Optical Path Length Difference Research Articles

LISA Pathfinder: OPD loop characterisation

The optical metrology system (OMS) of the LISA Pathfinder mission is measuring the distance between two free-floating test masses with unprecedented precision. One of the four OMS heterodyne interferometers reads out the phase difference between the reference and the measurement laser beam. This phase from the reference interferometer is common to all other longitudinal interferometer read outs and therefore subtracted. In addition, the phase is fed back via the digital optical pathlength difference (OPD) control loop to keep it close to zero. Here, we analyse the loop parameters and compare them to on-ground measurement results.

Optimization of excitation of fiber Fabry-Perot tunable filters used in swept lasers using a phase-correction method.

In this paper we investigate a phase-correction method for compensation of the nonlinearity of conventional wavelength-swept laser sources based on a fiber Fabry-Perot tunable filter as a wavelength selective element. A triangular waveform signal is commonly used to drive the filter. We, however, extract the zero crossings from the interferograms and modify the shape of the triangular signal accordingly. This algorithm was tested for different values of the optical path length difference in the interferometer setup. Significant compensation for the nonlinearity of the filter was obtained.

Investigation of a novel temperature-sensing mechanism based on strain-induced optical path-length difference in a multicore optical fiber

A four-core optical fiber is employed to investigate a novel temperature-sensing mechanism, which is based on the strain-induced optical path-length difference between the fiber core pairs. A short segment of a four-core fiber is wound around a solid stainless steel cylinder to form a tight circular loop, which is exposed to temperatures of up to 100 $^{\circ}$C. Temperature-induced radial expansion of the stainless steel cylinder causes a shear strain in the fiber and introduces an optical path-length difference between the fiber core pairs. This results in a total phase shift of about 20.40 $\pm $ 0.29 rad in the interference pattern of the four-core fiber, which is monitored by a CMOS camera. The temperature-induced phase and strain sensitivities are measured to be 3.74 rad/m$^{\circ}$C and 0.18 $\mu \varepsilon$/$^{\circ}$C, respectively.

Phase Measurement Using DIC Microscopy

The development of fluorescent probes and proteins has helped make light microscopy more popular by allowing the visualization of specific subcellular components, location and dynamics of biomolecules. However, it is not always feasible to label the cells as it may be phototoxic or perturb their functionalities. Label-free microscopy techniques allow us to work with live cells without perturbation and to evaluate morphological differences, which in turn can provide useful information for high-throughput assays. In this study, we use one of the most popular label-free techniques called differential interference contrast (DIC) microscopy to estimate the phase of cells and other nearly transparent objects and instantly estimate their height. DIC images provide detailed information about the optical path length (OPL) differences in the sample and they are visually similar to a gradient image. Our previous DIC construction algorithm outputs an image where the values are proportional to the OPL (or implicitly the phase) of the sample. Although the reconstructed images are capable of describing cellular morphology and to a certain extent turn DIC into a quantitative technique, the actual OPL has to be computed from the input DIC image and the microscope calibration settings. Here we propose a computational method to measure the phase and approximate height of cells after microscope calibration, assuming a linear formation model. After a calibration step the phase of further samples can be determined when the refractive indices of the sample and the surrounding medium is known. The precision of the method is demonstrated on reconstructing the thickness of known objects and real cellular samples.

Optoelectronic Feedback Loop for Phase Noise Suppression in THz Self-Heterodyne Detection

A novel terahertz (THz) self-heterodyne detection system using an optoelectronic feedback loop is proposed. Conventional THz self-heterodyne detection system is inherently vulnerable to phase noise associated with the optical path length difference between the laser sources and the photomixer. The proposed THz self-heterodyne detection system utilizes the optoelectronic feedback loop to suppress the phase noise of the intermediate frequency signal at the output of the photomixer. The optoelectronic feedback loop requires a feedback loop with a relatively small loop bandwidth and thus is implemented without using rather sophisticated integrated photonics technology. The proposed THz self-heterodyne detection system with the optoelectronic feedback loop suppresses the phase noise by more than 25 dB.

Detection-dependent six-photon Holland-Burnett state interference.

The NOON state, and its experimental approximation the Holland-Burnett state, have important applications in phase sensing measurement with enhanced sensitivity. However, most of the previous Holland-Burnett state interference (HBSI) experiments only investigated the area of the interference pattern in the region immediately around zero optical path length difference, while the full HBSI pattern over a wide range of optical path length differences has not yet been well explored. In this work, we experimentally and theoretically demonstrate up to six-photon HBSI and study the properties of the interference patterns over a wide range of optical path length differences. It was found that the shape, the coherence time and the visibility of the interference patterns were strongly dependent on the detection schemes. This work paves the way for applications which are based on the envelope of the HBSI pattern, such as quantum spectroscopy and quantum metrology.

Four-core optical fiber as a calorimetric gauge.

A four-core optical fiber is demonstrated as a calorimetric gauge for investigation of one-dimensional heat transfer measurements. Transient heat pulses from a Nd:YAG laser of 600 ms duration with a repetition rate of the order of 10 s are delivered onto the cleaved distal end face of the four-core fiber, aiming at one of the single cores only, which cause an optical path length difference between four guiding cores due to the temperature-induced change in the index of refraction and physical length of the targeted fiber core of concern. This results in a shift in the fringe pattern, which is operated in the reflection scheme. A phase shift of 0.43±0.015 rad is measured with a CMOS camera for 40 mW pulses. The thermal heat diffusion length in the selected fiber core is determined to be 2.8 mm, which contains 10.9±0.38 kJ/m2s heat, causing a temperature rise of 1.43±0.05 K.

Self-adaptive thermal-lensing compensation for a high-power laser

In this study, we present the analytic temperature profile in cylindrical geometry for transmissive optics. The model permits the explicit calculation of the optical path length difference across the radial direction of a rod. This allows us to determine the specific length of the compensation material to remove the thermal effect not only for a small region at the beam’s center but also for the entire geometry of the optics, including high-order aberrations for various power ranges.

Detection of low intensity sound with laser Doppler anemometry

Laser Doppler anemometry (LDA) sound measurement systems have traditionally been designed to achieve point measurements of a sound field so they keep the laser path lengths through the water short to minimize the signal contribution from the acousto-optic effect and use relatively large beam separation angles to minimize the interference fringe volume. While the traditional LDA approaches provide reasonable sensitivity to the Doppler shifts from microparticles oscillating in a low frequency sound field, at high frequencies the sound measurement sensitivity depends on the optical path length difference (OPD). OPD increases due to the acousto-optic effect as the sound pressure is integrated over the entire path length. An LDA system using a small beam separation angle and long laser light paths through the water is shown to be capable of detecting low intensity sound pressure signals. Theoretical and experimental results are presented.

Investigating the optical properties and molecular structure of PEEK fiber

The automatic variable wavelength interferometry, VAWI, technique is used to determine the optical properties of Poly(ether ether ketone), PEEK, highly oriented fiber. The main part of this technique is the Pluta polarizing interference microscope attached with the automatic moving interference filter via stepper motor. The VAWI technique depends on measuring the optical path length differences at certain positions in microinterferogram. These positions are the coincidence and anti-coincidence of the fiber fringe with the free medium fringes. The measured refractive indices and birefringence values are utilized to calculate some optical constants of PEEK fiber using Cauchy and Sellmeier's equations. Also using some structure relationship, some molecular structure and orientation parameters of PEEK fiber as a function of the wavelength of the incident light are calculated. The method allows us to determine any molecular structure parameters of PEEK fiber at any wavelength in the visible spectrum. Microinterfrograms are given for illustration.

Noninvasive and Continuous Hematocrit Measurement by Optical Method without Calibration

SUMMARYHematocrit monitoring in an extracorporeal circulation apparatus is required for detection of adverse events such as hypotension and bleeding. Nevertheless, we have researched noninvasive and continuous hematocrit measurements using optical methods, it remains a challenge to measure absolute levels of hematocrit without calibration. The purpose of this study is to develop an optical hematocrit measurement method without calibration, and to confirm the effectiveness in in vitro blood experiments. We have developed an improvement method for dual wavelength and detector model by maximizing the difference of optical path lengths. Based on the proposed method, a measurement system has been developed. In the basic blood experiment, the correlation of hematocrit and calculated values by the proposed method has been confirmed. Then, we have conducted hematocrit measurement experiments with attachment errors and change of blood flow. The data indicate that the accuracy of the proposed method without calibration has been equivalent to that of an invasive method, which is employed in clinical practice. In conclusion, we have confirmed that the proposed method is effective for noninvasive and continuous hematocrit measurements.

DIC image reconstruction using an energy minimization framework to visualize optical path length distribution.

Label-free microscopy techniques have numerous advantages such as low phototoxicity, simple setup and no need for fluorophores or other contrast materials. Despite their advantages, most label-free techniques cannot visualize specific cellular compartments or the location of proteins and the image formation limits quantitative evaluation. Differential interference contrast (DIC) is a qualitative microscopy technique that shows the optical path length differences within a specimen. We propose a variational framework for DIC image reconstruction. The proposed method largely outperforms state-of-the-art methods on synthetic, artificial and real tests and turns DIC microscopy into an automated high-content imaging tool. Image sets and the source code of the examined algorithms are made publicly available.

Active stabilization of a fiber-optic two-photon interferometer using continuous optical length control

The practical realization of long-distance entanglement-based quantum communication systems strongly rely on the observation of highly stable quantum interference between correlated single photons. This task must accompany active stabilization of the optical path lengths within the single-photon coherence length. Here, we provide two-step interferometer stabilization methods employing continuous optical length control and experimentally demonstrate two-photon quantum interference using an actively stabilized 6-km-long fiber-optic Hong-Ou-Mandel interferometer. The two-step active control techniques are applied for measuring highly stable two-photon interference fringes by scanning the optical path-length difference. The obtained two-photon interference visibilities with and without accidental subtraction are found to be approximately 90.7% and 65.4%, respectively.

Comparison of methods for determining the coherence of semiconductor laser light based on interference fringe contrast and speckle pattern morphology

We compare the classical technique for determining the coherence length of semiconductor laser light based on the slope of the interference-fringe visibility curve against a speckle technique based on the number of connected domains in the speckle-field interference pattern as determined using the morphological Euler number. The study was performed using a Michelson interferometer where the difference in optical path length between the legs can be adjusted over a range of several centimeters. We report the results from a comparison of these techniques for determining coherence of radiation from semiconductor lasers in the red (650 nm), green (532 nm), and blue (450 nm) regions. We show that the interference-fringe visibility curves and the curves for the morphological Euler numbers as a function of the phase delay induced by the adjustable arm of the interferometer are clearly correlated. The morphological radiation-coherence determination technique based on the speckle-field interference pattern is quite fast and is simpler than the traditional interference-fringe contrast-visibility technique.

Measurement of the optical path length difference in an interferometer using a sinusoidally frequency-modulated light source.

We develop a technique for measuring the optical path length difference (OPLD) in an interferometer using a frequency-modulated light source. Compared with conventional methods, this technique offers a high sampling rate, high precision, and cost efficiency, and is capable of determining which of the two optical paths is longer. In addition, we show that this technique works properly even when the OPLD is significantly longer than the coherence length of the light source.

Mid-Infrared Silicon-on-Insulator Fourier-Transform Spectrometer Chip

Mid-infrared absorption spectroscopy is highly relevant for a wide range of sensing applications. In this letter, we demonstrate a Fourier-transform spectrometer chip based on the principle of spatial heterodyning implemented in the silicon-on-insulator waveguide platform, and operating near 3.75- $\mu \text{m}$ wavelength. The spectrometer comprises a waveguide splitting tree feeding to an array of 42 Mach–Zehnder interferometers with linearly increasing optical path length differences. A spectral retrieval algorithm based on calibration matrices is applied to the stationary output pattern of the array, compensating for any phase and amplitude errors arising from fabrication imperfections. A spectral resolution below 3 nm is experimentally demonstrated.

Evaluation of absolute form measurements using a tilted-wave interferometer.

Tilted-wave interferometry is a promising measurement technique for the highly accurate measurement of aspheres and freeform surfaces. However, the interferometric fringe evaluation of the sub-apertures causes unknown patch offsets, which currently prevent this measurement technique from providing absolute measurements. Simple strategies, such as constructing differences of optical path length differences (OPDs) or ignoring the piston parameter, can diminish the accuracy resulting from the absolute form measurement. Additional information is needed instead; in this paper, the required accuracy of such information is explored in virtual experiments. Our simulation study reveals that, when one absolute OPD is known within a range of 500 nm, the accuracy of the final measurement result is significantly enhanced.

Direct Visualization of Mucus Production by the Cold-Water Coral Lophelia pertusa with Digital Holographic Microscopy

Lophelia pertusa is the dominant reef-building organism of cold-water coral reefs, and is known to produce significant amounts of mucus, which could involve an important metabolic cost. Mucus is involved in particle removal and feeding processes, yet the triggers and dynamics of mucus production are currently still poorly described because the existing tools to study these processes are not appropriate. Using a novel microscopic technique—digital holographic microscopy (DHM)–we studied the mucus release of L. pertusa under various experimental conditions. DHM technology permits μm-scale observations and allows the visualization of transparent mucoid substances in real time without staining. Fragments of L. pertusa were first maintained in flow-through chambers without stressors and imaged with DHM, then exposed to various stressors (suspended particles, particulate food and air exposure) and re-imaged. Under non-stressed conditions no release of mucus was observed, whilst mucus strings and sheaths were produced in response to suspended particles (activated charcoal and drill cuttings sediment) i.e. in a stressed condition. Mucus strings and so-called ‘string balls’ were also observed in response to exposure to particulate food (brine shrimp Artemia salina). Upon air-exposure, mucus production was clearly visible once the fragments were returned to the flow chamber. Distinct optical properties such as optical path length difference (OPD) were measured with DHM in response to the various stimuli suggesting that different mucus types are produced by L. pertusa. Mucus produced to reject particles is similar in refractive index to the surrounding seawater, suggesting that the energy content of this mucus is low. In contrast, mucus produced in response to either food particle addition or air exposure had a higher refractive index, suggesting a higher metabolic investment in the production of these mucoid substances. This paper shows for the first time the potential of DHM technology for the detection, characterization and quantification of mucus production through OPD measurements in L. pertusa.

Synthetic-wavelength based absolute distance measurement using heterodyne interferometry of a femtosecond laser

Large-scale and high precision absolute distance measurement is essential in aerospace technology and advanced manufacturing. Traditional method of measuring distance cannot meet this requirement. Since the advent of optical frequency comb, it has brought a revolutionary breakthrough to absolute distance measurement. In the past decade, there were proposed many methods to measure long absolute distances with high accuracy. Especially, the simple method of using adjacent pulse-to-pulse distance as a ruler for distance measurement has been widely used. The accuracy of this method depends mainly on the knowledge of relative positions of the two overlapped pulses, i.e., pulse-to-pulse alignment. In our previous study, we have proposed a heterodyne interferometer based on synthetic wavelength method with femtosecond laser. The synthetic wavelength is derived from the virtual second harmonic and the real second harmonic, and the real second harmonic is produced by a piece of periodically poled LiNbO3 (PPLN) crystal. However, the second harmonic generation system makes the system complicated, and causes a great optical energy loss. In order to solve this problem, we generate the synthetic wavelength by two spatial band-pass filters in our present study, which can simplify the system greatly. Moreover, we can reduce the optical energy loss and tune the synthetic wavelength by controlling the angle of the filter. The synthetic wavelength used in the present system is 71.39 m. The interferometric phase of the synthetic wavelength is used as a mark for the pulse-to-pulse alignment. In order to reduce the influences of air disturbance and temperature variation, we set up a thermal-insulated cover for the interferometer to stabilize the environment in the system. By using this cover, the optical path length difference of the system in 450 s can be reduced from 8.56 m to 0.21 m. To demonstrate the efficacy of the method described above, the target mirror is moved by eight steps in steps of 5 mm. We compare the measurement results with those obtained by a commercial interferometer, and the residual error is less than 100 nm. Since the measurement range is larger than our previous study, the relative accuracy is better than the previous system. In conclusion, we demonstrate a synthetic-wavelength based absolute distance measurement by using heterodyne interferometry of a femtosecond laser. Two spatial band-pass filters are used to generate the synthetic wavelength, which can simplify the system. The comparison results show that the system has an accuracy better than 100 nm in a displacement of 40 mm. The accuracy of the experimental system can be further improved by making the common-path of the two interferometers longer, locking the fceo to the atomic clock and sampling the data synchronously.

Proposed ultralow-energy dual photonic-crystal nanobeam devices for on-chip N x N switching, logic, and wavelength multiplexing.

Silicon-on-insulator Mach-Zehnder interferometer structures that utilize a photonic crystal nanobeam waveguide in each of two connecting arms are proposed here as efficient 2 × 2 resonant, wavelength-selective electro-optical routing switches that are readily cascaded into on-chip N × N switching networks. A localized lateral PN junction of length ~2 μm within each of two identical nanobeams is proposed as a means of shifting the transmission resonance by 400 pm within the 1550 nm band. Using a bias swing ΔV = 2.7 V, the 474 attojoules-per-bit switching mechanism is free-carrier sweepout due to PN depletion layer widening. Simulations of the 2 × 2 outputs versus voltage are presented. Dual-nanobeam designs are given for N × N data-routing matrix switches, electrooptical logic unit cells, N × M wavelength selective switches, and vector matrix multipliers. Performance penalties are analyzed for possible fabrication induced errors such as non-ideal 3-dB couplers, differences in optical path lengths, and variations in photonic crystal cavity resonances.