A novel subaperture stitching method based on monoscopic deflectometry in single point diamond turning is introduced in this study for measuring large-aperture optical surfaces. This method not only solves the phase position deviation between subapertures, but also eliminates the system calibration error. The objective optimization is achieved by utilizing the gradient deviation and form deviation at the overlapped areas of adjacent subapertures. To achieve full-aperture measurement of the SUT, the global gradient is integrated to reconstruct the SUT. Experimental validation confirms the feasibility of the method.
Phase measuring deflectometry (PMD) is a high-precision and low-cost measurement method for specular surface. The simple system configuration and nanoscale measurement accuracy make it possible to integrate the fabrication and testing systems of ultra-precision components, which is of great significance to the improvement of manufacturing efficiency and reliability. In machining, workpiece clamping is a key step before turning. However, repeated the clamping error of the workpieces will reduce the accuracy of manufacturing. Therefore, an alignment method is needed to obtain the actual position of the remounted workpiece to ensure machining quality. A method is proposed to realize non-contact workpiece self-positioning using PMD. A positioning method is proposed with strong anti-noise ability based on PMD in this paper. By adding different centroid positioning errors to the camera target surface, it is verified that the positioning accuracy of the model can achieve a micron level and strong noise immunity. The method solves the problem of workpiece positioning using PMD without increasing the complexity of the system.
Recently, the full-area defect inspection of high-performance optical components such as large telescope mirrors is urgently demanded. An industrial robotic arm is suitable for conducting the scanning movement of defect inspection systems, and another monitoring system is needed to guide the moving trajectory of the robotic arm. An efficient and precise guiding system is developed based on a laser projection measuring system. After the calibration of the measuring system, real-time point clouds of the component under test can be acquired. Denoising and registration of the point clouds are conducted to align the robot coordinate system with the workpiece coordinate system. Then, the scanning inspection can be conducted all over the component under test. Experimental results demonstrate that the system has high efficiency and accuracy within 17.59 μm
Sparse sampling of spectral components in Segmented Planar Imaging Detector for Electro-Optical Reconnaissance is an essential limiting factor to the imaging resolution. A dictionary learning method is proposed to improve the imaging quality. The images are segmented into patches, and data are extracted directly from small patches and taken as dictionary elements. By training high-and-low resolution image pairs, a coupled dictionary is obtained. The TV/L1 minimization and alternating direction multiplier method are used to restore high-resolution images. In this way, the quality metric RMSE of images is improved from 20.99 to 14.99, and PSNR from 21.69 dB to 24.62 dB.
Stereo deflectometry can specify the position of a workpiece and reduce the difficulty of geometrical calibration. But the measurement scope is limited, and this issue is especially severe for the measurement of complex surfaces. A method is proposed to extend the measuring scope of stereo deflectometry. The nominal model of the surface under test is aligned with the overlapped measurement area of the stereo vision system, and the other areas outside overlapped region are measured using the monoscopic SCOTS approach with each camera, respectively. This method effectively combines the advantages of stereo and monoscopic deflectometry, and the measuring accuracy and flexibility can be improved.
The phase measuring deflectometry is a powerful technique for the in-situ measurement of of complex optics. Its measurement accuracy is comparable with conventional interferometry, but with higher flexibility, stability and efficiency. The three main challenges in the deflectometric measurement, namely the position-angle uncertainty in calculating the pixel correspondences, height-slope ambiguity in specifying the normal vectors, and rank deficiency in surface reconstruction are analyzed. Some significant error factors and effective solutions are introduced. The measuring accuracy of complex surfaces can achieve a level of 100 nm RMS.
Deflectometry is a powerful measuring technique of complex optical surfaces. Usually a series of binary patterns or sinusoidal fringes are displayed on a screen, and correspondences are established between the screen and camera points according to their gray levels or phases. The image associated with a screen pixel is blurred due to the defocus and aberrations of the off-axis imaging system, and the calculated location of the correspondence point will in turn be biased. The space variant point spread function associated with the catadioptric system is analyzed based on the light field method, and the resulting blurring effect is then addressed using Wiener deconvolution algorithm. Henceforth the phase errors in the captured images can be compensated effectively. Experimental results are presented to demonstrate the feasibility and effectiveness of the proposed method.
The measurement of freeform optical surfaces is a challenging task in precision manufacturing. Those widely used instruments such as the point-scanning profiler and sub-aperture stitching interferometer are costly expensive and time consuming. The phase measuring deflectometry is a powerful measuring technique for complex optical surfaces. To image the measuring efficiency and reduce the number of the captured images, the modulating information can be reutilized in the second direction in the bi-directional phase shifting, so that totally only 6 images are needed. The tracing deviations caused by the form errors behave differently with those caused by the position errors. Then precise localization of the measured surface can be realized by error separation, so that detecting of feature points can be avoided. Experimental results demonstrate that the measurement error is below 150 nm.
The dual wavelength interferometry in digital holography can eliminate 2π ambiguities with a large synthetic wavelength, but the measurement error tends to be amplified. In this paper, a new numerical algorithm is proposed to reduce the amplification error, and further expand the measurement range. The wrapped phase map associated with one wavelength is used to assist unwrapping the phase map associated with the other wavelength. Since these two phase maps correspond to the same step height, an exhaustive searching method is applied. The measurement error will not be amplified linearly with the synthetic wavelength, but controlled at the same level with the single wavelength interferometry. In consideration of the measurement errors such as the environmental vibration, instability of wavelength and so on, a tolerance is set to guarantee the stability of the solution. The performance and feasibility of the proposed algorithm is verified by the numerical demonstration.
The segmented planar imaging detectors have attracted intensive attention because of its superior imaging performance and structural compactness. The structure of radial SPIDER is investigated and the imaging progress is mathematically analyzed according to the Van Cittert-Zernike theorem. Due to the sparse sampling density in the frequency domain resulted from restriction of the structure, the imaging quality of SPIDER is unsatisfactory. In this paper, a reconstruction algorithm based on the compressed sensing theory is proposed to reconstruct the sparse signal from far fewer sampling density than the Nyquist–Shannon sampling criterion. The objective function, measurement matrix and sparse matrix are discussed according to the physical mechanism of SPIDER. The TV/L1 minimization and alternating direction multiplier method (ADMM) are used to obtain high-resolution images. Simulation results of image reconstruction demonstrate that the imaging resolution is improved remarkably than the original image.
In the phase measuring deflectometry, the phase error caused by the nonlinear intensity response, called the gamma distortion, can negatively affect the measurement quality of specular surfaces. Based on the generic exponential four-step phase-shifting fringe modal, this paper proposes a flexible and simple phase retrieval method to eliminate the phase errors without complex calibration or additional fringe patterns. The experimental results illustrate that the proposed method can accurately retrieve the phases from the distorted fringe patterns with the Gamma distortion, and the measurement precision can henceforth be improved.
Phase measuring deflectometry is a powerful in-situ measuring technique for complex specular surfaces. Its measuring accuracy depends on the quality of geometric calibration. An in-situ deflectometric measuring system is integrated into a single point diamond turning machine. An accurate self-calibration method is proposed to refine the positions of the camera and the screen. A world coordinate system is established by introducing a flat mirror without markers. The geometric positions are solved by minimizing the deviations of the traced screen pixels. The tracing deviations caused by the form errors behave differently with those caused by the position errors. Precise localization of the measured surface can be realized by error separation, so that detecting of feature points can be avoided. Experimental results demonstrate that the measurement error is below 300 nm.
The measurement of aspheric optics has attracted intensive attention in precision engineering, and efficient in-situ measurement technologies are required urgently. Phase measuring deflectometry is a powerful measuring method for complex specular surfaces. In this paper, an in-situ measurement method is developed based on the sub-aperture deflectometry. A complete measuring procedure is developed, including initial calibration, self-adaptive calibration, route planning, imaging acquisition, phase retrieval, gradient calculation, surface reconstruction and sub-aperture stitching. Several key points concerning the sub-aperture measurement are investigated, and effective solutions are proposed to balance the measuring accuracy and aperture, to overcome the height/slope ambiguity and to eliminate the stitching errors caused by point sampling and measuring errors. The measuring flexibility and stability can be greatly improved compared to the existing SCOTS measuring approach.
Industrial robots have great potential for efficient and flexible polishing of large optical components, but the low positioning accuracy and control stability limits the polishing form quality. A model is established to describe the pressure distribution at the edge based on FEA analysis, and the effects of form deviation between the workpiece and the polishing pad is also investigated, thus TIFs can be calculated reliably. Polishing paths are planned to avoid sharp turning angles and fast movement, which can lead to unstable material removal. The dwell time is calculated via deconvolution with the space-variant TIFs. Experiments are conducted and the results show that the edge-roll error is significantly reduced and the polishing time is saved by 80%. Hence the robotic polisher can be comparable to the conventional polishing machines, which has a great significance for the ultra-precision optical manufacturing.
In recent years, the measurement of specular aspheric surface has attracted intensive attention in precision engineering. Phase measuring deflectometry is a powerful measuring technique, which could accurately measure specular surfaces. The software configurable optical test system and a four step phase shifting approach are applied to obtain the normal vectors of the measured surface. The geometric parameters are recalculated by optimization to improve the calibration accuracy. Then the surface is reconstructed using a optimization algorithm. The configuration parameters should be set according to specific surface shapes and measuring conditions. Numerical experiments demonstrate that good performance can be achieved using this method.
The measurement of microstructured components is a challenging task in optical engineering. Digital holographic microscopy has attracted intensive attention due to its remarkable capability of measuring complex surfaces. However, speckles arise in the recorded interferometric holograms, and they will degrade the reconstructed wavefronts. Existing speckle removal methods suffer from the problems of frequency aliasing and phase distortions. A reconstruction method based on the antialiasing shift-invariant contourlet transform (ASCT) is developed. Salient edges and corners have sparse representations in the transform domain of ASCT, and speckles can be recognized and removed effectively. As subsampling in the scale and directional filtering schemes is avoided, the problems of frequency aliasing and phase distortions occurring in the conventional multiscale transforms can be effectively overcome, thereby improving the accuracy of wavefront reconstruction. As a result, the proposed method is promising for the digital holographic measurement of complex structures.
KEYWORDS: Reconstruction algorithms, Wavelets, Digital holography, Speckle, Holography, Wavelet transforms, Interferometry, Holograms, Signal to noise ratio
Digital holography is a promising measurement method in the fields of bio-medicine and micro-electronics. But the captured images of digital holography are severely polluted by the speckle noise because of optical scattering and diffraction. Via analyzing the properties of Fresnel diffraction and the topographies of micro-structures, a novel reconstruction method based on the dual-tree complex wavelet transform (DT-CWT) is proposed. This algorithm is shiftinvariant and capable of obtaining sparse representations for the diffracted signals of salient features, thus it is well suited for multiresolution processing of the interferometric holograms of directional morphologies. An explicit representation of orthogonal Fresnel DT-CWT bases and a specific filtering method are developed. This method can effectively remove the speckle noise without destroying the salient features. Finally, the proposed reconstruction method is compared with the conventional Fresnel diffraction integration and Fresnel wavelet transform with compressive sensing methods to validate its remarkable superiority on the aspects of topography reconstruction and speckle removal.
Digital holography has become a powerful method for measuring three-dimensional topography of complex shapes. The application of optical-fibers can make the system more compact and flexible. However, some problems are also brought into the system by the use of optical-fibers. In order to facilitate the analysis and optimization of the measurement system, the digital holographic interferometry system is simulated in the optics software which is based on field-tracing. This allows the seamless combination of different numerical analysis techniques in different subdomains of the system. The fiber coupling efficiency is optimized. Hereby the parameters of the coupling lens and the splitting ratio can be determined. Finally the object wave is reconstructed from the interferograms, which verifies the reliability of the optimization results.
Currently the measurement of complex surfaces is a challenging task in precision engineering. Full aperture measurement is difficult to meet the requirements on accuracy and range at the same time, thus sub-aperture stitching measurement is conducted in turn. A robust six degrees of freedom stitching method is proposed for the in-situ subaperture measurement. The partial-partial-iterative closest point (PPICP) algorithm with a point-to-plane minimization approach is used. To avoid the potential over-influence of outliers, robust M-estimation techniques is applied for the processing of data. The optimal motion parameters are solved iteratively using the Levenberg-Marquardt algorithm. Curved surface interpolation technology based on the Delaunay triangulation is used to complete the surface integration for achieving seamless surface stitching. The PPICP method can effectively eliminate the systematic measurement errors, such as tilt, translation and rotation errors. Experimental results show that the proposed method has higher accuracy, efficiency and stability for precision in-situ measurements.
As an important measuring technique, white light interferometry can realize fast and non-contact measurement, thus it is now widely used in the field of ultra-precision engineering. However, the traditional recovery algorithms of surface topographies have flaws and limits. In this paper, we propose a new algorithm to solve these problems. It is a combination of Fourier transform and improved polynomial fitting method. Because the white light interference signal is usually expressed as a cosine signal whose amplitude is modulated by a Gaussian function, its fringe visibility is not constant and varies with different scanning positions. The interference signal is processed first by Fourier transform, then the positive frequency part is selected and moved back to the center of the amplitude-frequency curve. In order to restore the surface morphology, a polynomial fitting method is used to fit the amplitude curve after inverse Fourier transform and obtain the corresponding topography information. The new method is then compared to the traditional algorithms. It is proved that the aforementioned drawbacks can be effectively overcome. The relative error is less than 0.8%.
Due to the limitation of traditional interferometry, digital holographic microscopy has attracted intensive attention for its capability of measuring complex shapes. However, speckles are inevitable in the recorded interferometric patterns, thereby polluting the reconstructed surface topographies. In this paper, a phase-shifting interferometer is built to realize the in-axis digital holographic microscopy. The anti-aliasing shift-invariant contourlet transform (ASCT) is used for reconstructing the measured surfaces. By avoiding subsampling in the scale and directional filtering schemes, the problems of frequency aliasing and phase distortion can be effectively solved. Practical experiments show that speckles can be recognized and removed straightforwardly. Therefore the proposed method has excellent performance for reconstructing structured surfaces.
Deflectometry is a promising method for freeform surfaces due to its wide applications and ease of implementation, but it is not robust against environmental noise and vibrations. A new deflectometry method using the quaternary orthogonal grid fringes is proposed to retrieve the surface slopes. Combined with a classic N-step phase-shifting technique, only one image is required to extract the two perpendicular directional phases instead of two groups of phase shifted fringes. The color of each pixel can be encoded by red, green and blue components. In each color component, two perpendicular fringe patterns compose quaternary orthogonal grid fringes. In practice, the relative shift between different colors is set depending on the lateral resolution of the camera lens and the zoom relation of the object-image. The object-image relationship can be established by using only one distorted colorful orthogonal fringe pattern reflected via the surface. This process is fast and stable because the RGB codes of every block are significantly different to its neighbor in at least one color component. This method is suitable for dynamic measurement of specular objects, and the influence of varying environment and moving objects can then be eliminated.
The polishing convolution theory is widely used in CCOS optical manufacture. In the paper, it is found that the practical amount of material removal is largely different to the theoretical results when the polishing pad does an accelerated motion. The change of the feed rate will cause a huge deviation while the change of the direction will not cause the deviation. Several experiments have finished by using ABB robot polisher and laser interferometer. The cause of the deviation primarily lies in the accumulation of the abrasive grains. To ensure the stability of the amount of material removal in the sub-aperture polishing process, the large change of feed rate should be avoided and the effect on the change of direction can be neglected.
KEYWORDS: Digital holography, Error analysis, Phase shifting, Holographic interferometry, Holography, Microscopy, Interferometry, Near field diffraction
Digital holographic microscopy is an attractive technology of precision measurement. Phase shifting is required to correctly reconstruct the measured surfaces from interferograms. Spectral phase shifting scheme, as an alternative approach of phase shifting, has drawn intensive attention in recent years. However, the wavelength modulated by the acousto-optic tunable filter (AOTF) is not sufficiently precise. As a consequence, severe measurement errors will be caused. In this paper, an iterative calibration algorithm is proposed. It estimates the unknown wavelength errors in the 3-step spectral phase shifting interferometry and then reconstructs the complex object wave. The actual wavelength is obtained by minimizing the difference between the measured and calculated intensities. Numerical examples have demonstrated that this algorithm can achieve very high accuracy over a wide range of wavelengths.
Freeform surfaces are widely used in precision components to realize novel functionalities. In order to evaluate the form qualities of the manufactured freeform parts, surface matching/fitting is required. The uncertainty of the obtained form deviations needs to be estimated to assess the reliability of form error evaluation. The GUM approach is extensively adopted for uncertainty assessment in precision metrology, but it is not suited for assessing the nonlinear matching/fitting problems of freeform models. In this paper a Monte-Carlo method is developed to estimate the uncertainty of the fitted position, shape and form error metrics. Based on the correlation analysis, the effects of objective functions in numerical optimization, noise amplitudes in measurement, shapes of freeform surfaces and so on are determined. Then the significant factors dominating the reliability of the fitted results can be identified. Henceforth the matching/fitting procedures can be arranged appropriately to reduce the uncertainty of the evaluation results and improve the reliability of freeform surface characterization.
Micro optical components are more and more widely used in precision engineering due to their small sizes and novel functionalities. Characterization of the surface topography of these components is very difficult due to the existence of sharp edges and complex features. Conventional filtering algorithms cannot be used directly for non-smooth structured surfaces. In this paper we present a filtering algorithm using the non-local means method. Instead of assigning weights according to the closeness or similarity between individual data points, this method are based on the similarity of the patches surrounding data points. This method can effectively separate the detailed textures of non-smooth surfaces while preserving primary features. Proper adaptation and improvement are made for the applications in precision engineering. The k-means clustering method is used to reduce the computational cost. Numerical experiments prove that the non-local means method is able to separate small-scaled textures from the primary surface shapes without ruining the sharp features.
Uncertainty evaluation, which is an effort to set reasonable bounds for the measurement results, is important for assessing the performances of precision measuring systems. The three dimensional measurement is affected by a large number of error sources. The distributions of the primary error sources are analyzed in this paper. The multiple-try Metropolis (MTM) algorithm is applied for sampling and propagation of uncertainty for these error sources due to its advantage in dealing with large dimensional problems. The uncertainties of the three coordinates of a measured point on the workpiece r, z, and θ are evaluated before and after error separation, respectively. The differences between the two types of uncertainties are compared to find out the influence of the error separation to the uncertainty. Finally, numerical experiments are implemented to demonstrate the uncertainty assessment process.
Surface roughness in Single Point Diamond Turning (SPDT) is affected by a number of factors, which collectively
contribute to the final finish of diamond-turned surface. This paper analyzes the dominant factors affecting surface
roughness in SPDT. Considering the mechanism of SPDT, the generation of surface roughness is closely related to
the material properties of workpieces, especially some material aspects such as anisotropy, impurity, inclusions and
microstructures. The conditions of the tool such as the rake angle, the nose radius, the tool cutting edge waviness
and the degree of wear exert significant influence on the surface roughness. The cutting process parameters,
including the spindle speed and the depth of cut, especially the feed rate, influence the surface roughness as well,
and the cutting conditions can be optimized for given materials and workpieces. The usage of mist also have to be
considered carefully. Based on the analysis above, appropriate diamond tools are chosen, and cutting process
parameters are optimized for particular workpieces, and some successful control of the surface roughness have
been achieved for some materials such as Al alloy6061, Si, Ge, and KDP.
With the development of manufacturing technologies of large-scale polymeric micro-patterns, the Roll-to-Roll
fabrication has received more and more attention. Its advantages of large area, high efficiency and low cost make this
process very competitive. Requirements on high accuracy for functional optical micro-structures impose new challenges
for processing precision of the roll stamper. Taking into account the difference between traditional imprinting and Roll
imprinting, we build a mathematical model to optimize the tooth shapes of the rolls for compensating the structure
distortion during the rolling motion. Squared patterns are adopted to demonstrate the validity of this compensation
method. Through simulation and testing, the results indicate that after optimization of structure, the manufacturing
accuracy of the polymer structure can be improved by 78.7%.
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