Transport of intensity equation (TIE) provides a powerful QPI means due to its simplicity and high efficiency. However, it is limited in dynamic measurement because it requires at least two defocus intensity images acquisition. Therefore, a simple, accurate, full-field single-shot QPI method is proposed based on TIE and wavelength multiplexing scheme. By ultizing the different phase modulation capabilities of liquid crystal spatial light modulator (LC-SLM) for different wavelengths of light, multiple intensity images of different defocus distances can be produced by a Fresnel-lens-loaded LC-SLM. In this manner, those images can be acquired by a color camera with single exposure, enabling dynamic QPI application. computational imaging.
Phase-shifting profilometry (PSP) is considered to be the most accurate technique for phase retrieval with fringe projection profilometry (FPP) systems. However, PSP requires that multiple phase-shifted fringe patterns be acquired, usually sequentially, which limits PSP to static or quasistatic imaging. We introduce color FPP (CFPP), which provides three-dimensional (3D) imaging using a single acquisition, for the application of real-time profiling. A single frame acquisition provides all three phase-shifted fringe patterns needed for the PSP phase retrieval algorithm. However, some problems must be overcome in CFPP, namely, color coupling and imbalance. Following up on the study, we propose a fixed coefficient decoupling method based on point-to-point correction and then introduce the empirical mode decomposition algorithm to decompose a color fringe pattern into three high-frequency components and three low-frequency components for imbalance correction, which improves measurement accuracy and realizes a single frame measurement for complex and discontinuous objects. After correction by the proposed method, the shape of the tested object can be recovered by one a single frame color fringe pattern, which meets the need for dynamic measurement, and the accuracy is not limited by the movement speed of object. The simulations and experimental results show that the proposed method can significantly reduce the influence of color coupling and imbalance in CFPP, and thus realize dynamic and high-precision 3D reconstruction.
KEYWORDS: Cameras, Modulation transfer functions, Optical engineering, Temperature metrology, Monochromatic aberrations, Picosecond phenomena, Thermal effects, Satellites, Signal to noise ratio
Thermal design is highly related to the performance of space cameras as temperature changes cause thermal displacements of the cameras’ optical and mechanical systems, consequently affecting imaging quality. However, most existing thermal design methods for space cameras focus on several thermal design parameters without a comprehensive and quantitative analysis. Therefore, we proposed an optimization thermal design method for space cameras based on thermo-optical analysis and the Taguchi method. We first established the thermal balance equations of space cameras, and by analyzing the thermal design parameters in the equations, we identified the key parameters that affect the temperature field, thermal displacements, and imaging quality of the camera. Furthermore, we evaluated the influence of each thermal design parameter on imaging quality based on the integrated thermo-optical analysis. Thereafter, we applied the Taguchi method to quantitatively calculate the effect of each thermal design parameter on imaging quality. Finally, we implemented an optimal thermal control scheme for space cameras based on the results of the Taguchi method. The experimental results demonstrated that the proposed method is reliable and efficient and would be beneficial to researchers working on the thermal design of optical instruments.
A fast and precise spatial-carrier phase-shifting algorithm based on the matrix VU factorization strategy that can realize dynamic real-time phase detection is proposed. First, the proposed algorithm divides the spatial-carrier interferogram into four phase-shifting subinterferograms. Second, the matrix VU factorization strategy, an excellent fast iterative algorithm, is used to accurately obtain the measured phase from these subinterferograms. Numerical simulation and experimental comparison verify that this method is an efficient and accurate single-frame phase demodulation algorithm. Meanwhile, the performance of the proposed method is analyzed and discussed for the influencing factors, such as random noise level, carrier-frequency value, and carrier-frequency direction. The results show that the method proposed is a fast and precise phase detection method that provides another effective solution for dynamic real-time phase measurement.
The extreme value of interference (EVI) algorithm is a very fast and efficient method for the fringe pattern phase demodulation. It requires only two arbitrarily phase-shifted frames in which the phase shift between interferograms can be determined by searching the maximum and the minimum of the normalized interference patterns, then the measured phase is obtained by an arctangent function. Compared with other two-frame demodulation algorithms, the EVI algorithm has great advantages. Firstly, the EVI algorithm is simple and the calculation speed is fast. Secondly and more importantly, it works very well even if the number of fringes of the interferogram is less than one. However, to make this method work, the fringe should be normalized in advance, which is sometimes not a satisfactory requirement. The effects of uneven background terms, modulation amplitude variations, and random noise in the fringe pattern will make the normalization of the fringes extremely complex. Therefore, by employing the HilbertHuang transform (HHT) based prefiltering in this paper, the background intensities and modulation amplitudes of the two interferograms are suppressed and normalized respectively. Then, phase demodulation is implemented using the EVI method. Because of the HHT process, the demodulation result is greatly improved in plenty of situations. Both simulation and experimental studies have shown that the proposed improved method makes it easier to determine the phase distribution with high precision even under complex conditions.
Transport of Intensity Equation (TIE) is a simple and efficient method for phase retrieval by solving the equation between the intensity axial derivative and phase. In this method, the estimation of the axial derivative of intensity is very crucial. Simply, we use two defocused intensity images to estimate the axial derivative by finite difference method. However, the result is still unsatisfactory even though the optimal defocused distance is adopted. The reason lies in that the intensity’s axial change is not linear in the propagation of light. Simply using the finite difference between the two defocused images will ignore higher order axial derivatives. In other words, the estimation of the axial derivative of intensity will contain nonlinear errors. To solve this problem, we propose an extrapolation-based method to estimate the axial derivative of intensity using multiple intensity images. With Taylor expansion and a series of combination and eliminations on these images, high order terms of axial derivative errors are removed. As a result, the nonlinear errors in estimation of the axial derivative will be reduced. The performance of our proposed method for different types of phases under different illumination conditions is investigated. Compared with normal TIE, our method can obtain a much more accurate phase profile.
Shadow moiré fringes have a complex intensity distribution, which makes the existing arcsine function or arccosine function that is used in random phase-shift extraction algorithms unstable in applications. We propose a high-precision algorithm to determine the random phase shift in a robust way. The idea consists of constructing three consecutive fringe patterns by the addition of two background terms suppressed fringe patterns. Then, an iterative self-tuning phase-shifting algorithm is developed to extract the measurement phase in a pointwise manner. Due to the use of an iterative procedure and tangent function, the present method can evaluate the phase shift accurately and robustly and can be implemented easily in many applications. In addition, the proposed method provides a solution for the development of the two-frame random shadow moiré technique. We present simulation and optical experiments to demonstrate the correctness of the proposed method. The results show that the proposed method performs better than other methods.
Annular sub-aperture stitching interferometry (ASSI) has provided an alternative solution to measure rotationally symmetric aspheric surfaces with low cost and high flexibility. It is an effective way to test the aspheric surface with a larger aperture and larger relative aperture without null compensation. In this paper, two kinds of annular sub-aperture stitching algorithms, pairwise sequential stitching (PSS) and global synchronously stitching (GSS), were studied. The detailed mathematical expressions are shown in the form of matrix. Besides, the influence of the noise and number of sub-apertures to the two algorithms was also studied by simulation. At last, experimental results of a convex hyperboloid surface by using the two stitching algorithms are presented.
Point diffraction interferometry (PDI) combined with annular subaperture stitching is proposed for ultrahigh-accuracy measurements of aspheric surfaces. By adding an axial movement to the test optics in the PDI system, aspheric surfaces with large departures can be measured with high accuracy by stitching the annular measurement data of different axial positions. We examine the principle of PDI-based annular subaperture stitching and the stitching algorithm. Simulations and experiments demonstrate the feasibility and effectiveness of our proposed method. Our method retains the ultra-high accuracy of PDI while extending the vertical dynamic range of the interferometer, enabling nanometer or even subnanometer accuracy measurements of large-departure rotationally symmetric aspheric surfaces.
A ball-based intermediary target technique is presented to position moving machine vision measurement system and
to realize data registration under different positions. Large-sized work-piece measurement based on machine vision faces
several problems: limited viewing angle, range and accuracy of measurement inversely proportional. To measure the
whole work-piece conveniently and precisely, the idea that using balls as registration target is proposed in this paper.
Only a single image of the ball target is required from each camera then the vision system is fully calibrated (intrinsic
and extrinsic camera parameters). When the vision system has to be moved to measure the whole work-piece, one
snapshot of the ball target in the common view can position the system. Then data registration can be fulfilled. To
achieve more accurate position of ball’s center, an error correction model is established.
Sub-aperture stitching (SAS) testing method is an effective way to extend the lateral and vertical dynamic range of a
conventional interferometer. However, the center of each sub-aperture could be in error because of the complex motion
of the mechanical platform. To eliminate the affection of lateral location error in the final stitching result, a lateral
location error compensation algorithm is introduced and the ability of the algorithm to compensate the lateral location
error is analyzed. Finally, a 152.4mm concave parabolic mirror is tested using SAS method with the compensation
algorithm. The result showed that the algorithm can effectively compensate the lateral location error caused by the
mechanical motion. The proposal of the algorithm can reduce high requirement of mechanical platform, which provides
a feasible method for the practical application of the engineering.
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