Optical Path Length Difference Research Articles

Optical path length difference of ray paths inside a reference sphere: a new approach for determining wavefront aberrations in axially symmetrical systems with an object at infinity

A new, to the best of our knowledge, method is proposed to analyze the wavefront aberrations in an axially symmetrical system with an object at infinity. The study commences by determining the optical path length (OPL) difference between two ray paths from the object to the reference sphere. The proposed method is then used to explore the claim in J. Opt. Soc. Am. A 19, 1187 (2002)JOAOD60740-323210.1364/JOSAA.19.001187 that wavefront aberrations do not depend on the radius of the reference sphere. It is found that this claim does not hold when the image plane is non-Gaussian. The proposed approach is applied to determine the primary wavefront aberrations of an axially symmetrical system with an object at infinity. The numerical values of the primary aberrations (spherical, coma, astigmatism, and field curvature) are in excellent agreement with those determined by Zemax simulations. The superiority of the proposed method over Zemax in determining the distortion aberration is confirmed through raytracing. Overall, the proposed method provides a useful contribution to the development of optical systems for applications requiring high-resolution imaging.

Optical phase and amplitude measurements of underwater turbulence via self-heterodyne detection

The creation of underwater optical turbulence is driven by density variations that lead to small changes in the water’s refractive index, which induce optical path length differences that affect light propagation. Measuring a laser beam’s optical phase after traversing these turbulent variations can provide insight into how the water’s turbulence behaves. The sensing technique to measure turbulent fluctuations is a self-heterodyne beatnote enhanced by light’s orbital angular momentum (OAM) to obtain simultaneous optical phase and amplitude information. Experimental results of this method are obtained in a water tank that creates a thermally driven flow called Rayleigh–Bénard (RB) convection. The results show time-varying statistics of the beatnote that depend on the incident OAM mode order and the strength of the temperature gradient. Beatnote amplitude and phase power spectral densities are compared to analytic theory to obtain estimates of the turbulent length scales using the Taylor hypothesis that include mean flow speed, turbulent strength, and length scales, and flow dynamics due to intermittency in the RB process.

Sensor noise in LISA Pathfinder : Laser frequency noise and its coupling to the optical test mass readout

The (LPF) mission successfully demonstrated the feasibility of the technology needed for the future space borne gravitational wave observatory LISA. A key subsystem under study was the laser interferometer, which measured the changes in relative distance in between two test masses (TMs). It achieved a sensitivity of 32.0−1.7+2.4 fm/Hz, which was significantly better than the prelaunch tests. This improved performance allowed direct observation of the influence of laser frequency noise in the readout. The differences in optical path lengths between the measurement and reference beams in the individual interferometers of our setup determined the level of this undesired readout noise. Here, we discuss the dedicated experiments performed on LPF to measure these differences with high precision. We reached differences in path length difference between (368±5) μm and (329.6±0.9) μm which are significantly below the required level of 1 mm or 1000 μm. These results are an important contribution to our understanding of the overall sensor performance. Moreover, we observed varying levels of laser frequency noise over the course of the mission. We provide evidence that these do not originate from the laser frequency stabilization scheme which worked as expected. Therefore, this frequency stabilization would be applicable to other missions with similar laser frequency stability requirements. Published by the American Physical Society 2024

Easy-to-Fabricate UV-Glue-Based Cascaded Fabry–Perot Fiber Sensor Probe for Temperature Measurement

In this paper, we propose an in-line fiber sensor probe based on UV-glue-assisted cascaded Fabry–Perot cavities for temperature measurement. The UV-curable adhesive in the sensing cavity plays an important role due to its high thermo-optic coefficient. We show that the temperature sensitivity depends on the optical path length difference between both cavities. We report a maximum value of 12.57 nm/°C in the range of 20 to 30 °C. This original sensor architecture features a low cost and simple structure that can be straightforwardly manufactured with readily available materials and a short production time.

Polarization state tomography technique based on coherent synthesis of polarization state and orthogonal polarization state separation method for comprehensive optical imaging.

Comprehensive optical imaging of the intensity, phase, and birefringent information of the biological sample is important because important physical or pathological changes always accompany the changes in multiple optical parameters. Current studies lack such a metric that can present the comprehensive optical property of the sample in one figure. In this paper, a polarization state synthesis tomography (PoST) method, which is based on the principle of polarization state coherent synthesis and demodulation, is proposed to achieve full-field tomographic imaging of the comprehensive information (i.e., intensity, phase, and birefringence) of the biological sample. In this method, the synthesis of the polarization state is achieved by the time-domain full-field low coherence interferometer, where the polarization states of the sample beam and the reference beam are set to be orthogonal for the synthesis of the polarization state. The synthesis of the polarization state enables two functions of the PoST system: (1) Depth information of the sample can be encoded by the synthesized polarization state because only when the optical path length difference between the two arms is within the coherence length, a new polarization state can be synthesized; (2) Since the scattering coefficient, refractive index and the birefringent property of the sample can modulate the intensity and phase of the sample beam, the synthesized polarization state is sensitive to all these three parameters and can provide the comprehensive optical information of the sample. In this work, the depth-resolved ability and the comprehensive optical imaging metric have been demonstrated by the standard samples and the onion cells, demonstrating the potential application value of this method for further investigation of the important physical or pathological process of the biological tissues.

Phase noise suppression technique based on an improved reference interferometer scheme.

The reference interferometer scheme is an effective noise reduction method, but the optical path length difference (OPD) of the two interferometers must be strictly equal, which limits its application in practical environments. In this paper, an improved reference interferometer demodulation technique without strictly equal OPDs is proposed to suppress phase noise. By introducing a reference interferometer, the phase noise can be removed from the demodulation results. The combination of the differential self-multiplication algorithm and the fitted phase modulation depth calculation formula can evaluate the phase modulation depth of both interferometers in real time and simultaneously eliminate the nonlinear distortion caused by phase modulation depth drift and the effect of different OPDs on the reference interferometer scheme. The experimental results show that the technique can obtain highly stable and accurate demodulation results even if the OPDs of the two reference interferometers are different. The phase modulation depth calculation error is less than 0.57%, the maximum phase noise reduction is 15 dB, the average reduction is 9 dB, the minimum total harmonic distortion is 0.17%, and the SINAD reaches 35.90 dB.

High-resolution on-chip spatial heterodyne Fourier transform spectrometer based on artificial neural network and PCSBL reconstruction algorithm.

A novel compact on-chip Fourier transform (FT) spectrometer has been proposed based on the silicon-on-insulator (SOI) platform with wide operating bandwidth and high resolution. The spectrometer consists of a 16-channel power splitter and a Mach-Zehnder interferometer (MZI) array of 16 MZIs with linearly increasing optical path length (OPL) difference. We have also developed a spectral retrieval algorithm based on the pattern-coupled sparse Bayesian learning (PCSBL) algorithm and artificial neural network (ANN). The experimental results show that the designed spectrometer has a flat transmission characteristic in the wavelength range between 1500 nm and 1600 nm, indicating that the device has a wide operating bandwidth of 100 nm. In addition, with the assistance of the spectral retrieval algorithm, our spectrometer has the ability to reconstruct narrowband signals with full width at half maximum (FWHM) of 0.5 nm and a triple-peaked signal separated by a 3-nm distance.

Graphical Explanations of Optical Path Length Difference Amplification Effect in Fiber-Optic Optical Delay Line using Chirped Fiber Bragg Gratings

Graphical Explanations of Optical Path Length Difference Amplification Effect in Fiber-Optic Optical Delay Line using Chirped Fiber Bragg Gratings

Optical visualization of heat transfer in supercritical carbon dioxide under near-critical, liquid-like, and gas-like conditions

Heat transfer in supercritical carbon dioxide (sCO2) is experimentally visualized, and a measurement method is proposed for evaluating the transport phenomena in near-critical, liquid-like, and gas-like conditions. There are various uses for sCO2 in engineering applications, such as abstraction, material processing, and soil remediation. However, the heat and mass transfer under supercritical conditions have not been fully revealed, and innovative measurement techniques with higher spatial and temporal resolutions are required. This study focuses on the evaluation of heat transfer in sCO2 using a high-speed phase-shifting interferometer. The density distribution of sCO2 under different temperature and pressure conditions is successfully visualized with the proposed interferometer. Characteristics of the density field patterns are observed near the critical point and in liquid-like and gas-like conditions. It is demonstrated that the sensitivity of the density (i.e., refractive index) to temperature changes is different for each condition. The transient heat transfer under gas-like condition is evaluated by the interferometer, and numerical simulations with 3D model are performed to evaluate the experimental results. Finally, the interference fringes pattern obtained by the interferometer is shown to be qualitatively in good agreement with the numerical temperature field change. Additionally, transient variations of optical path length difference obtained in the experiment, which means apparent temperature distribution, were compared with numerical simulations. Experimental results are quantitatively in good agreement with the numerical results under a thermal diffusivity of order 10−8 m2/s, confirming the feasibility of the proposed measurement technique for the transient heat transfer in sCO2.

Multiple motion picture recording in light-in-flight recording by holography with an angular multiplexing technique.

Light-in-flight recording by holography (LIF holography) is an ultrafast imaging technique for recording light pulse propagation as a motion picture. In this study, we propose and demonstrate multiple motion picture recordings of light pulse propagation by use of LIF holography with angular multiplexing. We set incident angles of reference light pulses to remove the difficulty in adjusting the optical path length difference between an object light pulse and reference light pulses and the complexity of the optical system. In the experiment, by using LIF holography with angular multiplexing, we succeeded in recording a propagating light pulse as two motion pictures with durations of 129.6ps without an inseparable superimposition of the reconstructed images. In addition, cross talk between the recorded images, noise caused by cross-terms in an image plane, and the number of motion pictures that can be recorded are discussed.

Sub-nanometer measurement of transient structural changes in dye-doped polystyrene microspheres

We present an interferometric spectral-domain optical coherence tomography microscopy setup to detect structural changes using interference of light reflected from different interfaces of the sample. We induce a reproducible nanometer-scale size change in dye-doped 10-µm polystyrene microspheres by the release of Stokes shift energy of dye molecules inside the microspheres, excited by a modulated 532-nm laser. The resulting optical path length difference was measured with a sensitivity of 0.4 p m / H z limited by photodetection noise, and reveals elastic as well as inelastic responses, which opens up possibilities for measuring the response of cell-sized biological objects.

Experimental demonstration of non-contact and quasi OPD-independent nanoscale-displacement measurement by phase-diversity optical digital coherent detection and comb filtering.

We experimentally demonstrated and quantitatively evaluated a non-contact nanometer-displacement measurement using phase-diversity optical digital coherent detection implemented by a 90 ° optical hybrid and a narrow-linewidth probe laser without fine-tuning of optical path length difference (OPD). Combined with a comb filter, the system exhibits 99.99% linearity detection with a scale and resolution of approximately 7 nm and 2 nm respectively, as well as a wideband vibration of 5.85 MHz. We also experimentally analyzed the effect of noise arising from the OPD and demonstrated the detection of displacement down to 85 nm with a resolution of 24 nm at an OPD of 342 cm.

Improved Phase Noise Cancellation Technology for Auxiliary Reference Interferometer Demodulation Scheme

In an unbalanced interferometer, the phase noise level is positively related to the optical path length difference (OPD) and the wavelength instability of the light source. The effective current solution for reducing phase noise is to use an auxiliary reference interferometer to measure the phase noise signal. However, this method requires that all interferometers have the same OPD, otherwise the phase modulation depth of different interferometers with the same light source will be different and the noise reduction effect will be severely reduced. It is difficult to provide interferometers with precisely the same OPD in practical. In this paper, an improved phase-generated carrier (PGC) demodulation technique for phase noise cancellation that does not require strictly equal OPDs of interferometers is proposed. Combining an auxiliary reference interferometer scheme with an ellipse fitting algorithm (EFA) can eliminate the effect of different phase modulation depths due to different OPDs, and phase modulation depth drift on demodulation results, significantly reducing harmonic distortion. The additional phase modulation signal ensures the correct calculation of small signals by the EFA, while the OPDs of the interferometers are evaluated in real time to achieve constant phase noise cancellation capability under different OPD. Experimental results show that the proposed technique achieves a highly stable phase demodulation result with a maximum phase noise reduction of about 9dB and a minimum THD of -74.59 dB in interferometers with non-strict equal OPD.

Non-invasive probing of dynamic ion migration in light-emitting electrochemical cells by an advanced nanoscale confocal microscope

In this study, we firstly propose an optical approach to investigate the ion profile of organic films in light-emitting electrochemical cells (LECs) without any invasive sputtering processes. In contrast to previous literatures, this pure optical strategy allows us to record clear and non-destructive ion profile images in the (Ru(dtb-bpy)3(PF6)2) consisted organic layer without interferences of complex collisions from the bombardment of secondary sputter induced ions in a conventional time-of-flight secondary ion mass spectrometry. By using the advanced position sensitive detector (PSD)-based Nanoscale Confocal Microscope, ion distribution profiles were successfully acquired based on the observation of nanoscale optical path length difference by measuring the refractive-index variation while the thickness of the LEC layer was fixed. Dynamic time-dependent ion profile displayed clear ion migration process under a 100 V applied bias at two ends of the LEC. This technique opens up a new avenue towards the future investigations of ion distributions inside organic/inorganic materials, Li-ion batteries, or micro-fluid channels without damaging the materials or disturbing the device operation.

Dual-Polarization Bandwidth-Bridged Bandpass Sampling Fourier Transform Spectrometer from Visible to Near-Infrared on a Silicon Nitride Platform.

On-chip broadband optical spectrometers that cover the entire tissue transparency window (λ = 650–1050 nm) with high resolution are highly demanded for miniaturized biosensing and bioimaging applications. The standard spatial heterodyne Fourier transform spectrometer (SHFTS) requires a large number of Mach–Zehnder interferometer (MZI) arrays to obtain a broad spectral bandwidth while maintaining high resolution. Here, we propose a novel type of SHFTS integrated with a subwavelength grating coupler (SWGC) for the dual-polarization bandpass sampling on the Si3N4 platform to solve the intrinsic trade-off limitation between the bandwidth and resolution of the SHFTS without having an outrageous number of MZI arrays or adding additional active photonic components. By applying the bandpass sampling theorem, the continuous broadband input spectrum is divided into multiple narrow-band channels through tuning the phase-matching condition of the SWGC with different polarization and coupling angles. Thereby, it is able to reconstruct each band separately far beyond the Nyquist criterion without aliasing error or degrading the resolution. We experimentally demonstrated the broadband spectrum retrieval results with the overall bandwidth coverage of 400 nm, bridging the wavelengths from 650 to 1050 nm, with a resolution of 2–5 nm. The bandpass sampling SHFTS is designed to have 32 linearly unbalanced MZIs with the maximum optical path length difference of 93 μm within an overall footprint size of 4.7 mm × 0.65 mm, and the coupling angles of SWGC are varied from 0° to 32° to cover the entire tissue transparency window.

High-stability PGC demodulation technique with an additional sinusoidal modulation based on an auxiliary reference interferometer and EFA.

In the reference interferometer demodulation scheme, it's difficult to guarantee in practice that both interferometers have the same optical path length difference (OPD), which makes the phase modulation depth different in different interferometers with the same laser modulation. The random shift of phase modulation depth also affects the demodulation results. An improved phase-generated carrier (PGC) technique is proposed based on an auxiliary reference interferometer and the ellipse fitting algorithm (EFA). The technique ensures the correct fitting of the EFA for small amplitude signals by introducing a sinusoidal signal as an additional phase modulation. The combination of the reference interferometer and EFA can eliminate the effect of different phase modulation depths of the two interferometers caused by different OPDs, the non-linear distortion caused by phase modulation depth shifts, and improve the accuracy of the demodulation results. The experiment results are consistent with the theoretical analysis, and the method extends the application of the EFA in the reference interferometer phase demodulation technique.

Substantial Improvement of Color-Rendering Properties of Conventional White LEDs Using Remote-Type Red Quantum-Dot Caps.

A new type of remote red quantum-dot (QD) component was designed and fabricated to improve the color-rendering properties of conventional white LED (light-emitting diode) lightings. Based on an optical simulation, the rectangular cavity-type QD cap was designed with an opening window on the top surface. Red QD caps were fabricated using a typical injection molding technique and CdSe/ZnS QDs with a core/shell structure whose average size was ~6 nm. Red QD caps were applied to conventional 6-inch, 15-W white LED downlighting consisting of 72 LEDs arrayed concentrically. The red QD caps placed over white LEDs enhanced the red components in the long-wavelength range resulting in the increase of the color rendering index (CRI) from 82.9 to 94.5. The correlated color temperature was tuned easily in a wide range by adopting various configurations consisting of different QD caps. The spatial and angular homogeneities were secured on the emitting area because QD caps placed over the white LEDs did not exhibit any substantial optical path length difference. The present study demonstrates that adopting QD caps in conventional LED lightings provides a flexible and efficient method to realize a high color-rendering property and to adjust correlated color temperature appropriately for a specific application.

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.

Investigation of dynamic influences in tilted-wave interferometry

Aspherical and freeform lenses allow for compact optical systems and have therefore gained high interest in optics. The interferometric measurement of these forms is a challenge, for which the tilted-wave interferometer (TWI) has been developed. To evaluate the measurement uncertainty of the TWI, both the static and the dynamic influence parameters have to be investigated. In this work, we focus on the dynamic influences on the measurement data of the interferometer. To this end, the individual influences as well as their point of insertion into the process chain are identified. Then the measurement of the interferogram data is modelled as a Monte Carlo simulation. The propagation of different influences through the data process chain to the optical path length differences (OPDs) is also simulated, and the resulting variation of the OPDs is estimated. Furthermore, the variation of the OPDs resulting from measured interferogram data is investigated for comparison. The analysis and quantification of variation of the OPDs along with its contributing influence sources are important steps on the way towards a full uncertainty estimation of optical form measurement with the TWI.

Graphene Superconductivity at Room‐Temperature of a Wide Range and Standard Atmosphere, Based on Vacuum Channels and White‐Light Interferometry

AbstractThe thickness of a monolayer graphene is extremely thin, ≈0.34 nm, so exact measurement of the optical path length and optical path length difference of graphene is challenging. This paper uses white‐light interferometry and a horizontal grating to obtain the optical characteristic curve of graphene. Then, the real existence of vacuum channels (VCs) in monolayer graphene is discovered. These VCs naturally eliminate the collision phenomena, and provide zero electrical resistance and superconductivity (SC) states. Multiple SC states (SCSs), SC persistence, magnetic field response, VCs transmitting a SC current with high efficiency, screen characteristics of VCs, etc. are discussed. Experiments show that only when a graphene ribbon is located at the exact position of the VC, does it transmit the SC current and provide a SCS. The duration of the persistence tests is 2 months. All experiments are conducted in a completely open space of a laboratory. Graphene SC at room‐temperatures of a wide range and standard atmosphere is achieved. This paper uses the optical technology to realize graphene SC, points out the basic reason of realizing it, and provides the experimental evidences.