Optical Path Length Changes Research Articles

In Situ Measurement of Deep-Sea Salinity Using Optical Salinometer Based on Michelson Interferometer

Ocean salinity plays an important role in oceanographic research as one of the fundamental parameters. An optical salinometer based on the Michelson interferometer (MI) suitable for in situ measurement in deep-sea environments is proposed in this work, and it features real-time calibration and multichannel multiplexing using the frequency modulated continuous wave (FMCW) technique. The symmetrical sapphire structure used to withstand deep-sea pressure can not only achieve automatic temperature compensation, but also counteract the changes in optical path length under deep-sea pressure. A model formula suitable for optical salinity demodulation is proposed through the nonlinear least squares fitting method. In vertical profile testing, the optical salinometer demonstrated remarkable tracking performance, achieving an error of less than 0.001 psu. The sensor displays a stable salinity demodulation error within ±0.002 psu during a three-month long-term test at a depth of 4000 m. High stability and resolution make this optical salinometer have broad development prospects in ocean observation.

Dynamic Interferometry With Retrace Error Correction Using Fringe Projection For High-Gradient Fields

This paper introduces an innovative approach aimed at advancing the characterization of high-gradient flow fields through the integration of dynamic interferometry and fringe projection techniques. Traditional interferometry offers a precise tool sensitive to optical path changes, typically used to measure refractive index variations induced by factors such as density changes in fluid flow. Rays are usually considered as straight lines, and refraction can be neglected. However, in scenarios involving high-gradient fields, such as supersonic flow with shock waves, optical path changes due to ray bending become significant. In these high-gradient fields, the trajectory of the ray is altered, leading to longer optical paths (resulting in incorrect values) and geometric distortions of the image (resulting in inaccuracies in position). Although retrace error corrections using numerical models of refractive index distribution can mitigate some effects, complete compensation is often challenging. To address this, our proposed technique integrates fringe projection, which is highly sensitive to ray deflections caused by variations in the index of refraction within a transparent medium. The method involves projecting a precisely defined multiplexed cosine fringe pattern across the measured area. Modifications in the pattern indicate ray bending, providing data for interferometric corrections. Real-time interferometry is seamlessly combined with the fringe projection technique to compensate for optical path length changes and mitigate mapping errors induced by ray deflections. The dynamic nature of this combined approach enables the instantaneous capture of both interferometric and fringe-projection data, making it a suitable tool for real-time measurements. Experimental verification of the technique demonstrates its efficacy, with a comparative study against traditional interferometry showcasing a significant reduction in mapping errors.

Thermal defocus-free Hartmann Wavefront Sensors for monitoring aberrations in Advanced Virgo

Earth-based gravitational waves interferometric detectors are shot-noise limited in the high-frequency region of their sensitivity band. While enhancing the laser input power is the natural solution to improve on the shot noise limit, higher power also increases the optical aberration budget due to the laser absorption in the highly reflective coatings of mirrors, resulting in a drop of the sensitivity of the detector. Advanced Virgo exploits Hartmann Wavefront Sensors (HWSs) to locally measure the absorption-induced optical aberrations by monitoring the optical path length change in the core optics. Despite the very high sensitivity of Hartmann sensors, temperature fluctuations can cause a spurious curvature term to appear in the reconstructed wavefront due to the thermal expansion of the Hartmann plate, that could affect the accuracy of the aberration monitoring. We present the implementation and validation of a control loop to stabilize the Advanced Virgo HWS temperature at the order of ΔT⩽0.01 K, keeping the spurious curvature within the detector’s requirements on wavefront sensing accuracy.

A novel interferometry-based method to study the anisotropy and kinetics of liquid to solid transition in polymer

We propose and demonstrate a first Twin -interferometry based optical approach for studying and exploring anisotropy and directional dependent crystallization kinetic of curing polymers under isothermal condition. A commercial polymeric solution of polyvinylidene fluoride hexa-fluoropropylene (PVDF-HFP) with five different concentrations were prepared and utilised for this study. A Twin-interferometer (TIM) is designed to record the rate of shift in Michelson’s fringes caused by rate of change of optical path length of a transparent polymeric solution in two orthogonal directions during curing. Pair of interferogram referred as Twin- interferogram (TIG) is recorded for the sample of all concentration during its liquid to solid transition. An extraction approach for various crystallization parameters such as anisotropy, crystallization half-life time, constants governing the rate and dimensionality of crystallization, and their variation along distinct direction from TIM is demonstrated. The results provided by TIM are verified by a method of anisotropy annihilation and other experimental techniques includes Scanning electron microscopic (SEM), Polarising optical microscopic (POM) and Dielectric spectroscopic studies.

Refractivity corrected distance measurement using the intermode beats derived from a supercontinuum.

Simultaneous distance measurements on two or more optical wavelengths enable dispersion-based correction of deviations that result from insufficient knowledge of the refractive index along the signal propagation path. We demonstrate a supercontinuum-based approach for highly accurate distance measurements suitable for such an inline refractivity compensation. The distance is estimated from the phase delay observations on the intermode beats. We use a supercontinuum (SC) coherently broadened from a 780 nm frequency comb and spanning the spectral range of 570-970 nm. Experiments are performed on the 590 and 890 nm wavelength bands filtered from the SC spectrum. Results show distance measurements with standard deviations of around 0.01 mm at 50 m, and a distance-dependent component below 0.2 ppm on the individual spectral bands. Distance residuals compared to a reference interferometer are on the order of 0.1 ppm for displacements up to 50 m. Controlled pressure-induced refractivity variations are created over a length of 15 m, resulting in an optical path length change of 0.4 mm. Using the two-color method, we demonstrate refractivity-corrected distance measurement with a standard deviation of around 0.08 mm for a 60 s averaging window. The current experimental configuration can be easily extended to distance measurements on more than two wavelengths. The results highlight its potential for practical long-distance measurements through inline refractivity compensation.

Contributed Session I: Correlating cone structure and function in retinitis pigmentosa using coarse-scale optoretinography (CoORG).

Optoretinography (ORG) has the potential to serve as a powerful diagnostic biomarker, owing to its sensitive and objective localization of function and dysfunction. Majority of ORG implementations employ adaptive optics (AO) for imaging activity at a cellular scale. Coarse-scale Optoretinography (CoORG), an ORG paradigm without AO, offers rapid, extended-field recordings and wider applicability in patients with retinal disease, by compromising cellular resolution. This study investigates the feasibility of CoORG in assessing cone dysfunction in patients diagnosed with retinitis pigmentosa (RP). Five RP patients aged 26 - 60 were recruited, alongside age-similar controls. The stimulus for evoking cone activity had a photon density between 15.5x10e6 - 19.7x10e6 photons/μm2, and was centered at 532 ± 5nm. Eight imaging trials per bleach were performed, allowing for 1 min. between successive trials for dark adaptation. The total experimental time for each bleach was 10-20 mins. In RP, cone function, estimated as the change in optical path length in the outer segment in response to a stimulus, was diminished and generally lower than normal controls. This deficit was observed in areas of seemingly normal outer retinal structure. Contrary to normals, no correlation was observed between outer segment length and cone function in RP. This highlights CoORG's potential for early, sensitive detection of retinal dysfunction prior to apparent structural degradation.

Poster Session: Optoretinography-based frequency characterization of the retinal response to a chirped flickering light.

In this contribution, we present experimental results of in vivo characterization of the photoreceptor's response to a chirped flickering white light stimulating the retina. We acquire the ORG signal with Spatio-Temporal Optical Coherence Tomography (STOC-T) setup, which combines both temporal and coherence gating to overcome limitations present in Full Field Fourier Domain Optical Coherence Tomography. From the acquired volumes, we extract the changes in optical path length (OPL) between the inner and outer photoreceptor junction (ISOS) and the cone outer segment tips (COST). We perform the measurements for frequencies ranging from 5 Hz to 50 Hz. The chirped flickering facilitates significantly shorter data acquisition time. We present results of in vivo measurement from three volunteers. Our results show that we can measure OPL changes between ISOS and COST occurring in response to a chirped flickering stimulation in a reproducible manner and resolve the amplitude of the response in the function of flicker frequency.

Evolution of sample optical pathlength during diffuse reflectance FT-IR analyses

In situ and operando diffuse reflectance FT-IR (DRIFTS) studies are often carried out over samples that may undergo changes in optical properties due to stronger absorptivity (darkening), for instance when coking or being reduced. The variation of IR optical pathlength of two Fe and Co-based Fischer-Tropsch catalysts treated at different temperatures was investigated through the use of an internal standard CaCO3 that was physically mixed with the catalyst. The CaCO3 overtone band at 1795 cm-1 was used, exhibiting an integral molar absorption coefficient ε = 2.68 × 105 cm mol-1. The IR penetration depth was negligible over the iron oxide sample once reduced above 400 °C, due to the formation of a strongly absorbing material. A reduction of the cobalt sample up to 350 °C revealed large changes of optical pathlength (dropping four-fold from 66 to 16 µm), likely related to the onset of cobalt oxide deep reduction. These data indicate that changes in optical pathlength should be considered when attempting quantitative DRIFTS analyses and that mixing a small concentration of CaCO3, e.g. 2 wt%, is a suitable way of doing so.

Zn_{1-x}Ni_xTe semiconductor nanocrystals in transparent glass for optoelectronic device applications

Doping glass with semiconductors, particularly with nanostructured semiconductors, has attracted attention due to the large optical absorption cross-sections of the latter. Based on this property, Ni^{2+} (5 wt%) doped phosphate glass and Zn_{1-x}Ni_xTe (x = 0.5, 1.0, 5.0 and 10.0 wt% of Ni^{2+}) nanocrystals (NCs) doped phosphate glasses (GCs) were prepared by fusion method and subsequent heat treatment. Influence of Ni^{2+} on structural, thermo-optical and third-order nonlinear optical properties have been analysed through various spectroscopic characterizations. The XRD pattern of the glass (G) exhibits the amorphous nature of the host material while GCs exhibit not only amorphous halo but also the presence of quantum dots (QDs) or nanocrystals (NCs) phases. TEM analysis of the studied GCs samples confirm the presence of quantum dots (QDs) and bulk NCs with an average diameter of approximately 4.2 {pm } 0.3 nm and 13.4 {pm } 0.2 nm, respectively. Several phosphate groups were observed and reported from Raman and FTIR-ATR spectra. The absorption band positions confirmed that Ni^{2+} ions resemble to the octahedral symmetry. The intensity of absorption band around 1352 nm (^3T{_1}(F) rightarrow^3A{_2}(F)) increased with the increase of Ni^{2+} in GCs which is an indicative of the ^{[6]}Ni^{2+} coordination. The emission properties such as emission cross-sections ({sigma }_{emi}) full width at half maxima (FWHM) for the ^1T{_2}(D) rightarrow^3T{_2}(F) (visible) and ^3A{_2}(F) rightarrow^3T{_1}(F) (near-infrared) emission transitions were reported. Among the glass-containing semiconductor nanocrystals (GCs), the emission cross-sections in GC4 sample (x = 10% of Ni^{2+}) are the largest for both the visible (11.88 times 10^{-18} cm^2) and infrared (0.98 times 10^{-20} cm^2) transitions. Thermal diffusivity (D), thermal conductivity (K) and temperature dependent optical path length change (ds/dT) were obtained through time-resolved thermal lens (TL) and thermal relaxation (TR) methods. The D and K parameters do not change significantly with increase of Ni^{2+} ions (0.5–5%) in GCs. Nonlinear-refractive index and nonlinear absorption of the studied samples were also obtained using femtosecond Z-scan technique. The increase of nonlinear absorption coefficient (beta) is observed from GC2 (2.53 {times } 10^{-10} cm/W) to GC4 (7.98 {times } 10^{-10} cm/W). The GC4, sample with 10 wt% of Ni^{2+}, showed the lowest ds/dT (1.22 times 10^{-6} K^{-1}) with good lasing (FOM and emission cross-sections) and nonlinear absorption properties suggesting that it can be a good candidate for visible-red emission light conversion in LED technology.

Non-geometric tilt-to-length coupling in precision interferometry: mechanisms and analytical descriptions

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.

Characterizing cone spectral classification by optoretinography.

Light propagation in photoreceptor outer segments is affected by photopigment absorption and the phototransduction amplification cascade. Photopigment absorption has been studied using retinal densitometry, while recently, optoretinography (ORG) has provided an avenue to probe changes in outer segment optical path length due to phototransduction. With adaptive optics (AO), both densitometry and ORG have been used for cone spectral classification based on the differential bleaching signatures of the three cone types. Here, we characterize cone classification by ORG, implemented in an AO line-scan optical coherence tomography (OCT), and compare it against densitometry. The cone mosaics of five color normal subjects were classified using ORG showing high probability (∼0.99), low error (<0.22%), high test-retest reliability (∼97%), and short imaging durations (< 1 hour). Of these, the cone spectral assignments in two subjects were compared against AO-scanning laser opthalmoscope densitometry. High agreement (mean: 91%) was observed between the two modalities in these two subjects, with measurements conducted 6-7 years apart. Overall, ORG benefits from higher sensitivity and dynamic range to probe cone photopigments compared to densitometry, and thus provides greater fidelity for cone spectral classification.

Interferometric sphere surface metrology with cylindrical reference for precision topography.

We demonstrate a method for measuring a surface map of a spherical body with interferometric optical point sensors while rotating the test subject. The setup takes advantage of the excellent performance of heterodyne interferometry at nanometer levels and suppression of common-mode errors, as a cylindrical mirror mounted adjacent to the sphere is used as a reference. Future space based missions for gravitational wave research demand an improved inertial reference sensor with reduced acceleration noise levels. Spherical test masses can enable increased performance by suspension-free operation, contrary to cuboid solutions suffering from cross-coupling of attitude control noise into test mass position. However, interferometric readout is affected by surface irregularities and test mass attitude. An accurate surface map for compensation of the center of gravity readout should be established, by characterization either a priori or in-flight, when optical path length changes due to the surface occur in the measurement bandwidth.

Selectable microwave‐frequency doubling and quadrupling via optical path‐length tuning

A technique to selectively double or quadruple the frequency of a microwave signal is experimentally demonstrated based on a commercial single-output Mach–Zehnder modulator (MZM). Selectability is achieved by only a change in optical path length in a post-MZM optical subsystem, without filtering and without changing the MZM drive voltage. This path length controls the synchronisation of two similarly shaped optical signals that are incoherently combined. Multiplication from 2 GHz (S-band) to 4 GHz (C-band, doubling) and to 8 GHz (X-band, quadrupling) is demonstrated with side-tone suppression greater than 24 dB. At a 10-kHz offset from the quadrupled frequency, the phase-noise degradation is only 7.9 dB, a 4.1-dB improvement over traditional quadrupling techniques.

“Loop Stabilized” Improved Transfer Cavity-Based Laser Frequency Stabilization

We describe an improved laser frequency stabilization technique that overcomes limitation of the conventional Transfer Cavity (TC) method by prohibiting frequency drift of the desired (working) laser arising due to change in differential optical path length of the Fabry-Perot (FP) cavity with respect to the reference laser. Unlike the TC where noise at each stage propagates and cascades to the working laser, in this novel “Loop Stabilized Transfer Cavity (LSTC)” technique, different stages like the reference and working lasers, FP cavity constitute a loop which is stabilized altogether rather than stabilizing the individual component. As a result, frequency of the working laser is restricted from drifting and overall noise is also reduced as compared to that in the TC. Theoretical and experimental results comparing both the techniques are presented here.

Light-adapted flicker optoretinograms captured with a spatio-temporal optical coherence-tomography (STOC-T) system.

For many years electroretinography (ERG) has been used for obtaining information about the retinal physiological function. More recently, a new technique called optoretinography (ORG) has been developed. In one form of this technique, the physiological response of retinal photoreceptors to visible light, resulting in a nanometric photoreceptor optical path length change, is measured by phase-sensitive optical coherence tomography (OCT). To date, a limited number of studies with phase-based ORG measured the retinal response to a flickering light stimulation. In this work, we use a spatio-temporal optical coherence tomography (STOC-T) system to capture optoretinograms with a flickering stimulus over a 1.7 × 0.85 mm2 area of a light-adapted retina located between the fovea and the optic nerve. We show that we can detect statistically-significant differences in the photoreceptor optical path length (OPL) modulation amplitudes in response to different flicker frequencies and with better signal to noise ratios (SNRs) than for a dark-adapted eye. We also demonstrate the ability to spatially map such response to a patterned stimulus with light stripes flickering at different frequencies, highlighting the prospect of characterizing the spatially-resolved temporal-frequency response of the retina with ORG.

Lens-Free Optical Scanners for Metal Additive Manufacturing

Galvanometer scanners (GSs) driving selective laser sintering (SLS)/selective laser melting (SLM) printers for additive manufacturing (AM) have mechanical limits. They provide inconsistent energy density across the print surface because of changes in optical path length, surface beam speed, and angle of incidence. The resulting thermal gradients may be particularly problematic for metal, whose high heat conductivity makes temperature prediction during printing critical. In this paper, we mathematically analyze and compare GSs with a new lens-free optical scanner. The results show that the latter can facilitate metal printing by providing consistent energy deposition across the print surface.

Interferometric imaging of thermal expansion for temperature control in retinal laser therapy.

Precise control of the temperature rise is a prerequisite for proper photothermal therapy. In retinal laser therapy, the heat deposition is primarily governed by the melanin concentration, which can significantly vary across the retina and from patient to patient. In this work, we present a method for determining the optical and thermal properties of layered materials, directly applicable to the retina, using low-energy laser heating and phase-resolved optical coherence tomography (pOCT). The method is demonstrated on a polymer-based tissue phantom heated with a laser pulse focused onto an absorbing layer buried below the phantom's surface. Using a line-scan spectral-domain pOCT, optical path length changes induced by the thermal expansion were extracted from sequential B-scans. The material properties were then determined by matching the optical path length changes to a thermo-mechanical model developed for fast computation. This method determined the absorption coefficient with a precision of 2.5% and the temperature rise with a precision of about 0.2°C from a single laser exposure, while the peak did not exceed 8°C during 1 ms pulse, which is well within the tissue safety range and significantly more precise than other methods.

Analysis and suppression of thermal effect of an ultra-stable laser interferometer for space-based gravitational waves detection

In this paper, we present a suppression method for the thermal drift of an ultra-stable laser interferometer. The detailed analysis on the Michelson interferometer indicates that the change in optical path length induced by temperature variation can be effectively reduced by choosing proper thickness and/or incident angle of a compensator. Taking the optical bench of the Laser Interferometer Space Antenna Pathfinder as an example, we analyze the optical bench model with a compensator and show that the temperature coefficient of this laser interferometer can be reduced down to 1 pm/K with an incident angle of 0.267828 rad. The method presented in this paper can be used in the design of ultra-stable laser interferometers, especially for space-based gravitational waves detection.

Quantification of intrinsic optical signals in the outer human retina using optical coherence tomography.

Intrinsic optical signals constitute a noninvasive biomarker promising the objective assessment of retinal photoreceptor function. We employed a commercial optical coherence tomography (OCT) system and an OCT signal model for evaluation of optical path length (OPL) changes in the temporal outer retina of five healthy subjects during light adaptation. Data were acquired at 30 time points, in ambient light and during long duration stimulation with white light, and analyzed, employing a signal model based on the sum of seven Gaussian curves corresponding to all relevant anatomical structures of the outer retina. During light stimulation, mean OPL between rod outer segment tips (ROST) and the retinal pigment epithelium (RPE) decreased by 21.4 ± 3.5%. Further, OPL between the external‐limiting membrane (ELM) and the RPE decreased by 5.2 ± 0.9% versus baseline, while OPL between ELM and ROST showed an initial decrease by 2.1 ± 1.6% versus baseline and, thereafter, increased by 2.8 ± 2.1% versus baseline. Thus, the presented approach allowed for assess to dynamic changes in the outer retina in response to light. The change in the subretinal space occurring in the context of light adaptation could be measured using a standard OCT platform and a dedicated signal model.

Electrowetting-actuated optofluidic phase modulator.

In this paper, an optofluidic phase modulator based on electrowetting is presented. The modulator consists of an inner and outer chamber. Two immiscible liquids are filled into the chambers, and a transparent sheet is fixed between the liquid-liquid interface to obtain a flat interface. By applying different voltages to the modulator, the flat interface moves up and down leading to the change of optical path length. Consequently, the variation of the optical path in the proposed modulator exploits the ability to alter the optical phase. To prove the concept, a prototype of the phase modulator is fabricated in experiment, and the ability of phase modulation is detected. Our proposed modulator performs optical phase shift up to ∼6.68 π driven with 150 V. Widespread applications of such an optofluidic phase modulator is foreseeable.