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Distance measurement based on the accumulated phase of intensity-modulated continuous-wave lasers is an established approach for pointwise geometry acquisition in uncontrolled conditions, enabling some of the most accurate Lidar/laser-scanning solutions. Inherently affected by cycle ambiguities due to the modulo 2 π phase observations, several modulation wavelengths are typically used in practical implementations to extend the measurement range. One of the main limitations of these systems arises from their inability to decouple mixed signals affected by different delays. This is especially relevant when the laser beam illuminates simultaneously two or more surfaces at significantly different distances, producing mixed-pixel measurements in which the estimated distance does not reliably correspond to any of the involved scatterers. Algorithms for detection and filtering of mixed pixels within point-cloud data have been proposed based on analyzing consistency across local neighborhoods. The resolution of multiple scatterers on individual measurements, however, has not been yet reported nor is provided by undisclosed commercial implementations. In this work, we analyze the problem of signal mixing in multi-wavelength phase-based distance estimation, and propose an algorithm for joint phase ambiguity resolution and mixed pixel detection based on mixed integer linear programming. We first analyze theoretically the performance limits of the proposed solution, demonstrating unbiasedness in the presence of noise and robustness in the presence of multiple scatterers. In addition, we investigate empirically the impact of noise, mixed measurements and choice of modulation wavelengths on the performance of the proposed algorithm. The results demonstrate the capacity of the presented approach, given an adequate wavelength selection, to provide unambiguous distance estimates under realistic noise conditions and to identify measurements affected by mixed pixels while approximating the position of the dominant scatterer. Aside from contributing to improving the reliability and resolution capability of Lidar and laser-scanning data, the proposed solution sets a promising step towards fully resolved multi-target distance measurement. [ABSTRACT FROM AUTHOR]

In case of in-line inspection of optical functional micro-structured surfaces with phase response as well as amplitude response, higher resolution than the diffraction limit and phase measurability are needed. We proposed a novel coherent super-resolution method named complex-amplitude-response SIM (structured illumination microscopy). An equation is derived that enables extraction of frequencies higher than the diffraction limit of the complex-amplitude response distribution of a sample from multiple acquired images, which had not been obtained previously. This equation was validated through theoretical analysis by using images calculated by numerical optical simulation that were assumed to be acquired. Numerical analyses using the derived equation and simulations of image acquisition revealed that the proposed method is able to measure phase- and amplitude-response distributions of samples with a resolution higher than the diffraction limit. It was demonstrated that the proposed method is able to separate two points at a submicron distance of 500 nm under conditions of visible light and long W.D. (NA 0.2) and measure the phase difference with a maximum error of approximately 0.03 rad (∼π/100). When the amplitude response distribution of a sample is uniform and consists only of phase responses, the structure of the sample cannot be observed by standard optical microscopy. Numerical simulations revealed that the proposed method is able to visualise such samples with fine periodic phase responses on the submicron scale (∼500 nm) beyond the diffraction limit. Furthermore, we have shown that the proposed method is able to detect phase defects in ultra-fine optical functional structures with periods of less than 100 nm, which is expected to characterise the next generation metasurfaces. • Long working distance optical measurement of submicron-structured surfaces with amplitude and phase response distributions. • The proposed method enables extraction of high frequencies of a sample beyond the diffraction limit not only for amplitude but also phase response measurement. • Visualisation of fine periodic phase structures under constant amplitude distribution condition beyond the diffraction limit. • Phase defect of 20 nm in ultra-fine periodic phase structures can be detected in long working distance measurement. [ABSTRACT FROM AUTHOR]

Finding the optimal phase matching angle of a potassium dihydrogen phosphate (KDP) crystal is vital for increasing the harmonic conversion efficiency, which plays a key role in Inertial Confinement Fusion (ICF). The aim of this study was to build and optimize an instrument, which can measure the optimal phase matching angle of a KDP crystal accurately. We designed and tested a new beam path, which made the alignment process much simple. We studied the temperature compensation method and applied it in the instrument. Several methods were used to investigate and reduce the errors of the instrument. The errors from laser energy, transmission unit, alignment system, energy meter, temperature, and environmental vibration were analyzed and optimized. The measurement accuracy of the instrument is 10 μ r a d i a n s in phase matching angle. The instrument had been manufactured and applied well in the laser fusion facility, which can save a lot of time and money. • A much simple type of CPMI had been designed and manufactured, which can measure the optimal phase matching angle of KDP crystal accurately. • By analyzing and optimizing the errors of the CPMI, the instrument had the accuracy of 10 μ radians in optimal phase-matching angle measurement. • The precise reference flat had been removed from the instrument, which made the alignment process more effective. [ABSTRACT FROM AUTHOR]

[Display omitted] • A new 3D microscope is designed by combining telecentric imaging and multi-angle Scheimpflug projection. • The improved and practical joint calibration method realizes high-accuracy system calibration. • The point-cloud registration error correction model achieves complete and high-precision microscopic 3D measurement. • A simple and effective approach is provided for 3D measurement of complex micro-structures. 3D measurement of complex micro-structures has becoming increasingly important for precision manufacturing. In this paper, a multi-angle Scheimpflug projection 3D microscope (MASP-3DM) is proposed, and the detailed design procedure is given. The system deployed four Scheimpflug projections and one telecentric imaging to overcome the shortcomings of limited depth of field (DOF), occlusion and reflection. Then, an improved and practical system calibration method is proposed, which utilizes pinhole projection model to calibrate the telecentric imaging. Meanwhile, local homography is combined with perspective-n-point (PnP) strategy to improve the calibration accuracy. Further, a point-cloud registration error correction model is established to achieve complete and high-precision measurement. The experimental results indicate that the re-projection error is within ±0.5μm and the registration error is less than 2μm for system calibration, the maximum of mean deviation, measurement bias, standard deviation, and type A uncertainty are respectively less than 3μm, 7μm, 4μm, and 1μm for 3D measurement, within the 10(H) mm ×50(W) mm ×40(D) mm volume. [ABSTRACT FROM AUTHOR]

• Fringe projection techniques for 3D shape measurement usually employ linear fringes. • This method has a limit on measurable whole plane displacement. • New method based on circular fringes is able to overcome this limitation. • It provides whole plane displacement measurement without affecting resolution. • New method of fringe analysis using single frame is developed. Fringe projection is a widely used technique for measurement of out-of-plane deformation of diffusely reflecting objects. Among the various fringe patterns employed for projection, usage of linear fringes is most common. However, the phase function of linear fringes has 2 π periodicity, thereby leading to ambiguity in determining whole-field out-of-plane deformation of dynamic objects. This paper presents a new method of measurement of whole-field out-of-plane deformation of targets by projecting a circular fringe pattern. New technique of fringe analysis is introduced to estimate the underlying phase distribution of the fringe pattern from a single image. In this technique, the fringe pattern is coordinate transformed into polar coordinates, and then Fourier fringe analysis technique is employed to obtain its phase. Subsequent to unwrapping, the phase map is re-transformed to Cartesian coordinates. The phase map obtained after coordinate transformation is converted to out-of-plane deformation map using camera calibration parameters. Simulations are carried out to establish the analysis method. Experimental validation is performed with the development of circular grating based fringe projection system. [ABSTRACT FROM AUTHOR]

• This algorithm can accurately retrieve the phase of the intensity transfer equation. • The phase can be retrieved under complex boundary condition. • The phase can be retrieved under non-uniform light-field illumination. • This algorithm is capable of handling irregular samples with taint. Phase retrieval based on the transport-of-intensity equation (TIE) illuminated with incoherent light reveals the advantages of simplicity and practicability, but the corresponding algorithm still needs accuracy improvement and applicability extension. An orthogonal direction iteration (ODI) algorithm is proposed to perform iterative calculations using the phase partial derivative information of the orthogonal directions. Under complex boundary conditions and non-uniform light-field illumination, the proposed ODI algorithm also can achieve an accurate solution of the TIE for periodic or non-periodic phase distributions. Moreover, the proposed ODI algorithm can fully utilise the phase partial derivative information of the orthogonal directions to perform phase compensation, and then achieve an accurate solution of the TIE for a phase object with shadows under non-uniform illumination. Both the simulation and experimental results demonstrate the obvious advantages of the proposed ODI algorithm for boundary condition relaxation and the accuracy improvement of solving the TIE. [ABSTRACT FROM AUTHOR]

Highlights • The CPMI was built to measure the optimal phase-matching angle of KDP crystal. • The measurement accuracy of CPMI is rather high which is 10 μrad. • Working posture adjustment system and temperature control system are applied to CPMI. Abstract An instrument has been developed to measure the optimal phase-matching angle of large-aperture potassium dihydrogen phosphate (KDP) crystal. KDP crystal in the frequency converter is applied to generate a third harmonic generation, which is important to achieve inertial confinement fusion (ICF). To achieve high harmonic conversion efficiency, the tuning angle of KDP crystal should be optimal when the frequency converter is working online in ICF facilities. The optimal tuning angle of KDP crystal must be measured off-line before KDP crystal is mounted in the facility. The Crystal Phase-matching angle Metrology Instrument (CPMI) can measure the optimal phase-matching angle and harmonic conversion efficiency of KDP crystal off-line. The CPMI is housed in ISO 5 clean room and several methods are taken to keep the temperature stable. The automatic alignment system is built in the CPMI which makes the measurement convenient and fast. The working posture adjustment system is applied to measure the optimal phase-matching angle when KDP crystal is in the working posture. The integration control system is assisted to measure the phase-matching angle automatically, which can increase the work efficiency immensely. Some experiments are done to test the measuring accuracy. The experiments indicate that the measuring error does not exceed 10 μrad and the repeated accuracy does not exceed 3 μrad. The CPMI can replace on-line measuring of the optimal phase-matching angle, which is economical and time-saving. [ABSTRACT FROM AUTHOR]

Fringe-based optical flow is a novel method for measuring the deformation of an object with a high sensitivity. When it is used for out-of-plane displacement measurement, there would be greatly error in low fringe-frequency area. To solve the problem, a new method is proposed, in which an optical vortex beam is used as the object light and a spherical wave as the reference light in double-optical-path interferometry. The interference system and principle are introduced. Some simulations are completed. The results show that there is an unmeasurable area with the circular closed fringe patterns formed by two plane waves. But with the non-closed circular fringe patterns formed by the OV object light and the spherical wave reference light, the measured phase differences are in good agreement with the standard values. And then the measurement errors would be decreased greatly. Besides, the method by using patterns obtained by the interference of an OV light and a spherical wave have a certain degree of anti-noise performance. [ABSTRACT FROM AUTHOR]

Abstract Recently, moving object reconstruction based on PSP has been attracted intensive research. The errors caused by the inner movement of PSP have been addressed successfully. However, when the object with discontinuities or isolated surface is measured and the temporal phase unwrapping method is applied, additional fringe patterns are required to unwrap the phase map. The object movement between the PSP fringe patterns and additional fringe patterns will cause unwrapping errors. This paper proposes a new method to reconstruct the moving object with discontinuous or isolated surface. The object movement is tracked and the influence on the phase map caused by the movement is analyzed. Then, the phase variation caused by the movement is obtained. The phase map of the object before movement is obtained by compensating the phase map of the object after movement based on the phase variations. Finally, the object is reconstructed by dual-frequency phase unwrapping method. A new projection strategy increasing the efficiency of the 3D frame rate is also presented in this paper. The 3D frame rate achieves half of the camera capture speed. The proposed method has high potential to be applied in industrial applications for real-time measurement of moving objects. Experiments are presented to verify the effectiveness. [ABSTRACT FROM AUTHOR]

Highlights • A numerical phase aberration compensation method for DHM is proposed. • This method needs no manual intervention or prior knowledge of recording setup. • Not only phase curvature but also high order aberrations could be corrected. • It outperforms the PVM method in terms of the noise robustness and calculation speed. • Simulated and experimental results prove the effectiveness of the proposed method. Abstract We propose a purely automatic and accurate phase aberration compensation method in digital holographic microscopy for phase-contrast imaging of living cells. At first, a least-squares fitting procedure is implemented to correct a large proportion of the phase aberrations. Subsequently, the flat phase background is retrieved based on phase gradient and image segmentation. Finally, the residual phase aberrations are eliminated in another least-squares fitting procedure performed within the background region. This method needs no manual intervention or prior knowledge of optical setup. Not only phase curvature but also high order aberrations could be corrected without extra components. It outperforms the phase-variation-minimization method in terms of noise robustness and calculation speed. The performance of the proposed method is demonstrated with simulated and experimental results. [ABSTRACT FROM AUTHOR]

Highlights • The method of Surface profiles of both surfaces of a transparent plate by using a series of fringe patterns obtained at different phase shifting caused by wavelength changing is proposed. • Iterative algorithm and the least square method is applied together to improve the precision of results. • Analyzing the influence of error from phase shifting value. • The experiment set up is simple and save time for measurement. Abstract An interferogram obtained from a transparent plate contains information about the profiles of both surfaces of the plate. This information can be extracted by processing fringe patterns measured at different wavelengths. The conventional Fourier analysis applied to solve such problems for a set of a restricted number of the fringe patterns is quite sensitive to the error of detuning the wavelength shifting and suffers from fringe patterns interference noise. This study proposes a method for finding surface profiles of a transparent plate using a series of fringe patterns obtained at different phase shifts caused by wavelength changes. The data treatment is based on the analytical approach for describing spatial distributions of irradiance in interference patterns. The results show that the proposed method is feasible. The experimental setup used herein was a Fizeau interferometer with tunable wavelength laser. A glass plate approximately 1 cm thick was as the test sample. According to the obtained results, the root mean square (RMS) errors for determining both surface profiles did not exceed 2.3 nm. [ABSTRACT FROM AUTHOR]

Highlights • This manuscript developed an efficient phase retrieval algorithm for phase shifting interferometry (PSI). • The SNR limit in the traditional PSI algorithm has been obtained and further broken by the proposed method. • This method although allow the self-calibration of phase shifts error even when the fringe number is less than one. Abstract We propose a novel phase demodulation algorithm for phase shifting interferometry (PSI) named as advanced spatial spectrum fitting (ASSF) algorithm. By utilizing dual-operation of singular value decomposition (SVD) and hybrid temporally and spatially estimating the background intensity, the retrieved phase distribution will become more robust to the noise distribution compared with the traditional PSI. At the same time, with no particular temporal phase shifts distribution requirement, it realize stable self-calibration phase retrieval with few interferograms containing less than one fringe. Therefore, even when the interferograms are seriously corrupted by the random noise or the fringe number is small, the high quality phase retrieval is possible. Both simulation and experimental results will be used to demonstrate the outstanding performance of the proposed ASSF algorithm. [ABSTRACT FROM AUTHOR]

Abstract We developed an interferometric system capable of generate four interferograms simultaneously with independent phase shifts employing modulation by polarization. The proposed system consists of three coupled interferometers: A polarized Mach–Zehnder interferometer (PMZI) which generates a primary pattern with crossed polarizations, coupled to two Michelson systems that serve as replicators of the primary pattern. In the proposed system, coupled three interferometers which generate four interference patterns with π /2 phase shifts. The four interference patterns can be detected simultaneously carrying a controllable phase shift by placing a linear polarizer in each replica obtained. To show the novelty and usage of the developed system on phase varying information temporal stability is presented and experimental results for static and dynamic variations. Highlights • Simultaneous phase shifting interferometry. • Experimental analysis of dynamic fast processes. • Coupled interferometers. [ABSTRACT FROM AUTHOR]

For the past few decades or so, tremendous research effort has been directed towards correction and compensation for system errors in phase map retrieval due to gamma-effect of the digital light processing projector used in the measurement system setup. In this paper, an update on the state-of-the-art in finding solution to the well-known nonlinear gamma problem and related effects in digital fringe projection profilometry is discussed. Using numerical experiments and illustrative simulations, recent progresses, developments, and shortcomings in remedying the gamma and its related effects in optical phase-shifting measurement profilometry using digital fringe projection techniques is broached, demonstrated, and reviewed. We further encompass the fundamental principles adopted in various nonlinear gamma calibration techniques together with viable possibilities for prospective research in optical fringe-projection metrology with phase measurement techniques. [ABSTRACT FROM AUTHOR]

Phase extraction of interferometry is a crucial step of optical measurement. In this paper, a machine learning method is proposed to extract the phase from the interferometric signal with the least squares support vector machine, which eliminates the phase unwrapping procedure and enhances the phase measuring accuracy greatly when compared with traditional phase unwrapping methods. Furthermore, it can also work well in the undersampling situation to some extent. Our method is capable of extracting both linear and nonlinear phases. A Michelson interferometer was constructed to demonstrate the validity of the method proposed, which can be potentially applied in many significant fields. [ABSTRACT FROM AUTHOR]

• A high-speed digital holographic tomography system is developed. • Interference information from four optical paths is recorded in a single hologram based on off-axis multiplexing. • 3-D dynamic phase measurement of an asymmetric gas flow is achieved. A high-speed digital holographic tomography system based on off-axis multiplexed recording is proposed for fast three-dimensional (3-D) phase measurements of transparent gasses. Object beams pass through the object at 0, 45, 90, and 135° and interfere with the reference beam to form a hologram that is recorded by a single camera. The phase information of each optical path is reconstructed by the Fresnel diffraction integral calculation, and then the 3-D phase information of the object can be obtained by the simple back-projection algorithm. The recording speed of the system depends entirely on the frame rate of the camera. In the experiments, we successfully measured the 3-D phase information of an asymmetric gas flow with the proposed system at 65 frames per second. [ABSTRACT FROM AUTHOR]

The synchronization of radio frequency (RF) systems in hadron synchrotrons relies on the availability of reference RF signals with a precise phase. For accelerators with a large frequency swing, frequency dependent phase errors can exceed the required phase margin and therefore have to be compensated. In this paper a new method for the phase calibration of RF signals with variable frequency is described. All the signals are measured with a digital oscilloscope and no complex signal processing is necessary. The described approach utilizes a three-parameter sine wave fit algorithm to estimate the phase of the relevant sine wave signals. A phase difference between RF signals with different frequencies is then calculated with respect to a reference pulse train. A detailed analysis of the measurement parameters is given. The method is applied for the calibration of the RF reference signals of the heavy ion synchrotron SIS18 at GSI. [ABSTRACT FROM AUTHOR]

We present a measurement scheme of the refractive index profile of optical fibers which does not require accurate index oil match using dual wavelength diffraction phase microscopy. Using dual wavelength algorithm, we solved phase wrapping problem caused by large optical path length difference between the optical fiber and its medium and final phase image was obtained without 2π ambiguity. The index profile was obtained by the filtered back projection algorithm that applies inverse Radon transformation of the phase profile matrix. As an example, a single mode fiber with a known index profile was measured by using this method. The measured profile is well agreed with index profile of the preform, which had been designed by a preform analyzer before the fiber being fabricated from the preform. [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]

To improve the grating wavefront quality especially the grating size, which is more than 1 m, we provide a method based on conical diffraction theory and grating groove active control technology to correct the grating substrate surface error. We apply the grating groove active control technology to carry out an echelle grating ruling experiment whose line density is 79 lines/mm in 36th order. Compared with the grating substrate surface error, the grating wavefront value reduces from 0.105 λ to 0.056 λ i.e., decreases by 47%. The experimental result proves that the grating substrate surface error compensation method can be used to improve the grating wavefront quality effectively. [ABSTRACT FROM AUTHOR]

Highlights • A novel dual-wavelength iterative method (DWIM) is described. • The phases and the phase shifts at each wavelength are simultaneously and accurately obtained from generalized dual-wavelength interferograms using DWIM. • Simulation results of the spherical cap are presented to verify the proposed method. • We give the basic relationship between the number of wavelengths, the second-order harmonics and the requirement of the minimum number of interferograms. • The applicability of DWIM is proved by the results of the biological cells. Abstract To address dual-wavelength interferograms with arbitrary phase shifts and second-order harmonics, a novel dual-wavelength iterative method (DWIM) based on the least-squares algorithm is proposed. In generalized dual-wavelength phase-shifting interferometry, to compensate for the phase-shift errors consisting of systematic and random phase-shift error, the wrapped phases of single-wavelength with high accuracy can be simultaneously obtained from generalized dual-wavelength interferograms without second-order harmonics. In addition, this method is also employed to deal with randomly phase-shifted dual-wavelength interferograms with the second-order harmonics, and then the effects of the fringe number in interferogram and the number of interferograms used on the accuracy of phase extraction are investigated by numerical simulations. Based on theoretical analysis and simulation results of DWIM, we present the basic relationship between the number of wavelengths, the second-order harmonics and the requirement of the minimum number of interferograms. Finally, the effectiveness of this method is proved by the simulation results of the spherical cap, and its applicability is verified with the results of the micro-sphere, the HeLa cell and the red blood cell, respectively. [ABSTRACT FROM AUTHOR]

Highlights • This paper presents a novel holistic calibration method for stereo deflectometry system to improve the system measurement accuracy. • The initial value of the system parameters are calculated from the fringe patterns displayed on the systemic LCD screen through a reflection of a markless flat mirror. • An iterative algorithm is proposed to compensate system distortion and optimize camera imaging parameters and system geometrical relation parameters based on a cost function. • The PV (peak value) of measurement error of a flat mirror can be reduced to 69.7 nm by applying the proposed method from 282 nm obtained with the conventional calibration approach. Abstract This paper presents a novel holistic calibration method for stereo deflectometry system to improve the system measurement accuracy. The reconstruction result of stereo deflectometry is integrated with the calculated normal data of the measured surface. The calculation accuracy of the normal data is seriously influenced by the calibration accuracy of the geometrical relationship of the stereo deflectometry system. Conventional calibration approaches introduce form error to the system due to inaccurate imaging model and distortion elimination. The proposed calibration method compensates system distortion based on an iterative algorithm instead of the conventional distortion mathematical model. The initial value of the system parameters are calculated from the fringe patterns displayed on the systemic LCD screen through a reflection of a markless flat mirror. An iterative algorithm is proposed to compensate system distortion and optimize camera imaging parameters and system geometrical relation parameters based on a cost function. Both simulation work and experimental results show the proposed calibration method can significantly improve the calibration and measurement accuracy of a stereo deflectometry. The PV (peak value) of measurement error of a flat mirror can be reduced to 69.7 nm by applying the proposed method from 282 nm obtained with the conventional calibration approach. [ABSTRACT FROM AUTHOR]

Highlights • A wavefront reconstruction method for multi-lateral shearing interferometry is proposed. • The test wavefront can be recovered from the multidirectional phase differences using the difference Zernike polynomials fitting method. • Computational burden can be reduced by representing the multidirectional phase differences with difference Zernike polynomials in only two orthogonal shear directions. • Accuracy and noise resistance of the method are verified theoretically and experimentally. Abstract For the multi-lateral shearing interferometers (multi-LSIs), the measurement accuracy can be enhanced by estimating the wavefront under test with the multidirectional phase information encoded in the shearing interferogram. Usually the multi-LSIs reconstruct the test wavefront from the phase derivatives in multiple directions using the discrete Fourier transforms (DFT) method, which is only suitable to small shear ratios and relatively sensitive to noise. To improve the accuracy of multi-LSIs, wavefront reconstruction from the multidirectional phase differences using the difference Zernike polynomials fitting (DZPF) method is proposed in this paper. For the DZPF method applied in the quadriwave LSI, difference Zernike polynomials in only two orthogonal shear directions are required to represent the phase differences in multiple shear directions. In this way, the test wavefront can be reconstructed from the phase differences in multiple shear directions using a noise-variance weighted least-squares method with almost no extra computational burden, compared with the usual recovery from the phase differences in two orthogonal directions. Numerical simulation results show that the DZPF method can maintain high reconstruction accuracy in a wider range of shear ratios and has much better anti-noise performance than the DFT method. A null test experiment of the quadriwave LSI has been conducted and the experimental results show that the measurement accuracy of the quadriwave LSI can be improved from 0.0054 λ rms to 0.0029 λ rms (λ = 632.8 nm) by substituting the DFT method with the proposed DZPF method in the wavefront reconstruction process. [ABSTRACT FROM AUTHOR]

In phase measuring deflectometry, two orthogonal sinusoidal fringe patterns are separately projected on the test surface and the distorted fringes reflected by the surface are recorded, each with a sequential phase shift. Then the two components of the local surface gradients are obtained by triangulation. It usually involves some complicated and time-consuming procedures (fringe projection in the orthogonal directions). In addition, the digital light devices (e.g. LCD screen and CCD camera) are not error free. There are quantization errors for each pixel of both LCD and CCD. Therefore, to avoid the complex process and improve the reliability of the phase distribution, a phase extraction algorithm with five-frame crossed fringes is presented in this paper. It is based on a least-squares iterative process. Using the proposed algorithm, phase distributions and phase shift amounts in two orthogonal directions can be simultaneously and successfully determined through an iterative procedure. Both a numerical simulation and a preliminary experiment are conducted to verify the validity and performance of this algorithm. Experimental results obtained by our method are shown, and comparisons between our experimental results and those obtained by the traditional 16-step phase-shifting algorithm and between our experimental results and those measured by the Fizeau interferometer are made. [ABSTRACT FROM AUTHOR]

The detection of broadband signal power spectrum based on spectral hole-burning (SHB) material has been investigated a lot, but the detection of phase is not reported yet. In this paper, a method of RF signal real-time phase detection is proposed by applying the SHB material. Phase measurement is performed through the in-phase and in-quadrature components of emitted field generated by the macro polarization at steady state. The time range of reaching steady state is determined by numerical solution of Bloch equation solved by Runge–Kutta method. Furthermore, the effect of phase change rate on the accuracy of real-time phase measurement is also given. The typical RF signals are performed in the simulation to demonstrate the feasibility of the method and agreeable results are obtained in the phase value. Through the analysis of the effect of noise on the phase accuracy, When SNR is greater than 24 dB, phase error is less than 0.83%, and the phase error does not accumulate with time. [ABSTRACT FROM AUTHOR]

Wavelength-tuning interferometry has been widely used to measure and estimate the surface profile of optical components. However, in multilayer interferometry, the coupling error between the higher harmonics and the phase-shift error causes a considerable systematic error in the calculated phase. In this research, the new 7 N − 6 phase-shifting algorithm was developed using the characteristic polynomial theory. The coupling errors calculated by various types of phase-shifting algorithms were analyzed. The surface profile and optical thickness deviation of the lithium niobate crystal wafer were measured simultaneously using wavelength-tuning Fizeau interferometry and the 7 N − 6 algorithm. The experimental results were compared in terms of observed ripples and measurement repeatability. [ABSTRACT FROM AUTHOR]

A circular-path polarization point-diffraction interferometer (PDI) is developed, in which the reference and test waves travel in a nearly same optical path and in opposite directions. Furthermore, a linear tilting modulation can be introduced into two interfering waves by rotating the polarization beam splitter (PBS). As a result, the fringe pattern with carrier frequency is captured and the Fourier transform method is employed to extract the tested wavefront. Furthermore, by analyzing the fringe parameters, i.e., fringe contrast and carrier frequency, it can be concluded that the proposed PDI can adjust easily these two fringe parameters. Therefore, the fringe pattern with the highest contrast and suitable carrier frequency can be captured, and so as this PDI with compact configuration can also obtain high accuracy of phase meausrement. [ABSTRACT FROM AUTHOR]

In this work, we have theoretically investigated three designs of common-path polarization heterodyne interferometry (CPHI) with the possibility of to enhance the phase sensitivity and sensitivity-tunable ability. The schemes are established by utilizing some quarter wave plates (QWP) to control the ellipticity of polarization of light, and adjusting the azimuthal angle to achieve adequate phase sensitivity. The theoretical analysis has been done by Jones calculus and the results will be compared with conventional polarization heterodyne interferometry. The proposed designs have high phase sensitivity and sensitivity-tunable ability. Additionally it causes to shift the point of the extreme slope to the smaller incidence angle which usually is more convenient for SPR measurement. By the simulation, the phase sensitivity and resolving power of refractive index measurement has been estimated 5.5 × 10 5 °/RIU and 1.8 × 10 −8 RIU, respectively. [ABSTRACT FROM AUTHOR]

In criminal investigations, latent fingerprints are one of the most significant forms of evidence and most commonly used forensic investigation tool worldwide. The existing non-contact latent fingerprint detection systems are bulky, expensive and require environment which is shock and vibration resistant, thereby limiting their usability outside the laboratory. In this article, a compact, full field, low cost technique for profiling of fingerprints using deflectometry is proposed. Using inexpensive mobile phone screen based structured illumination, and windowed Fourier transform (WFT) based phase retrieval mechanism, the 2D and 3D phase plots reconstruct the profile information of the fingerprint. The phase information is also used to confirm a match between two fingerprints in real time. Since the proposed technique is non-interferometric, the measurements are least affected by environmental perturbations. Using the proposed technique, a portable sensor capable of field deployment has been realized. [ABSTRACT FROM AUTHOR]

We report a novel approach to diffraction phase microscopy (DPM) with automatic pinhole alignment. The pinhole, which serves as a spatial low-pass filter to generate a uniform reference beam, is made out of a liquid crystal display (LCD) device that allows for electrical control. We have made DPM more accessible to users, while maintaining high phase measurement sensitivity and accuracy, through exploring low cost optical components and replacing the tedious pinhole alignment process with an automatic pinhole optical alignment procedure. Due to its flexibility in modifying the size and shape, this LCD device serves as a universal filter, requiring no future replacement. Moreover, a graphic user interface for real-time phase imaging has been also developed by using a USB CMOS camera. Experimental results of height maps of beads sample and live red blood cells (RBCs) dynamics are also presented, making this system ready for broad adaption to biological imaging and material metrology. [ABSTRACT FROM AUTHOR]

Dual-wavelength interferometry could extend the measured range of single-wavelength interferometry by combining the two single wavelength phases, particularly for the measurement of step height. When testing the high-reflectivity surfaces with the single wavelength Fizeau interferometer, we have presented the π ∕ 4 phase-shift carrier squeezing interferometry (QCSI) method for phase extraction with multi-beam interference ( Appl. Opt . 55, 1920–1928, 2016). In this paper, we propose an integer and decimal portions synthetization (IDS) method for the multi-beam interference in the dual-wavelength Fizeau interferometer. One of the single wavelength wrapped phases is demodulated by the multi-beam interference QCSI algorithm, while the second of the single wavelength wrapped phases is extracted by the conventional two-beam interference phase-shift algorithm, so the equivalent wavelength unwrapped phase is derived from the two single wavelength wrapped phase. The decimal portion of synthesized phase is then obtained directly from the first single wavelength wrapped phase, and the integer portion of synthesized phase is obtained from the fringe order of the first single wavelength wrapped phase determined by the equivalent wavelength unwrapped phase. The proposed non-iterative IDS method avoids the common error magnification effect in the two-wavelength techniques, and only requires no more than 8 frame phase-shift interferograms for each single wavelength. Its robust performance is validated by both simulations and experiments in the presence of multi-beam interference as well as phase-shift error for measuring objects with height discontinuities. [ABSTRACT FROM AUTHOR]

• An algorithm is proposed to improve the surface profilemeasurement accuracy in spectral interferometer. • Simulation is carried out to prove this algorithmhas the 96% possibility to correct the error in slope of the linear fitted phase and the 4% possibility to bring the additional minor errorunder the influence of three kinds of additive noise. • For the measurement of a reflecting mirror, the maximum variation of the surface and the repeatability are optimized to 10 nm and 2.2 nm from 30 nm and 4.9 nm, respectively. • For the measurement of a smooth profile with a step shape of nearly 3 μm height, the algorithm provides a surface variation less than 10 nm and minimum step height repeatability of 1.3 nm. The spectrally resolved interferometer (SRI) is used to measure the surface profile by the linear fitting line of its phase distribution of spectral interference signal. However, the noise existed in the phase cannot be ignored if the nano-scale measurement accuracy is required. In this paper, a novel algorithm is proposed to improve the measurement accuracy by using the constant term oflinear fitting line of phase distribution in wavenumber domain. The simulations indicate that the algorithm achieves the similar measurement accuracy under the influence of three kinds of noise. Even though the proposed algorithm has the possibility of 4% to bring the additional minor error, it provides a better performance on measurement of entire surface in different SNRs compared with the other two common algorithms. In experiments, the variations of surface less than 10 nm and 30 nm and the repeatability of 2.2 nm and 4.9 nm are obtained in the measurements of a protected aluminium mirror with and without proposed algorithm. A smooth profile with a step shape of nearly 3 μm height is tested, where the maximum repeatability of step height and maximum magnitude of variations of the surfaces reaches to 3.8 nm and 10 nm from the 15.3 nm and 30 nm by using this algorithm. Both the simulations and experimental results demonstrate that the proposed algorithm is feasible for high-precision measurement. [ABSTRACT FROM AUTHOR]

• An approach for phase measurement of structured light in optical manipulation is proposed and experimentally demonstrated. • The phase profiles can be accurately obtained, which is highly desirable in optical trapping systems. • Our proposed method exhibits remarkable advantages including strong flexibility, no environmental noise, and rapid measurement. Accurate phase measurement of structured light is highly desirable in holographic optical tweezers, since quality of phase profiles have a strong impact on performance of manipulating particles. Here, we report a novel interferometric phase measurement technique for accurately measuring phase profile of structured light. The related experiments are performed, in which the measured phase profiles agree well with the designed phase profiles. It reveals that the phase profiles of structured light can be accurately obtained. Importantly, the fast switch between phase measurement and particle manipulation in the experiment can be easily implemented, which are strongly preferable in holographic optical tweezers. This study offers a promising way for accurately obtaining phase profiles of structure light, which is very helpful for particle manipulation. [ABSTRACT FROM AUTHOR]

• A parameter estimation (PE) paradigm is proposed to achieve high-depth resolution tomography phase measurement. • The PE paradigm can break through the limitation of depth resolution in WSI with narrow scanning bandwidth. • The PE reaches the same depth resolution level as DFT even reducing 60% scanning bandwidth when PSNR is higher than 35dB. Wavelength scanning interferometry (WSI) is a promising tomographic imaging technique. However, the depth resolution is fundamentally limited by a narrow wavelength scanning bandwidth, which brings challenges to the frequency extraction for depth information. In this work, we proposed a parameter estimation (PE) paradigm via sinewaves separation, which allows high depth resolution tomographic measurement with narrow-band sources. To obtain accurate depth information, a sinewaves separation model is designed to estimate the frequency of the overlapped signals and it can achieve higher depth resolution without any prior knowledge even under limited scanning bandwidth. Moreover, the estimated frequency is used for phase retrieval and the multi-layer 3D profile measurement can be further implemented. The simulation and experimental results show that the PE method can reach the same depth resolution level as discrete Fourier transform (DFT) even reducing 60% scanning bandwidth when PSNR is higher than 35 dB. [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]

Phase map filtering is considered an indispensable process in the measurement delivered by speckle interferometric optics. For recent measurements, quite a lot of scenarios require an optimized time consumption. A notable feature of the raw phase map is the 2 π modulo of the phase distribution, as retrieved by the inverse tangent operation. Instead of employing the filtering method directly on the phase fringe pattern, the wrapped phase is converted into the sine–cosine domain with its sine and cosine components, and then the filtering method is applied to them. However, it is the nature of the sine–cosine filtering framework that consumes approximately 70% calculation resources for the recalculation of the intermediate phase map and the sine/cosine components at every loop, which limits the temporal property of related measurement. To address the issues of efficiency and quality at the same time, a new filtering domain is proposed, namely the complex amplitude domain filtering framework. The filtering is conducted at the stage of recovering the complex amplitude without calculating the intermediate phase map at every loop. The merit of complex amplitude domain filtering is that it has a good filtering efficiency to remove the speckle noise, preserves the details of the sharp edge in the phase-wrapped area at the same time, and no additional phase shift is generated during the filtering. Most of the existing filters and strategies used in the sine–cosine filtering domain can be directly applied in the proposed complex amplitude domain. Preliminary experiments show that, compared to the sine–cosine domain filtering, the proposed complex amplitude domain filtering accelerates the filtering process by at least 40% at no cost of filtering quality, and particularly shows a better filtering performance with the partial differential equations (PDE) noise reduction method. • Speckle suppression speed at least 40% faster than filtering in sine–cosine domain. • Preserving details of sharp edges at phase jumping area in phase measurement. • Existing filters being readily and effectively applied in complex amplitude domain. • No artificial phase shift generated during complex amplitude domain filtering. [ABSTRACT FROM AUTHOR]

Absolute phase information is required when multiple separated objects are being measured. The recent proposed phase-coding method can effectively achieve absolute phase retrieval by embedding the fringe order information in phase domain. However, it suffers from the limitation of codewords and the requirement of more coding patterns. To overcome these problems, this paper proposed several improved phase-coding methods to solve the absolute phase with fewer patterns. The four-frame and five-frame method are suitable when the fringes are sparse, since they can respectively encode N ∕ 2 and N fringe periods(generally N ≤ 16 ). If really dense fringe patterns with more than N periods are required, the improved two-step phase-coding algorithm can be adopted since it can encode about N 2 ∕ 2 fringe periods. Experiments were conducted and the results verify the success of the proposed methods. [ABSTRACT FROM AUTHOR]

A novel wavefront reconstruction algorithm for radial shearing interferometer (RSI) is proposed in this paper. Based on the shearing relationship of RSI, an interpolation coefficient matrix is established by the radial shearing ratio and the number of discrete points of test wavefront. Accordingly, the expanded wavefront is characterized by the interpolation coefficient matrix and the test wavefront. Consequently the test wavefront can be calculated from the phase difference wavefront. The numerical simulation is conducted to confirm the correctness of the proposed algorithm. Compared with the previous wavefront reconstruction methods, the proposed algorithm is more accurate and stable. [ABSTRACT FROM AUTHOR]

Phase unwrapping is one of the most challenging processes in many profilometry techniques. To sidestep the phase unwrapping process, Perciante et al. (2015) proposed a wrapping-free method to retrieve the phase based on the direct integration of the spatial derivatives of the fringe patterns. However, this method is only applicable to objects with phase continuity, so it may fail to handle fringe patterns containing complicated singularities such as noise, shadows, shears and surface discontinuities. In the light of this problems, a robust wrapping-free phase retrieval method is proposed that is based on the combined use of Perciante's method and the weighted least squares method. Two partial derivatives of the desired phase are obtained from the fringe patterns, while the carrier is eliminated using the direct phase difference method. The phase singularities are determined using a derivative variance correlation map (DVCM), and the weighting coefficient is obtained from the binary mask of the reverse DVCM. Simulations and experiments are conducted to prove the validity of the proposed method. The results are analyzed and compared with those of Perciante's method demonstrating that in addition to maintaining the advantage of sidestepping the phase unwrapping process, the proposed method is available for measuring objects with some types of singularities sources. [ABSTRACT FROM AUTHOR]

A film measuring method based on a new data model using a home-made microscopic white light spectral interferometer is proposed. It can improve the measuring accuracy of the thin film thickness at different OPDs. The influence of the effective thickness caused by the beam splitter prism in a Michelson interferometric objective is analysed and found not to be negligible while calculating the thin-film thickness. The linear relationship between the effective thickness and the optical path difference (OPD) can be removed by introducing a wavelength correction which made the effective thickness measurement more accurate. Some experiments on the film standard with calibrated film thickness showed that introducing a wavelength correction made the film thickness measurement more accurate at different OPDs. [ABSTRACT FROM AUTHOR]

Dimensional metrology for micro structure plays an important role in addressing quality issues and observing the performance of micro-fabricated products. In white light interferometry, the proposed method is expected to measure three-dimensional topography through modulation depth in spatial frequency domain. A normalized modulation depth is first obtained in the xy plane (image plane) for each CCD image individually. After that, the modulation depth of each pixel is analyzed along the scanning direction (z-axis) to reshape the topography of micro samples. Owing to the characteristics of modulation depth in broadband light interferometry, the method could effectively suppress the negative influences caused by light fluctuations and external irradiance disturbance. Both theory and experiments are elaborated in detail to verify that the modulation depth-based method can greatly level up the stability and sensitivity with satisfied precision in the measurement system. This technique can achieve an improved robustness in a complex measurement environment with the potential to be applied in online topography measurement such as chemistry and medical domains. [ABSTRACT FROM AUTHOR]

We present a new dual-wavelength dual-refractive-index digital holographic (DWDRIDH) technique that can be employed for simultaneously measuring the surface and subsurface three-dimensional topographies and does not involve the usual phase unwrapping by detection of phase discontinuity thanks to the resulting synthetic beat wavelength. The reconstructed unambiguous phase images for the synthetic beat wavelength are achieved by subtraction of the independent phase maps, which were obtained using four-phase step algorithm for each wavelength separately, and then both surface topography and subsurface shape can be decoupled from the phase maps on the beat wavelength by use of two separate refractive indices. By simulation technology, the feasibility of this method is demonstrated by the results concerning the surface and subsurface heights of a homocentric sphere and a simulated monocyte, respectively. [ABSTRACT FROM AUTHOR]

Phase retrieval technique is regarded as one of the most significant tools to solve optical inverse problems. Several phase retrieval algorithms are discussed in this review. The occurrence of ill-posed conditions often makes the calculation difficult. As a synthesis, the multiple-image phase retrieval technology is invented to obtain more accurate convergence result in iterative computation. The multiple-input retrieval scheme can attach new constraints on convergence as a new limitation. As an indirect measuring method, it will make it possible to reconstruct the distribution of intensity and phase in an imaging or measurement system, where data processing is executed by computer. Moreover, the retrieval method has been applied for image encryption successfully. Finally, the development and application of the iterative phase retrieval are overviewed. [ABSTRACT FROM AUTHOR]

A novel method for testing aspheric lenses using digital holography with an electrically tunable lens (ETL) is proposed and experimentally verified. The ETL generates a tunable deformed wavefront which helps to decrease the high gradient of aspheric lenses. By decomposing the aspheric surface into two resolvable ones, its absolute phase can be determined using a double-exposure measurement. In this method, the wavefront generated by the ETL need not be identical to the aspheric surface as in conventional null interferometer system, but just sufficient to resolve the high gradient surface. On the other hand, the tunability of the ETL allows generation of wavefronts which can be used to test different aspheric lens. Furthermore, advantages of the ETL such as low cost, fast response, and compact configuration make the proposed method a promising technique for aspheric surface measurement. [ABSTRACT FROM AUTHOR]

Spatial filtering, a key point to realize real-time measurement, is used commonly in digital off-axis holography to extract desired terms. In this paper, we propose a weighted adaptive spatial filtering method by weighting the adaptive filtering window (obtained from image segmentation) based on signal to noise ratio. The advantages of this method are evaluated by simulations and further verified by recorded digital image plane holograms. The results demonstrate that our method is effective in suppressing noise and retaining the sharp edges in the reconstructed 3D profiles. [ABSTRACT FROM AUTHOR]

A birefringent-refraction (BR) sensor for measuring refractive indices of liquid solutions based on phase interrogation in a heterodyne interferometer is proposed. We theoretically investigate a comprehensive performance comparison between a surface plasmon resonance (SPR) sensor and the proposed BR sensor in terms of sensitivity and the dynamic range in refractive index measurements. In comparison with a typical SPR sensor, the simulations and experiments show that BR sensors can achieve the same order of sensitivity but with a flexible incident angle and a wide RI range. [ABSTRACT FROM AUTHOR]

We report simultaneous measurement of thickness and refractive index (RI) using Coherent Gradient Sensing (CGS) based interferometric setup. The collimated light beam transmitted through the specimen is analyzed using two gratings in tandem and a spatial filtering arrangement. At the imaging plane, the desired orders superpose yielding interference fringes. Phase shifting interferometric (PSI) technique has been used to obtain the phase information directly. For decoding the information of thickness and RI, the specimen is rotated and the variation in interferometric phase before and after the specimen rotation determined. Simultaneous measurement on a glass plate of thickness 6.019 mm and refractive index of 1.4570 has been demonstrated. Detailed uncertainty analysis is also reported. The expanded uncertainty for thickness and RI in the measurement process was determined to be ±0.005 mm and ±0.00008 respectively. [ABSTRACT FROM AUTHOR]

Spherical concave surfaces with high numerical apertures are required in industry for lithography optics at ultraviolet and X-ray wavelengths. Among the systematic errors in these spherical-surface test, the gravitational deformation has not been separated from the other optical aberrations. We utilized a two-surface comparison method to quantify the gravitational deformation in a vertical Fizeau interferometer. Certain aberrations vary with rotation around the optical axis. We averaged the ordinary aberrations and isolated the aberration caused by gravitational deformation. Experimental results show that a 4-in concave surface with an F -number 0.75 reveals to have a gravitational deformation of 7 nm peak-to-valley. [ABSTRACT FROM AUTHOR]

Micro-metallic particles embedded in polymers are now widely used in several industrial applications in order to modify the mechanical properties of the bulk. A uniform distribution of these particles inside the polymers is highly desired for instance, when a biological backscattering is simulated or a bio-framework is designed. A 3D Fourier domain optical coherence tomography system to detect the polymer's internal homogeneity is proposed. This optical system has a 2D camera sensor array that records a fringe pattern used to reconstruct with a single shot the tomographic image of the sample. The system gathers the full 3D tomographic and optical phase information during a controlled deformation by means of a motion linear stage. This stage avoids the use of expensive tilting stages, which in addition are commonly controlled by piezo drivers. As proof of principle, a series of different deformations were proposed to detect the uniform or non-uniform internal deposition of copper micro particles. The results are presented as images coming from the 3D tomographic micro reconstruction of the samples, and the 3D optical phase information that identifies the in-homogeneity regions within the Poly methyl methacrylate (PMMA) volume. [ABSTRACT FROM AUTHOR]

• A strategy which combines the DFS-LSR and the FPL covers all-stage cophasing without any further hardware cost for the DFS is proposed and analyzed. • The DFS-LSR make up for shortcoming of the FPL in fine cophasing and is more robust than the MPP. • Testing and mathematical analysis indicate the robustness of the DFS-LSR. As a technique for quantitatively measuring wavefront piston of optical multi-aperture systems, dispersed fringe sensor (DFS) is considered to be a coarse phasing sensor which can be complemented by fine cophasing sensors. In this work, we presented a strategy for the DFS to cover coarse and fine co-phasing stages. The strategy that combines two estimating algorithms and the optical features makes the DFS feasible for both coarse and fine cophasing stages. Subsequent analysis proves the ability of DFS in coarse and fine stages and in particular the robustness of this strategy in fine co-phasing stage. Further, we use demonstration experiment to show the ability of this strategy in different situations compared with other methods. In addition, the robust anti-noise ability is proved by both demonstration and analysis. Thus, the strategy gives phasing system the ability to robustly cover coarse and fine co-phasing stages without any further hardware cost for DFS. [ABSTRACT FROM AUTHOR]