In x-ray dark-field imaging using dual phase grating interferometer,multi-contrast signals are extracted from a set of acquired phase-stepping data by using the least-squares fitting algorithm.The extracted mean inten...In x-ray dark-field imaging using dual phase grating interferometer,multi-contrast signals are extracted from a set of acquired phase-stepping data by using the least-squares fitting algorithm.The extracted mean intensity,amplitude and visibility signals may be intrinsically biased.However,it is still unclear how large these biases are and how the data acquisition parameters influence the biases in the extracted signals.This work set out to address these questions.Analytical expressions of the biases of the extracted signals were theoretically derived by using a second-order Taylor series expansion.Extensive numerical simulations were performed to validate the theoretical results.It is illustrated that while the estimated mean intensity signal is always unbiased,the estimated amplitude and visibility signals are both positively biased.While the biases of the estimated amplitude signals are proportional to the inverse of the total number of phase steps,the biases of the estimated visibility signals are inversely proportional to the product of the total number of phase steps and the mean number of photons counted per phase step.Meanwhile,it is demonstrated that the dependence of the biases on the mean visibility is quite different from that of Talbot-Lau interferometer due to the difference in the intensity model.We expect that these results can be useful for data acquisition optimizations and interpretation of x-ray dark-field images.展开更多
According to the measurement principle of the traditional interferometer,a narrowband signal model is established and used,however,for wideband signals or multiple signals,this model is invalid.For the problems of dir...According to the measurement principle of the traditional interferometer,a narrowband signal model is established and used,however,for wideband signals or multiple signals,this model is invalid.For the problems of direction finding with interferometer for wideband signals and multiple signals scene,a frequency domain phase interferometer is proposed and the concrete implementation scheme is given.The proposed method computes the phase difference in frequency domain,and finds multi-target results with judging the spectrum amplitude changing,and uses the frequency phase difference to compute the arrival angle.Theoretical analysis and simulation results show that the proposed method effectively solves the problem of the angle estimation with phase interferometer for wideband signals,and has good performance in multiple signals scene with nonoverlapping spectrum or partially overlapping.In addition,the wider the signal bandwidth,the better direction finding performance of this algorithm.展开更多
In this paper,we present a phase multiplication algorithm(PMA)to obtain scalable fringe precision in laser self-mixing interferometer under a weak feedback regime.Merely by applying the double angle formula on the sel...In this paper,we present a phase multiplication algorithm(PMA)to obtain scalable fringe precision in laser self-mixing interferometer under a weak feedback regime.Merely by applying the double angle formula on the self-mixing signal multiple times,the continuously improved fringe precision will be obtained.Theoretical analysis shows that the precision of the fringe could be improved toλ/2^(n+1).The validity of the proposed method is demonstrated by means of simulated SMI signals and confirmed by experiments under different amplitudes.A fringe precision ofλ/128 at a sampling rate of 500 k S/s has been achieved after doing 6 th the PMA.Finally,an amplitude of 50 nm has been proved to be measurable and the absolute error is 3.07 nm,which is within the theoretical error range.The proposed method for vibration measurement has the advantage of high accuracy and reliable without adding any additional optical elements in the optical path,thus it will play an important role in nanoscale measurement field.展开更多
A new type of polarization sensitive interferometer is proposed,named the Delta interferometer,inspired by its geometry resembling the Greek letter Delta.The main difference between the Delta interferometer and other ...A new type of polarization sensitive interferometer is proposed,named the Delta interferometer,inspired by its geometry resembling the Greek letter Delta.The main difference between the Delta interferometer and other existing interferometers,such as Michelson,Mach-Zehnder and Young's double-slit interferometers,is that the two interfering paths are asymmetrical in the Delta interferometer.The visibility of the first-order interference pattern observed in the Delta interferometer is dependent on the polarization of the incidental light.Optical coherence theory is employed to interpret this phenomenon and single-mode continuous-wave laser light is employed to verify the theoretical predictions.The theoretical and experimental results are consistent.The Delta interferometer is a perfect tool to study the reflection of electromagnetic fields in different polarizations and may find applications in polarization-sensitive scenarios.展开更多
Using only one optic element,the phase mask provides a robust and inherently stable methodfor reproducing fiber Bra gg gratings,and reduces the complexity of the fiber grating fabrication system.This paper reviews the...Using only one optic element,the phase mask provides a robust and inherently stable methodfor reproducing fiber Bra gg gratings,and reduces the complexity of the fiber grating fabrication system.This paper reviews the phase mask and phase mask techniques,and its application to inscribe the fiberBragg gratings.It is noteworthy that the wavelength of the fiber Bragg grating would be tuned via onlya phase mask in a phase mask interferometer.In these systems,the fiber Bragg grating is inscribed byultra violet(UV)interference stripes derived from the optical components,where the phase mask is usedas a beam splitter of±1 order diffraction light.展开更多
The change of the equivalent baseline and interferometric phase of cluster SAR satellites is analyzed when the constellation circles around the Earth and the satellites rotate around the center at the same time. The l...The change of the equivalent baseline and interferometric phase of cluster SAR satellites is analyzed when the constellation circles around the Earth and the satellites rotate around the center at the same time. The letter provides assessment of baseline error and phase error which influence the precision of height measurement in the across-track interferometric mode. The mathematical model of cluster satellite movement is built, simulation analyses and the curve of height error are presented. The simulation results show that height measurement error can be compensated by the formulae derived in this letter, therefore, the Digital Elevation Models (DEM’s) are recovered accurately.展开更多
In theory, we find that the actual function of the analyzer grating in the Talbot–Lau interferometer is segmenting the self-images of the phase grating and choosing integral areas, which make sure that each period of...In theory, we find that the actual function of the analyzer grating in the Talbot–Lau interferometer is segmenting the self-images of the phase grating and choosing integral areas, which make sure that each period of self-images in one detector pixel contributes the same signal to the detector. Furthermore, in the case of the lack of an analyzer grating, the shifting curves are still existent in theory as long as the number of fringes is non-integral in a detector pixel, which is a sufficient condition for creating shifting curve. The sufficient condition is available for not only the Talbot–Lau interferometer and the inverse geometry of Talbot–Lau interferometer, but also the x-ray phase contrast imaging system based on geometrical optics. In practical applications, we propose a method to improve the performances of the existing systems by employing the sufficient condition. This method can shorten the system length, is applicable to large period gratings, and can use the detectors with large pixels and large field of view. In addition, the experimental arrangement can be simplified due to the lack of an analyzer grating. In order to improve detection sensitivity and resolution, we also give an optimal fringe period.We believe that the theory and method proposed here is a step forward for x-ray phase contrast imaging.展开更多
This study shows that the principle of a recently proposed connnon-path laser interferometer containing a planar grating is nonexistent and apparently caused by a mathematical derivation error. Both p- and s-polarized...This study shows that the principle of a recently proposed connnon-path laser interferometer containing a planar grating is nonexistent and apparently caused by a mathematical derivation error. Both p- and s-polarized beams ill the proposed setup experience once the ＋lst-order diffraction and once the lst-order diffraction by tile grating. As a result, the phase of each beam remains unchanged and the interference fringes formed by the two beams are not expected to move when the grating is translated in the grating vector direction. We perform an experiment to confirm this prediction. Both our analysis and experimental observation cast doubt on the experimental results of the authors who proposed the interferometer.展开更多
A new direction finding(DF)method,in which the high-accuracy measuring can be realized only with single baseline,is presented used for airborne based on Doppler-phase measurement.The analysis discovers that the intege...A new direction finding(DF)method,in which the high-accuracy measuring can be realized only with single baseline,is presented used for airborne based on Doppler-phase measurement.The analysis discovers that the integer of wavelength in radial distance can be directly derived compositely,making use of the velocity vector equation and Doppler shift,as well as Doppler changing rate equation.From this,the integer difference of wavelength in path length difference of radial distance between two adjacent antenna elements can be obtained.As soon as the value less than a wavelength in path length difference is determined by phase difference measurement,the direction angle of target can be obtained.As compared with now existing interferometry first determining phase difference,this sort of direction finding method combining Doppler with phase difference first by determining path length difference does not have phase ambiguity nor require restricting base length.By simple mathematical identity transformation,we can prove that the equation derived in this paper is equivalent to an existing one from phase interferometry.The new method presented in this paper will certainly increase new developing force for the research and development of airborne single station direction finding system.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.U1532113,11475170,11905041)Anhui Provincial Natural Science Foundation(Grant No.2208085MA18)Fundamental Research Funds for the Central Universities(Grant No.JZ2022HGTB0244)。
文摘In x-ray dark-field imaging using dual phase grating interferometer,multi-contrast signals are extracted from a set of acquired phase-stepping data by using the least-squares fitting algorithm.The extracted mean intensity,amplitude and visibility signals may be intrinsically biased.However,it is still unclear how large these biases are and how the data acquisition parameters influence the biases in the extracted signals.This work set out to address these questions.Analytical expressions of the biases of the extracted signals were theoretically derived by using a second-order Taylor series expansion.Extensive numerical simulations were performed to validate the theoretical results.It is illustrated that while the estimated mean intensity signal is always unbiased,the estimated amplitude and visibility signals are both positively biased.While the biases of the estimated amplitude signals are proportional to the inverse of the total number of phase steps,the biases of the estimated visibility signals are inversely proportional to the product of the total number of phase steps and the mean number of photons counted per phase step.Meanwhile,it is demonstrated that the dependence of the biases on the mean visibility is quite different from that of Talbot-Lau interferometer due to the difference in the intensity model.We expect that these results can be useful for data acquisition optimizations and interpretation of x-ray dark-field images.
文摘According to the measurement principle of the traditional interferometer,a narrowband signal model is established and used,however,for wideband signals or multiple signals,this model is invalid.For the problems of direction finding with interferometer for wideband signals and multiple signals scene,a frequency domain phase interferometer is proposed and the concrete implementation scheme is given.The proposed method computes the phase difference in frequency domain,and finds multi-target results with judging the spectrum amplitude changing,and uses the frequency phase difference to compute the arrival angle.Theoretical analysis and simulation results show that the proposed method effectively solves the problem of the angle estimation with phase interferometer for wideband signals,and has good performance in multiple signals scene with nonoverlapping spectrum or partially overlapping.In addition,the wider the signal bandwidth,the better direction finding performance of this algorithm.
基金supported by the Natural Science Foundation of Fujian Province(No.2020J01705)the School Foundation of Jimei University(No.C150345)。
文摘In this paper,we present a phase multiplication algorithm(PMA)to obtain scalable fringe precision in laser self-mixing interferometer under a weak feedback regime.Merely by applying the double angle formula on the self-mixing signal multiple times,the continuously improved fringe precision will be obtained.Theoretical analysis shows that the precision of the fringe could be improved toλ/2^(n+1).The validity of the proposed method is demonstrated by means of simulated SMI signals and confirmed by experiments under different amplitudes.A fringe precision ofλ/128 at a sampling rate of 500 k S/s has been achieved after doing 6 th the PMA.Finally,an amplitude of 50 nm has been proved to be measurable and the absolute error is 3.07 nm,which is within the theoretical error range.The proposed method for vibration measurement has the advantage of high accuracy and reliable without adding any additional optical elements in the optical path,thus it will play an important role in nanoscale measurement field.
基金Project supported by the Shanxi Key Research and Development Project(Grant No.2019ZDLGY09-08)Shanxi Nature and Science Basic Research Project(Grant No.2019JLP-18).
文摘A new type of polarization sensitive interferometer is proposed,named the Delta interferometer,inspired by its geometry resembling the Greek letter Delta.The main difference between the Delta interferometer and other existing interferometers,such as Michelson,Mach-Zehnder and Young's double-slit interferometers,is that the two interfering paths are asymmetrical in the Delta interferometer.The visibility of the first-order interference pattern observed in the Delta interferometer is dependent on the polarization of the incidental light.Optical coherence theory is employed to interpret this phenomenon and single-mode continuous-wave laser light is employed to verify the theoretical predictions.The theoretical and experimental results are consistent.The Delta interferometer is a perfect tool to study the reflection of electromagnetic fields in different polarizations and may find applications in polarization-sensitive scenarios.
基金Supported by National Natural Science Foundation of China(No.60077023)"863"High-Technology Program(307)Tian jin Natural Science Foundation(No.013601711).
文摘Using only one optic element,the phase mask provides a robust and inherently stable methodfor reproducing fiber Bra gg gratings,and reduces the complexity of the fiber grating fabrication system.This paper reviews the phase mask and phase mask techniques,and its application to inscribe the fiberBragg gratings.It is noteworthy that the wavelength of the fiber Bragg grating would be tuned via onlya phase mask in a phase mask interferometer.In these systems,the fiber Bragg grating is inscribed byultra violet(UV)interference stripes derived from the optical components,where the phase mask is usedas a beam splitter of±1 order diffraction light.
文摘The change of the equivalent baseline and interferometric phase of cluster SAR satellites is analyzed when the constellation circles around the Earth and the satellites rotate around the center at the same time. The letter provides assessment of baseline error and phase error which influence the precision of height measurement in the across-track interferometric mode. The mathematical model of cluster satellite movement is built, simulation analyses and the curve of height error are presented. The simulation results show that height measurement error can be compensated by the formulae derived in this letter, therefore, the Digital Elevation Models (DEM’s) are recovered accurately.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11074172 and 11674232)the National Key Basic Research Program,China(Grant No.2012CB825804)the National Special Foundation for Major Science Instrument,China(Grant No.61227802)
文摘In theory, we find that the actual function of the analyzer grating in the Talbot–Lau interferometer is segmenting the self-images of the phase grating and choosing integral areas, which make sure that each period of self-images in one detector pixel contributes the same signal to the detector. Furthermore, in the case of the lack of an analyzer grating, the shifting curves are still existent in theory as long as the number of fringes is non-integral in a detector pixel, which is a sufficient condition for creating shifting curve. The sufficient condition is available for not only the Talbot–Lau interferometer and the inverse geometry of Talbot–Lau interferometer, but also the x-ray phase contrast imaging system based on geometrical optics. In practical applications, we propose a method to improve the performances of the existing systems by employing the sufficient condition. This method can shorten the system length, is applicable to large period gratings, and can use the detectors with large pixels and large field of view. In addition, the experimental arrangement can be simplified due to the lack of an analyzer grating. In order to improve detection sensitivity and resolution, we also give an optimal fringe period.We believe that the theory and method proposed here is a step forward for x-ray phase contrast imaging.
文摘This study shows that the principle of a recently proposed connnon-path laser interferometer containing a planar grating is nonexistent and apparently caused by a mathematical derivation error. Both p- and s-polarized beams ill the proposed setup experience once the ＋lst-order diffraction and once the lst-order diffraction by tile grating. As a result, the phase of each beam remains unchanged and the interference fringes formed by the two beams are not expected to move when the grating is translated in the grating vector direction. We perform an experiment to confirm this prediction. Both our analysis and experimental observation cast doubt on the experimental results of the authors who proposed the interferometer.
文摘A new direction finding(DF)method,in which the high-accuracy measuring can be realized only with single baseline,is presented used for airborne based on Doppler-phase measurement.The analysis discovers that the integer of wavelength in radial distance can be directly derived compositely,making use of the velocity vector equation and Doppler shift,as well as Doppler changing rate equation.From this,the integer difference of wavelength in path length difference of radial distance between two adjacent antenna elements can be obtained.As soon as the value less than a wavelength in path length difference is determined by phase difference measurement,the direction angle of target can be obtained.As compared with now existing interferometry first determining phase difference,this sort of direction finding method combining Doppler with phase difference first by determining path length difference does not have phase ambiguity nor require restricting base length.By simple mathematical identity transformation,we can prove that the equation derived in this paper is equivalent to an existing one from phase interferometry.The new method presented in this paper will certainly increase new developing force for the research and development of airborne single station direction finding system.
