Dynamic Phase Measurement Research Articles

Dynamic phase measurement based on two-step phase-shifting interferometry with geometric phase grating

Abstract This paper proposes a novel dynamic 2-step phase-shifting interferometry method with a geometric phase grating and direct aberration-free object phase recovery algorithm. By exploring the amplitude-phase modulation property of the geometric phase grating, two-step phase-shifting interferograms with π / 2 phase shift can be obtained in a single shot through two kinds of spatial-multiplexing arrangements. Then the restriction on the background uniformity of the 2-step phase-shifting algorithms and the system aberration can be avoided simultaneously, based on the presented direct and fast object phase demodulation strategy with an object-free state recorded in advance, so an accurate object measurement result can be guaranteed. Accordingly, a detailed analysis of the theoretical model of error sources is conducted by taking the depolarization error of geometric phase grating and phase measurement model error into consideration, with a Least Squares Iteration optimization strategy established to further improve the measurement accuracy. Experiments on various types of phase objects, such as a photo-etched quartz substrate, the spatial light modulator, and a silicon chip, validate the effectiveness and accuracy of our method when compared with the reference phase obtained from 4-step temporal phase-shifting method. The dynamic phase measurement capability is demonstrated by exhibiting the evaporation process of alcohol droplet.

One-shot self-calibrating phase-shifting interferometry by direct normalization of interferograms

Dynamic phase measurement is a valuable technique applied across various scientific and technological domains due to its high accuracy, non-contacting method, and numerous practical applications. In this manuscript, we present a phase retrieval method capable of measuring the object’s phase in real-time. Our proposal is based on a double aperture common-path interferometer adapted for polarization modulation in the input windows, enabling the superposition of two fields with orthogonal circular polarizations. Two interferograms and two intensities are captured in a single shot, showcasing the possibility of obtaining two normalized interferograms directly and straightforwardly. This allows for the derivation of expressions for phase recovery and, additionally, the determination of the arbitrary phase step. We demonstrate that this method is easy to implement, highly accurate, and sufficiently fast for real-time applications. To validate the effectiveness of the method, we conduct numerical error analysis and laboratory experiments.

Fast and precise single-frame phase demodulation interferometry

To achieve real-time phase detection, this paper presents a fast and precise spatial carrier phase-shifting interferometry based on the dynamic mode decomposition strategy. The algorithm initially produces a series of phase-shifted sub-interferograms with the aid of a spatial carrier interferogram. Subsequently, the measured phases are derived with great accuracy from these sub-interferograms through the use of the dynamic mode decomposition strategy, an outstanding non-iterative algorithm. Numerical simulation and experimental comparison show that this method is an efficient and accurate single-frame phase demodulation algorithm. The paper also analyzes the performance of the proposed method based on influencing factors such as random noise level, carrier frequency size, and carrier frequency direction. The results indicate that this method is a fast and accurate phase solution method, offering another effective solution for dynamic real-time phase measurement.

Fast and high precision phase recovery technology of single-shot ineterferogram based on depth convolution neural network

Phase retrieval from single interferogram is of great interest for the possibility of dynamic phase measurement. However, it is a very complicated process in reality since the unknowns and knows are highly unequal. In this paper, we propose a fast phase recovery method from single interferogram based on deep convolution neural network. The network is trained based on supervised learning to achieve the purpose of quickly obtaining unwrapped phase results from a single interferogram. To improve the detection accuracy, a modified set establishment model has been propose to improve the practicability of the fringe data. The simulation and experimental results show that the root mean square value of residual phase extraction error by this method is closed to 0.01λ (λ = 632.8 nm), and the constructed depth convolution neural network model has significant flexibility and effective generalization ability for phase recovery of single frame interference fringe.

RSAGAN: Rapid self-attention generative adversarial nets for single-shot phase-shifting interferometry

The phase-shift operation in phase-shifting interferometry (PSI) often introduces deviation and limits its application in the field of dynamic phase measurement. Based on this, a rapid self-attention generative adversarial nets (RSAGAN) is constructed and applied to realize single-shot PSI. By constructing the neural network of attention mechanism, we can quickly obtain the region dependency of the whole interferogram, so as to obtain a more realistic result after effective iterations. Accordingly, we can take one interferogram as the input of the network, get another interferogram with arbitrary phase shifts, and then combine the two-step phase-shifting algorithms to get the measured phase information. This method only needs one interferogram combined with the trained RSAGAN to achieve the acquisition of phase information with a simple experimental device, and has better generalization ability than the direct end-to-end phase acquisition method. Compared with the network without attention mechanism, the designed network has higher learning accuracy and has the potential to be applied in the related fields of dynamic phase measurement.

One-Shot Phase Retrieval Method for Interferometry Using a Multi-Stage Phase-Shifting Network

In this letter, we proposed a Multi-Stage phase-shifting network (MSPS-Net) based on Multi-Stage Progressive Image Restoration for one-shot phase retrieval interferometry. This network generates three interferograms with specific phase shifts from interferograms recorded in a single frame excellently, metrics such as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PSNR</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SSIM</i> indicate that the generated phase shift interferograms have high similarity to the real one. Further, By analyzing different types of aberrations, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RMS</i> value of error map retrieved by the proposed method is less than 1/200λ, which shows higher accuracy than latest phase-shifting network method built by Encoder and Decoder. All the experiment results show that our solution is available for the problem of high-accuracy dynamic phase measurement and has excellent generalization ability.

Synchronous Phase-Shifting Interference for High Precision Phase Imaging of Objects Using Common Optics.

Quantitative phase imaging and measurement of surface topography and fluid dynamics for objects, especially for moving objects, is critical in various fields. Although effective, existing synchronous phase-shifting methods may introduce additional phase changes in the light field due to differences in optical paths or need specific optics to implement synchronous phase-shifting, such as the beamsplitter with additional anti-reflective coating and a micro-polarizer array. Therefore, we propose a synchronous phase-shifting method based on the Mach-Zehnder interferometer to tackle these issues in existing methods. The proposed method uses common optics to simultaneously acquire four phase-shifted digital holograms with equal optical paths for object and reference waves. Therefore, it can be used to reconstruct the phase distribution of static and dynamic objects with high precision and high resolution. In the experiment, the theoretical resolution of the proposed system was 1.064 µm while the actual resolution could achieve 1.381 µm, which was confirmed by measuring a phase-only resolution chart. Besides, the dynamic phase imaging of a moving standard object was completed to verify the proposed system's effectiveness. The experimental results show that our proposed method is suitable and promising in dynamic phase imaging and measurement of moving objects using phase-shifting digital holography.

Dynamic phase measurement of fast liquid crystal phase modulators.

We present dynamic time-resolved measurements of a multi-pixel analog liquid crystal phase modulator driven at a 1 kHz frame rate. A heterodyne interferometer is used to interrogate two pixels independently and simultaneously, to deconvolve phase modulation with a wide bandwidth. The root mean squared optical phase error within a 30 Hz to 25 kHz bandwidth is <0.5° and the crosstalk rejection is 50 dB. Measurements are shown for a custom-built device with a flexoelectro-optic chiral nematic liquid crystal. However, the technique is applicable to many different types of optical phase modulators and spatial light modulators.

Phase-shifting interferometry from single frame in-line interferogram using deep learning phase-shifting technology

Phase-shifting interferometry is a highly accurate phase measurement technology. Its application in dynamic phase measurement is limited by the recording process of multiple phase-shifting interferograms. In this paper, a one-to-multiple deep learning (DL) framework is developed to generate an equivalent to multiple image phase shifting interferometry, using only a single in-line interferogram. The network is trained to map the single frame interferogram to three phase-shifting interferograms. And then, all these four phase-shifting interferograms are used for the phase-shifting phase recovery. Simulation and experimental results prove that the proposed method can realize phase measurement in in-line interference system by recording single interferogram. And it has similar precision with traditional phase-shifting holography by recording four frames phase-shifting interferograms. Further, compared with the strategy of generating the phase distribution from single frame interferogram by trained DL framework directly, the DL phase-shifting strategy can reduce the network error in the non-linear mapping partly owing to the introduction of phase-shifting algorithm and the network only needs to deal with the mapping relationship between the interferograms with different phase shifts, showing higher accuracy and better generalization ability. The proposed method can provide a new alternative approach for the high-accuracy dynamic phase measurement.

Dynamic phase measurement of a transparent object by parallel phase-shifting digital holography with dual polarization imaging cameras

Measurement of surface shape and refractive index for moving transparent objects is critical in various fields. A parallel phase-shifting digital holography system that can record and reconstruct the phase information of moving transparent objects using two high-resolution polarization imaging cameras was presented. In the developed system, two polarization imaging cameras with 3.45 µm pixel pitch passed through the object in different directions. These two polarization imaging cameras were controlled by LabVIEW and worked synchronously. The proposed system can obtain the object's integral phase distributions in different directions, which is more effective for measuring an asymmetric object. In the experiment, the resolution of the system was confirmed by using a transmission-type test target. Besides, the dynamic phase measurement of an irregularly shaped transparent object was completed to verify the proposed system's effectiveness.

Multi-wavelength phase-shifting interferometry based on a two-step phase-shifting phase retrieval algorithm with a color CMOS

By combining the advantages of multi-wavelength phase-shifting interferometry and two-step phase-shifting phase retrieval algorithm, a measured phase with high precision and a large measuring range can be retrieved rapidly from three multi-wavelength interferograms with unknown phase shifts, recorded by a single-chip color CMOS. Firstly, two normalized differential interferograms without backgrounds are obtained by means of subtraction followed by normalization between the three color interferograms. Next, the wrapped phases of a single wavelength are retrieved via the Gram–Schmidt orthonormalization approach. Finally, the unambiguous phase of the three synthetic wavelengths can be achieved by subtraction between the wrapped phases of corresponding wavelengths. To reduce the phase noise amplification introduced by the magnification of wavelengths, the phase unwrapping algorithm of reducing the noise of the three- synthetic wavelength to the level of a two-synthetic long wavelength, a single-wavelength, and a two-synthetic short wavelength are implemented in turn. Compared with conventional multi-wavelength phase shifting interferometry, only three interferograms with unknown phase shifts are needed to reconstruct the actual phase of the measured object to a high degree of measurement resolution, and with a large measurement range; this approach would be useful in dynamic phase measurement. Both simulation and experimental results validate the performance of the proposed method.

Fast and precise spatial-carrier phase-shifting algorithm with the matrix VU factorization

A fast and precise spatial-carrier phase-shifting algorithm based on the matrix VU factorization strategy that can realize dynamic real-time phase detection is proposed. First, the proposed algorithm divides the spatial-carrier interferogram into four phase-shifting subinterferograms. Second, the matrix VU factorization strategy, an excellent fast iterative algorithm, is used to accurately obtain the measured phase from these subinterferograms. Numerical simulation and experimental comparison verify that this method is an efficient and accurate single-frame phase demodulation algorithm. Meanwhile, the performance of the proposed method is analyzed and discussed for the influencing factors, such as random noise level, carrier-frequency value, and carrier-frequency direction. The results show that the method proposed is a fast and precise phase detection method that provides another effective solution for dynamic real-time phase measurement.

Fast 3D measurement based on improved optical flow for dynamic objects.

High resolution, real-time three-dimensional (3D) measurement plays an important role in many fields. In this paper, a multi-directional dynamic real-time phase measurement profilometry based on improved optical flow is proposed. In a five-step phase shifting dynamic measurement, pixel matching is needed to make the pixels one-to-one corresponding in five patterns. However, in the frequently-used pixel matching method at present, it is necessary to calculate the correlation and traverse the whole deformed pattern for the motion information of the measured object. The huge amount of computation caused by correlation computation takes up most of the time in the process of the entire 3D reconstruction, so it can not meet the requirement of real-time dynamic measurement. In order to solve the problem, the improved optical flow algorithm is introduced to replace correlation calculation in pixel matching. In one measurement, five captured patterns need to be dealt with, and the optical flow between each two adjacent frames is calculated. Then four two-dimensional vector matrices can be obtained. The vector matrices contain the complete motion information of the measured object. Experiments and simulations prove that this method can improve the efficiency of pixel matching by 42 times and 3D reconstruction by 32 times on the premise of ensuring the accuracy.

Dynamic phase measuring profilometry for rigid objects based on simulated annealing.

This paper presents a dynamic phase measurement profilometry (PMP) method based on the simulated annealing algorithm. In dynamic PMP for rigid objects, pixel matching is an effective method to make one-to-one pixel correspondence in each captured pattern. However, pixel matching by the global traversing algorithm takes up most of the time in the whole reconstruction process. For the purpose of optimizing pixel matching and enhancing performance in dynamic PMP, the simulated annealing algorithm is introduced. By generating a random path based on the simulated annealing algorithm, it is sufficient to locate the approximate area of the measured object. Then the accurate position can be calculated by combining it with a partial traversing algorithm. The proposed method can reduce pixel matching time by 63% and increase reconstruction efficiency by 58%. Simulations and experiments prove feasibility and precision.

条纹投影动态三维表面成像技术综述

The dynamic three-dimensional(3D) surface imaging technology based on fringe projection was summarized and the characteristics of typical strategies were analyzed. Firstly, the basic principle of the technique was introduced, including the basic structure of the system, the principle of 3D surface imaging, and the two typical phase extraction methods, phase shifting method and Fourier transform method. Secondly, the dynamic imaging scheme including high speed projection scheme and dynamic 3D surface imaging method using relatively low speed camera was introduced. Thirdly, the absolute phase acquisition methods in dynamic 3D image were introduced, mainly analog and digital coding and area statistical coding, were introduced. Finally, the methods of accurate dynamic phase measurement were introduced.

Dispersion spectroscopy with optical frequency comb-based single-shot dual-heterodyne mixing.

We present a novel approach to high-speed dispersion spectroscopy that realizes a wide dynamic range, by simultaneous and parallel phase measurement using scanless dual-heterodyne mixing of 50 and 1.4 GHz frequency intervals. This system can realize parallel measurements of the relative phases between adjacent frequencies by introducing an optical frequency comb and intensity modulator to generate adjacent frequency and arrayed waveguide grating to separate the sidebands. The experimental results using single-mode fibers, whose lengths range from 0 to 92 km, indicated a 26 nm dispersion spectrum, 1785 ps/nm measurement range, and 0.27 ps/nm measurement uncertainty in 1 ms.

Multi-target CW interferometric acoustic measurements on a single optical beam.

We present a free-space, continuous-wave laser interferometric system capable of multi-target dynamic phase measurement at acoustic frequencies up to a Nyquist bandwidth of 10.2 kHz. The system uses Digitally-enhanced Heterodyne Interferometry to range gate acoustic signals simultaneously from multiple in-line reflections while isolating coherent cross-talk between them. We demonstrate sub-nanometer displacement sensitivity across the audio band for each individual reflection surface and 1.2 m resolution between successive surfaces. Signals outside the 1.2 m range-gate of the system were suppressed by greater than 30 dB in amplitude, enabling high fidelity independent acoustic measurements.

Dynamic Phase Measurement Based on Two-Step Spatial Carrier-Frequency Phase-Shifting Interferometry

A dynamic phase measurement method based on a two-step spatial carrier-frequency phase-shifting (TS-SCFPS) technique is proposed. First, by the subtraction operation between a pair spatial carrier-frequency interferograms with a certain phase shifts, which are captured by dual-channel interferometry system, we can achieve one-frame background-removed carrier-frequency interferogram. Second, from two-frame phase-shifting subinterferograms splitting from the above background-removed carrier-frequency interferogram, we can rapidly achieve the accurate phase through using a two-step orthogonal and normalization algorithm. Compared with the existing SCFPS methods, the proposed TS-SCFPS method reveals good background deductions and antinoise performance. Moreover, by using a two-step phase-shifting algorithm, without any special requirement for the phase shifts, the proposed TS-SCFPS method can rapidly achieve high-accuracy phase retrieval relative to other SCFPS methods. Especially, the achieved experimental results demonstrate the outstanding performance of the proposed TS-SCFPS method in both static and dynamic phase measurements.

Low-dose and fast grating-based x-ray phase-contrast imaging

X-ray phase-contrast imaging has experienced rapid development over the last few decades, and in this technology, the phase modulation strategy of phase-stepping is used most widely to measure the sample's phase signal. However, because of its discontinuous nature, phase-stepping has the defects of worse mechanical stability and high exposure dose, which greatly hinder its wide application in dynamic phase measurement and potential clinical applications. In this manuscript, we demonstrate preliminary research on the use of integrating-bucket phase modulation method to retrieve the phase information in grating-based X-ray phase-contrast imaging. Experimental results showed that our proposed method can be well employed to extract the differential phase-contrast image, compared with the current mostly used phase-stepping strategy, advantage of integrating-bucket phase modulation technique is that fast measurement and low dose are promising.

A Rapid Spatial Carrier-Frequency Phase-Shifting Method Based on the Orthogonality of Diamond Diagonal Vectors

From a one-frame off-axis interferogram with unknown carrier-frequency, a rapid spatial carrier-frequency phase-shifting (SCFPS) method is proposed to achieve the phase measurement of the dynamic process. First, based on the SCFPS technique, four-frame phase-shifting subinterferograms are constructed from one-frame off-axis interferogram. Second, by using the orthogonality of diamond diagonal vectors, respectively, achieved through the subtraction and addition operations between two equal length vectors, which are generated from above four-frame phase-shifting subinterferograms, the accurate phase can be retrieved rapidly. Compared with current SCFPS methods, in addition to maintaining high accuracy of phase-shifting method, as well as no requirement for carrier-frequency calibration, the proposed method reveals an obvious advantage in processing speed of phase retrieval, and this will greatly facilitate its application prospect for dynamic phase measurement.