2π phase ambiguity problem is very important in phase measurement when a deformed object has a large out of plane displacement. The dual-frequency projection grating phaseshifting profilometry （PSP） can be used to ...2π phase ambiguity problem is very important in phase measurement when a deformed object has a large out of plane displacement. The dual-frequency projection grating phaseshifting profilometry （PSP） can be used to solve such an issue. In the measurement, two properchosen frequency gratings are utilized to synthesize an equivalent wavelength grating which ensures the computed phase in a principal phase range. Thus, the error caused by the phase unwrapping process with the conventional phase reconstruct algorithm can be eliminated. Finally, experimental result of a specimen with large plastic deformation is given to prove that the proposed method is effective to handle the phase discontinuity.展开更多
In Fourier transform profilometry （FTP）, we must restrain spectrum overlapping caused by the nonlinearity of the charge coupled device （CCD） and increase the measurement accuracy of the object shape. Firstly, the ...In Fourier transform profilometry （FTP）, we must restrain spectrum overlapping caused by the nonlinearity of the charge coupled device （CCD） and increase the measurement accuracy of the object shape. Firstly, the causes of producing higher-order spectrum components and inducing spectrum overlapping are analysed theoretically, and a simple physical ex- planation and analytical deduction are given. Secondly, aiming to suppress spectrum overlapping and improve measurement accuracy, the influence of spatial carrier frequency of projection grating on them is analysed. A method of increasing the spatial carrier frequency of projection grating to restrain or reduce the spectrum overlapping significantly is proposed. We then analyze the mechanism of how the spectrum overlapping is reduced. Finally, the simulation results and experimental measurements verify the correction of the proposed theory and method.展开更多
In order to study the strength of the composite material plate problems, need to adopt a nondestructive testing method to obtain the specimen surface under the effect of high-speed impact regularity of shape. The proj...In order to study the strength of the composite material plate problems, need to adopt a nondestructive testing method to obtain the specimen surface under the effect of high-speed impact regularity of shape. The projection profilometry was used to measure the surface profile or the full field deformation. Furtherly, by using the Fourier transform algorithm, there is only one frame of captured image</span><span style="font-family:Verdana;"> which</span><span style="font-family:Verdana;"> is needed in the measurement, so that it can be introduced into the high speed impaction procedure measurement. An experimental system, which was contained with an impact setup and the projection profilometry measurement part, was constructed for the impaction action characteristic research. The metallic impact object can be launched by a gas gun or a spin fan, respectively. The detected object </span><span style="font-family:Verdana;">is</span><span style="font-family:Verdana;"> manufactured by composite materials. In order to increase the surface deformation measurement accuracy, the calibration method and the error was discussed with different calibration specimen. And then, the proposed profilometry measurement method is proved by the gas gun and spin fan projectile test. The surface deformation of the manufactured composite plates and fan case are measured in the impaction procedure. So that the impact action details can be described much more clearly than the traditional video monitoring method.展开更多
Digital structured light （SL） profilometry is increasingly used in three-dimensional （3D） measurement technology. However, the nonlinearity of the off-the-shelf projectors and cameras seriously reduces the measure...Digital structured light （SL） profilometry is increasingly used in three-dimensional （3D） measurement technology. However, the nonlinearity of the off-the-shelf projectors and cameras seriously reduces the measurement accuracy. In this paper, first, we review the nonlinear effects of the projector-camera system in the phase-shifting structured light depth measurement method. We show that high order harmonic wave components lead to phase error in the phase-shifting method. Then a practical method based on frequency domain filtering is proposed for nonlinear error reduction. By using this method, the nonlinear calibration of the SL system is not required. Moreover, both the nonlinear effects of the projector and the camera can be effectively reduced. The simulations and experiments have verified our nonlinear correction method.展开更多
Three dimensional（3D） displacements, which can be translated further into 3D strain, are key parameters tor design, manufacturing and quality control. Using different optical setups, phase-shift methods, and algorit...Three dimensional（3D） displacements, which can be translated further into 3D strain, are key parameters tor design, manufacturing and quality control. Using different optical setups, phase-shift methods, and algorithms, several different 3D electronic speckle pattern interferometry（ESPl） systems for displacement and strain measurements have been achieved and commercialized. This paper provides a review of the recent developments in ESPI systems for 3D displacement and strain measurement. After an overview of the fundamentals of ESP! theory, temporal phase-shift, and spatial phase-shift techniques, 3D deformation measurements by the temporal phase-shift ESPI system, which is suited well for static measurement, and by the spatial phase-shift ESPI system, which is particularly useful for dynamic measurement, are discussed. For each method, the basic theory, a brief derivation and different optical layouts are presented. The state of art application, potential and limitation of the ESPI systems are shown and demonstrated.展开更多
The technique of phase measuring profilometry using a single phase step method is proposed.This method can automatically obtain phase value at each pixel by using a discret cosine transform algorithm.The method is abl...The technique of phase measuring profilometry using a single phase step method is proposed.This method can automatically obtain phase value at each pixel by using a discret cosine transform algorithm.The method is able to automatically recognize any position between depression and elevation on an object surface.Theoretical analysis and experimental verification are presented.展开更多
A fast 3D reconstruction method based on structured light to measure various parameters of the raceway groove is presented. Digital parallel grating stripes distributed with sine density are projected onto the raceway...A fast 3D reconstruction method based on structured light to measure various parameters of the raceway groove is presented. Digital parallel grating stripes distributed with sine density are projected onto the raceway groove by a DLP projector, and distorting of stripes is happened on the raceway. Simultaneously, aided by three-step phase-shifting approach, three images covered by different stripes are obtained by a high-resolution CCD camera at the same location, thus a more accuracy local topography can be obtained. And then the bearing is rotated on a high precision computer controlled rotational stage. Three images are also obtained as the former step at next planned location triggered by the motor. After one cycle, all images information is combined through the mosaics. As a result, the 3D information of raceway groove can be gained. Not only geometric properties but also surface flaws can be extracted by software. A preliminary hardware system has been built, with which some geometric parameters have been extracted from reconstructed local topography.展开更多
The dual-frequency grating measurement theory is proposed in order to carry out the measurement of a discontinuous object. Firstly, the reason why frequency spectra are produced by low frequency gratings and high freq...The dual-frequency grating measurement theory is proposed in order to carry out the measurement of a discontinuous object. Firstly, the reason why frequency spectra are produced by low frequency gratings and high frequency gratings in the field of frequency is analysed, and the relationship between the wrapped-phase and the unwrapping-phase is discussed. Secondly, a method to combine the advantages of the two kinds of gratings is proposed： one stripe is produced in the mutation part of the object measured by a suitable low frequency grating designed by MATLAB, then the phase produced by the low frequency grating need not be unfolded. The integer series of stripes is produced by a high frequency grating designed by MATLAB based on the frequency ratio of the two kinds of gratings and the high frequency wrapped-phase, and the high frequency unwrapping-phase is then obtained. In order to verify the correctness of the theoretical analysis, a steep discontinuous object of 600×600 pixels and 10.00 mm in height is simulated and a discontinuous object of ladder shape which is 32.00 mm in height is used in experiment. Both the simulation and the experiment can restore the discontinuous object height accurately by using the dual-frequency grating measurement theory.展开更多
A new error compensating five sample phase shifting algorithm which is insensitive to phase shift error is proposed to retrieve the phase distribution of a fringe pattern. It includes two steps. First, the linear ...A new error compensating five sample phase shifting algorithm which is insensitive to phase shift error is proposed to retrieve the phase distribution of a fringe pattern. It includes two steps. First, the linear phase shift error is estimated using four sample images. Then, the phase distribution is calculated with error corrected by using the phase shift error estimated in the first step. As the equations of error estimation and phase calculation are simple, this new algorithm is practical as well as effective. Computer simulations were carried out to verify the effectiveness of the algorithm. Results of two other well known error compensating algorithms are also presented, which show the new algorithm is the least sensitive to phase shift error.展开更多
Fringe projection profilometry(FPP)has been extensively studied in the field of three-dimensional(3D)measurement.Although FPP always uses high-frequency fringes to ensure high measurement accuracy,too many patterns ar...Fringe projection profilometry(FPP)has been extensively studied in the field of three-dimensional(3D)measurement.Although FPP always uses high-frequency fringes to ensure high measurement accuracy,too many patterns are projected to unwrap the phase,which affects the speed of 3D reconstruction.We propose a high-speed 3D shape measurement method using only three high-frequency inner shifting-phase patterns(70 periods),which satisfies both high precision and high measuring speed requirements.Besides,our proposed method obtains the wrapped phase and the fringe order simultaneously without any other information and constraints.The proposed method has successfully reconstructed moving objects with high speed at the camera's full frame rate(1700 frames per second).展开更多
A novel phase-shifted long-period fiber grating(PS-LPFG)for the simultaneous measurement of torsion and temperature is described and experimentally demonstrated.The PS-LPFG is fabricated by inserting a pretwisted stru...A novel phase-shifted long-period fiber grating(PS-LPFG)for the simultaneous measurement of torsion and temperature is described and experimentally demonstrated.The PS-LPFG is fabricated by inserting a pretwisted structure into the long-period fiber grating(LPFG)written in single-mode fiber(SMF).Experimental results show that the torsion sensitivities of the two dips are?0.114 nm/(rad/m)and?0.069 nm/(rad/m)in the clockwise direction,and?0.087 nm/(rad/m)and?0.048 nm/(rad/m)in the counterclockwise direction,respectively.The temperature sensitivities of the two dips are 0.057 nm/℃ and 0.051 nm/℃,respectively.The two dips of the PS-LPFG exhibit different responses to torsion and temperature.Simultaneous measurement of torsion and temperature can be implemented using a sensor.The feasibility and stabilization of simultaneous torsion and temperature measurement have been confirmed,and hence this novel PS-LPFG demonstrates potential for fiber sensing and engineering applications.展开更多
Phase measurement profilometry(PMP) uses a digital projector and a camera for 3D shape measurement.However,the nonlinear response of the measurement system causes the captured perfect sinusoidal fringe patterns to bec...Phase measurement profilometry(PMP) uses a digital projector and a camera for 3D shape measurement.However,the nonlinear response of the measurement system causes the captured perfect sinusoidal fringe patterns to become non-sinusoidal waveforms,which results in phase and measurement errors.We perform a theoretical analysis of the phase error resulting from non-sinusoidal fringe patterns.Based on a derived phase-error expression,the empirical mode decomposition(EMD) method is introduced to restrain nonlinear phase error and improve the precision in evaluating the phase distribution.A computer simulation and experimental results prove that the proposed method can eliminate possible phase-error in PMP.展开更多
In this study, an improved phase-shi^ng diffraction interferometer for measuring the surface topography of a microsphere is developed. A common diode-pumped solid state laser is used as the light source to facilitate ...In this study, an improved phase-shi^ng diffraction interferometer for measuring the surface topography of a microsphere is developed. A common diode-pumped solid state laser is used as the light source to facilitate ap- paratus realization, and a new polarized optical arrangement is designed to filter the bias light for phase-shifting control. A pinhole diffraction self-calibration method is proposed to eliminate systematic errors introduced by optical elements. The system has an adjustable signal contrast and is suitable for testing the surface with low reflectivity. Finally, a spherical ruby probe of a coordinate measuring machine is used as an example tested by the new phase-shifting diffraction interferometer system and the WYKO scanning white light interferometer for experimental comparison. The measured region presents consistent overall topography features, and the resulting peak-to-valley value of 84.43 nm and RMS value of 18.41 nm are achieved. The average roughness coincides with the manufacturer＇s specification value.展开更多
Phase-shifting measurement and its error estimation method were studied according to the holographic principle.A function of synchronous superposition of object complex amplitude reconstructed from N-step phase-shifti...Phase-shifting measurement and its error estimation method were studied according to the holographic principle.A function of synchronous superposition of object complex amplitude reconstructed from N-step phase-shifting through one integral period(N-step phase-shifting function for short)was proposed.In N-step phase-shifting measurement,the interferograms are seen as a series of in-line holo-grams and the reference beam is an ideal parallel-plane wave.So the N-step phase-shifting function can be obtained by multiplying the interferogram by the original reference wave.In ideal conditions,the proposed method is a kind of synchro-nous superposition algorithm in which the complex ampli-tude is separated,measured and superposed.When error exists in measurement,the result of the N-step phase-shifting function is the optimal expected value of the least-squares fitting method.In the above method,the N+1-step phase-shifting function can be obtained from the N-step phase-shifting function.It shows that the N-step phase-shifting function can be separated into two parts:the ideal N-step phase-shifting function and its errors.The phase-shifting errors in N-steps phase-shifting phase measurement can be treated the same as the relative errors of amplitude and intensity under the understanding of the N+1-step phase-shifting function.The difficulties of the error estimation in phase-shifting phase measurement were restricted by this error esti-mation method.Meanwhile,the maximum error estimation method of phase-shifting phase measurement and its formula were proposed.展开更多
基金the National Natural Science Foundation of China(No.10672065).
文摘2π phase ambiguity problem is very important in phase measurement when a deformed object has a large out of plane displacement. The dual-frequency projection grating phaseshifting profilometry （PSP） can be used to solve such an issue. In the measurement, two properchosen frequency gratings are utilized to synthesize an equivalent wavelength grating which ensures the computed phase in a principal phase range. Thus, the error caused by the phase unwrapping process with the conventional phase reconstruct algorithm can be eliminated. Finally, experimental result of a specimen with large plastic deformation is given to prove that the proposed method is effective to handle the phase discontinuity.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61173122, 60970098, 60803024, 90715043, and 61144006)the Postdoctoral Startup Foundation of Central South University, China (Grant No. 1332/74341016030)
文摘In Fourier transform profilometry （FTP）, we must restrain spectrum overlapping caused by the nonlinearity of the charge coupled device （CCD） and increase the measurement accuracy of the object shape. Firstly, the causes of producing higher-order spectrum components and inducing spectrum overlapping are analysed theoretically, and a simple physical ex- planation and analytical deduction are given. Secondly, aiming to suppress spectrum overlapping and improve measurement accuracy, the influence of spatial carrier frequency of projection grating on them is analysed. A method of increasing the spatial carrier frequency of projection grating to restrain or reduce the spectrum overlapping significantly is proposed. We then analyze the mechanism of how the spectrum overlapping is reduced. Finally, the simulation results and experimental measurements verify the correction of the proposed theory and method.
文摘In order to study the strength of the composite material plate problems, need to adopt a nondestructive testing method to obtain the specimen surface under the effect of high-speed impact regularity of shape. The projection profilometry was used to measure the surface profile or the full field deformation. Furtherly, by using the Fourier transform algorithm, there is only one frame of captured image</span><span style="font-family:Verdana;"> which</span><span style="font-family:Verdana;"> is needed in the measurement, so that it can be introduced into the high speed impaction procedure measurement. An experimental system, which was contained with an impact setup and the projection profilometry measurement part, was constructed for the impaction action characteristic research. The metallic impact object can be launched by a gas gun or a spin fan, respectively. The detected object </span><span style="font-family:Verdana;">is</span><span style="font-family:Verdana;"> manufactured by composite materials. In order to increase the surface deformation measurement accuracy, the calibration method and the error was discussed with different calibration specimen. And then, the proposed profilometry measurement method is proved by the gas gun and spin fan projectile test. The surface deformation of the manufactured composite plates and fan case are measured in the impaction procedure. So that the impact action details can be described much more clearly than the traditional video monitoring method.
基金Project supported by the Science and Technology Major Projects of Zhejiang Province,China(Grant No.2013C03043-5)
文摘Digital structured light （SL） profilometry is increasingly used in three-dimensional （3D） measurement technology. However, the nonlinearity of the off-the-shelf projectors and cameras seriously reduces the measurement accuracy. In this paper, first, we review the nonlinear effects of the projector-camera system in the phase-shifting structured light depth measurement method. We show that high order harmonic wave components lead to phase error in the phase-shifting method. Then a practical method based on frequency domain filtering is proposed for nonlinear error reduction. By using this method, the nonlinear calibration of the SL system is not required. Moreover, both the nonlinear effects of the projector and the camera can be effectively reduced. The simulations and experiments have verified our nonlinear correction method.
基金supported by National Natural Science Foundation of China(Grant Nos.51275054,51075116)
文摘Three dimensional（3D） displacements, which can be translated further into 3D strain, are key parameters tor design, manufacturing and quality control. Using different optical setups, phase-shift methods, and algorithms, several different 3D electronic speckle pattern interferometry（ESPl） systems for displacement and strain measurements have been achieved and commercialized. This paper provides a review of the recent developments in ESPI systems for 3D displacement and strain measurement. After an overview of the fundamentals of ESP! theory, temporal phase-shift, and spatial phase-shift techniques, 3D deformation measurements by the temporal phase-shift ESPI system, which is suited well for static measurement, and by the spatial phase-shift ESPI system, which is particularly useful for dynamic measurement, are discussed. For each method, the basic theory, a brief derivation and different optical layouts are presented. The state of art application, potential and limitation of the ESPI systems are shown and demonstrated.
文摘The technique of phase measuring profilometry using a single phase step method is proposed.This method can automatically obtain phase value at each pixel by using a discret cosine transform algorithm.The method is able to automatically recognize any position between depression and elevation on an object surface.Theoretical analysis and experimental verification are presented.
基金This project is supported by National Natural Science Foundation ofChina (No.50375047).
文摘A fast 3D reconstruction method based on structured light to measure various parameters of the raceway groove is presented. Digital parallel grating stripes distributed with sine density are projected onto the raceway groove by a DLP projector, and distorting of stripes is happened on the raceway. Simultaneously, aided by three-step phase-shifting approach, three images covered by different stripes are obtained by a high-resolution CCD camera at the same location, thus a more accuracy local topography can be obtained. And then the bearing is rotated on a high precision computer controlled rotational stage. Three images are also obtained as the former step at next planned location triggered by the motor. After one cycle, all images information is combined through the mosaics. As a result, the 3D information of raceway groove can be gained. Not only geometric properties but also surface flaws can be extracted by software. A preliminary hardware system has been built, with which some geometric parameters have been extracted from reconstructed local topography.
基金Project supported by the Science-Technology Program Research Foundation of Hunan Province, China (Grant No 2009FJ3187)the 11th Five-year Plan for Key Construction Academic Subject (Optics) of Hunan Province, China (Grant No 06GXCD02)
文摘The dual-frequency grating measurement theory is proposed in order to carry out the measurement of a discontinuous object. Firstly, the reason why frequency spectra are produced by low frequency gratings and high frequency gratings in the field of frequency is analysed, and the relationship between the wrapped-phase and the unwrapping-phase is discussed. Secondly, a method to combine the advantages of the two kinds of gratings is proposed： one stripe is produced in the mutation part of the object measured by a suitable low frequency grating designed by MATLAB, then the phase produced by the low frequency grating need not be unfolded. The integer series of stripes is produced by a high frequency grating designed by MATLAB based on the frequency ratio of the two kinds of gratings and the high frequency wrapped-phase, and the high frequency unwrapping-phase is then obtained. In order to verify the correctness of the theoretical analysis, a steep discontinuous object of 600×600 pixels and 10.00 mm in height is simulated and a discontinuous object of ladder shape which is 32.00 mm in height is used in experiment. Both the simulation and the experiment can restore the discontinuous object height accurately by using the dual-frequency grating measurement theory.
文摘A new error compensating five sample phase shifting algorithm which is insensitive to phase shift error is proposed to retrieve the phase distribution of a fringe pattern. It includes two steps. First, the linear phase shift error is estimated using four sample images. Then, the phase distribution is calculated with error corrected by using the phase shift error estimated in the first step. As the equations of error estimation and phase calculation are simple, this new algorithm is practical as well as effective. Computer simulations were carried out to verify the effectiveness of the algorithm. Results of two other well known error compensating algorithms are also presented, which show the new algorithm is the least sensitive to phase shift error.
基金supported by the National Key Research and Development Program of China(No.2018YFB2001400)the Innovation Group Science Fund of Chongqing Natural Science Foundation(No.cstc2019jcyj-cxttX0003)。
文摘Fringe projection profilometry(FPP)has been extensively studied in the field of three-dimensional(3D)measurement.Although FPP always uses high-frequency fringes to ensure high measurement accuracy,too many patterns are projected to unwrap the phase,which affects the speed of 3D reconstruction.We propose a high-speed 3D shape measurement method using only three high-frequency inner shifting-phase patterns(70 periods),which satisfies both high precision and high measuring speed requirements.Besides,our proposed method obtains the wrapped phase and the fringe order simultaneously without any other information and constraints.The proposed method has successfully reconstructed moving objects with high speed at the camera's full frame rate(1700 frames per second).
基金supported by the National Natural Science Foundation of China(No.11527804)Joint Research Fund in Astronomy under cooperative agreement between the National Natural Science Foundation of China(NSFC)and Chinese Academy of Sciences(CAS)(Nos.U1831115 and U1631239)+3 种基金Open Project of Key Laboratory of Astronomical Optics&Technology,Nanjing Institute of Astronomical Optics&Technology,Chinese Academy of Sciences(No.CAS-KLAOT-KF201806)Fundamental Research Funds for the Central Universities111 Project(No.B13015)the Harbin Engineering University.
文摘A novel phase-shifted long-period fiber grating(PS-LPFG)for the simultaneous measurement of torsion and temperature is described and experimentally demonstrated.The PS-LPFG is fabricated by inserting a pretwisted structure into the long-period fiber grating(LPFG)written in single-mode fiber(SMF).Experimental results show that the torsion sensitivities of the two dips are?0.114 nm/(rad/m)and?0.069 nm/(rad/m)in the clockwise direction,and?0.087 nm/(rad/m)and?0.048 nm/(rad/m)in the counterclockwise direction,respectively.The temperature sensitivities of the two dips are 0.057 nm/℃ and 0.051 nm/℃,respectively.The two dips of the PS-LPFG exhibit different responses to torsion and temperature.Simultaneous measurement of torsion and temperature can be implemented using a sensor.The feasibility and stabilization of simultaneous torsion and temperature measurement have been confirmed,and hence this novel PS-LPFG demonstrates potential for fiber sensing and engineering applications.
基金sipported by the National Natural Science Foundation of China (61128012,60978043,61061160503)the Research Grants Council of the Hong Kong Special Administrative Region (9041577)
文摘Phase measurement profilometry(PMP) uses a digital projector and a camera for 3D shape measurement.However,the nonlinear response of the measurement system causes the captured perfect sinusoidal fringe patterns to become non-sinusoidal waveforms,which results in phase and measurement errors.We perform a theoretical analysis of the phase error resulting from non-sinusoidal fringe patterns.Based on a derived phase-error expression,the empirical mode decomposition(EMD) method is introduced to restrain nonlinear phase error and improve the precision in evaluating the phase distribution.A computer simulation and experimental results prove that the proposed method can eliminate possible phase-error in PMP.
基金supported by the National Natural Science Foundation of China under Grant Nos.61275096 and 51275120
文摘In this study, an improved phase-shi^ng diffraction interferometer for measuring the surface topography of a microsphere is developed. A common diode-pumped solid state laser is used as the light source to facilitate ap- paratus realization, and a new polarized optical arrangement is designed to filter the bias light for phase-shifting control. A pinhole diffraction self-calibration method is proposed to eliminate systematic errors introduced by optical elements. The system has an adjustable signal contrast and is suitable for testing the surface with low reflectivity. Finally, a spherical ruby probe of a coordinate measuring machine is used as an example tested by the new phase-shifting diffraction interferometer system and the WYKO scanning white light interferometer for experimental comparison. The measured region presents consistent overall topography features, and the resulting peak-to-valley value of 84.43 nm and RMS value of 18.41 nm are achieved. The average roughness coincides with the manufacturer＇s specification value.
基金supported by the National Natural Science Foundation of China (Grant No.60467003 and 60277032)。
文摘Phase-shifting measurement and its error estimation method were studied according to the holographic principle.A function of synchronous superposition of object complex amplitude reconstructed from N-step phase-shifting through one integral period(N-step phase-shifting function for short)was proposed.In N-step phase-shifting measurement,the interferograms are seen as a series of in-line holo-grams and the reference beam is an ideal parallel-plane wave.So the N-step phase-shifting function can be obtained by multiplying the interferogram by the original reference wave.In ideal conditions,the proposed method is a kind of synchro-nous superposition algorithm in which the complex ampli-tude is separated,measured and superposed.When error exists in measurement,the result of the N-step phase-shifting function is the optimal expected value of the least-squares fitting method.In the above method,the N+1-step phase-shifting function can be obtained from the N-step phase-shifting function.It shows that the N-step phase-shifting function can be separated into two parts:the ideal N-step phase-shifting function and its errors.The phase-shifting errors in N-steps phase-shifting phase measurement can be treated the same as the relative errors of amplitude and intensity under the understanding of the N+1-step phase-shifting function.The difficulties of the error estimation in phase-shifting phase measurement were restricted by this error esti-mation method.Meanwhile,the maximum error estimation method of phase-shifting phase measurement and its formula were proposed.
