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• We analyze the problem areas and distorted signals that can arise when measuring CSMU using basic white-light interferometry. We specifically focus on addressing the structural areas that are prone to errors, ensuring reliable processing results and improving efficiency. • In the signal processing of the problem areas, we employ characteristic analysis of the distorted signal. By filtering out the disturbed part of the signal and extracting the desired portion containing accurate height information, we are able to reconstruct the 3D topography. • This algorithm can be applied to any traditional optical system utilizing white-light interferometry. It is a simple and accurate approach that only requires a standard experimental setup, making it highly practical. Micro-nanostructures refer to technologies that operate at the nanoscale and provide materials and devices with unique mechanical, physical, and chemical properties. These structures have diverse applications in fields such as microelectronics, biotechnology, aerospace, and metamaterials. As precision machining technology advances, the demand for smaller sizes and higher accuracy of structural units has increased, leading to more compact integration. Consequently, the lossless and high-precision 3D measurement of highly integrated micro-nanostructure components has become increasingly challenging. In this study, we analyzed measurement errors in compactly spaced microstructural units using white-light scanning interferometry and proposed an algorithm to optimize this technology. By combining coherent peak-histogram processing with signal correlation analysis, we were able to improve the measurement accuracy by approximately ten times compared to current mainstream algorithms. To validate our algorithm, we performed experiments using metasurfaces with structural unit spacing at the order of sub-micrometer. The results obtained demonstrated the effectiveness of our algorithm in achieving accurate measurements. [ABSTRACT FROM AUTHOR]

The absolute testing technique has been widely employed in sub-nanometer optical surface metrology, we have presented a generalized shift-rotation absolute measurement method for high-numerical-aperture spherical surfaces (Yang et al., 2017). In this paper, a simple and effective three-step shift-rotation absolute testing technique for optical surface figure with irregular shaped aperture is presented. The test surface is tested in an original, a rotational and a shift position. Based on the orthonormal polynomials over irregular shaped aperture, the absolute figure of the test surface is separated from the reference surface errors by the two measurement difference data. Simulation results presented in the paper indicated the validity of the three-step shift-rotation absolute measurement method. The measurement results show a good agreement with the results measured by commercial profiler. The novel three-step shift-rotation absolute testing technique is a promising method to measurement the optical flat and spherical with the irregular shaped aperture. [ABSTRACT FROM AUTHOR]

We demonstrate a lensless phase-shifting point diffraction interferometer with a tiny pinhole to measure spherical mirror surface figures. The interferograms used to reconstruct the surface figure are formed without imaging optics. Fresnel diffraction calculations with a coordinate transformation are studied as a means of reconstruction method for wavefront amplitude and phase. The Radon transform is used to determine the distance from the tiny pinhole to the CCD target, which guarantees the accuracy of the diffraction calculations. Our lensless phase-shifting point diffraction interferometer not only retains the higher measurement precision by the ideal reference wavefront, but also overcome the fabrication and mounting limitation of the imaging optics. The simulations and experiments have validated the accuracy and feasibility of the spherical mirror measurement by proposed lensless phase-shifting point diffraction interferometer. [ABSTRACT FROM AUTHOR]

Non-null interferometry could use to measure the radius of curvature (ROC), we have presented a virtual quadratic Newton rings phase-shifting moiré-fringes measurement method for large ROC measurement (Yang et al., 2016). In this paper, we propose a large ROC measurement method based on the evaluation of the interferogram-quality metric by the non-null interferometer. With the multi-configuration model of the non-null interferometric system in ZEMAX, the retrace errors and the phase introduced by the test surface are reconstructed. The interferogram-quality metric is obtained by the normalized phase-shifted testing Newton rings with the spherical surface model in the non-null interferometric system. The radius curvature of the test spherical surface can be obtained until the minimum of the interferogram-quality metric is found. Simulations and experimental results are verified the feasibility of our proposed method. For a spherical mirror with a ROC of 41,400 mm, the measurement accuracy is better than 0.13%. [ABSTRACT FROM AUTHOR]

We propose a high-order shift-rotation absolute ultra-precision measurement method to calibrate the misalignment aberration and reference surface deviation in high-numerical-aperture spherical surface testing. Based on high-order approximation, the high-order misalignment aberrations are deduced. Both the computer simulation and experimental results confirm the feasibility of the proposed absolute ultra-precision measurement method. The high-order misalignment aberrations and reference surface deviation can be removed from the measured results by our absolute measurement method. The high-order shift-rotation absolute measurement method can get the accuracy of nanometer level in high-numerical-aperture spherical surface testing. [ABSTRACT FROM AUTHOR]

Misalignment aberrations in Fizeau interferometric testing system can significantly influence the measurement results in the case of high-numerical-aperture test spherical surfaces, and it is hard to separate the high-order misalignment aberrations from the measured data. The traditional calibration method, which is based on linear-approximation, is applicable in calibrating only the linear misalignment aberration in measurement of high-numerical-aperture spherical surfaces. Based on modified power term for interferometry and 4-overlapping averaging 9-frame algorithm, sub-nanometer accuracy high-order calibration method is proposed to calibrate the linear misalignment aberrations as well as high-order misalignment aberrations. Both the computer simulation and experimental results confirm the feasibility and accuracy of the proposed calibration technique, and sub-nanometer misalignment aberrations can be calibrated. The proposed method can also used in spherical surface ultra-precision measurement by other interferometric setups without foreknowledge of numerical aperture of the test surface. [ABSTRACT FROM AUTHOR]

Abstract: A method for measuring the radius of curvature with a pinhole point diffraction interferometer (PDI) is proposed. Using the wavefront difference method and the Gaussian imaging equation, the longitudinal displacement of the converging rays passing through a standard plane-parallel-plate sample in PDI interference cavity is determined. Based on this longitudinal displacement, a precise formula for radius of curvature calculation is deduced. An experimental system for radius of curvature measurements is set up to verify the principle. With this testing system, the radius of curvature of spherical mirrors and the surface figure can be measured in a higher precision simultaneously. Some sources of uncertainty in measurement are discussed based on detailed error analysis. The experimental results indicate that the measurement accuracy is in the order of 10−4. [Copyright &y& Elsevier]

• STP method can retrieve the synthetic-wavelength phase from moiré fringe patterns in simultaneous dual-wavelength interferometry. • In STP method, by the additive-to-multiplicative moiré fringe transition, the measured synthetic-wavelength interferometry information exists directly and is demodulated conveniently. • STP method is implemented with π/(2k) phase shift at the synthetic wavelength to be retrieved by the conventional phase-shift algorithm. • STP method releases the restriction of spatial carrier for spectrum separation and the requirement of quadratic polar coordinate transform for the circle carrier. • The separation distance of the phase lobes in spectrum for STP method is longer than 9.56 times of the distance for traditional temporal FT method. Simultaneous dual-wavelength interferometry (SDWI) could extend the measured range of each single-wavelength interferometry, and has higher efficiency when the two single wavelengths work simultaneously. However, the directly measured phase demodulation at the long synthetic wavelength (λ S) from the generated moiré fringe patterns in SDWI is rather arduous. To reduce the difficulty of the processing for the moiré fringe patterns, a synthetic wavelength temporal phase retrieval method (STP) with the π/(2k) phase shift at λ S was proposed in this paper. By the additive-to-multiplicative moiré fringe transition, the synthetic-wavelength interferometry information exists in the form of the superposition with other wavelength information. And then for the longer separation distance of the phase lobes in spectrum, the synthetic-wavelength spectrum in STP method could be filter out more easily than traditional temporal Fourier transform (FT) method. After a low-pass filtering in the spectrum of the multiplicative moiré fringe intensity and adopting the π/(2k) phase shift at λ S , the synthetic-wavelength phase is retrieved by the conventional phase-shift algorithm from the obtained synthetic-wavelength phase-shift interferograms with the interval of π/2 phase shift. Compared with the spatial FT method with the introduction of spatial carrier, STP method releases the restriction of spatial carrier for spectrum separation and the requirement of quadratic polar coordinate transform for the circle carrier. Finally, the feasibility and applicability of the STP method are verified using simulation and experimental results. [ABSTRACT FROM AUTHOR]

Dual-wavelength interferometry (DWI) could extend the measured range of each single-wavelength interferometry. The synchronization of the two working wavelengths in DWI is of high efficient, and the generated moiré fringe indirectly represents the information of the measured long synthetic-wavelength ( λ S ) phase. However, the extraction of the measured synthetic-wavelength phase is rather arduous from the moiré fringe. To retrieve the synthetic-wavelength phase from the moiré fringe patterns, we present a carrier squeezing dual-wavelength interferometry method (CSDI) in simultaneous DWI (SDWI). After the mathematical square of the moiré fringe patterns, the multiplicative moiré phase-shift fringe patterns with π/2 phase shift at λ S are combined into a single spatial-temporal fringe (STF). By converting the temporal phase shift into spatial carrier and the introduction of the carrier, the measured synthetic wavelength phase is retrieved by the filter and inverse Fourier transform of the STF spectrum. Compared with other methods, CSDI method could suppress the influence of the phase-shift error and only requires 4 frame phase-shift interferograms. Numerical simulations are executed to demonstrate the performance of the CSDI method in SDWI with the peak-to-valley (PV) value of 1.46 nm and the root mean square (RMS) values of 0.23 nm for the demodulated error. And the precision is better than PV of 20 nm (0.0059 λ s ) and RMS of 6 nm (0.0017 λ s ) even when the distribution range of the phase-shift error is as high as ± 10% relative to the π/2 phase shift step at λ S . Finally, our experimental results indicate that the measurement accuracy is better than 1.3% for a step with the height of 7.8 µm, and 0.5% for the step height of 6.233 µm for a Fresnel lens. [ABSTRACT FROM AUTHOR]

• Only a single interferogram is needed to complete the high-precision measurement of large ROC, which avoids the time-consuming process of acquiring interferograms. • This method uses a large step size to find a rough solution in a wide search range, and then constructs a shrunken range with a small step size based on the rough solution to quickly determine the high-precision measurement results. • Simulation and experimental results show that our method has high measurement accuracy in different interference models but also measurement efficiency is significantly improved. The method, based on searching the maximum or minimum of the metric function in the defined range that can be used to confirm the expected value, has been applied for measuring the large radius of curvature (ROC). The small step size is always needed in the searching range to ensure the measurement accuracy. But in the wide searching range, it will consume much time for finding the expected value. In order to improve the measurement efficiency, this paper proposes a fast measurement strategy for large ROC. This method uses a large step size to find a rough solution in a wide search range, and then constructs a shrunken range with a small step size based on the rough solution to quickly determine the high-precision measurement results. Simulation and experimental results show that the proposed method can be flexibly applied to different interference systems and greatly improve their measurement efficiency. For the tested spherical mirrors with ROC of 41400 mm and 1000 mm, high precision ROC can be obtained in just a few seconds. [ABSTRACT FROM AUTHOR]

• The CCFC method could extract the synthetic-wavelength interferogram from moiré fringe patterns in simultaneous dual-wavelength interferometry without the introduction of other wavelength interferometric information. • Coupled by the multiplication for the conjugate complex functions, only the lower beat-frequency synthetic-wavelength interferometric fringe pattern is derived directly. • The half-band filter in used in CCFC method is appropriate for the different spectral width or carrier spatial frequency. • The necessary introduced linear carrier in CCFC method is merely about 0.0947 times of the carrier in the traditional spatial domain fourier transform demodulation theory numerically. • The introduced carrier is only used to pursue the separation between the ±1 order phase lobes instead of the separation between the different wavelength phase lobes in CCFC method. Simultaneous dual-wavelength interferometry (SDWI) supplies a better solution to extend the measurement range of traditional single-wavelength interferometry with higher efficiency. To decompose the needed longer beat-frequency synthetic-wavelength (λ S) information from the generated moiré fringe pattern in SDWI, a conjugate complex function coupling strategy (CCFC) of interferometric field is proposed in this study. By the Fourier transform and the half-band filter in one side of the spectrum, the positive half spectrum is obtained. The inverse Fourier transform and conjugate operation are performed on the half spectrums to obtain the two conjugate complex functions of the interferometric field. Coupled by the multiplication for the conjugate complex functions, the lower beat-frequency synthetic-wavelength interferometric fringe pattern is derived directly. And if the SDWI is implemented with the π/2 phase shift at λ S , the obtained phase-shift interferogram for λ S could be demodulated by the conventional phase-shift algorithm. Compared with other spatial-domain Fourier transform demodulation theory, the half-band filter used in CCFC method is appropriate for the different spectral width and carrier spatial frequency. The necessary introduced linear carrier is merely about 0.0947 times of the carrier in the former numerically. And it is only used to pursue the separation between the ±1 order phase lobes instead of the separation between the different wavelength phase lobes. The feasibility and applicability of the CCFC method are verified using simulation and experimental results. [ABSTRACT FROM AUTHOR]

• This strategy only uses a single interferogram, which will reduce data acquisition requirements and improve measurement efficiency. • Based on the theoretical analysis of the optical propagation path in the experimental system, a simple method is derived to correct the retrace error and established a matching model. • Simulation and experimental results show that our method not only has high-accuracy of measuring small ROC, but also performs well in the measurement of large ROC. We proposed an iterative correlation coefficient matching strategy for the high-precision measurement of the radius of curvature (ROC), which only needs a single-frame interferogram. This strategy includes two parts: one is to obtain an initial ROC by using the relationship between the ROC and the diameter of the dark ring; other is to further solve a high-precision value by an iterative method. In the iterative part, we simulated a series of interference patterns with each ROC in the setting range, and calculated the correlation coefficient between the each simulated interferogram and the measured interferogram, and searched the maximum of the correlation coefficient that would be used to confirm a new ROC in the next iteration. When the calculated ROCs in the adjacent iterations meet the termination condition, the high-accuracy ROC can be solved. The feasibility of our proposed method has been verified by simulations and experiments. The errors of the test mirrors with the ROC of 101.6 mm and 1000 mm are 0.013% and 0.024% in experiments, respectively. This research provides a simple and feasible method for realizing the high-precision ROC measurement. [ABSTRACT FROM AUTHOR]

A novel white-light interference signal leakage sampling points (LSPs) correction method based on Morlet wavelet transform and phase seven-step phase shift algorithm (PSA) is presented in this paper. During the correction process, the method can eliminate the LSPs error accurately without changing traditional optical system. Meanwhile, it can effectively de-noise the interference signals and calculate a relatively smooth recovery shape. • The main advantage of the LSPs correction method is that we use wavelet transform to find LSPs in white-light interference signals innovatively for its characteristic of the wavelet coefficient at the distortion points position are different from the general positions, which is different from the traditional method of using wavelet transform for noise reduction and ZOPD extraction. • Furthermore, the algorithm can be applied for any traditional optical system of white-light interferometry. It is simple, accurate and easy to optimize other algorithms. White-light scanning interferometry has become a well-established tool for measuring the microscopic three-dimensional morphology of objects. However, it is sensitive to external disturbances and suffers from leakage sampling, which compromises the accuracy of the measurements. To avoid the error, a robust correction method is proposed, based on wavelet transform, to find leakage sampling point (LSP), and the cubic spline interpolation method is used to complete the interference signal to achieve the signal correction. Further, phase evaluation at each pixel provides a high vertical resolution to characterize the microstructure. In addition, the proposed method exhibits a good denoising performance. Simulations and comparison experiments demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]