Change In Optical Path Difference Research Articles

Impact of mechanical disturbances to the placement of reference light in Fourier transform interferometers.

Fourier transform interferometers usually need a dedicated reference light to precisely track optical path difference changes. There are a few different ways to incorporate the reference light into the optical system. This paper conducted experiments to give a test of how different ways of incorporating reference light are affected by mechanical disturbances. It found that placing the reference light in a different path than the test light can be very sensitive to mechanical disturbance errors, while propagating the reference light together with the test light can be very robust against mechanical vibrations of optical components.

A novel interferometry-based optical sensor to study the coagulation of human plasma

We propose and demonstrate a Twin-interferometry (TIM) based optical approach for studying and exploring anisotropy and directional dependent coagulation kinetics in human plasma under isothermal condition. Human plasma is obtained by centrifuging blood samples collected in Ethylenediamine tetra acetic acid (EDTA) coated vials at 6000 RPM in a laminar flow unit. 0.5 ml of plasma is collected in an optically flat disposable glass cuvette and subjected to induced coagulation by adding equal amounts of CaCl2 solution as coagulant at seven different concentrations. A Twin-interferometer is designed to record the rate of shift in Michelson’s fringes caused by rate of change of optical path difference of coagulating plasma in two orthogonal directions. A pair of interferograms, referred to as the Twin- interferogram (TIG), are recorded for all plasma samples with different CaCl2 concentration during its coagulation. A new approach for extracting various coagulation parameters from TIG, such as anisotropy, half coagulation time, constants governing the rate and dimensionality of coagulation, and their variation along distinct direction is demonstrated. TIG results are validated using polarizing optical microscopic (POM) and optical extinction techniques.

Highly Sensitive Balloon-like Fiber Interferometer Based on Ethanol Coated for Temperature Measurement.

A highly sensitivity balloon-like fiber interferometer based on ethanol coating is presented in this paper. The Mach-Zehnder interferometer is formed by bending a single-mode fiber to a balloon-like structure and nested in the Teflon tube. Then, an ethanol solution was filled into the tube of the balloon-like fiber interferometer by the capillary effect. Due to the high sensitivity of the refractive index (RI) of ethanol solutions to temperature, when the external temperature varies, the optical path difference changes. The change in temperature can be detected by the shift in the interference spectrum. Limited by the size of the balloon-like structure, three kinds of these structures with different sensitive lengths were prepared to select the best parameters. The sensitive lengths were 10, 15 and 20 mm, respectively, and the RI detection performance of each structure in 10~26% NaCl solutions was investigated experimentally. The results show that when the sensitive length is 20 mm, the RI sensitivity of the sensor is the highest, which is 212.88 nm/RIU. Ultimately, the sensitive length filled with ethanol is 20 mm. The experimental results show that the temperature sensitivity of the structure is 1.145 nm/°C in the range of 28.1 °C~35 °C, which is 10.3 times higher than that of an unfilled balloon-like structure (0.111 nm/°C). The system has the advantages of low cost and easy fabrication, which can potentially be used in high-precision temperature monitoring processes.

Effects of Shock Waves on Shack–Hartmann Wavefront Sensor Data

Shock waves will form by turning supersonic or locally supersonic flow and result in an increase in the freestream density downstream of the shock. This increase leads to optical distortions that limit the effectiveness of aircraft-mounted laser systems. In this paper, analytic expressions are developed to describe these optical distortions in terms of the optical-path difference (OPD). Pupil-plane disturbances imposed by the shock are studied for two cases: when the shock is parallel to the propagation direction and when the shock is on an angle relative to the propagation direction. Upon propagation from the pupil plane, the analysis shows that shock-induced phase discontinuities can sometimes cause the irradiance pattern in the image plane to bifurcate. Despite a large amount of tilt in the pupil plane, the bifurcated irradiance pattern does not map to a proportional shift in the image plane. The implications that these findings have on Shack–Hartmann wavefront sensor (SHWFS) data are also explored. The results show that least-squares reconstruction from the SHWFS data yield accurate estimates of the change in OPD across the shock when the magnitude of the phase difference caused by the shock is between 0 and approximately . However, when , the results show that least-squares reconstruction begins to severely underestimate the change in OPD across the shock. Such results will inform future efforts looking to develop aircraft-mounted laser systems.

Optofluidic Micromachined Platform for Refractive Index Measurement

We present a combination of micromachined optofluidic platforms equipped with a fiber-optic sensing configuration based on a three-path Mach–Zehnder interferometer (MZI) for simultaneous measurement of the refractive index of liquids and the autocalibration in dynamic regime. The sensing principle is based on the low-coherence interferometry, characterized by a generation of Gaussian enveloped interferograms, for which the position of its maximum depends on the optical path difference (OPD) between the sensing and reference arm of the MZI. When liquid flows through the central microchannel of the optofluidic platform it crosses the light beam between the two optical fibers in the sensing arm causing the OPD change. An algorithm has been applied for the calculation of the refractive index of liquids out of the raw interference signals. We obtained a very good agreement between the experimental results and literature data of refractive indices of subjected fluids. The accuracy of refractive index measurement is approximately 1%, predominantly determined by the accuracy of reading the position of the mechanical scanner. The proposed sensor is attractive for the label-free biological, biochemical, and chemical sensing owing autocalibration and high sensitivity yet consuming a very small sample volume of 1 µL. It is capable to measure the refractive index of various liquids and/or gases simultaneously in the process.

Iterative normalized cross-correlation method for absolute optical path difference demodulation of dual interferometers.

It is still a challenge to realize the absolute optical path difference (OPD) demodulation of multi-interference systems with a narrow spectral interval and small OPD interval. In this paper, an iterative normalized cross-correlation algorithm is firstly proposed for demodulating the multiple absolute OPDs of a dual-interference system and applied to optical fiber sensing system. By constructing a template function in combined form, the optimal solutions of its components and OPDs are solved iteratively based on the reconstruction matrix method and cross-correlation algorithm, respectively. The simulation and experiment show that the demodulation accuracies near the OPDs of 560 µm and 660 µm are both up to 5 nm in different spectral intervals from 45 to 80 nm. The simulation results show that all demodulation precisions at the spectral interval of 55 nm do not exceed 4 nm when the OPD changes in the range of 650-670 µm. Besides, the experimental verification shows the temperature accuracy (0.125 °C) with 95% confidence of T-distribution is very close to the control accuracy (0.1 °C). The proposed algorithm can improve the multiplexing capability of optical fiber sensor system and reduce its cost.

Rhombic optical path difference bias white light interferometric fiber-optic gyroscope.

We present a novel, to the best of our knowledge, white light interferometric fiber-optic gyroscope (IFOG) scheme using a fiber-optic rhombic optical path difference (OPD) bias structure to interrogate with a sensing coil to realize rotation rate measurement without a phase modulator. The OPD bias structure composed of four (2×1) 3 dB single-mode fiber couplers was constructed to implement non-reciprocal OPD bias. White light interferometric demodulation was utilized to acquire the change in OPD due to the Sagnac-phase shift. Absolute linear output can be obtained. We produced the principle prototype of rhombic OPD bias white light IFOG without utilizing a phase modulator. An experimental demonstration of the IFOG prototype system achieves linear output with respect to the OPD difference in detecting rotation rate.

High-accuracy measurement system for the refractive index of air based on a simple double-beam interferometry.

A measurement system based on a simple double-beam interferometry is built to realize the measurement of air refractive index with high accuracy. The basic principle of the system is that, through measuring the change of optical path difference caused by rapid and smooth vacuumization, measurement of refractive index of air is converted to length measurement. Error correction and signal processing are studied to ensure high-accuracy measurement of the refractive index of air. Three applicable methods are used in system. The system based on the methods realize the subdivision and counting of interference fringe by software with three-error correction, error compensation for the end-window plates' thickness change caused by vacuumization, steady realization of high vacuum conditions. To verify the accuracy and reliability of the system, the measurement results are compared with that obtained from the method based on empirical Edlén's formula. Analysis result shows that the expanded measurement uncertainty of the system is U = 5×10-9, with k = 2. The system can be used to compensate the laser wavelength error caused by the refractive index of air with high accuracy.

Electron Cloud Spectroscopy Using Micro-Ring Fabry–Perot Sensor Embedded Gold Grating

An electron cloud spectroscopy system consisting of a microring and Bragg grating Fabry-Perot is proposed. It has the form of a Panda-ring formed by an add-drop filter with nonlinear two-phase modulators. The input light of $1.50\mu \text{m}$ center wavelength is fed into the system. By using suitable two-phase modulator parameters, the whispering gallery mode (WGM) of light is formed at the center ring. The gold plate at the center microring illuminated by light leads to electron cloud oscillations forming the electron density that results in the spin up and spin down of electrons. The electron cloud spins (spin up and spin down) form the qubits which can be transmitted to the Fabry-Perot sensing unit by the spin waves. The Fabry-Perot sensing unit measures the spectral profile of the electron cloud spins. To observe the spectral profile of the electron cloud spins a large bandwidth is employed. The space-time function is applied to distinguish the electron cloud spins, which leads to having the selected spin switching time and sensor sensitivity resolution. By varying the input power and the gold grating gaps, the change in optical path difference formed in terms of the electron cloud spins at the center ring, where the optimum of ~10Pbit is obtained. Both the reflection and transmission schemes of the microring Fabry-Perot circuit have bit rates of ~6Pbit $s^{-1}$ . The reflection and transmission spectra have a free spectral range of ~0.04–0.14 $\mu \text{m}$ . The optimum sensitivity of the microring Fabry-Perot sensor is $0.31\mu \,\,\text{m}^{-1}$ .

Modulation of Second-Harmonic Generation in Bulk MoS2 via Excitation Wavelength and Metal Film Thickness

We numerically investigated the impact of the excitation wavelength and metal film thickness on second-harmonic generation (SHG) in bulk MoS2, which originates from the change in optical-path difference and phase difference among the multistage reflected lights during the thin-film interference process. The enhancement factor of SHG for a MoS2 layer on metal-dielectric substrates was calculated using the finite-difference time-domain technique. It was shown that the intensity of SHG was strongly affected by the excitation wavelength and the thickness of the metal film. We also obtained the dependence of the thickness of the MoS2 layer with the strongest SHG on the excitation wavelength. The reflection, transmission, and absorption of MoS2 layers with different thicknesses were studied by changing the metal film thickness of substrates, and the MoS2 thickness with the strongest SHG was found at different excitation wavelengths. We found that changing the metal film thickness has little effect on the color of the MoS2 layer, indicating that the thickness of the MoS2 layer can still be roughly estimated from the color. Therefore, it is inferred that MoS2 layers with the strongest SHG have the potential to be used for optical information storage or in the design of optical devices provided that the excitation wavelength or the thickness of the metal film is selected appropriately.

Polyvinylidene fluoride coated optical fibre for detecting perfluorinated chemicals

This work reports the development of a Fabry-Perot Interferometry (FPI) based optical fibre to detect perfluorooctanoic acid (PFOA) and other perfluoroalkyl substances (PFAS) in aqueous solutions. A novel and simple sensor fabrication procedure utilizing an immersion precipitation-based phase inversion process to form a thin polyvinylidene fluoride (PVDF) coating at the end-faces of freshly cleaved optical fibres is presented. The PVDF coating was rich in the electroactive β-phase, which enhances dipole-dipole and hydrophobic interaction with PFAS at binding sites. Sensor testing with model PFOA solutions showed that the PVDF coated FPI optical fibre can detect PFOA. The change in optical path difference (OPD) with change in PFOA concentration was considered as a measure of sensitivity and it corresponded to a value of 0.9–5 nm/ppm for PFOA. In real PFAS solutions obtained from fire-fighting foams, the OPD was found to be significantly more sensitive at 178 nm/ppb.

Design and Experimental Test of a Common-path Coherent-dispersion Spectrometer for Exoplanet Searches

A coherent-dispersion spectrometer (CODES) system using the radial velocity (RV) method for exoplanet searches is established in this paper. This spectrometer utilizes a new Sagnac interferometer with common-path and asymmetric designs. Compared with the traditional Michelson interferometer-based spectrometer for exoplanet detection, these designs markedly improve the stability of the optical path difference (OPD) to positional changes in optical elements or air density changes, reducing the need for active cavity stabilization. Furthermore, the asymmetric Sagnac design allows convenient separation of the two complementary outputs. In order to verify the feasibility of the CODES, an optical Doppler shift experiment is constructed in the laboratory. The RV signal was extracted by the phase shifts of the interference fringes produced by the spectrometer. The experimental results show that the obtained retrieved RV is 76.7 m s−1, with an absolute error of 0.3 m s−1 compared to simulated values. And the root mean square error (RMSE) and the standard deviation (STD) are 21.3 m s−1 and 21.4 m s−1, respectively. Error analyses show that the OPD change caused by the temperature variation is the main factor for the RMSE and STD.

Beam quality improvement in an end-pumped Nd:YAG slab amplifier by the increase of the super-Gaussian order of laser diode beam profile

This work focuses on a new estimation to pave the way for an easier optical design of a slab amplifier according to optical path difference (OPD) distribution via laser diode (LD) as a pump source. In general, the output of LD consists of super-Gaussian beams with order 1 in the fast axis and order 3 in the slow axis. The thermal lens (TL) effect is the most important challenge in the optical design of the slab amplifier chain for transferring light from one single-module slab to the next. The formed TL in the slab volume is compensated via the zigzag path of the seed laser in the slab thickness direction. Aforementioned, to improve the output beam quality (BQ) of the slab amplifier, TL effect must be covered by using external optical elements in the slab width direction. In the present paper, the OPD spatial distribution of LD pumped Nd:YAG slab (0.6% Nd3+ dopant) is estimated by using math functions that can be matched. It follows both aspheric and super-Gaussian functions in the slab width direction. Our results show that the super-Gaussian estimation could portray a better understanding of OPD changes and create the conditions for optimizing the slab amplifier output BQ which relates to the super-Gaussian parameter of LD beam in the slow axis. Experimental measurement of TL-diopter in the slab thickness direction proves our simulation results.

Terahertz continuous wave system using phase shift interferometry for measuring the thickness of sub-100-μm-thick samples without frequency sweep.

A terahertz continuous wave system is demonstrated for thickness measurement using Gouy phase shift interferometry without frequency sweep. One arm of the interferometer utilizes a collimated wave as a reference, and the other arm applies a focused beam for sample investigation. When the optical path difference (OPD) of the arms is zero, a destructive interference pattern is produced. Interference signal intensity changes induced by the OPD changes can be easily predicted by calculations. By minimizing the difference between the measured and the calculated signal against the OPD, the thicknesses of sub-100-μm-thick samples are determined at 625 GHz.

Thermal behavior characterization of a kilowatt-power-level cryogenically cooled Yb:YAG active mirror laser amplifier

We present an analysis of the thermal behavior of a high-energy kilowatt-average-power diode-pumped cryogenically cooled Yb:YAG active mirror laser amplifier based on measurements and simulations. Maps of the temperature distribution of the laser material at pump powers up to 1 kW were obtained for the first time by spatially and spectrally resolving the fluorescence induced by a scanning probe beam. The wavefront distortion resulting from the front surface deformation and the overall deformation of the gain medium assembly were measured using a Mach–Zehnder interferometer. The measured deformations agree well with the results of thermomechanical modeling using finite element method simulations, and with the results of focal length shift measurements. The relative contributions to the optical path difference (OPD) of the mechanical deformations, refractive index changes, and electronic contribution are discussed. We show that the Cr4+:YAG cladding plays a significant role in both the temperature distribution and the overall OPD changes. The pump-induced mechanical deformations of the assembly dominate the OPD changes in this kilowatt-average-pump-power cryogenically cooled Yb:YAG active mirror laser.

Determination of Nonlinear Refractive Index of Zinc Phthalocyanine by Pump Induced Fizeau Interferometry

Experimental measurement of intense light induced refractive index is demonstrated using Fizeau interferometer. Refractive index is induced in a specific region of the sample with intense light pulse of a linearly polarized, Q- switched Nd:YAG laser at 1064nm wavelength. The respective change in optical path difference (OPD) is measured using Fizeau interferometer. The OPD so obtained is mapped in terms of change in refractive index in the area of interaction of pump beam and sample. The measured induced refractive index is then used to calculate thermo-optic coefficient of the ZnPc embedded polymeric sample.

EHoloNet: a learning-based end-to-end approach for in-line digital holographic reconstruction.

It is well known that in-line digital holography (DH) makes use of the full pixel count in forming the holographic imaging. But it usually requires phase-shifting or phase retrieval techniques to remove the zero-order and twin-image terms, resulting in the so-called two-step reconstruction process, i.e., phase recovery and focusing. Here, we propose a one-step end-to-end learning-based method for in-line holography reconstruction, namely, the eHoloNet, which can reconstruct the object wavefront directly from a single-shot in-line digital hologram. In addition, the proposed learning-based DH technique has strong robustness to the change of optical path difference between reference beam and object light and does not require the reference beam to be a plane or spherical wave.

Multifunction interferometry using the electron mobility visibility and mean free path relationship.

A conventional Michelson interferometer is modified and used to form the various types of interferometers. The basic system consists of a conventional Michelson interferometer with silicon-graphene-gold embedded between layers on the ports. When light from the monochromatic source is input into the system via the input port (silicon waveguide), the change in optical path difference (OPD) of light traveling in the stacked layers introduces the change in the optical phase, which affects to the electron mean free path within the gold layer, induces the change in the overall electron mobility can be seen by the interferometer output visibility. Further plasmonic waves are introduced on the graphene thin film and the electron mobility occurred within the gold layer, in which the light-electron energy conversion in terms of the electron mobility can be observed, the gold layer length is 100 nm. The measurement resolution in terms of the OPD of 50 nm is achieved. In applications, the outputs of the drop port device of the modified Michelson interferometer can be arranged by the different detectors, where the polarized light outputs, the photon outputs, the electron spin outputs can be obtained by the interference fringe visibility, mobility visibility and the spin up-down splitting output energies. The modified Michelson interferometer theory and the detection schemes are given in details.

A Method for Measurement of Nonlinearity of Laser Interferometer Based on Optical Frequency Tuning.

A method for measuring the nonlinearity of laser interferometer using optical frequency tuning technique is presented in this paper. The basic principle of this method is to make the fractional part of an interference fringe change by tuning the laser frequency and determining the nonlinearity of interferometer by comparing the fractional fringe change measured by the interferometer to that calculated from the laser frequency change. An experimental interferometric system with a wavelength tunable laser source is set up and the nonlinearity of the interferometer is measured. Since it does not require the precise displacement mechanism to produce the optical path difference change, this method is more convenient to use and may achieve a higher accuracy than the conventional measurement methods. The nonlinearity of the arbitrary interferometric phase can be measured by changing the laser frequency with this method. Experiments results have shown that the repeatability of nonlinearity measurement is less than 0.2 nm. This method can be applied to interferometry-based high precision dimensional measurements, such as coordinate measurement and displacement sensor calibration.

CO$_{2}$ Gas Sensing Using Optical Fiber Fabry–Perot Interferometer Based on Polyethyleneimine/Poly(Vinyl Alcohol) Coating

An optical fiber Fabry–Perot interferometer (FPI) based on poly (ethyleneimine) (PEI)/ poly (vinyl alcohol) (PVA) blend membrane is proposed and realized experimentally as a sensor for the pressure of CO $_{2}$ in the atmosphere. The functional material layer based on PEI/PVA blend polymer exhibits reversible optical path difference change because of absorption and release of CO $_{2}$ gas molecules. The cavity of the FPI is fabricated by coating a 15- $\mu$ m PEI/PVA blend film on the end-face of a cleaved single-mode fiber. An interference spectrum with fringe contrast of 19.5 dB and free spectra range of 33.15 nm is obtained. The proposed FPI sensor is sensitive to the changes of concentration of CO $_{2}$ , as well as a sensitivity of 0.281 nm/ $\%$ within an interval which ranges from 7.6 $\%$ to 86.9 $\%$ .