Measurement Of Optical Path Length Research Articles

The Suppression Effect of an Imaging System on the Geometric Tilt-to-Length Coupling in a Test Mass Interferometer

Tilt-to-length (TTL) coupling noise arises from angular misalignments of interfering beams in optical path length (OPL) measurements and significantly impacts the accuracy of interferometry measurement systems. This paper focuses on geometric TTL coupling in a test mass (TM) interferometer and examines how an imaging system influences TTL noise suppression. First, the analytical expression of the geometric TTL coupling in a TM interferometer with alignment errors is derived and confirmed through numerical simulation. Subsequently, an imaging system is incorporated into the geometric model and the corresponding analytical expressions are obtained under two common conjugate relationships. Nevertheless, the TTL coupling remains beyond the requirement of TM interferometer, as the residual TTL coupled with alignment errors persists even with the imaging system. Therefore, an optimal position of the imaging system capable of eliminating the second-order term of the TTL coupling is determined. Meanwhile, the first-order term can be mitigated through in-orbit calibrations. These findings offer valuable guidance for the design and adjustment of imaging systems in space-borne gravitational wave detection missions, which require high-precision laser interferometry.

Effective optical path length measurement of integrating cavity using time-resolved spectroscopy and tunable diode laser absorption spectroscopy

Integrating cavities are commonly used in trace gas detection and weak absorption measurement. The effective path length (L) is an important index for evaluating the ability to increase the optical path length of an integrating cavity. Studies have demonstrated that the effective path length (L) is related to the inner surface reflectivity, cavity shape and dimension, and port fraction. However, the measured effective path length (L) of an integrating cavity generally varies with the spectroscopic technique used in practical applications. In this study, the effective path lengths (L) of a cubic integrating cavity with different port fractions were measured using time-resolved spectroscopy and tunable diode laser absorption spectroscopy (TDLAS). The value of L gradually decreased with an increase in the port fraction. Further, the measured L results showed a deviation between the two measurement techniques. The reason for the different effective optical paths obtained by the two spectroscopic techniques was investigated. An analysis showed that the difference in the effective optical paths was due to the reflectivity difference at the different laser wavelengths used for the two spectral methods. Correcting the reflectivity eliminates the difference in the effective optical paths.

Simultaneous measurement of H2O concentration and effective absorption optical path length under unknown optical path length condition based on a single spectral line

Quantitative gas measurement under the condition of unknown optical path length is a challenge in laser absorption spectroscopy technology field. In this paper, we proposed a tunable diode laser absorption spectroscopy line shape analysis (TDLAS-LSA) method for simultaneous measurement of water vapor concentration and effective optical path length (EOPL) under unknown optical path conditions. A single H2O absorption line near 1383.9 nm (7226.02 cm−1) was selected, and its line strength, self-broadening coefficient and temperature-dependence coefficient were measured experimentally to improve the HITRAN databases. The Lorentz broadening and line area were accurately extracted by Hartmann-Tran profile (HTP) fitting, and the gas concentration and EOPL were calculated based on the spectral line shape analysis method. Eight concentrations of water vapor in the range of 146 ppm ∼ 4.39% were measured experimentally, and the maximum average deviation between the TDLAS-LSA method and the commercial sensor was less than 7.1%. Comparing the EOPL with mechanical measurement, the maximum deviation of multiple measurements is less than 5.7%. The results showed that the TDLAS-LSA method can effectively perform gas sensing under unknown optical path conditions, and has great application potential in low-cost, in-situ and multi-parameter simultaneous measurement.

Analyses of Laser Propagation Noises for TianQin Gravitational Wave Observatory Based on the Global Magnetosphere MHD Simulations

Abstract TianQin is a proposed space-borne gravitational-wave (GW) observatory composed of three identical satellites orbiting around the geocenter with a radius of 105 km. It aims at detecting GWs in the frequency range of 0.1 mHz–1 Hz. The detection of GW relies on the high-precision measurement of optical path length at the 10−12 m level. The dispersion of space plasma can lead to the optical path difference (OPD, Δl) along the propagation of laser beams between any pair of satellites. Here, we study the OPD noises for TianQin. The Space Weather Modeling Framework is used to simulate the interaction between the Earth magnetosphere and solar wind. From the simulations, we extract the magnetic field and plasma parameters on the orbits of TianQin at four relative positions of the satellite constellation in the Earth magnetosphere. We calculate the OPD noise for single link, Michelson combination, and Time-Delay Interferometry (TDI) combinations (α and X). For single link and Michelson interferometer, the maxima of ∣Δl∣ are on the order of 1 pm. For the TDI combinations, these can be suppressed to about 0.004 and 0.008 pm for α and X. The OPD noise of the Michelson combination is colored in the concerned frequency range; while the ones for the TDI combinations are approximately white. Furthermore, we calculate the ratio of the equivalent strain of the OPD noise to that of TQ, and find that the OPD noises for the TDI combinations can be neglected in the most sensitive frequency range of TQ.

Practical application of microsphere samples for benchmarking a quantitative phase imaging system.

Quantitative phase imaging (QPI) provides an approach for monitoring the dry mass of individual cells by measuring the optical pathlength of visible light as it passes through cells. A distinct advantage of QPI is that the measurements result in optical path length quantities that are, in principle, instrument independent. Reference materials that induce a well‐defined optical pathlength shift and are compatible with QPI imaging systems will be valuable in assuring the accuracy of such measurements on different instruments. In this study, we evaluate seven combinations of microspheres embedded in index refraction matching media as candidate reference materials for benchmarking the performance of a QPI system and as calibration standards for the optical pathlength measurement. Poly(methyl metharylate) microspheres and mineral oil were used to evaluate the range of illumination apertures, signal‐to‐noise ratios, and focus positions that allow an accurate quantitative optical pathlength measurement. The microsphere‐based reference material can be used to verify settings on an instrument that are suitable for obtaining an accurate pathlength measurement from biological cells. The microsphere/media reference material is applied to QPI‐based dry mass measurements of a population of HEK293 cells to benchmark and provide evidence that the QPI image data are accurate.

Measurement of the effective optical path length of diffusing integrating cavities using time-resolved spectroscopy.

A method to measure the effective optical path length (EOPL) of a diffusing cavity using time-resolved spectroscopy is presented. A 710nm short-pulsed laser was employed as the light source with a FWHM of 0.7ns. From the temporal response curves, the time to establish a uniform optical field was obtained as approximately 4ns for this cavity. Correspondingly, light was scattered 5-6 times by the inner coating. EOPLs with different port fractions were obtained by the selection of an appropriate initial time. Moreover, we verified a previously reported theoretical EOPL law using time-resolved spectroscopic results. This work provides a method to measure the EOPL of a diffusing cavity at different wavelengths.

Label-free tissue scanner for colorectal cancer screening.

The current practice of surgical pathology relies on external contrast agents to reveal tissue architecture, which is then qualitatively examined by a trained pathologist. The diagnosis is based on the comparison with standardized empirical, qualitative assessments of limited objectivity. We propose an approach to pathology based on interferometric imaging of “unstained” biopsies, which provides unique capabilities for quantitative diagnosis and automation. We developed a label-free tissue scanner based on “quantitative phase imaging,” which maps out optical path length at each point in the field of view and, thus, yields images that are sensitive to the “nanoscale” tissue architecture. Unlike analysis of stained tissue, which is qualitative in nature and affected by color balance, staining strength and imaging conditions, optical path length measurements are intrinsically quantitative, i.e., images can be compared across different instruments and clinical sites. These critical features allow us to automate the diagnosis process. We paired our interferometric optical system with highly parallelized, dedicated software algorithms for data acquisition, allowing us to image at a throughput comparable to that of commercial tissue scanners while maintaining the nanoscale sensitivity to morphology. Based on the measured phase information, we implemented software tools for autofocusing during imaging, as well as image archiving and data access. To illustrate the potential of our technology for large volume pathology screening, we established an “intrinsic marker” for colorectal disease that detects tissue with dysplasia or colorectal cancer and flags specific areas for further examination, potentially improving the efficiency of existing pathology workflows.

Direct high-precision measurement of the effective optical path length of multi-pass cell with optical frequency domain reflectometer.

Multi-pass cells (MPCs) are commonly used in trace-gas detection and weak spectrum measurement. It is essential to accomplish a high-precision measurement of MPCs' effective optical path length (EOPL). A direct high-precision measuring method of MPCs' EOPL with optical frequency domain reflectometer (OFDR) was reported and demonstrated in this paper. Several important parameters of a MPC, such as EOPL and base length, were derived with high-precision by identifying the complicated signal of OFDR. The MPC's EOPL was also verified with the prevailing absorbance method. The results showed that the MPC's EOPL measured by each of these two methods is highly consistent. However, the relative uncertainty with the OFDR dramatically decreased 2 orders of magnitude (about 0.0085%) than that with the absorbance method. It demonstrated that the OFDR method with fewer measurement links is more conducive to a direct measurement. The performances of beam spread and stray light in the White-cell were also evaluated with the method.

TD-PCI system based on an angle modulation for in vivo measurements of the human eye

In this study, a "time domain" system based on a partial coherence interferometry method is presented. The classic technique of varying the reference arm using a linear motor is replaced by the use of a rotating glass cube. The theoretical definition of the variation of the optical path length and first measurements in a human model eye and a real human eye are presented.

The transport of intensity equation for optical path length recovery using partially coherent illumination

We investigate the measurement of a thin sample's optical thickness using the transport of intensity equation (TIE) and demonstrate a version of the TIE, valid for partially coherent illumination, that allows the measurement of a sample's optical path length by the removal of illumination effects.

Phase-preserved optical elevator.

The unique superiority of transformation optics devices designed from coordinate transformation is their capability of recovering both ray trajectory and optical path length in light manipulation. However, very few experiments have been done so far to verify this dual-recovery property from viewpoints of both ray trajectory and optical path length simultaneously. The experimental difficulties arise from the fact that most previous optical transformation optics devices only work at the nano-scale; the lack of intercomparison between data from both optical path length and ray trajectory measurement in these experiments obscured the fact that the ray path was subject to a subwavelength lateral shift that was otherwise not easily perceivable and, instead, was pointed out theoretically [B. Zhang et al. Phys. Rev. Lett. 104, 233903, 2010]. Here, we use a simple macroscopic transformation optics device of phase-preserved optical elevator, which is a typical birefringent optical phenomenon that can virtually lift an optical image by a macroscopic distance, to demonstrate decisively the unique optical path length preservation property of transformation optics. The recovery of ray trajectory is first determined with no lateral shift in the reflected ray. The phase preservation is then verified with incoherent white-light interferometry without ambiguity and phase unwrapping.

Final report on Pilot Study CCQM-P110: Study on the accuracy and uncertainty of FT-IR methods calibrated with synthetic spectra for NO2 concentration measurements

The results of the first pilot study designed to evaluate the level of comparability of measurements of nitrogen dioxide (NO2) mole fractions in nitrogen based on measurement procedures that rely on FT-IR spectroscopy as an absolute method of quantification with the traceability of measurement results to line strength data are reported.Participants were required to report measurement results using FT-IR for the gas standard (nominal mole fraction of 10 µmol/mol NO2 in nitrogen) received from the BIPM as part of the CCQM-K74 exercise. In addition, they were required to provide infrared spectra and instrument parameter information to enable a recalculation of their results by the BIPM's, using only its own synthetic spectra calibration procedure with values traceable to the line parameters contained in HITRAN 2004.The relative standard uncertainties based on FT-IR measurements reported by participating laboratories ranged from 0.6% to 4.3%. The relative standard uncertainty of the reference value for each gas standard was 0.4%, as determined during the CCQM-K74 exercise. Of the ten results submitted, only five agreed with the reference value within their expanded uncertainties. Furthermore, major contributions to the uncertainty of FT-IR measurements arose from the optical path length measurements and the uncertainty that could be attributed to line strength data from the HITRAN molecular database. The inclusion of these uncertainty contributions was estimated by the BIPM to result in achievable relative standard uncertainties of 3.4% for its FT-IR measurements using synthetic spectra calibration procedures.Finally the recalculation of the participants' results by the BIPM using the laboratories' submitted experimental characteristics and infrared spectra showed good agreement with the submitted results, indicating that the calculation algorithms were not in themselves a major reason for the spread of results.Main text.To reach the main text of this paper, click on Final Report.The final report has been peer-reviewed and approved for publication by the CCQM-GAWG.

Use of common path phase sensitive spectral domain optical coherence tomography for refractive index measurements

We report the use of a common path phase sensitive spectral domain optical coherence tomography setup for the measurement of the refractive index (RI) of a biomimetic material (glucose solution in water having intralipid as the scattering medium) and a single biological cell (keratinocyte). The RI of glucose solutions could be measured with a precision of ∼0.00015, which corresponds to a precision of ∼2 nm in the optical path length measurement in our setup. The precision obtained in the measurement of the RI of a single keratinocyte cell was ∼0.0004.

Measuring light speed with a modulated laser diode

The time of flight (TOF) of a light pulse travelling back and forth and optical path length measurements are used to estimate the velocity of light. The light pulse has a duration of 10 ns, and is obtained from a suitably modified CW commercial laser diode. The TOF is read with a digital oscilloscope connected to two fast sensors, detecting the signals at the switch-on of a laser diode and at the arrival of the light pulse reflected from a plane mirror placed at a known distance.

Evaluation of Indicator-Based pH Measurements for Freshwater over a Wide Range of Buffer Intensities

Two different sulfonephthalein indicators, cresol red (CR) with a pKa of approximately 8.3 and bromothymol blue (BTB) with pKa of approximately 7.4, were tested for an analysis of freshwater over a broad range of pH and total alkalinity values. Measurements from an autonomous sensor system using a 1 cm optical path length were compared to those using a 10 cm path length on a benchtop spectrophotometer. The indicator pH perturbation was quantified with a thermodynamic model and nonlinear least-squares analysis. The laboratory study found that the perturbation-corrected pH differed between the 1 cm (large indicator perturbation) and 10 cm (small indicator perturbation) optical path length measurements from -0.017 to +0.15 with a median of +0.0041 pH units for CR and from -0.015 to +0.026 with a median of -0.0008 pH units for BTB. Precision was +0.0005-0.013 and +0.0001-0.0027 pH units for the 1 and 10-cm-path-length measurements, respectively. The autonomous sensor was deployed for 14 days in a local creek. Simultaneous glass pH electrode measurements had a large negative and drifting offset (-0.15 to -0.40 pH units) compared to the indicator-based measurements. This study is the first in situ comparison between potentiometric and spectrophotometric pH methods in a freshwater system.

Measurements of Optical Pathlength Using Phase-Resolved Spectroscopy in Patients Undergoing Cardiopulmonary Bypass

Near infrared spectroscopy (NIRS) has been used during cardiac surgery to monitor cerebral oxygenation although the validity of this technique has yet to be established. Although optical pathlength included in the algorithm for calculating NIRS values is supposed to be constant, recent evidence has suggested that optical pathlength could be affected by acute hemodilution in animals. We conducted the present study to investigate whether optical pathlength changes during cardiopulmonary bypass (CPB), and whether these changes affect NIRS values in adult patients. Nine patients undergoing elective cardiac surgery with CPB were enrolled in this study. Optical pathlength and cerebral NIRS values (oxyhemoglobin [DeltaO(2)Hb] and tissue oxygen index) were measured by phase-resolved spectroscopy and NIRO 100, respectively. Optical pathlength, hemoglobin concentration, and NIRS values were measured at the following points: 1) after the induction of anesthesia, 2) 10 min after the start of CPB, 3) 60 min after the start of CPB, and 4) 1 h after CPB. The associations between optical pathlength and other variables were analyzed by Pearson correlation coefficients and multiple regression analysis. Optical pathlength significantly increased starting at 27.7-30.8 cm at 10 min, and 31.3 cm at 60 min after the start of CPB (P < 0.0001). Hemoglobin concentrations significantly decreased (from 11.2 to 7.1 g/dL at 10 min and 7.7 g/dL at 60 min P < 0.0001). There was a significant correlation (r = 0.55, P < 0.001) between percentage changes in pathlength and hemoglobin concentration. Multiple regression analysis showed that optical pathlength was a significant determinant of DeltaO2Hb. The results indicate that optical pathlength can change during CPB and its changes may affect DeltaO2Hb.

Phase retrieval in low-coherence interferometric microscopy

We present compensating methods that address inherent errors in quantitative phase reporting for low-coherence interferometric techniques. A brief theoretical treatment of the problem and experimental validation using spectral domain phase microscopy demonstrate mitigation of the degrading effects of phase leakage on accurate measurement of optical path length in the vicinity of closely spaced reflectors. This result has direct implications for phase-sensitive interferometry techniques, such as Doppler imaging, as well as amplitude-based quantitative reporting. Corrected phase retrieval is demonstrated for conversion of interferometric phase to optical path length in cell surface deflections of beating cardiomyocytes.

Self-calibrating hybrid wavelength, polarization, and time-multiplexed heterodyne interferometers for Angstrom precision measurements

Propose here unique wavelength and hybrid wavelength-polarization and wavelength-polarization-time-multiplexed heterodyne optical interferometers using an internal self-referencing scheme enabling Angstrom level sensitivity optical path-length measurements. As a first step, a proof-of-concept wavelength multiplexed scanning heterodyne interferometer is built to test the surface quality of a test mirror, demonstrating ±100 A profile variations with a 0.9 A accuracy. The hybrid wavelength-polarization and wavelength-polarization-time-multiplexed interferometers can be used to form spectrally coded distributed sensors.

A measurement system for determining the thickness of an optical wave plate

This study proposes a non-destructive measurement method for determining the thickness of an optical wave plate. The measurement system comprises a laser interferometer to conduct optical path length measurement, a stepping motor to adjust the angle of the incident light on the wave plate, and a computer to perform data calculations. The optical path difference is obtained by adjusting the angle of rotation of the wave plate using the stepping motor. The thickness of the optical wave plate can be obtained accurately and rapidly from the mathematical relations describing the optical path length difference. The proposed measurement method is capable of measuring large thicknesses (i.e., at the cm scale) with nano-scale precision. As such, the method provides a valuable contribution to the field of precision thickness measurement.

Measurement of Cerebral Optical Pathlength as a Function of Oxygenation Using Near-infrared Time-resolved Spectroscopy in a Piglet Model of Hypoxia

Near-infrared spectroscopy (NIRS) has been used for measurement of changes in cerebral hemoglobin concentrations in neonates to study cerebral oxygenation and hemodynamics. In this study, measurements by time-resolved reflectance spectroscopy (TRS) were performed in a piglet model with various degrees of cerebral oxygenation to estimate the differential pathlength factor (DPF). A portable three-wavelength TRS system (TRS-10, Hamamatsu Photonics K.K.) with a probe attached to the head of a piglet was used. Eleven newborn piglets were anesthetized and respired by a ventilator to induce stepwise hypoxia loading. The DPF showed positive linear relationship with arterial hemoglobin (Hb) oxygen saturation and sagittal sinus venous Hb oxygen saturation at 761 and 795 nm. The DPF at 835 nm also showed very slight positive linear relationship with arterial hemoglobin oxygen saturation. The DPF values obtained in this study should contribute to a better understanding of noninvasive measurements by NIRS in neonates.