Dual-wavelength Interferometry Research Articles

Dual-wavelength real-time simultaneous phase imaging based on off-axis interferometry

Dual-wavelength interferometry is widely used in optical measurement, including the of great significance phase imaging of transparent samples. Here, we present a dual wavelength real-time phase imaging system based on off-axis interferometry with two cameras for recording complex fields transmitted through transparent samples in a wide-field and non-intrusive manner. The method of phase unwrapping based on combing dual wavelength with Fourier transform was derived in detail. The advantage of the proposed system is, compared with single-shot dual wavelength holograms methods, that it can easily extract the complex fields at both wavelengths without consideration of spectrum overlap or needing extra optic device to create lateral shearing. For phase noise, we calculated and removed the phase signal without sample in Fourier domain, which can also ensure the measured phase accurately. Experimental results on standard sample (polystyrene microspheres) demonstrated the efficiency of this imaging system. Implementation in quantitative imaging of living cells showed the time of single-shot acquisition of samples was only 0.025s, which indicated that the system can be applied to real-time and label-free identification of phase objects.

Conjugate complex function coupling strategy of interferometric field: Synthetic-wavelength interferometric fringe extraction in simultaneous dual-wavelength interferometry

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 (λS) 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 λS, the obtained phase-shift interferogram for λS 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.

In-situ characterization of double-diffusive convection during unidirectional solidification of a binary solution

ABSTRACT The work focuses on developing a detailed understanding of the effects of initial composition (C in ) and bottom cooling temperatures (TB ) on different characteristics of double-diffusive convection during unidirectional solidification of water-NH4Cl solution in a complete non-intrusive manner. The qualitative investigation, simultaneous quantification of transported parameters (composition and temperature) and fluid velocities associated with flow patterns are carried out using rainbow schlieren deflectometry, dual-wavelength interferometry and PIV (particle image velocimetry) technique respectively. The dependence of the characteristics of double-diffusive convection for different Cin and TB is explained on the basis of real-time whole-field investigation using a combination of aforementioned imaging techniques.

Simultaneous investigation of thermal and vapour concentration fields around an impinging droplet using dual wavelength interferometry

We report simultaneous investigation of temperature and vapour concentration fields around an evaporating droplet as it impinges on a heated surface using the concept of dual wavelength interferometry. Experiments have been conducted with acetone as the model fluid. To decouple the temperature and vapour concentration fields from a single interferogram, the interferometer employs two light sources of considerable spectral separation (λBlue= 458 nm and λRed= 632.8 nm). Dynamical aspects of impinging and evaporating droplet have been simultaneously recorded using high speed videography. Results have been presented in the form of spatio-temporally resolved temperature and concentration fields along with their polar plots around the droplet interface at different stages of droplet evaporation process. During the initial spreading phase, dominance of contact line evaporation was captured in quantitative terms as densely-spaced temperature and mole fraction contours in these regions. The spreading and receding phase of the droplet is followed by its sessile phase wherein polar plots of the transported properties indicated towards continuous evaporation at droplet interface with contact line evaporation being the dominant mechanism. Plausible signatures of thermo-capillary convection along the droplet interface have been explained on the basis of interferometric measurements. To the best of our knowledge, the work reported is one of the first attempts to simultaneously map the spatio-temporally resolved thermal and vapour concentration fields around an evaporating droplet and is important since the phenomenon of droplet heat transfer is governed by the coupled mechanisms of diffusion and buoyancy-induced convection, which, in turn, are affected by temperature and concentration distributions around the droplet.

Wavelength-multiplexed single-shot ptychography

We present the first experimental demonstration of wavelength-multiplexing in single-shot ptychography. Specifically, we experimentally reconstruct the complex transmission profile of a wavelength-independent and wavelength-dependent object simultaneously for 532 nm and 633 nm probing wavelengths. In addition, we discuss the advantages of a more general approach to detector segmentation in single-shot ptychography. A minimization to correct for uncertainties in a priori information that is required for single-shot geometries is presented along with a novel probe constraint. Furthermore, this technique is complementary to dual-wavelength interferometry without the need for an external reference. This work is enabling to imaging technologies and applications such as broadband single-shot ptychography, time-resolved imaging by multiplexed ptychography, real-time inspection for laser micro-machining, and plasma imaging.

Hybrid-net: a two-to-one deep learning framework for three-wavelength phase-shifting interferometry.

In this paper, we propose a two-to-one deep learning (DL) framework for three- wavelength phase-shifting interferometry. The interferograms at two different wavelengths are used as the input of the proposed hybrid-net, and the interferogram of the third wavelength is used as the output. Using the advantages of the hybrid learning network, the interferogram of the third wavelength can be obtained accurately. Finally, the three-wavelength phase-shifting interferometry is realized. Compared with the previous DL-based dual-wavelength interferometry (DWI), the proposed method can further improve the measurement range of the sample without changing the DWI system. Especially for the independent step sample, the problem of limited measurement range is solved due to the input of auxiliary information. More importantly, the third wavelength can be set freely according to the measurement requirements, which is no longer limited by the actual laser and can provide more measuring ruler for phase measurement. Both experimental results and simulation analysis demonstrate the proposed method in the feasibility and the performance in improving the measurement range.

Fast phase extraction of a synthetic wavelength from a dual-wavelength interferogram through Hilbert transformation.

Phase imaging is an important measurement method in optical metrology, and phase extraction is one of its essential components. A method using one-frame dual-wavelength interferometry (DWI) for fast phase extraction is proposed. Using this method, the Hilbert transform (HT) is applied twice to a wavelength-multiplexed interferogram to obtain two images. The HT is then applied twice to the sum of the squares of these two images. The synthetic wavelength phase can then be obtained. Compared with other common multiple-frame DWI methods, the proposed approach requires only one multiplexed interferogram and does not have to consider parameter changes in interferograms of different frames. Furthermore, the proposed method was determined to require the least calculation time, and the simulation and experimental results confirmed its high accuracy and efficiency. It suggests that the proposed method is suitable for real-time measurements.

Dual-wavelength interferogram decoupling method for three-frame generalized dual-wavelength phase-shifting interferometry based on deep learning

In dual-wavelength interferometry, the key issue is how to efficiently retrieve the phases at each wavelength using the minimum number of wavelength-multiplexed interferograms. To address this problem, a new dual-wavelength interferogram decoupling method with the help of deep learning is proposed in this study. This method requires only three randomly phase-shifted dual-wavelength interferograms. With a well-trained deep neural network, one can obtain three interferograms with arbitrary phase shifts at each wavelength. Using these interferograms, the wrapped phases of a single wavelength can be extracted, respectively, via an iterative phase retrieval algorithm, and then the phases at different synthetic beat wavelengths can be calculated. The feasibility and applicability of the proposed method are demonstrated by simulation experiments of the spherical cap and red blood cell, respectively. This method will provide a solution for the problem of phase retrieval in multiwavelength interferometry.

双波长干涉技术中改进的最小公倍数有效波长法

双波长干涉技术中改进的最小公倍数有效波长法

Derivative method for dual-wavelength three-frame phase-shifting interferometry

Dual-wavelength interferometry is an important technique, which is widely used in optical measurement and microscopy imaging. In this study, a phase extraction method using derivative algorithm for simultaneous dual-wavelength three-frame phase-shifting interferometry is proposed. Only by calculating the difference between the first and other interferograms as well as its first-order and second-order derivatives, one can separate the information of single-wavelength and obtain continuous phase of the synthetic wavelength. The phase shift can be any value between ( 0 , 2 π ) . Simulation and experimental results demonstrate that this method can be used to dual-wavelength on-axis and off-axis interferometric imaging systems with high accuracy. Since only three phase-shifted interferograms are required and only partial derivative algorithm is used, the imaging speed is faster.

Unambiguous measurement range and error tolerance in dual-wavelength interferometry.

In dual or multiwavelength interferometry, the traditional equivalent wavelength method is widely used for phase recovery to enlarge the unambiguous measurement range (UMR). In fact, however, this method ignores information of size and sign (positive or negative) of single wavelength wrapped phases, and the extension of the UMR is not sufficient. For the reflective measurement, the largest UMR of the dual or multiwavelength interferometry is half of the least-common multiple (LCM) of single wavelengths, called the LCM effective wavelength, which is often several times the equivalent wavelength. But why do we often use the equivalent wavelength and seldom use the larger UMR in practice? Existing research reveals that the actual UMR is related to the measurement error of single-wavelength-wrapped phases, and half of the LCM effective wavelength is only the theoretical value. But how do errors affect the UMR? We think the quantitative analysis and description are lacking. In this paper, we continue to study this problem, analyze it in a graphical method, and give quantitative descriptions. The simulation experiments are carried out and verify our analysis.

Quantitative phase imaging in dual-wavelength interferometry using a single wavelength illumination and deep learning.

In this manuscript, we propose a quantitative phase imaging method based on deep learning, using a single wavelength illumination to realize dual-wavelength phase-shifting phase recovery. By using the conditional generative adversarial network (CGAN), from one interferogram recorded at a single wavelength, we obtain interferograms at other wavelengths, the corresponding wrapped phases and then the phases at synthetic wavelengths. The feasibility of the proposed method is verified by simulation and experiments. The results demonstrate that the measurement range of single-wavelength interferometry (SWI) is improved by keeping a simple setup, avoiding the difficulty caused by using two wavelengths simultaneously. This will provide an effective solution for the problem of phase unwrapping and the measurement range limitation in phase-shifting interferometry.

Radial Hilbert transform for phase retrieval using two-wavelength three-frame phase-shifting interferometry

Dual-wavelength interferometry (DWI) without phase unwrapping is widely applied in optical measurement and imaging. For improving measurement efficiency and increasing the range of applications, a method of retrieving a phase using fewer interferograms and shorter calculating time is proposed in this study. The proposed method requires only three multiplexed and phase-shifted interferograms. By subtracting the other two interferograms from the first frame image and using the Hilbert transform (HT), we first obtained the phase at each wavelength and then calculated the continuous phase at the synthetic wavelength. The method is applicable to open-loop fringes obtained in an off-axis interferometric system and closed-loop fringes obtained in an on-axis system. We used a combination of the radial HT and coordinate conversion method to solve the problem of having to use the conventional HT for closed-loop fringes. The feasibility and applicability of the method are verified using simulation and experimental results.

Two-step dual-wavelength interferometry for surface relief retrieval

Two-step dual-wavelength interferometry for surface relief retrieval

Phase unwrapping in dual-wavelength digital holographic microscopy with total variation regularization.

A two-step dual-wavelength phase imaging method with total variation (TV) regularization in digital holographic microscopy (DHM) is presented. The rough height map is first denoised with TV regularization, and then it is used as a guiding map for accurate phase unwrapping. By combining the principle of dual-wavelength interferometry and TV regularization, the problem of phase unwrapping is converted into a minimization problem that can be efficiently solved with the Split Bregman algorithm. The proposed algorithm allows a synthetic wavelength that can be arbitrarily large in principle to a single wavelength, while the accuracy of the phase map can achieve the same level in single-wavelength DHM. Moreover, the unwrapping method is robust to the change of weighting parameters. Comparative topographic measurements of a sample with abrupt steps are illustrated, and the results verified the effectiveness of the method.

Carrier squeezing interferometry with π/2 phase shift at the synthetic wavelength: Phase extraction in simultaneous dual-wavelength interferometry

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 (λS) 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 λS 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 (0.0059λs) and RMS of 6 nm (0.0017λs) even when the distribution range of the phase-shift error is as high as ± 10% relative to the π/2 phase shift step at λS. 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.

Phase retrieval from the phase-shift moiré fringe patterns in simultaneous dual-wavelength interferometry

Simultaneous dual-wavelength interferometry (SDWI) could extend the measured range of each single-wavelength interferometry. The moiré fringe generated in SDWI indirectly represents the information of the measured long synthetic-wavelength phase, thus the phase demodulation is rather arduous. To address this issue, we present a method to convert the moiré fringe pattern into a synthetic-wavelength interferogram (moiré to synthetic-wavelength, MTS). After the square of the moiré fringe pattern in the MTS method, the additive moiré pattern is turned into a multiplicative one. And the synthetic-wavelength interferogram could be obtained by a low-pass filtering in spectrum of the multiplicative moiré fringe pattern. Therefore, when the dual-wavelength interferometer is implemented with the π/2 phase shift at a sequence of synthetic-wavelength phase-shift interferograms with π/2 phase shift could be obtained after the MTS method processing on the captured moiré fringe patterns. And then the synthetic-wavelength phase could be retrieved by the conventional phase-shift algorithm. Compared with other methods in SDWI, the proposed MTS approach could reduce the restriction of the phase shift and frame numbers for the adoption of the conventional phase-shift algorithm. Following, numerical simulations are executed to evaluate the performance of the MTS method in processing time, frames of interferograms and the phase shift error compensation. And the necessary linear carrier for MTS method is less than 0.11 times of the traditional dual-wavelength spatial-domain Fourier transform method. Finally, the deviations for MTS method in experiment are 0.97% for a step with the height of 7.8 μm and 1.11% for a Fresnel lens with the step height of 6.2328 μm.

Extended depth-range dual-wavelength interferometry based on iterative two-step temporal phase-unwrapping

For dual-wavelength interferometry (DWI), we propose an extended depth-range phase-shifting interferometry technique of extracting phase distributions from randomly phase-shifted interferograms. First, the generalized phase-shifting algorithm is utilized to retrieve the single-wavelength phase from interferograms with random phase shifts. Then, the phase difference and phase-sum are calculated from the wrapped single-wavelength phases, and iterative two-step temporal phase-unwrapping is introduced to unwrap the phase-sum. Finally, the height of objects is determined. Simulations and experiments are conducted to demonstrate the excellent precision and overall performance of the proposed method. As the limitation of being exclusively applicable to interferograms with special phase shifts is broken, the proposed method will greatly facilitate the practical application of DWI. Furthermore, because the phase-sum and iterative two-step temporal phase-unwrapping is introduced to extend the depth-range, the sensitivity and precision of the retrieved phase are greatly improved.

Phase extraction for dual-wavelength phase-shift Fizeau interferometry in the presence of multi-beam interference

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.

Simultaneous phase-shifting dual-wavelength interferometry based on independent component analysis.

An independent component analysis-based simultaneous phase-shifting dual-wavelength interferometry approach is proposed. By using a one-time phase-shifting procedure, the simultaneous phase-shifting operation of two illumination wavelengths can be implemented, and then the background intensity and two orthogonal independent components of each single wavelength can be separated from a sequence of simultaneous phase-shifting dual-wavelength interferograms with random phase shifts. Subsequently, the wrapped phases of single wavelength can be calculated by above two orthogonal independent components; thus the unambiguous phase of synthetic wavelength can be achieved. Both the simulation and experimental results show that the proposed approach reveals the advantages of high accuracy, rapid speed, high stability, and good adaptability for arbitrary phase shifts.