Phase Retardation Measurement Research Articles

Time-resolved retardance and optic-axis angle measurement system for characterization of flexoelectro-optic liquid crystal and other birefringent devices.

A new polarimeter is presented which gives time-resolved measurements of both the optic-axis angle and the linear phase retardation for modulated birefringent optical devices. It is suitable for characterizing dynamic waveplate devices based on liquid crystal and other materials. It is fully automated and requires no angular alignment of the device under test. The system has an absolute angle error of < ± 0.3° and a retardance error of < ± 0.44°, with considerably better relative accuracy. The method has been tested with a chiral nematic liquid crystal device exhibiting flexoelectro-optic switching at 3 kHz in the uniform lying helix mode. These results represent the first time-resolved tilt-angle and phase retardation measurements for a liquid crystal device operating at fast switching frequencies.

Environment-noise-free optical heterodyne retardation measurement using a double-pass acousto-optic frequency shifter.

We demonstrate an environment-noise-free optical heterodyne interferometer (OHI) based on a double-pass acousto-optic frequency shifter (AOFS) for phase retardation measurements. The OHI generates intermediate-frequency (IF) heterodyne beat signals for each orthogonal linear polarization mode of a birefringence sample. The phase differences of the IF signals are compared by using a wide-bandwidth lock-in amplifier. This scheme provides 20dB rejection of common-mode environmental disturbances. Measurements of the half-wave voltage of an electro-optics modulator and the electro-optic coefficient of an LiNbO3 plate are demonstrated as application examples.

Measurement of phase retardation of optical multilayer films based on laser feedback system

The phase property of optical films is becoming a new research focus in optoelectronics. The retardation caused by reflection on multilayer optical films can be utilized to make phase retarders and modulate the polarization state of optical systems. In this paper, a novel method based on laser feedback is presented to measure the retardance. The laser feedback system can realize fast and stable measurement with high accuracy. Two samples of K9 glass covered with different multilayer optical films are measured at different angles of incidence. The results show that the retardance is sensitive to the incident angle and can provide guidance for the usage of reflective optical films.

Generation of phase difference between self-mixing signals in a-cut Nd:YVO₄ laser with a waveplate in the external cavity.

We present a novel method using Nd:YVO4 laser with a waveplate in the external cavity to generate two orthogonally polarized signals with stable and adjustable phase difference. The phase difference is observed in the presence of external interference, and it is determined by the phase retardation of the waveplate. A model based on birefringent external-interference effect is proposed to theoretically explain the phase difference phenomenon, and the arithmetic solution of the relation between the phase difference and the phase retardation of waveplate is given. The simulated results accord with the experimental phenomena. This Letter provides the possibility for the measurement of phase retardation and also offers guidance to the design of interferometers based on fringe counting technique.

Repeatability of corneal phase retardation measurements by polarization-sensitive optical coherence tomography.

Polarization-sensitive optical coherence tomography (PS-OCT) can evaluate internal tissue structures of the cornea, such as collagen fibers, by phase retardation measurement. In this study, we assessed the repeatability of corneal phase retardation measurements using anterior segment PS-OCT. A total of 173 eyes of 173 patients were measured using PS-OCT. In total, 58 eyes of young subjects with normal corneas, 28 eyes of old subjects with normal corneas, 26 eyes with corneal dystrophy or degeneration, 37 eyes with corneal transplantation, and 24 eyes with keratoconus were evaluated. The 3-mm diameter average of en face phase retardation of the posterior corneal surface was examined using PS-OCT. To evaluate the repeatability, intraclass correlation coefficients (ICCs) were calculated for intraobserver repeatability and interobserver repeatability analysis. Polarization-sensitive OCT showed good repeatability for corneal measurements. Intraclass correlation coefficients of intraobserver and interobserver repeatability of all the subjects were 0.989 and 0.980, respectively. Intraclass correlation coefficients of the intraobserver for each group, that is, young and old subjects with normal cornea, cornea dystrophy/degeneration, corneal transplantation, and keratoconus, were 0.961, 0.975, 0.984, 0.978, and 0.996, respectively. Interobserver ICCs for the above-mentioned respective groups were 0.952, 0.964, 0.988, 0.959, and 0.975, respectively. Polarization-sensitive OCT showed good repeatability for phase retardation measurements of central corneas not only for normal corneas, but also for various diseased corneas. Polarization-sensitive OCT might be useful for evaluating corneal phase retardation, which is one of the parameters that defines birefringence.

A Simple Method to Measure Pretilt Angles of Inverse Twisted Nematic Liquid Crystal Cells

We have developed a simple optical method based on measurements of phase retardation versus out-of-plane cell rotation angle and data analyzed by extended Jones matrix method to obtain pretilt angles of inverse twisted nematic (ITN) and tilted homeotropic liquid crystal (LC) cells. In our Jones-matrix calculations, we have assumed a constant pretilt angle as the LC-director tilt angles throughout the ITN cell as well as the tilted homeotropic cell. We have compared the measured pretilt angles of the ITN cell with those of an accompanying tilted homeotropic (ATH) cell. The results showed increasing discrepancies between them with increasing rubbing depth for LC alignments. However, these discrepancies could be explained by assuming that the surface-LC tilt angle of the ITN cell was equal to the measured pretilt angle of the ATH cell to generate a convex-type LC-director-deformation profile within the ITN cell based on Oseen-Frank elastic continuum theory with infinite anchoring energies. The average of the LC-director tilt angles over this profile was equivalent to the measured pretilt angle of the ITN cell.

Elimination of the measurement error induced by piezoelectric ceramic nonlinearity in phase retardation measurement

We introduce a displacement measurement system based on the isotropic optical feedback technique to measure length variations in the feedback cavity. The principle of the system is based on frequency shifting and heterodyne phase-measuring. Using this system, displacements of some feature points in the intensity output of the laser such as polarization switching are measured. Based on the measured results, a linear relation is established between the position of the polarization switching and the anisotropy. This forms the basis of future applications of the polarization control technique in the field of optical measurement.

Note: error elimination for ellipsometry by laser feedback instrument.

Ellipsometry has in recent decades been used in measuring optical phase retardation. Known for its high resolution but uncertain accuracy, we analyze the systematic error involved with this technique and give error values regarding phase retardation measurements. We developed a laser-feedback assembly to measure phase retardation to a higher resolution and accuracy compared with that from ellipsometry. We eliminated the systematic error associated with ellipsometry using results obtained with this assembly and improved measurement accuracies for ellipsometry to about 0.2°. Such high-precision ellipsometry would greatly improve the manufacturing of wave plates.

Methods for optical phase retardation measurement: A review

Optical-phase-retardation elements are widely used in many fields. Accurate measurement of their phase retardation is crucial to the practical effect of the element’s processing and application. The development and present situation of the methods for optical phase retardation measurement are reviewed, with the wave plate, the most typical phase-retardation element, as an example. The latest research progress in this field is introduced; the principles and characteristics of individual measurement method are summarized and discussed. Three new methods based on laser frequency splitting or laser feedback are presented in detail, in which the laser is not only regarded as a light source but also plays a role of sensor. Moreover, no standard wave plates are needed and arbitrary phase retardation can be measured. Traceability, high precision and high repeatability are achieved as well.

Multi-Wavelength Conversion Based on Single Wavelength Results in Phase Retardation Measurement

We introduce an instrument for single wavelength measurement of phase retardation based on the laser feedback phenomenon. A method of multi-wavelength conversion for this instrument is proposed and the conversion results are analyzed. System calibration is used to eliminate the conversion error. The experimental results show that the maximum error after conversion is 0.26°. Through the present work, the application of laser feedback instrument for single wavelength measurement of a wave plate is expanded to the multi-wavelength range. This will expand the application area of the instruments.

Measuring Stress in Si Ingots Using Linear Birefringence

We report near infrared (NIR) linear birefringence measurements on shaped and surface finished Czochralski (CZ) - grown silicon ingots. The linear birefringence was measured using a commercially available NIR system. All measurements were done with the NIR beam configured parallel to one of the <100> directions of silicon. Stress- optic coefficient values of silicon were used to calculate the residual stress from phase retardation values. Two- dimensional scans were performed along flat surface, i.e. the crystallographic [001] and [010] directions. Examples of both, higher and lower stressed Si ingots are presented. Due to the large diameter of silicon ingots, stress resolution and stress detection limits are much enhanced for ingots than for silicon wafer. Phase retardation measurements for most ingots showed only low stress distribution of <30kPa. However, some ingot sections show stress as high as nearly 1.0MPa.

POLARIZATION-SENSITIVE OPTICAL COHERENCE TOMOGRAPHY USING A MODIFIED BALANCE DETECTOR

In conventional polarization-sensitive optical coherence tomography (PS-OCT), phase retardation is obtained by the amplitude of P and S polarization only, and the fast axis angle is obtained by the phase difference in P and S polarizations via Hilbert transformation. In this paper, we proposed a modified PS-OCT setup in which the phase retardation and fast axis angle are simply expressed as the function of the amplitude of P and S polarization and their differential signal. Due to the common-path feature between the two channels of P and S polarization, the fluctuation in the measurement of phase retardation and fast axis angle caused by excess noise and phase noise from the laser source can be reduced by the differential signal of P and S polarization via a modified balance detector. Thus, the signal of phase retardation and fast angle axis in the deep layer of a porcine sample can be improved.

Semi-classical theory and experimental research for polarization flipping in a single frequency laser with feedback effect

In this paper, we propose a semi-classical theory to successfully explain the polarization flipping in a single frequency laser. An experimental setup is built to verify this theory. The observed experimental phenomena are consistent with the theoretical analysis. We perform phase retardation measurements of birefringent components using this experimental system. The results show that the measurement repeatability is 0.12° and the measurement accuracy is 0.22°.

Phase retardation measurement by analyzing flipping points of polarization states in laser with an anisotropy feedback cavity

Phase retardation of wave plate is measured by analyzing flipping points of polarization states. Measured result and system error are analyzed. Nonlinearity of piezoelectric ceramic is an important error source. The nonlinearity is measured with an interferometer based on microchip Nd:YAG laser feedback phenomenon. The measured system of phase retardation, in this paper, is calibrated to the frequency splitting system. The accuracy of the system is improved. The measurement repeatability is better than 0.12° and the accuracy is better than 0.22°. This paper has a very important significance for wave plate high precision manufacture.

Measurement of phase retardation of waveplate online based on laser feedback

Polarization flipping accompanying with intensity transfer between two eigenstates of one laser mode happens when waveplate is placed in external cavity. The position of polarization flipping of two eigenstates is a function of phase retardation of waveplate. Phase retardation of waveplate is measured through analyzing the position of polarization flipping of two eigenstates. The measurement accuracy of phase retardation is 0.22°. A new structure of optical cement tray which can eliminate stress birefringence from optical cement process is invented. The accuracy of waveplate manufacture can be improved greatly based on the work of this article.

自校准法测量波片相位延迟

自校准法测量波片相位延迟

Monte-Carlo-based phase retardation estimator for polarization sensitive optical coherence tomography

A Monte-Carlo-based phase retardation estimator is developed to correct the systematic error in phase retardation measurement by polarization sensitive optical coherence tomography (PS-OCT). Recent research has revealed that the phase retardation measured by PS-OCT has a distribution that is neither symmetric nor centered at the true value. Hence, a standard mean estimator gives us erroneous estimations of phase retardation, and it degrades the performance of PS-OCT for quantitative assessment. In this paper, the noise property in phase retardation is investigated in detail by Monte-Carlo simulation and experiments. A distribution transform function is designed to eliminate the systematic error by using the result of the Monte-Carlo simulation. This distribution transformation is followed by a mean estimator. This process provides a significantly better estimation of phase retardation than a standard mean estimator. This method is validated both by numerical simulations and experiments. The application of this method to in vitro and in vivo biological samples is also demonstrated.

Birefringence measurement of the retinal nerve fiber layer by swept source polarization sensitive optical coherence tomography

A Swept Source Polarization-Sensitive Optical Coherence Tomography (SS-PS-OCT) instrument has been designed, constructed, and verified to provide high sensitivity depth-resolved birefringence and phase retardation measurements of the retinal nerve fiber layer. The swept-source laser had a center wavelength of 1059 nm, a full-width-half-max spectral bandwidth of 58 nm and an A-line scan rate of 34 KHz. Power incident on the cornea was 440 µW and measured axial resolution was 17 µm in air. A multiple polarization state nonlinear fitting algorithm was used to measure retinal birefringence with low uncertainty. Maps of RNFL phase retardation in a subject measured with SS-PS-OCT compare well with those generated using a commercial scanning laser polarimetry instrument. Peak-to-valley variation of RNFL birefringence given here is less than values previously reported at 840nm.

基于最小二乘拟合的波片相位延迟测量

基于最小二乘拟合的波片相位延迟测量

Precise measurement of optical phase retardation of a wave plate using modulated-polarized light

We propose a new method for precisely measuring the optical phase retardation of a wave plate using modulated-polarized light. Modulated-polarized light is used such that the zeros of the system can be accurately determined. A Babinet-Soleil compensator is employed to measure the optical phase retardation. A cross-wavelength measurement is also proposed for determining the phase retardation at a wavelength, which is not the measuring wavelength.