Phase Retardation Measurement Research Articles

Fiber-based single-channel polarization-sensitive spectral interferometry

We present a novel, to our knowledge, fiber-based single-channel polarization-sensitive spectral interferometry system that provides depth-resolved measurement of polarization transformations of light reflected from a sample. Algebraic expressions for the Stokes parameters at the output of the interferometer are derived for light reflected from a birefringent sample by using the cross-spectral density function. By insertion of a fiber-optic spectral polarimetry instrument into the detection path of a common-path spectral interferometer, the full set of Stokes parameters of light reflected from a sample can be obtained with a single optical frequency scan. The methodology requires neither polarization-control components nor prior knowledge of the polarization state of light incident on the sample. The fiber-based single-channel polarization-sensitive spectral interferometer and analysis are demonstrated by measurement of phase retardation and fast-axis angle of a birefringent mica plate.

Spatial refractive index measurement of porcine artery using differential phase optical coherence microscopy

We describe a methodology to record spatial variation of refractive index of porcine renal artery using differential phase optical coherence microscopy (DP-OCM). The DP-OCM provides quantitative measurement of thin specimen phase retardation and refractive index by measuring optical path-length changes on the order of a few nanometers and with a lateral resolution of 3 microm. The DP-OCM instrumentation is an all-fiber, dual-channel Michelson interferometer constructed using a polarization maintaining (PM) fiber. Two-dimensional en face dual-channel phase images are taken over a 150 x 200 microm region on a microscopic slide, and the images are reconstructed by plotting a two-dimensional refractive index map as the OCM beam is moved across the sample. Because the DP-OCM can record transient changes in the optical path-length, the system may be used to record quantitative optical path-length alterations of tissue in response to various stimuli. A fiber-based DP-OCM may have the potential to substantially improve in vivo imaging of individual cells for a variety of clinical diagnostics, and monitoring applications.

P-140: Simultaneous Phase Retardation and Optic Axis Measurements of A- and C-Plates

We demonstrate a new method for simultaneously measuring the phase retardation and optic axis of a compensation film by using an axially-symmetric sheared polymer network liquid crystal (AS-SPNLC). With overlaying a tested compensation film with a calibrated AS-SPNLC cell between crossed polarizers, the optic axis and phase retardation value of the compensation film can be determined. This method is applicable to both A- and C-plate phase compensation films.

Polarization-Sensitive Optical Coherence Tomography using only Linearly Polarized Light

This work presents polarization-sensitive optical coherence tomography (PS-OCT) using only linearly polarized light. The main characteristics of linear PS-OCT include the following. (1) In a turbid medium with linear birefringence, the degree of polarization (DOP) of backscattered linearly incident polarized light does not change significantly with the increase of birefringence value; (2) the phase retardation of the sample can be obtained from only the phase difference between the orthogonal polarization heterodyne signals, so a common phase noise rejection mode is introduced. These advantages may not only support the immunity of background phase noise and laser frequency noise, but also increase the sensitivity of phase retardation measurements; (3) the dynamic range of phase retardation in this system is between 0° and 180°

A novel method to measure the cell gap and pretilt angle of a reflective liquid crystal display

A powerful method for the phase retardation measurement of a reflective liquid crystal cell is presented. The proposed method is based on the heterodyne interferometer theory for probing cell parameters. Due to common-path optical arrangement, a fast measurement with high accuracy and sensitivity was possible. Both theoretical analysis and experimental procedures are presented. The experimental results agree well with that obtained theoretically.

Orthogonal linear polarized lasers(III)—Applications in self-sensing*

Abstract In this paper, the applications of orthogonal linear polarized lasers in self-sensing are reviewed. The properties for such a laser include the production of new frequency in one longitudinal mode spacing, the tuning of frequency difference, the change of polarization states as cavity turning, the control of mode competition intesity, the optical feedback, and so on. The orthogonal polarized lasers have been used as a laser nanometer ruler based on competition between two polarized lights in a HeNe laser and as a displacement measurement tool based on the optical feedback in the orthogonal polarized lasers. They are also used in the phase retardation measurement of a waveplate, the angle measurement, the vibration measurement, the pressure/force measurement, theweak magnetic field measurement, and so on. The structures of these new divices are simple and compact with the great advantages of high resolution and hight accuracy. Some of these divices can trace to the source of the laser wavelength. Thenanometer laser ruler is an example whose measurement range is 12mm, resolution is 79nm and linearity is less than 5 ×10−5. The repeatability of the phase retardation measuring system of waveplate can reach 3′

Simultaneous measurement of phase retardation and optic axis of a phase compensation film using an axially-symmetric sheared polymer network liquid crystal

A new method for simultaneously measuring the phase retardation and optic axis of a uniaxial compensation film is demonstrated using an axially-symmetric sheared polymer network liquid crystal (SPNLC). By overlaying a tested compensation film with a calibrated SPNLC cell between crossed polarizers, two dark spots are clearly observed in a CCD image. From the orientation direction and distance of these two spots, the optic axis and phase retardation value of the compensation film can be determined. This method is particularly useful for those optical systems whose optic axis and phase retardation are dynamically changing.

Depth-resolved phase retardation measurements for laser-assisted non-ablative cartilage reshaping

Since polarization-sensitive optical coherence tomography (PS-OCT) is emerging as a new technique for determining phase retardation in biological materials, we measured phase retardation changes in cartilage during local laser heating for application to laser-assisted cartilage reshaping. Thermally-induced changes in phase retardation of nasal septal cartilage following Nd:YAG laser irradiation were investigated using a PS-OCT system. A PS-OCT system and infrared imaging radiometer were used to record, respectively, depth-resolved images of the Stokes parameters of light backscattered from ex vivo porcine nasal septal cartilage and radiometric temperature changes following laser irradiation. PS-OCT images of cartilage were recorded before (control), during and after laser irradiation. From the measured Stokes parameters (I, Q, U and V), an estimate of the relative phase retardation between two orthogonal polarizations was computed to determine birefringence in cartilage. Phase retardation images of light backscattered from cartilage show significant changes in retardation following laser irradiation. To investigate the origin of retardation changes in response to local heat generation, we differentiated two possible mechanisms: dehydration and thermal denaturation. PS-OCT images of cartilage were recorded after dehydration in glycerol and thermal denaturation in heated physiological saline. In our experiments, observed retardation changes in cartilage are primarily due to dehydration. Since dehydration is a principal source for retardation changes in cartilage over the range of heating profiles investigated, our studies suggest that the use of PS-OCT as a feedback control methodology for non-ablative cartilage reshaping requires further investigation.

Simultaneous Measurement of Phase Retardation and Fast-Axis Angle of Phase Retardation Plate

A phase retardation plate, such as a quarter-wave plate, is able to control the state of polarization. Thus, a precise simultaneous determination of phase delay between two eigen-polarization states and its fast-axis angle is essential to the performance of the phase retardation plate to control the state of polarization. Consequently, the measurement of the two-dimensional spatiotemporal distribution of phase retardation and the fast-axis angle become crucial when a large-area of phase retardation plate, such as that for a liquid crystal display, is characterized, due to the inhomogeneity of the retardation plate. In order to measure the linear birefringence parameters, phase retardation and fast-axis angle at the same time, a novel polarized optical heterodyne interferometer is developed, with which the parameters of a quarter-wave plate are successfully measured and verified. The features of this device are (1) a common-path configuration, (2) measurement independent of laser intensity, and (3) the capability of simultaneously determining the spatiotemporal distributions of phase retardation and fast-axis angle of a retardation plate.

Polariscope for simultaneous measurement of the principal axis and the phase retardation by use of two phase-locked extractions

A novel polariscope with electro-optic modulation that is capable of simultaneous measurement of the principal axis and the phase retardation of an optical linear birefringent medium by means of two phase-locked extractions is described. A phase compensator is used to suppress the transmission phase-retardation effect of the beam splitter, thereby enhancing the precision of the measuring performance. The validity of the proposed design is demonstrated by measurement of the principal axis and phase retardation of a quarter-wave plate sample. There are absolute errors of 0.25 degrees on average and 0.58 degrees at maximum in the principal-axis measurement and of 0.75 degrees (0.83%) on average and 3.11 degrees at maximum in the phase-retardation measurement. Meanwhile, the retardation error lies within a 5% uncertainty range of a commercial wave plate. The root-mean-square resolutions for the principal-axis angle and phase-retardation measurements are 0.042 degrees and 0.081 degrees, respectively. Finally, the dynamic ranges of the principal-axis angle measurement and the phase-retardation measurement extend as far as 180 degrees.

Measurements of phase retardation and principal axis angle using an electro-optic modulated Mach–Zehnder interferometer

This paper presents an electro-optic modulated circular heterodyne modified Mach–Zehnder interferometer and a convenient two-phase signal-processing algorithm for the measurement of variations in the magnitude of phase retardation and the angle of principal axis in optical materials. The developed method solves the problems of normalized intensity jump and limited phase retardation measurement range associated with the circular heterodyne interferometer proposed previously. The present method uses a saw-tooth wave signal to drive an electro-optic (EO) modulator, and employs a lock-in amplifier to demodulate the principal axis angle and the phase retardation. Specifically, this paper considers two main sources of measurement errors, namely the misorientation of the EO modulator and the reflection phase retardation of the beam splitter. Furthermore, the study develops calibration procedures and identifies a means to minimize measurement errors induced by the reflection phase retardation of the beam splitter.

Thickness and birefringence of healthy retinal nerve fiber layer tissue measured with polarization-sensitive optical coherence tomography.

Thinning of the retinal nerve fiber layer and changes in retinal nerve fiber layer (RNFL) birefringence may both precede clinically detectable glaucomatous vision loss. Early detection of RNFL changes may enable treatment to prevent permanent loss of vision. Polarization-sensitive optical coherence tomography (PS-OCT) can provide objective information on RNFL thickness and birefringence. PS-OCT scans around the optic nerve head (ONH) of two healthy young volunteers were made using 10 concentric circles of increasing radius. Both the mean RNFL thickness and mean retinal nerve fiber birefringence for each of 48 sectors on a circle were determined with data analysis. Both the RNFL thickness and birefringence varied as a function of sector around the ONH. The RNFL became thinner with increasing distance from the ONH. In contrast, the birefringence did not vary significantly as a function of radius. Birefringence of healthy RNFL is constant as a function of scan radius but varies as a function of position around the ONH, with higher thickness values occurring superior and inferior to the ONH. Measured double-pass phase retardation per unit depth around the ONH ranged between 0.10 and 0.35 deg/microm, equivalent to birefringences of 1.2 x 10(-4) and 4.1 x 10(-4) respectively, measured at a wavelength of 840 nm. Consequently, when a spatially constant birefringence around the ONH is assumed, the conversion of scanning laser polarimetry (SLP) phase-retardation measurements to RNFL thickness may yield incorrect values. The data do not invalidate the clinical value of a phase-retardation measurement, but affect the conversion of phase retardation to RNFL thickness.

The new circular polariscope and the Senarmont setup with electro-optic modulation for measuring the optical linear birefringent media properties

The new common-path circular polariscope and the Senarmont setup with electro-optic modulation for measuring the optical linear birefringent media properties are presented. It enables the measurement of not only the phase retardation but also the principal axis angle. The measurement procedure is carried out in two setups. In the first one, we use the electro-optic modulated circular heterodyne interferometer and the phase-lock technique to precisely measure the principal axis angle. After removing the first quarter-wave plate in the first setup, a Senarmont setup is designed to determine the phase retardation also using the phase-lock technique. The simple phase extraction algorithm for the principal axis angle and the phase retardation measurement is presented. The root-mean-square resolutions for the principal axis angle and phase retardation are found to be 0.0247° and 0.0304°, respectively, with corresponding dynamic ranges of 0–180° and 0–90°.

A compact circular heterodyne interferometer for simultaneous measurements of variation in the magnitude of phase retardation and principal axis angle

This paper presents a compact configuration for simultaneous measurements of variation in the magnitude of phase retardation and principal axis angle in optical materials. The configuration comprises a circular heterodyne common-path interferometer, in which a sawtooth voltage waveform is used to regulate an electro-optic (EO) modulator. Changes in phase retardation and in the angle of the principal axis are demodulated by a lock-in amplifier via a simple signal-processing algorithm. Compared to the conventional configurations, the proposed interferometer offers an easier setup, has only one detection channel, and employs a simpler signal-processing operation. The validity of the proposed measurement system is demonstrated using a quarter-wave plate as a sample. The results indicate that the average absolute errors of the phase retardation and principal axis angle of quarter-wave plate are 4.88% and 0.94°, respectively. Furthermore, the root-mean-square resolutions of the magnitude of phase retardation and the principal axis angle are shown to be 1.59° and 0.10°, respectively. The dynamic range of phase retardation measurement is up to 90° and that of the principal axis angle measurement is up to 180°.

Simultaneous absolute measurements of principal angle and phase retardation with a new common-path heterodyne interferometer.

This study demonstrates a new method for simultaneously measuring both the angle of the principal axis and the phase retardation of the linear birefringence in optical materials. We used a circular common-path interferometer (polariscope) as the basic structure modulated by an electro-optic (EO) modulator. An algorithm was developed to simultaneously measure the principal axis and the phase retardation of a lambda/4 or lambda/8 plate as a sample. In the case of a lambda/4 plate, the average absolute error of the principal axis is approximately 3.77 degrees, and that of the phase retardation is approximately 1.03 degrees (1.09%). The retardation error is within the 5% uncertainty range of a commercial wave plate. Fortunately, the nonlinear error caused by the reflection phase retardation of the beam splitter dose not appear in the new system. Therefore the error could be attributed to misalignment and defects in the EO modulator or the other optical components. As for the repeatability of this new common-path heterodyne interferometer, the average deviation for the principal axis is 0.186 degrees and the phase retardation is 0.356 degrees. For the stability, the average deviation for the principal axis is 0.405 degrees and the phase retardation is 0.635 degrees. The resolution of this new system is estimated to be approximately 0.5 degrees, and the principal axis and phase retardation could be measured up to pi and 2pi, respectively, without ambiguity.

Kerr effect in gas and its application to noncontact measurement of electric field

A noncontact measurement of electric field is proposed based on the Kerr effect in gases. With the Kerr sensing technique, the electric field can be measured without causing any field disturbance. Kerr constants of gases are, however, very small compared with those of liquids, and this ideal technique has not been applied to electric field measurement in gas. In this study, a system is developed for a highly sensitive measurement of the small phase retardation caused by the Kerr electro-optic effect in gases. An optical phase modulation technique is effectively adopted to improve the sensitivity of the system. With this optical system, (i) dc stressed uniform electric fields in sulfur hexafluoride, nitrogen, and carbon dioxide gases at the pressure of 0.2–0.5 MPa and (ii) ac stressed uniform electric fields in atmospheric air are measured.

Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates

The modification of the Senarmont compensator is presented. It uses standard simple and reverse Senarmont setups, however, the phase retardances of unknown medium as well as the element used as a quarterwave plate in classical setups could be measured. It leads to conclusion that retardations of two unknown elements could be obtained and no calibrated quarter wave plate is needed.

Photoinduced Birefringence in Poly(malonic ester) Containing p-Cyanoazobenzene with Photoexcitation of cis Conformer

Photoinduced birefringence in a poly(malonic ester) containing two symmetrical p-cyanoazobenzene groups has been investigated using two pumping beams with different wavelengths of 365 and 488 nm, which are assignable to the absorption wavelengths of trans and cis conformers of azobenzene, respectively. We observed unexpected photoinduced birefringence even by the pumping beam of 488 nm as large as that by 365 nm. To describe such specific phenomenon, we measured the magnitude and direction of the induced birefringence by means of a new experimental setup, adding I/4 waveplate between the polymer film and the analyzer of conventional a pair of crossed polarizers setup. The measurement of the photoinduced phase retardation by simultaneous illumination with two perpendicularly polarized beams of 365 and 488 nm supports the fact that there is another process for the photoinduced birefringence besides a typical trans -cis photoisomerization of azobenzene.

Photoalignment of liquid crystals by liquid crystals

We observed light-induced alignment of the nematic liquid crystal, 4, 4(')-n-pentylcyanobiphenyl (5CB), on a fused quartz. Irradiation of the adsorbed layer with polarized ultraviolet light produced homogeneous alignment in a 5CB-filled liquid crystal cell with the easy orientation axis perpendicular to the polarization direction. The measured anchoring energy increases with illumination up to 10(-4) erg/cm (2). Phase retardation and pretilt measurements confirmed near homogeneous alignment of the LC in a cell, while the polarization dependence of second harmonic generation suggested a near normal alignment of the adsorbed layer. We believe that light-induced rearrangement or phototransformation of the adsorbed layer causes the observed phenomenon.

Nematic polar anchoring strength measured by electric field techniques

We analyze the high-electric-field technique designed by Yokoyama and van Sprang [J. Appl. Phys. 57, 4520 (1985)] to determine the polar anchoring coefficient W of a nematic liquid crystal-solid substrate. The technique implies simultaneous measurement of the optical phase retardation and capacitance as functions of the applied voltage well above the threshold of the Frederiks transition. We develop a generalized model that allows for the determination of W for tilted director orientation. Furthermore, the model results in a new high-field technique, (referred to as the RV technique), based on the measurement of retardation versus applied voltage. W is determined from a simple linear fit over a well-specified voltage window. No capacitance measurements are needed to determine W when the dielectric constants of the liquid crystal are known. We analyze the validity of the Yokoyama–van Sprang (YvS) and RV techniques and show that experimental data in real cells often do not follow the theoretical curves. The reason is that the director distribution is inhomogeneous in the plane of the bounding plates, while the theory assumes that the director is not distorted in this plane. This discrepancy can greatly modify the fitted value of 1/W, and even change its sign, thus making the determination of W meaningless. We suggest a protocol that allows one to check if the cell can be used to measure W by the YvS or RV techniques. The protocol establishes new criteria that were absent in the original YvS procedure. The results are compared with other data on W, obtained by a threshold-field technique for the same nematic-substrate pair.