppression of coherent noise can produce higher-quality reconstructed images in digital holographic microscopy. A robust and effective phase coherent noise denoising algorithm is proposed in this paper that combines the anisotropic diffusion equation and the phase quality map. In order to accurately identify the noise and signal pixels, we introduce the phase quality map and edge detection to quantify the quality of the pixel information. In addition, a synthetic diffusion function is established to control the speed of the anisotropic diffusion process based on the quality coefficient. Several experiments have been carried out to validate the effectiveness of the proposed algorithm for coherent noise reduction. The results demonstrate that the proposed algorithm can reduce coherent noise and preserve edge details well.

Shape reconstruction based on zero-curl gradient field estimation in a fringe reflection technique.

A novel shape reconstruction method based on zero-curl gradient field estimation is presented in this paper. Zero-curl field estimation makes the most of curl information to obtain the ideal gradient data, and achieves the reconstruction with the quality map path integration method. In the estimation process, an algebraic approach is adopted to enforce integrability, which maintains the local information well. Moreover, we use the residual gradients of surface obtained from the Southwell zonal reconstruction algorithm as the raw gradient data in zero-curl field estimation, which has a stable tradeoff between smoothness and local shape confinement. The performance of the proposed method over antinoise capability is discussed and demonstrated by the simulations. The measurement experiment of an ultraprecision sphere mirror identifies the validity over general shapes, and the reconstruction results of hyperbolic surface with a local shape map demonstrate the better performance on local details retention. Therefore, this method performs well in handling complex objects with local mutation regions and high accuracy requirement of local information in practical measurement.

High-precision rotation angle measurement method based on a lensless digital holographic microscope.

To accurately measure ultrasmall rotation angles, a robust and effective method based on lensless digital holographic microscopy is proposed in this paper. The method combines holographic microscopy, solid geometry, and 3D measurement, including holographic measurement and angle measurement processes. We can calculate the 3D shape by the angular spectrum algorithm and the least-squares phase-unwrapping algorithm in the holographic process. According to the relationship between the surface shape and rotation angles, the real-time rotation angles can be calculated. To validate the feasibility and practicability of the proposed approach, numerical noise simulations and experiments were performed. The measurement precision of rotation angle can reach 0.5″ in the range of 1000″ in this paper's experiments. The holographic method has high measurement precision and good stability. In addition, the compact small volume has great potential in small-angle sensor applications.

Further investigation on the phase stitching and system errors in digital holography.

In this work, an improved phase stitching algorithm is proposed in digital holography (DH) based on a deduced phase errors model and a global optimization algorithm. In addition, to correct the relative rotation error between the coordinate systems of a CCD and xy-motion stages, we presented a simple and reliable image-based correction method. The experimental results obtained from our proposed method are compared with those calculated from the existing phase stitching method to verify the performance of the presented method. It is shown that our new proposed methods are robust and valid for measurement of a large microstructure element. As far as we know, the improved phase stitching algorithm and image-base correction method have not been discussed in DH, as we presented in this paper.

Modified stitching algorithm for annular subaperture stitching interferometry for aspheric surfaces.

In this paper, a modified stitching algorithm for annular subaperture stitching interferometry (ASSI) for aspheric surfaces is proposed. The mathematical model of adjustment error is deduced based on the wavefront aberration theory and rigid body movement; meanwhile, its basic principle and theory are introduced. The modified stitching algorithm is established based on the mathematical model and the simultaneous least-squares method, which keeps the error from transmitting and accumulating. So the adjustment error can be compensated efficiently. In addition, the standard deviation (SD) in the overlapped regions is used as the figure of merit to determine the stitching accuracy. Finally, simulations and experiments are given to verify the validity and rationality of the proposed algorithm. The results show that the introduced method is quite efficient.

Universal calculation formula and calibration method in Fourier transform profilometry.

We propose a universal calculation formula of Fourier transform profilometry and give a strict theoretical analysis about the phase-height mapping relation. As the request on the experimental setup of the universal calculation formula is unconfined, the projector and the camera can be located arbitrarily to get better fringe information, which makes the operation flexible. The phase-height calibration method under the universal condition is proposed, which can avoid measuring the system parameters directly. It makes the system easy to manipulate and improves the measurement velocity. A computer simulation and experiment are conducted to verify its validity. The calculation formula and calibration method have been applied to measure an object of 22.00 mm maximal height. The relative error of the measurement result is only 0.59%. The experimental results prove that the three-dimensional shape of tested objects can be reconstructed exactly by using the calculation formula and calibration method, and the system has better universality.