Mapping local retardance in birefringent samples using polarization sensitive optical coherence tomography

We proposed a method to extract depth-resolved local retardance in birefringent samples from conventional polarization-sensitive optical coherence tomography (PSOCT) that uses one circularly polarized incident light. Despite the wide use of such PSOCT systems in characterizing birefringent samples, the measured cumulative retardance does not represent the true cumulative retardance when optical axis varies with depth. A Jones calculus based algorithm was designed to derive the local depth-resolved retardance from conventional cumulative PSOCT results. The algorithm was tested in samples with homogeneous optical axis as well as samples with depth-dependent optical axis.     

Simple system for evaluating retardation of liquid crystal cells using grating type liquid crystal polarization splitters

We propose a unique optical system for measuring the retardation of birefringent films using a pair of liquid crystal (LC) gratings; that is, the examined birefringent films are inserted between two LC gratings. Because the LC grating functions as a polarization beam splitter for circularly polarized light, the proposed system is optically equivalent to the measurement system using a pair of two circular polarizers. First, the polarization splitting performance of the LC grating is discussed. It is found that a sufficiently high voltage (such that the retardation is less than a half wavelength) has to be applied for the almost pure circularly polarized diffracted light. Next, the measurement of the retardation of a homogeneous LC cell as an examined birefringent film was demonstrated using the proposed method. The proposed method is revealed to have the same measurement performance as that of the conventional method using a pair of linear polarizers and has an advantage that there is no need for the optic axis of the test birefringent specimen to be set at a specific angle.     

双折射调谐器设计的等色图原理

提出双折射调谐器设计的等色图方法，给出原理。分析表明当晶片光轴处在以折射光线为轴线、顶角为４５°的圆锥面上时，双折射调谐器具有最快的波长调谐速率；当光轴位于过折射光线并与入射面成４５°或１３５°的平面内时，调谐器抑制非所需波长的能力最强。由此给出光轴相对晶片表面的两个优化取向，对石英晶片它们分别为１８．７１２°和５９．９２２°。文中还给出了三块晶片组合的调谐器的设计例子，对其调谐特性进行了简要的讨论。     

Polychromatic intensity point spread function of a birefringent lens

We study the intensity point spread function (IPSF) of a uniaxial birefringent lens sandwiched between two linear polarizers under broadband illumination having flat-top spectral profile. The optic axis of the birefringent crystal is perpendicular to the lens axis. For monochromatic input illumination, a low-power birefringent lens offers enhanced resolution under parallel-polarizers configuration and apodization under crossed-polarizers configuration with a single focus as well. At a relatively high value of birefringence parameter, the proposed system behaves as a double-focus lens. The present communication uses a novel technique to study the effect of polychromatic illumination on the imaging characteristics of birefringent lenses. The studies reveal that the imaging characteristics of the low-power birefrigent lens does not deteriorate considerably under polychromatic illumination. However, for a polychromatic beam with large bandwidth, the imaging behavior of the system having high birefringence parameter deviates appreciably from that under strictly monochromatic illumination. The said system even loses its inherent bi-focal nature due to depolarization of polarized polychromatic light upon passage through the birefringent crystal.     

Effect of the orientation of the optic axis on simulated scattering matrix elements of small birefringent particles

We study how the orientation of the optic axis affects single-scattering properties for small, birefringent calcite particles simulated using DDSCAT 7.1.1. We consider two irregular model particles, a flake and a rhomboid, in either a (i)?fixed or (ii)?random orientation. Simulations are performed for three volume-equivalent radii of 0.1, 0.45, and 1.0?μm. For each target, we repeat the computations for three sets of orientations of the optic axis. When a fixed spatial orientation of the target is considered, the simulations are significantly affected by the orientation of the optic axis. However, the effect is considerably weaker when assuming the same targets in random spatial orientation.     

Evaluation of polychromatic image quality of a birefringent lens by means of optical transfer function

Polychromatic or white-light optical transfer function (OTF) is put forward as a criterion to evaluate the performance of a uniaxial birefringent lens sandwiched between two linear polarizers. The optic axis of the birefringent crystal is perpendicular to the lens axis. The results show that the same system may be adapted for both enhanced resolution and apodization just by rotating any of the polarizers included in the system even under broadband illumination. The proposed system may also be exploited for image processing applications under polychromatic input illumination.     

Optimum design of birefringent filter

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Light transmission in inhomogeneous birefringent medium as a function of propagation and observation angles

We use the Mueller matrix for inhomogeneous linear birefringent media derived in Savenkov et al. [Mueller-matrix model of an inhomogeneous linear birefringent medium: single scattering case. JQSRT 2007;106:475–86] to generate new results on the forward scattering of light using Cloude's coherence matrix method. We show that the intensity of scattered light (m₁₁) as a function of observation angle depends on the difference between refractive indices along the eigen polarizations resulting in intensity lost when unpolarized light propagates parallel to the optical axes compared to propagation orthogonal to the optical axis. For a given inhomogeneity (roughness), depolarization strongly depends on the direction of light propagation in the medium. The depolarization at 90° propagation angle is minimal for any value of inhomogeneity. Sample calculations are based on calcite.     

A sensitive method of determining optic axis azimuth based on laser feedback

A sensitive method to determine the optic axis azimuth of the birefringence element is presented, which is based on laser feedback. The phase difference between the two intensities in birefringence feedback changes with the angle between the optic axis of the birefringence element and laser original polarization. The phase difference is highly sensitive to the relative position of the optic axis and the laser original polarization. This method is used to highly precisely determine the optic axis azimuth, and is able to distinguish between the fast axis and the slow axis of the birefringence element. Theoretical analysis and experimental results are both demonstrated.     

A new type Lyot filter insensitive to incident angle

The shifting direction of a central wavelength for a quartz birefringent filter is found different when the filter is rotated around the axis parallel and perpendicular to the quartz optical axis in this paper. Based on this result, a new type of two-stage modified-Lyot quartz filter is presented, which show that the central wavelength of this new type Lyot filter is actually insensitive to incident angle through theory analysis when incident angle is less than 18°, and the maximum transmission decrease only about 66% compared to normal incidence. Moreover, this conclusion is in good agreements with relative experiment results.     

光学玻璃应力双折射叠加

为解决在光学玻璃应力双折射测量中遇到的双折射叠加问题,利用光学等效原理,使用一个线性双折射模型和一个旋转器来代替叠加模型。对叠加的情况做了分析和计算,得到了叠加后的特征延迟、主应力方向和旋转角随两个应力模型主应力方向夹角变化的曲线。理论分析表明,应力双折射叠加不是应力双折射的简单相加,而是与叠加模型各自的应力双折射值和主应力方向的夹角有关。实验结果与理论计算相吻合。应力双折射叠加对实际光学玻璃测试造成不良影响,使测量精度降低,特别是有透光支撑机构或折射液容器的情况下,应力双折射叠加的影响不可忽略。     

The Local-Sampling Phase Shifting Technique for Precise Two-Dimensional Birefringence Measurement

A precise method for measurement of two-dimensional birefringence distribution is described and discussed. This method can determine the relative retardation and the azimuthal angle of the fast axis in an optical component. In order to detect relative retardation with high resolution, a local-sampling phase shifting technique is proposed. This method can measure 256 × 256 values of the birefringent phase difference and azimuthal angle in a short time with ± 0.02 deg (0.03 nm) of retardation accuracy.     

Determination of the optical-axis orientation of a uniaxial crystal by frequency-domain interferometry

Frequency-domain interferometry has been used to find the optical axis of a uniaxial, birefringent crystal. The dependence of the interference fringe spacing on the incident angle and the direction of the optical axis were determined in a 4.6-cm-thick KDP crystal.     

高双折射光纤环镜改善40 GHz光时钟消光比的研究

时钟信号的好坏在同步、解复用和光判决中起着决定性的作用,双折射光纤环镜具有灵活可调的滤波特性,光时钟信号通过双折射环形镜可以使其消光比得到改善,从而提高时钟信号的质量。为此提出了利用高双折射光纤环形镜提高光时钟信号消光比的方案,数值上模拟了环形镜透射谱随双折射器件偏振延时量(Δt)、偏振控制器快慢轴角度以及偏振控制器所引入光程差的变化而变化的情况,并理论分析了消光比不理想的时钟信号经过环形镜后的光谱形式。用法布里-珀罗滤波器提取的40 GHz时钟信号进行实验,时钟经过环形镜后消光比改善了13 dB,实验结果和理论模拟得到了很好的匹配。     

Optic axis determination accuracy for fiber-based polarization-sensitive optical coherence tomography

We present a generalized analysis of fiber-based polarization-sensitive optical coherence tomography with an emphasis on determination of sample optic axis orientation. The polarization properties of a fiber-based system can cause an overall rotation in a Poincaré sphere representation such that the plane of possible measured sample optic axes for linear birefringence and diattenuation no longer lies in the QU-plane. The optic axis orientation can be recovered as an angle on this rotated plane, subject to an offset and overall indeterminacy in sign such that only the magnitude, but not the direction, of a change in orientation can be determined. We discuss the accuracy of optic axis determination due to a fundamental limit on the accuracy with which a polarization state can be determined as a function of signal-to-noise ratio.     

Optical activity of a cadmium diphosphide crystal

We have experimentally studied the characteristic features of a laser beam, polarized at angles of ± 45° to the horizontal (vertical), passing through plates of varying thickness cut from a CdP₂ crystal and placed between crossed polarizers, as a function of their angle of rotation relative to the vertical axis. We show that a periodic variation in the intensity is connected with the variation in polarization of the laser beam. We have established that the laser beam remains linearly polarized not only when it passes through the sample along the optic axis, but also when it travels at up to a 17.5° angle to the optic axis. In this case, the specific rotation of the plane of polarization along the optic axis is 68.2 degrees/mm for a thicker plate and 83.3 degrees/mm for a thin plate. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 5, pp. 690–693, September–October, 2006.     

A quartz birefringent filter insensitive to incident angle

The shifting direction of a central wavelength for a quartz birefringent filter is found different when the filter is rotated around the axis parallel and perpendicular to the quartz optical axis in this paper. Based on this result, a new type of two-stage modified-Lyot quartz filter is presented, which shows that the central wavelength of this new type filter is actually insensitive to incident angle through theory analysis. Moreover, this conclusion is in good agreement with the relative experiment results.     

改进型基于径向双折射晶体的超分辨滤波器

改进了现有的基于径向双折射晶体的横向超分辨滤波器.通过调整偏振器的偏振方向和晶体光轴之间的夹角,改进的滤波器可以实现更广的超分辨可调范围,并且在相同的条件下,相对于现有的连续振幅型超分辨光瞳滤波器,超分辨性能和焦深都有较大提高.改进的超分辨滤波器,为实际应用提供了更多方便.     

Imaging characteristics of a birefringent lens under broadband illumination

This paper reports the imaging characteristics of an optical system consisting of a lens made of a uniaxial birefringent crystal sandwiched between two linear polarizers under polychromatic input illumination. The optic axis of the birefringent crystal is perpendicular to the lens axis and for an initial investigation, the spectral profile of the input beam is considered to be uniform for all wavelengths. The study reveals that if the variation of the birefringence parameters of the device with the wavelength is less, a larger bandwidth may be used without considerably deviating from the imaging characteristics under strictly monochromatic illumination. The nonlinear variation of birefringence with wavelength results in an asymmetric axial irradiance distribution. This obviates an optimal operating wavelength as well as a proper choice of the lens material. It is found that no appreciable change in image quality under diffraction-limited condition results for an input beam having 632 nm operating wavelength and 60 nm bandwidth. Therefore, it may be feasible to use this system with a white light source in conjunction with a wavelength-selective filter.