Direct optical path measurement in fibre-optic gyroscopes: A potential method for compensating slow-drifting errors

Researchers at the University of Queensland, Australia, have developed and refined an optical feedback technique for measuring surface roughness. We spoke to one of the authors, Jeremy Herbert, to find out more. Optical feedback interferometry is a non-contact sensing technique that uses a laser as not only a coherent light source, but also as a receiver of information. The beam from the laser is reflected off a target where it is modulated by some property of the material. This light is then reinjected back into the laser cavity where it mixes with the standing wave and disturbs the normal operation of the laser. By monitoring this disturbance through either the output power or the terminal voltage of the laser, information about the target can be determined. Schematic of the roughness measurement experiment showing the direction of translation as parallel to the lasing axis The primary advantage of optical feedback is that a sensor can detect changes in optical path length on the order of nanometres, and/or minute changes in target reflectivity using compact and low cost components; in some configurations, a laser diode is the only optical component. This allows extremely sensitive measurement of quantities such as displacement, velocity and refractive index of transparent media. Another more recent application is the imaging of targets using exotic wavelengths (such as terahertz radiation) for which simple detectors are not widely available. The sensitivity of instrumentation based on optical feedback is a double-edged sword. While this type of sensor can measure minute changes in the properties of the target, it is also very sensitive to changes in environmental parameters such as temperature and vibration. A common approach to minimise the effects of these unwanted influences on the output signal is to perform repeated measurements and average them. Unfortunately in some circumstances, such as the one outlined in the article, it is not possible to perform repeated measurements, and so an alternative strategy is required. Roughness target locations where a focused translating beam would experience higher (green) and lower reflectivity (red). The black arrow shows the direction of scanning. In the article, a method of determining information about the roughness of a surface using optical feedback was described and demonstrated. The method does not rely on repeated measurement, but instead uses the windowed standard deviation of the optical feedback signal to track the effective reflectivity of the surface as it moves. A method to compute the windowed standard deviation in a real-time manner was presented in an earlier article also published in Electronics Letters (Herbert, J, Wilson, S, Rakic, A and Taimre, T, ‘FPGA implementation of a high-speed, real-time, windowed standard deviation filter’, Electronics Letters, 2016, 52, (1), pp. 22–23). This work is significant because it demonstrates a viable method for the use of optical feedback signals to measure surface roughness without necessitating repeated measurements of the target. It provides evidence for the idea that an online surface roughness sensor could be developed, with the small size and low cost advantages of laser feedback, for use in the manufacturing process of objects with specific roughness tolerances. More broadly, this approach could be applicable to other scenarios in which repeating a measurement is impossible, such as in determining information about a particle randomly passing through the beam. Possible applications of this work in the short term could be in the area of tribology, the measurement of mechanical wear, and in manufacturing processes that require tight control of surface roughness. Longer-term applications are also possible in areas where the measurement quantity of interest can be modelled as the problem of surface roughness, such as in the measurement of particle size. Since this work was completed, further efforts have been directed toward applying the methods in the article to other scenarios in which repeated measurements are not possible. Examples of these situations include the characterisation of uniquely shaped particles passing through the beam, and in the online control of manufacturing processes such as polishing. Optical feedback sensors are unusual in that they are able to measure nanometre-sized changes in optical path length, and yet can be constructed using a small number of compact and relatively inexpensive components. As manufacturers compete to have the most effective quality control and manufacturing processes, sensing techniques such as the one outlined in this article become more and more relevant. Over the coming years, further work in this area could result in low cost sensors that could improve the yield of manufacturing processes through the increased availability of information about process parameters.

With the Fizeau interferometer method, the change in optical path length with temperature is measured at six wavelengths for twenty new Corning optical glasses. The sample, a polished block with a few seconds of wedge, is held in a double-walled chamber with temperature control provided over the range -20 degrees C to +80 degrees C by a circulating water-glycol mixture. A Gaertner interferometer viewing apparatus is modified by addition of a monitor head that permits simultaneous photoelectric fringe detecting and viewing. Measurement of thermal expansion with the Plummer-Hagy high precision dilatometer permits the extraction of the temperature coefficient of absolute refractive index from the optical path measurement. The coefficient of refractive index relative to standard air at the temperature of the glass is found by further data reduction using Edlén's equations. The experimental values of the index change as a function of temperature are curve-fitted by a FORTRAN program, and the slopes are computed to give instantaneous values of the coefficients. The average residual for the fit is about 1.0 x 10(-6). The precision of the absolute coefficient values is estimated to be +/-0.05 x 10(-6). Representative data for one glass are presented to illustrate the results available from this work.

This paper reports the demonstration of a widely-translatable fiber-optic mirror based on the motion of liquid metal through the hollow core of a photonic bandgap fiber. By moving a liquid metal mirror within the hollow core of an optical fiber, large, continuous changes in optical path length are achieved in a comparatively small package. A fiber-optic device is demonstrated which provided a continuously-variable optical path length of over 3.6 meters, without the use of free-space optics or resonant optical techniques (i.e. slow light). This change in path length corresponds to a continuously-variable true-time delay of over 12 ns, or 120 periods at a modulation frequency of 10 GHz. Wavelength dependence was shown to be negligible across the C and L bands.

Hypoxic-ischemia of the brain (tissue oxygen deficiency due to obstructed circulation) during birth can result in neurological impairment and consequently patients that may require specialised care for the remainder of their life. An accurate method for measuring fetal brain oxygenation is therefore required. Traditional clinical techniques do not directly measure cerebral oxygenation and are unpleasant for both the mother and fetus. Near infrared (NIR) spectroscopy is a technique that allows changes in tissue chromophore concentrations to be measured non-invasively. Most NIR spectrometers use algorithms which assume that the optical pathlength of the light in the tissue does not change during the measurement. In the area of fetal NIR spectroscopy, it is of interest to determine whether contraction induced optical pathlength changes produce significant errors in the estimated concentration changes. An intensity modulated optical spectrometer (MOS) can provide optical pathlength information in addition to the pure intensity data provided by traditional NIR spectrometers. An MOS is used here to investigate the influence of contractions on the change in the oxy- and deoxy-hemoglobin status in the fetal brain. It was found that in most cases the changes in optical pathlength did not contribute significantly to any error. It appears that the pathlength changes are primarily due to contraction induced absorption changes. It also appears that artefactual pathlength and absorption changes, which occur due to maternal movement, while to0 complicated to physically characterise are readily recognisable in the raw data.

This paper is the second in a set of two investigating tilt-to-length (TTL) coupling. TTL describes the cross-coupling of angular or translational jitter into an interferometric phase signal and is an important noise source in precision interferometers, including space gravitational wave detectors like LISA. We discussed in Hartig et al (2022 J. Opt. 24 065601) the TTL coupling effects originating from optical path length changes, i.e. geometric TTL coupling. Within this work, we focus on the wavefront and detector geometry dependent TTL coupling, called non-geometric TTL coupling, in the case of two interfering fundamental Gaussian beams. We characterise the coupling originating from the properties of the interfering beams, i.e. their absolute and relative angle at the detector, their relative offset and the individual beam parameters. Furthermore, we discuss the dependency of the TTL coupling on the geometry of the detecting photodiode. Wherever possible, we provide analytical expressions for the expected TTL coupling effects. We investigate the non-geometric coupling effects originating from beam walk due to the angular or translational jitter of a mirror or a receiving system. These effects are directly compared with the corresponding detected optical path length changes in Hartig et al (2022 J. Opt. 24 065601). Both together provide the total interferometric readout. We discuss in which cases the geometric and non-geometric TTL effects cancel one-another. Additionally, we list linear TTL contributions that can be used to counteract other TTL effects. Altogether, our results provide key knowledge to minimise the total TTL coupling noise in experiments by design or realignment.

A novel highly sensitive intensity detection method has been proposed based on a self-interference ring resonator, where it is obtained by introducing an additional interference sensing arm between two coupling regions in the conventional planar add-drop micro-ring resonator. By means of dissipative and dispersive coupling mechanisms, optical path length changes of sensing arm not only bring the shift in a resonant wavelength, but also result in the variation of the linewidth and extinction of the spectrum. Using the analytical expression of the transmittance, it is proved that this sensor can monitor optical path length changes of sensing arm with a theoretical detection limit ( $5.6\times 10^{-3}$ nm) by measuring intensity variations at a certain transmission valley.

The optical paths on the LISA bench must have a length instability of less than 10~pm/square root Hz over time scales of 1s to 1000s. A small rigid interferometer has been constructed to measure the optical path length changes using various bonding techniques. The interferometer was constructed entirely from ultra-low expansion (ULE) glass by optically contacting ULE beamsplitters to a ULE bench. Preliminary results taken with the interferometer operating in air indicate optical path length fluctuations of approximately 100 pm/ sqaure root Hz or less for frequencies between 1 mHz and 1 Hz.

Fiber optic gyroscopes (FOGs) are vital components for manned, unmanned, and autonomous platforms, as well as applications requiring extremely accurate data for stabilization, pointing, orientation of payloads, and navigation and control. FOG-based inertial systems also provide highly accurate data for all types of navigation, positioning, and georeferencing systems. Substantial improvements in the performance of FOGs and FOG-based inertial systems at KVH are directly related to advancements in the design and manufacture of optical fiber, as well as in manufacturing operations and signal processing. Open-loop FOGs, such as those developed and manufactured by KVH Industries, offer tactical-grade performance in a robust, small package. The success of KVH FOGs and FOG-based inertial systems is due to a series of key innovations including the development of proprietary D-shaped fiber with an elliptical core, as well as KVH's ThinFiber. KVH continually improves its FOG manufacturing processes and its signal processing, with the goal of improving accuracies across its entire FOG product line. KVH acquired its FOG capabilities, including its patented E·Core® fiber, when the company purchased the assets of Andrew Corporation's Sensor Products Group in 1997. E·Core fiber is unique in that the light-guiding fiber core — critical to the FOG's performance — is elliptically-shaped. The elliptical core results in an optical path with low loss and high polarization-maintaining ability. In 2011, KVH developed its ThinFiber, a 170-micron diameter dual acrylate-coated fiber that retains the full performance characteristics of E·Core fiber. ThinFiber has enabled the development of compact, high-performance open-loop FOGs, which are also used in a line of FOG-based inertial measurement units (IMUs) and inertial navigation systems (INS).

The development of lasers, new electro-optic light modulation methods, and improved electronic techniques have made possible significant improvements in the range and accuracy of optical distance measurements, thus providing not only improved ranging methods but also useful techniques for the study of other geo-physical, meteorological, and astronomical problems. One of the main limitations, at present, to the accuracy of distance measurements is the uncertainty in the average propagation velocity of the radiation resulting from inhomogeneity of the atmosphere. Accuracies as high as a few parts in ten million now appear feasible, however, through the use of the dispersion method, in which simultaneous measurements of optical path length at two widely separated wavelengths are used to determine the average refractive index over the path and hence the true geometrical distance. The design of a new instrument based on this method, which utilizes wavelengths of 63281 and 3681X and 3-GHz polarization modulation of the light, is presented. Preliminary measurements over a 5.3-km path with this instrument haXe demonstrated a sensitivity of 3 x 107 in detecting changes in optical path length for either wavelength using 1-sec averageing, and a standard deviation of 3 x 10-7 in corrected length. The principal remaining sources of error are summarized.

“Experimental Techniques” is an intermediate laboratory course designed in part to help students decide whether they want to pursue experimental physics. Key to this goal are meaningful opportunities for creative exploration and problem solving which mimic real-world research. Despite the COVID-19 pandemic, by building an interferometer at home using inexpensive department-provided materials, students were afforded opportunities for real creativity while proving that changes in optical path length – not just arm length – lead to fringe evolution. Though the physics involved was significantly simpler than in other experiments, students developed a better understanding of optical path length and interferometry while being introduced to instrumentation and some of the fundamental skills used by experimentalists in the lab. Members of the class also gained a meaningful sense of accomplishment and excitement. Consequently, we are now considering implementing this experiment as part of the in-person version of the course.

Noninvasive functional imaging of molecular and cellular processes of vision may have immense impact on research and clinical diagnostics. Although suitable intrinsic optical signals (IOSs) have been observed ex vivo and in immobilized animals in vivo, detecting IOSs of photoreceptor activity in living humans was cumbersome and time consuming. Here, we observed clear spatially and temporally resolved changes in the optical path length of the photoreceptor outer segment as a response to an optical stimulus in the living human eye. To witness these changes, we evaluated phase data obtained with a parallelized and computationally aberration-corrected optical coherence tomography system. The noninvasive detection of optical path length changes shows neuronal photoreceptor activity of single cones in living human retina, and therefore, it may provide diagnostic options in ophthalmology and neurology and could provide insights into visual phototransduction in humans.

A computer-adapted fiber-optic temperature sensing system has been developed which aims to study both the theoretical aspect of fiber temperature sensing and the experimental aspect of such system. The system consists of a laser source, a fiber sensing element, an electronic fringes counting device, and an on-line personal computer. The temperature measurement is achieved by the conventional double beam fringe counting method with optical path length changes in the sensing beam due to the fiber expansion. The system can automatically measure the temperature changes in a sensing fiber arm which provides an insight of the heat generation and dissipation of the measured system. Unlike the conventional measuring devices such as thermocouples or solid state temperature sensors, the fiber sensor can easily be wrapped and shaped to fit the surface of the measuring object or even inside a molded plastic parts such as a computer case, which gives much more flexibility and applicability to the analysis of heat generation and dissipation in the operation of these machine parts. The reference beam is being set up on a temperature controlled optical bench to facilitate high sensitivity and high temperature resolution. The measuring beam has a motorized beam selection device for multiple fiber beam measurement. The project has been demonstrated in the laboratory and the system sensitivity and resolution are found to be as high as 0.01 degree Celsius. It is expected the system will find its application in many design studies which require thermal budgeting.

Nanometer-scale displacement sensing using self-mixing interferometry with a correlation-based signal processing technique

This paper proposes a more accurate eccentricity and tilt measurement method based on Young's interference experiment. The basic principle of the method is introduced first before the method is simulated. Then the results are obtained when a to-be-adjusted focusing lens with eccentricity and tilt is simulated. The optical sensitivity also is obtained from these simulation results, and the expression for the change in optical path length caused by eccentricity and tilt is analyzed. Use of this method to detect eccentricity and tilt and assist in adjustment of the system allows the instrument to achieve higher accuracy and thus obtain improved imaging quality and spectral resolution.

Experiments for cell identification are presented using a high-precision cell phase measurement system that does not require any phase unwrapping. This system is based on a Mach-Zehnder interferometer using a phase-locking technique, and it measures the change in optical path length while the sample is scanned across the optical axis. The spatial resolution is estimated to be less than 1.1μm. The sensitivity of optical path length difference is estimated to be less than 2nm. Using experiments, we investigate the potential of this approach for cancer cell identification. In our preliminary experiments, cancer cells were distinguished from normal cells through comparison of optical path length differences.