Phase Retardation Measurement Research Articles

Insights into atypical segmental layer thicknesses and phase retardation in thick corneas using ultrahigh-resolution polarization-sensitive optical coherence tomography

BackgroundAccurately assessing corneal structural status is challenging when thickness deviates from the average. Polarization-sensitive optical coherence tomography (PS-OCT) measures tissue-specific polarization changes, providing additional contrast for accurate segmentations and aids in phase retardation (PR) measurements. Previous studies have shown PR's effectiveness in identifying sub-clinical keratoconus (KC) in asymmetric cases. Thus, this study aims to assess PR distribution in thick corneas with and without KC.MethodsIn this retrospective and cross-sectional study, 45 thick corneas from 30 Asian-Indian subjects, categorized into healthy (n = 26) and KC (n = 19) groups were analyzed. All eyes underwent standard clinical evaluations, tomographic assessments, and corneal biomechanics measurements. PR and individual layer thicknesses were measured using custom-designed ultrahigh-resolution PS-OCT. PR en-face maps were generated. Individual layer thicknesses and PR analysis was conducted across multiple zones, extending up to 8–10 mm in diameter. All eyes in the study had not undergone interventions, received topical medications, or had previous corneal disease history.ResultsSignificant differences were found in spherical and cylindrical powers, keratometry, pachymetry, and biomechanical indices (all P < 0.01). Thickness profiles from PS-OCT showed significant differences in the 4–8 mm zones only. Bowman's layer thickness significantly differed only in the central 2 mm zone (P = 0.02). The median PR values showed marginal differences in the central 2 mm zone (P = 0.0565). Additionally, there were significant differences observed in the 2–4 mm and 4–6 mm zones (P = 0.0274 and P = 0.0456, respectively). KC eyes exhibited an atypical PR distribution and corneal thinning, while normal eyes maintained a uniform Bowman’s layer thickness and PR maps with larger areas of higher PR.ConclusionThe study revealed distinctive PR distribution in thick corneas among healthy and KC groups. Using an ultrahigh-resolution PS-OCT the significance of Bowman's layer thickness in these groups was also emphasized. The study offered potential improvements in clinical diagnostics by enhancing our understanding of corneal structure and its altered function.

One-shot measurement of birefringence by radial analysis

Due to complexity and bulky configuration of conventionally mechanical rotation approaches, a more convenient approach is to measure the birefringence effect (phase retardation and fast axis) by nano-fabricated spatial devices. Previous literature introduced radially-polarized illumination and eliminated the need for rotation mechanics in the illumination optics but still required rotation devices in the analyzer part. This work aims to achieve a compact and one-shot birefringence measurement by introducing spatial concepts in both the modulator and analyzer. By proposing a novel birefringence measurement by the combination of radial illumination and radial analyzer, this work is the first time to integrate no-mechanical motion and one-shot birefringence measurement in a single light path. What’s more, we are the first to introduce Fourier analysis in birefringence measurement, replacing the previous average intensity calculation, which is easily influenced by light source fluctuations. Based on our one-shot & non-mechanical measurement design and Fourier analysis algorithm, our birefringence measurement achieved very stable phase retardation measurement (standard deviation < 0.3°) and high accuracy fast axis measurement (average absolute error < 0.04°).

Reducing noise in polarization-sensitive optical coherence tomography for high-quality local phase retardation imaging

Local phase retardation (LPR) is increasingly recognized as a crucial biomarker for assessing disease progression. However, the presence of speckle noise significantly challenges its accuracy and polarization contrast. To address this challenge, we propose a signal-processing strategy aimed at reducing the impact of noise on LPR measurements. In this approach, the LPR is reconstructed by polar decomposition after averaging multiple Mueller matrices from different overlapping sub-spectra. To optimize measurement accuracy, we systematically combined and traversed different sub-spectral numbers and bandwidths. By examining the quarter-wave plate and glass slide, high-accuracy phase retardation measurements were successfully verified, and the maximum polarization contrast was improved by 23%. Moreover, experimental results from multi-tissue imaging vividly illustrate that the equivalent number of looks (ENL) and polarization contrast were improved by 18% and 19%, respectively. This outcome indicates that our proposed strategy can effectively reduce the noise spikes, enhancing tissue discrimination capabilities.

White light OPD scanning polariscope for whole-field optical path retardation and principal angle examinations

Fringe-scanning (or TFP/RGB) and phase-stepping are now the most acceptable techniques for examining stressed photoelastic samples; however the former requires a calibration table, which is sensitive to the geometrical and optical parameters of the corresponding polariscope, and concentrates only on phase retardation measurements; the latter suffer from three potential issues: 1) the principal angle is indeterminate when the corresponding phase retardation is close or equal to an integer multiple of π, 2) the obtained phase retardation and principal angle are wrapped, and 3) the phase retardation and principal angle may couple together in certain situations. Free from the disadvantages of the fringe-scanning and phase-stepping polariscopes, a white light OPD (optical path difference) scanning polariscope composed of a white light laser, an OPD modulator, and a dark-field circular polariscope was proposed for whole-field optical path retardation (proportional to the phase retardation) and principal angle determinations. This paper introduces the theory of the polariscope, demonstrates the experimental setup for implementing the polariscope, and presents the results from the uses of the setup. The results manifest a standard deviation of 8 nm when repeatedly measuring an optical path retardation and 1.21ο when repeatedly measuring a principal angle; moreover, the results confirm the polariscope's validity and feasibility, but showing a limitation while adopting the polariscope to evaluate fringe orders < 3.

Rapid measurement method of intracavity phase retardation based on laser frequency splitting.

We present a method for phase retardation measurement of intracavity optical elements which is based on frequency splitting caused by weak phase anisotropy of Nd: YAG. The measurement range covers 0-π and the measurement uncertainty is less than 0.0300 rad. A theoretical analysis is provided to obtain the phase retardation of intracavity optical elements by using the phase difference or frequency difference of two eigenmodes. The minimum error is 0.0036 rad by using the composite wave plate to verify various phase retardation conditions. This work provides a rapid and accurate intracavity method for measuring the phase retardation of optical elements.

Method for Measurement of Phase Retardation of a Wave Plate Based on Spectral Interference Technology

Method for Measurement of Phase Retardation of a Wave Plate Based on Spectral Interference Technology

Fourier-Domain Phase Retardation Vortex Measurement

Optical vortices have found a wide range of applications thanks to their helical phase topology allowing to carry the orbital angular momentum. In this work, self-interfering vortex beams are utilized in a new single-shot holographic method for the circular phase retardation measurement. The vortices carrying information about the phase retardation introduced between two orthogonal circular polarization modes are generated by the spin to orbital angular momentum conversion. The phase retardation is stored in off-axis holographic records acquired in a common-path setup using a geometric-phase grating. In the proposed method, the circular phase retardation is reconstructed in the Fourier domain, surpassing the measurement precision provided by methods restoring the retardation from the rotation of a Double-Helix Point Spread Function (DH PSF). The developed method can be adapted for application to polarimetry, orientation imaging and diagnostics of nano-emitters.

Simultaneous measurement of phase retardation and fast axis azimuth of wave plate based on equivalent component and phase detection

Wave plates (WPs) are key components in optical polarization systems whose phase retardations and fast axis azimuths should be determined accurately. At present many measurement methods are based on light intensity detection which is inevitably affected by light intensity fluctuations so that the measurement accuracy is limited. What’s more, quite a few methods cannot measure WPs’ fast axis azimuths simultaneously. In this paper a method of simultaneously measuring the phase retardation and fast axis azimuth of arbitrary WP is proposed, which is based on equivalent component and phase detection. A rotatable half wave plate (HWP) and a retroreflector are used and its effect is equivalent to measuring an equivalent WP whose phase retardation is twice that of the measured wave plate, which is equivalent to doubling the measurement resolution. Phase detection is used to process the signals which means the measurement accuracy is better than that by usual light intensity detection. What’s more, the presented method eliminates the angle positioning errors of birefringent components in principle which exists in many present WP measurement methods. Finally, the measurement system setup is simple as well as the measurement process. The measurement formulae are deduced and corresponding WP measuring system is established. The error analysis shows that the system measurement uncertainty is about 3.9′ for the phase retardation and 5” for the fast axis azimuth. Experiment results and comparisons of quarter WPs and HWPs show that the presented method is in good agreement with other method. The phase retardation measurement repeatability is also good with a standard deviation about 2′.

Analysis and reduction of noise-induced depolarization in catheter based polarization sensitive optical coherence tomography.

In catheter based polarization sensitive optical coherence tomography (PS-OCT), a optical fiber with a rapid rotation in the catheter can cause low signal-to-noise ratio (SNR), polarization state instability, phase change of PS-OCT signals and then heavy noise-induced depolarization, which has a strong impact on the phase retardation measurement of the sample. In this paper, we analyze the noise-induced depolarization and find that the effect of depolarization can be reduced by polar decomposition after incoherent averaging in the Mueller matrix averaging (MMA) method. Namely, MMA can reduce impact of noise on phase retardation mapping. We present a Monte Carlo method based on PS-OCT to numerically describe noise-induced depolarization effect and contrast phase retardation imaging results by MMA and Jones matrix averaging (JMA) methods. The peak signal to noise ratio (PSNR) of simulated images processed by MMA is higher than about 8.9 dB than that processed by JMA. We also implement experiments of multiple biological tissues using the catheter based PS-OCT system. From the simulation and experimental results, we find the polarization contrasts processed by the MMA are better than those by JMA, especially at areas with high depolarization, because the MMA can reduce effect of noise-induced depolarization on the phase retardation measurement.

Proposed method for phase retardation measurements using polarimetric techniques

Phase retardance elements such as quarter, half and full waveplates are essential elements in the most of the polarization systems. So, they should be determined precisely. Accurate determination of the phase retardation for these elements are necessary and critical due to its effect on the optical polarization measurements. In this paper we measure two-dimensional phase retardation distribution of half wave plate using four step phase shifting technique for accurate retardance measurements through the whole surface of the wave plate. By using this technique, four images are captured, which are related to different orientation of the azimuth angle of the analyzer, and mathematically analyzed to obtain the phase retardance measurements. The mean value of the phase retardance measurements is 182.57˚ with uncertainty 0.6˚.

Proposed method for phase retardation measurements using polarimetric techniques

Proposed method for phase retardation measurements using polarimetric techniques

A modified method for calibration of polarimetric components using polarizing interferometry

Polarization interferometer technique has been developed for calibration of phase retardation elements such as quarter/half wave plate with known tolerance in each one. In addition, this technique is used to measure unknown retardation elements to identify its phase retardation. A polarizing beam splitter is placed after Sagnac interferometer to split the produced fringes into p and s polarization interferograms to be analyzed. The phase retardation measurements depend on two states, the reference state which includes recording the reference p and s interferogram images without placing the sample then measuring state at which the p and s interferogram images are recorded after placing the sample inside Sagnac interferometer. Six images are recorded for each interferogram under a controlled environment to calculate the repeatability of measurements and for uncertainty estimation. The detected images are mathematically processed to determine the phase retardation of the polarimetric components. The results are found to be in a good consequent with the data measured by Senarmont compensator method.

Improved accuracy of quantitative birefringence imaging by polarization sensitive OCT with simple noise correction and its application to neuroimaging.

Polarization-sensitive optical coherence tomography (PS-OCT) enables three-dimensional imaging of biological tissues based on the inherent contrast provided by scattering and polarization properties. In fibrous tissue such as the white matter of the brain, PS-OCT allows quantitative mapping of tissue birefringence. For the popular PS-OCT layout using a single circular input state, birefringence measurements are based on a straight-forward evaluation of phase retardation data. However, the accuracy of these measurements strongly depends on the signal-to-noise ratio (SNR) and is prone to mapping artifacts when the SNR is low. Here we present a simple yet effective approach for improving the accuracy of PS-OCT phase retardation and birefringence measurements. By performing a noise bias correction of the detected OCT signal amplitudes, the impact of the noise floor on retardation measurements can be markedly reduced. We present simulation data to illustrate the influence of the noise bias correction on phase retardation measurements and support our analysis with real-world PS-OCT image data.

Investigation of the Clinical Potential of Polarization-Sensitive Optical Coherence Tomography in a Laryngeal Tumor Model.

The vocal cord tissue consists of three anatomical layers from the surface to deep inside: the epithelium that contains almost no collagen, the lamina propria that is composed of abundant collagen, and the vocalis muscle layer. It is clinically important to visualize the tissue microstructure using a non-invasive method, especially in the case of vocal cord nodules or cancer, since histological changes in each layer of the vocal cord cause changes in the voice. Polarization-sensitive optical coherence tomography (PS-OCT) enables phase retardation measurement to evaluate birefringence of tissue with varied organization of collagen fibers in different tissue layers. Therefore, PS-OCT can visualize structural changes between normal and abnormal vocal cord tissue. A rabbit laryngeal tumor model with different stages of tumor progression was investigated ex-vivo by PS-OCT. A phase retardation slope-based analysis, which quantifies the birefringence in different layers, was conducted to distinguish the epithelium, lamina propria, and muscle layers. The PS-OCT images showed a gradual decrease in birefringence from normal tissue to advanced tumor tissue. The quantitative analysis provided a more detailed comparison among different stages of the rabbit laryngeal tumor model, which was validated by the corresponding histological findings. Differences in tissue birefringence was evaluated by PS-OCT phase retardation measurement. It is also possible to indirectly infer the dysplastic changes based on the mucosal and submucosal alterations.

An interferometric method for simultaneously determination the phase retardation and fast-axis azimuth angle of a wave plate

In this study, an interferometric method was proposed for the simultaneous measurement of phase retardation and fast-axis azimuth angle of a wave plate by using a Mach–Zehnder interferometer. The wave plate to be tested is placed in one of the light passages in the interferometer, and two analyzers with transmission axes at horizontal and vertical orientations are arranged at the two output regions. When a linearly polarized laser light beam is passed through the interferometer, two interference light beams are simultaneously generated. Through an analysis of the intensities of the two light beams, the phase retardation and fast-axis azimuth angle of the tested wave plate can be simultaneously determined using specially derived equations. The feasibility of the proposed method was demonstrated using measurements of zero-order half-wave and zero-order quarter-wave plates. The proposed method is easy to operate, enables rapid measurement, and has high stability and accuracy.

Measurement of a birefringent sample based on ptychographical iterative engine using planar polariscope

Although it is a simple and convenient birefringence analysis instrument, the traditional planar polariscope is difficult to use for the quantitative measurement of phase retardation and azimuth angle. A novel 2D quantitative birefringence measurement method based on ptychographic iterative engine (PIE) in a planar polariscope is proposed. The birefringent sample is placed in the parallel probe-forming path. By inserting an isotropic diffractive object with good modulation property for the probe, the ptychographic scan measurements are performed under two different dark-field states. The amplitudes and phases of the two probes containing different birefringence information were reconstructed, and the phase retardation and azimuth angle obtained with a simple and straightforward extraction approach. The approach was verified using a classic diametrically compressed disc. The proposed method solves the problem of quantitative birefringence measurement in planar polariscopes by introducing the phase information. It reduces the PIE scans and shortens the data collection time, which provides a practical measurement means for birefringence in materials, biophysics and opto-mechanical system.

Slope-based segmentation of articular cartilage using polarization-sensitive optical coherence tomography phase retardation image.

.A segmentation method based on phase retardation measurements from polarization-sensitive optical coherence tomography (PS-OCT) is developed to differentiate the structural zones of articular cartilage. The organization of collagen matrix in articular cartilage varies over the different structural zones, generating different tissue birefringence. Analyzing the slope of the accumulated phase retardation at different depths can detect the variation in tissue birefringence and be used to segment the structural zones. The method is validated on phantoms composed of layers of different materials. Articular cartilage samples from adult swine are segmented with the method. The characteristics in each segmented zone are also examined by histology and high-resolution second-harmonic generation imaging, showing distinctive properties that match with the anatomical structure of articular cartilage. The segmentation algorithm is also applied on PS-OCT images acquired at multiple illumination angles, where the angular dependence of tissue birefringence in the deep zone is detected. This method offers a noninvasive imaging approach to differentiating the structural zones of articular cartilage, as well as a quantification approach based on the phase retardation measurements of PS-OCT. This method has great potential in studying depth-related progression of cartilage degeneration.

波片相位延迟量测量和快轴标定系统

波片相位延迟量测量和快轴标定系统

基于双弹光差频调制的中红外波片相位延迟高精度测量

基于双弹光差频调制的中红外波片相位延迟高精度测量

Phase retardation measurement of an arbitrary wave plate based on magneto-optical modulating and residue detecting of the base frequency component of the signal

Wave plates (WPs) are key components in optical polarization systems whose phase retardations should be measured accurately. The key point of most light extinction methods focuses on how to precisely judge the system's extinction state and then confirm corresponding angle positions of the optical components. Usually the extinction state of a measurement system is judged by detecting residue of outgoing light intensity. In this Letter, a method of measuring the phase retardation of an arbitrary WP based on magneto-optical modulation is proposed. A magneto-optical modulator is placed between the standard quarter-WP and the second polarizer on the basis of the traditional optical path. The measurement signal is obtained after the outgoing light passing through a band-pass filter whose center frequency is the same as the frequency of the magneto-optic modulator's driving voltage. This method detects the base frequency component instead of the whole intensity of the outgoing light, so as to get better judgement accuracy of the system's extinction state. The arbitrary WP's phase retardation can be accurately derived by detecting the residue of the base frequency component of the outgoing light signal and then judging the angle position of the second polarizer when the system is in the state of extinction. The corresponding theoretical formulas are deduced by the Jones matrix, and the WP measuring system is established. The error analysis shows that the system measurement uncertainty is about 4.5' if the experiment temperature varies in the range of 0.1°C. Experiment results on half-WPs and quarter-WPs show that the presented method is in good agreement with other methods. The measurement repeatability is also good, with the standard deviation about 2'.