Two-beam interferometry with a definitive phase-shift sign

Mach-Zehnder Interferometer (MZI) is used to measure the phase shift (Δφ) between two light beams related to relative length difference (ΔL) of MZI's two arms. The phase shift of the interferometer output is represented by output Free Spectral Range (FSR). Thus the FSR can be configured by setting its length difference of the two arms, to vary the phase shift. In this paper, the FSR of two couplers MZI are compared with three couplers MZI with two configurations based on the two couplers MZI's length difference. Length difference of the two couplers MZI is utilized for both of the length differences for the first configuration of three couplers MZI. As for the second configuration, each of the three couplers MZI length differences is half of the two couplers MZI length difference. The two couplers MZI are designed to have FSR at 10 nm, which can be obtained by using 0.166 mm as the length difference. 3 dB couplers are used for all of the configurations. Only one input port is utilized and the outputs are simulated in a normalized graph form. The MZIs simulation shows that the FSR of three couplers MZI first configuration is 5 nm, half of the FSR of two couplers MZI, while the FSR of three couplers MZI second configuration is 10 nm, the same as the FSR of two couplers MZI.

This paper is intended to bridge the present gap in publications on the subject between the very simple illustrative paper and the detailed account that can be understood only by an expert. An outline of the types of problem that can be tackled with a Mach-Zehnder interferometer is followed by a discussion of the principle of formation of interference fringes in two-beam interferometry and an account of the principle of operation of the Mach-Zehnder interferometer. The relations between fringe shift and temperature change are derived for liquids and for gases at constant pressure and the factors that control the sensitivity are indicated. A description is given of the operations to be performed to produce fringes and some attention is given to practical details of the instrument and associated apparatus. The methods of analysing interferograms, including the use made of white-light fringes when measuring absolute temperatures are described, and some attention is given to sources of error. After an account of the application of the interferometer to temperature measurement in convective heat transfer systems, illustrated by examples from steady state and transient processes, the advantages of the instrument over other methods of temperature measurement for some problems are discussed briefly.

In order to achieve precise control of phase shift amplitude and position in the echo spectrum of phase-shifted fiber Bragg grating (PSFBG) sensor, the method to control PSFBG sensor using mechanical micro-strain was proposed. There were micrometer screws, strain beams, phase shifting fiber gratings, demodulators, etc. in this method. The micro-strain control was performed by a micrometer screw, and the strain was transmitted to the PSFBG by the beam, thereby changing the echo spectrum. Finally, a functional model of spectrum offset and microdisplacement Δy was constructed. Experimental results show that stretching and compression can cause positive phase shift and negative phase shift of PSFBG, and the phase shift fit curve is linear, and its comprehensive fit slope is 0.9914. The system can achieve continuous tuning of the phase shift by bending the micro-strain of the beam. The magnitude of the phase shift can be linearly controlled by changing the load displacement. The method is simple, high precision, large control range and passive. It has certain application value.

Silicon photonic sensors based on Mach Zehnder Interferometers (MZIs) have applications spanning from biological and olfactory sensors to temperature and ultrasound sensors. Although a coherent detection scheme can solve the issues of sensitivity fading and ambiguity in phase direction, the measured phase remains 2π periodic. This implies that the acquisition frequency should ensure a phase shift lower than π between each measurement point to prevent 2π phase jumps. Here, we describe and experimentally characterize two methods based on reference MZIs with lower sensitivities to alleviate this drawback. These solutions improve the measurement robustness and allow the lowering of the acquisition frequency. The first method is based on the phase derivative sign comparison. When a discrepancy is detected, the reference MZI is used to choose whether 2π should be added or removed from the nominal MZI. It can correct 2π phase jumps regardless of the sensitivity ratio, so that a single reference MZI can be used to correct multiple nominal MZIs. This first method relaxes the acquisition frequency requirement by a factor of almost two. However, it cannot correct phase jumps of 4π, 6π or higher between two measurement points. The second method is based on the comparison between the measured phase from the nominal MZI and the phase expected from the reference MZI. It can correct multiple 2π phase jumps but requires at least one reference MZI per biofunctionalization. It will also constrain the corrected phase to lie in a limited interval of [-π, +π] around the expected value, and might fail to correct phase shifts above a few tens of radians depending on the disparity of the nominal sensors responses. Nonetheless, for phase shift lower than typically 20 radians, this method allows the lowering of the acquisition frequency almost arbitrarily.

Transmission optical coherence tomography (tOCT) is gaining interest for imaging biological samples; however, so far, quantitative phase information has not been directly obtained. This study introduces SOPHAST-OCT, an approach for integrated 2D phase recovery in Off-Axis Full-Field Swept-Source tOCT. It uses phase-shifting to leverage OCT’s inherent phase changes between recorded interferograms. SOPHAST-OCT demonstrates promising phase agreement with the simulated ground truth phase. This approach represents a first step toward quantitative imaging in tOCT. Full Text: PDF References Y. Park, C. Depeursinge, G. Popescu, "Quantitative phase imaging in biomedicine", Nature Photon 12, 578 (2018). CrossRef K. Alm, H. Cirenajwis, L. Gisselsson, A.G. Wingren, B. Janicke, A. Mölder, et al., in Holography, Research and Technologies (IntechOpen, 2011). CrossRef W. Drexler, J. Fujimoto, editors , Optical Coherence Tomography: Technology and Applications, 2nd ed. (Springer Cham, 2015). CrossRef W. Krauze, P. Ossowski, M. Nowakowski, M. Szkulmowski, M. Kujawińska, "Enhanced QPI functionality by combining OCT and ODT methods", Quantitative Phase Imaging VII, 11653, 19 (2021). CrossRef B.C. Wilson, S.L. Jacques, "Optical reflectance and transmittance of tissues: principles and applications", IEEE J. Quantum Electron. 26, 2186 (1990). CrossRef J. van der Horst, A.K. Trull, J. Kalkman, "Deep-tissue label-free quantitative optical tomography", Optica 7, 1682 (2020). CrossRef P. Hosseini, Y. Sung, Y. Choi, N. Lue, Z. Yaqoob, P. So, "Scanning color optical tomography (SCOT)", Opt. Expr. 23, 19752 (2015). CrossRef P. de Groot, "Phase Shifting Interferometry" in Optical Measurement of Surface Topography, edited by R. Leach (Springer, Berlin, Heidelberg, 2011). CrossRef M. Wojtkowski, A. Kowalczyk, R. Leitgeb, A.F. Fercher, "Full range complex spectral optical coherence tomography technique in eye imaging", Opt. Lett. 27, 1415 (2002). CrossRef Q. Zhang, S. Zhong, J. Lin, W. Chen, M. Luo, J. Zhong, Y. Yu, Z. Peng, S. Cheng, "Full-range Fourier-domain optical coherence tomography based on Mach–Zehnder interferometer", Opt. Lasers Engin. 124, 105794 (2020). CrossRef R. Juarez-Salazar, C. Robledo-Sanchez, F. Guerrero-Sanchez, A. Rangel-Huerta, "Generalized phase-shifting algorithm for inhomogeneous phase shift and spatio-temporal fringe visibility variation", Opt. Express 22, 4738 (2014). CrossRef R. Juarez-Salazar, C. Robledo-Sánchez, C. Meneses-Fabian, F. Guerrero-Sánchez, L. M. Arévalo Aguilar, "Generalized phase-shifting interferometry by parameter estimation with the least squares method", Opt. Lasers Engin. 51, 626 (2013). CrossRef M.A. Herráez, D.R. Burton, M.J. Lalor, M.A. Gdeisat, "Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path", Appl. Opt. 41, 7437 (2002). CrossRef Z. Wang, A.C. Bovik, "A universal image quality index", IEEE Signal Proc. Lett. 9, 81 (2002). CrossRef

We numerically studied an ultracompact folded-path photonic crystal waveguide Mach–Zehnder interferometer (MZI) thermo-optic switch based on a small-bend radius double 180° waveguide bend MZI arm. The design can at least double the active waveguide length and sensitivity while maintaining a small heater size compared to the conventional MZI design. From 3D finite difference time domain simulation, a refractive index increase of 0.019 in the 25 μm long heated arm that is induced by a temperature difference of 102 K produces a π phase shift in the output of the MZI.

A quantitative phase measuring technique is presented that estimates the object phase from a series of phase shifted interferograms that are obtained in a common-path configuration with unknown phase shifts. The derived random phase shifting algorithm for common-path interferometers is based on the Generalized Phase Contrast theory [pl. Opt.40(2), 268 (2001)10.1063/1.1404846], which accounts for the particular image formation and includes effects that are not present in two-beam interferometry. It is shown experimentally that this technique can be used within common-path configurations employing nonlinear liquid crystal materials as self-induced phase filters for quantitative phase imaging without the need of phase shift calibrations. The advantages of such liquid crystal elements compared to spatial light modulator based solutions are given by the cost-effectiveness, self-alignment, and the generation of diminutive dimensions of the phase filter size, giving unique performance advantages.

We apply an AM-FM surface albedo model to analyze the projection of surface patterns viewed through a binocular camera system. This is used to support the use of modulation-based stereo matching where local image phase is used to compute stereo disparities. The local image phase is an advantageous feature for image matching, since the problem of computing disparities reduces to identifying local phase shifts between the stereoscopic image data. Local phase shifts, however, are problematic at high frequencies due to phase wrapping when disparities exceed +/-pi. We meld powerful multichannel Gabor image demodulation techniques for multiscale (coarse-to-fine) computation of local image phase with a disparity channel model for depth computation. The resulting framework unifies phase-based matching approaches with AM-FM surface/image models. We demonstrate the concepts in a stereo algorithm that generates a dense, accurate disparity map without the problems associated with phase wrapping.

A new method is proposed and demonstrated for fabricating phase-shifted fiber Bragg gratings (FBGs) using a variable-velocity scanning UV laser beam in combination with a shielded phase mask. The transmission properties of phase-shifted FBGs were analyzed based on coupled-mode theory and a transfer matrix method. The grating is divided into three parts to allow for easier analysis of FBG properties. These segments included a uniform FBG1 and FBG2 which were separated by a shielded section. A novel phase-shifted FBG was fabricated using this method, in which the refractive indices of FBG1 and FBG2 were different. Transmission properties of these phase-shifted FBGs were simulated numerically using MATLAB, and the experimental results and simulated results are in good agreement. In addition to the length and effective refractive index of the shielded section, the phase shift value of a phase-shifted FBG was also found to be dependent on the lengths and effective refractive indices of FBG1 and FBG2. Moreover, we predicted that changing the scanning velocity for fabricating FBG2 would adjust phase shift value, which exhibits a positive linear relationship with the scanning velocity. These results can provide guidelines for fabricating any phase shift value FBGs. This technique is simple, convenient, and may be developed further for use in fabricating novel tunable fiber filters or DFB fiber lasers.

Hazelnut proteins detection in cookies using an immersible label-free photonic chip sensor

A method for determining soil hydraulic parameters based on periodic point source solutions of the linearized Richards equation is proposed. Closed‐form solutions were derived for buried and surface point sources with a sinusoidally varying flux. These solutions describe the dependence of the matric flux potential (MFP) amplitude and phase shift on the distance from the point sources, frequency of source flux alternations, and soil hydraulic parameters. The Fourier series representation of square waves was used to extend the point source solutions for sinusoidally varying flux to square‐wave cyclic inputs of water with a 50% duty cycle—a preferable operating mode for field experiments. Close to the sources, the amplitudes and shape of MFP waves from a step input were more pronounced than those from a sinusoidal input, but the difference diminished as distance increased. The proposed method involves recording the pressure head variations with a continuously reading tensiometer installed below a pressure‐compensating emitter controlled by an irrigation computer. Among 16 cyclic step‐input irrigation tests, one series involved pressure‐head measurements at a single depth and varied water‐pulse durations; the second involved pressure‐head measurements at various depths with a fixed water‐pulse duration. The soil saturated hydraulic conductivity, the coefficient α of Gardner's conductivity model, and the coefficient k of the linearized unsteady‐flow equation were estimated by matching the periodic solution for cyclic step inputs to the measured pressure‐head data with a two‐step inversion procedure: an amplitude‐shift (AS) estimation procedure followed by the Levenberg–Marquardt (LM) optimization algorithm. The AS procedure was effective, and the LM optimization yielded only minor improvements. Our main findings are: (i) the periodic solution for step inputs yields reasonably good predictions of pressure‐head variations measured at various depths below an emitter for different periods of water application; and (ii) the proposed point‐source method seems to yield consistent and reliable estimates of the three soil hydraulic parameters.

We present a method for predicting the geometric phase introduced by wave plates and a polarizer, wherein mathematical formulas to calculate the phase using the Mueller formalism are visualized as a triangle on the surface of the Poincare sphere. These constructions are used to describe a simple experiment with a birefringent medium in a Mach–Zehnder interferometer and polariscopic setup. A geometric radio frequency (RF) phase shifter for controlling the geometric phase introduced by the birefringent medium is also presented. The RF phase generated from orthogonally polarized light signals was shifted from 0 deg to 360 deg; this phase shift exhibited nonlinear characteristics. Thus, the proposed phase-shifter device improves phase control sensitivity in the partial region.

We developed simultaneous phase-shifting system based on a Mach–Zehnder interferometer and a replicating system integrated by a Michelson configuration and a cube beam splitter. The system is capable to obtain four simultaneous interferograms in a single capture, and the phase shifts are controlled by placing a linear polarizer in each replica obtained. The system retrieves four interferograms with a relative phase shift of π/2 and the optical phase map is calculated using the four-step algorithm. In addition, the configuration presents potential capabilities for generating spiral interference patterns. To show the advantage of the technique, experimental results are presented for static and dynamic samples.

The Mach-Zehnder interferometer is a fundamental tool for measuring phase shifts between two light paths, serving as a crucial prototype for achieving high-precision measurements in various scientific and technological applications. In this study, we analyze different models for estimating relative phase shift in a general two-arm Mach-Zehnder interferometer. We demonstrated that single- parameter estimation models can be reduced from the two-parameter estimation model by imposing appropriate constraints on the parameter space. To make quantum Fisher information of the single- parameter estimation models meaningful, the corresponding constraints must be guaranteed in the experiment implementation. Furthermore, we apply the quantum Fisher information approach to analyze the Mach-Zehnder interferometer with the an input state composed of a displaced squeezed vacuum state and a coherent state, providing insights into the precision limits of such configurations.

We present a simple mathematical method for phase shifting that overcomes some phase shift errors and limitations of commonly used methods. The method is used to generate a sequence of phase-shifted interferograms from a single interferogram. The generated interferograms are employed to reconstruct the wavefront aberrations, as an application. The approach yields results with only very small deviations compared to both simulated wavefront aberrations, including the first 25 Zernike polynomials (0.05%) and those measured with a Shack-Hartmann sensor (0.5%).