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Journal ArticleDOI

Measurement of birefringence using polarization phase-shifting Mach–Zehnder interferometer

01 Nov 2015-Optical Engineering (International Society for Optics and Photonics)-Vol. 54, Iss: 11, pp 113112-113112

AbstractAn interferometric method for quantitative evaluation of the magnitude and direction of birefringence of an arbitrarily oriented birefringent sample is developed and presented. The analysis shows that full-field analysis of a spatially varying birefringence is possible by suitably combining several interferogram frames obtained by varying the polarization parameters involved. The preliminary experimental result for a uniformly birefringent sample with a known direction of birefringence is presented. © 2015 Society of Photo-Optical Instrumentation Engineers

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Journal Article
TL;DR: The data support a positive relationship between spermatozoa with total SHBF in their head and increased DNA fragmentation.
Abstract: Sao Paulo State Univ UNESP, Botucatu Med Sch, Ctr Human Reprod Prof Franco Jr,Res Unit, Paulista Ctr Diag Res & Training,Dept Gynecol & O, Ribeirao Preto, Brazil

38 citations

Journal ArticleDOI
Abstract: In order to measure the transmission wavefront of laser rods and to improve the edge diffraction effect of small-aperture laser rods measured by Tayman or Fizeau interferometer, a variable-inclination Mach-Zehnder interferometer was proposed. The incident angle was changed by adjusting the tilting attitude of the phase shifting reflector, then the optical path difference was changed that the phase shift was introduced to the coherent light and the phase shifting interferometry was realized. The transmission wavefront of a laser rod (Nd:YAG) with the diameter of 6 mm and the length of 60 mm was measured by this interferometer, the peak-valley (PV) and root mean square (RMS) of the wavefront were 0.391λ and 0.056λ. The same laser rod was measured by ZYGO GPI XP interferometer, the peak-valley (PV) and root mean square (RMS) were 0.370λ and 0.064λ. The comparison results show that the interferometer can achieve high-precision detection of transmission wavefront of laser robs. The variable-inclination Mach-Zehnder interferometer has high phase-shifting precision and wide phase-shifting range, and the beam in the system can pass through the laser rod only once, which can suppress the multi-beam interference and improve the edge diffraction effect of the small-aperture laser rods.

5 citations


Additional excerpts

  • ...Opto-Electronic Engineering, 2020, 47(2): 190254 1 引 言 激光棒是固体激光器的核心工作物质,其透射波 前质量可以衡量激光棒的折射率非均匀性、两端面平 行差以及剩余应力等指标,直接影响了激光器输出激 光的模式和能量。美国检测与材料协会于 20 世纪 80 年代正式确立激光棒波前检测的标准方法,规定采用 干涉测量的方法,将待测激光棒放置于干涉腔中,并 通过干涉图标准判读方法进行相位解算。陈进榜等[1] 采用 LTY80 型棱镜干涉仪对小口径激光棒进行了测 量,讨论了干涉图与激光棒端面平行差的关系并详细 介绍了手工作图法获得波前畸变的分析过程。何勇等 [2]将移相干涉技术引入激光棒测量领域,采用改进的 泰曼-格林型光路并结合四步移相算法实现了 Ф5 mm 口径的激光棒波前畸变检测。吴志飞等[3]在斐索干涉 仪中对比了单双通法测量激光棒的优劣,并采用棱镜 反射单通方案测量了口径为 Ф6 mm 激光棒的透射波 前,有效提高了检测精度。 马赫-曾德尔干涉仪中参考光与测试光分光路传 输,可以独立调节并进行光程补偿,其属于单通干涉 仪即测试光单次透过被测件,扩展了干涉仪的测量范 围,避免了一般干涉仪中测试光束两次通过被测件引 入的回程误差和四次边缘衍射,对大像差、小口径的 被测对象,优势尤为突出。 马赫-曾德尔干涉仪中常用的波面恢复技术是基 于单帧干涉图的处理方法。Bone等[4]首先提出了二维 快速傅里叶变换方法,并用该方法对单幅载频干涉图 进行处理以提取相位信息[5]。然而,对于小口径的测 试件而言,增加条纹数量则意味着更大的倾斜角度, 导致相干光之间的夹角增大,引入较大回程误差[6], 在测量长度较长的小口径激光棒时,相干光之间的剪 切量增大,导致较大的波前遮拦,加剧边缘衍射效应。 在移相干涉测量技术中,压电陶瓷晶体(PZT)是最 为常见的移相器件[7],在适当的电压作用下,压电陶 瓷产生微米量级的微位移,驱动反射镜实现移相[8]。 在马赫-曾德尔干涉仪中,利用压电陶瓷晶体在斜 45° 方向上推动反射镜,改变相干光束间的光程差,以实 现移相。但是,压电装置较为昂贵,需要放大器和控 制系统,增加了干涉仪结构复杂度,不适用于小口径 干涉仪。 另一种常用的移相方式是波长调谐移相[9]。以激 光器作为移相器,通过改变其输出波长实现移相,简 化了干涉仪的装置结构。电流调制波长移相方案中, 激光器注入电流的变化会引起输出光功率与激光器相 干长度的改变[10-12],导致移相干涉图的背景光强和对 比度不一致,在利用干涉图进行相位解算时会出现较 大误差。Brid等[13]采用光栅作为选频器件,通过机电 调谐的方法,实现了稳定的高精度波长调谐。但是, 光栅调制的频率不高,移相速度慢,激光器的整体价 格昂贵,难以用于现场检测的一体化结构干涉仪中。 偏振移相技术也是马赫-曾德尔干涉仪中常用的 时域移相方法。Santa等[14]在测量双折射材料的幅值和 方向时,通过旋转偏振片引入相移;Tania等[15]采用偏 振移相术得到全内反射液体样本的折射率和相位分 布。然而偏振移相术系统结构复杂,且很难控制偏振 器件的透振方向,容易导致移相误差,影响测量结果。 Carlos 等[16]基于等厚干涉光路提出了一种新型的 移相方式,以激光点源作为移相器,在垂直于光轴方 向上移动点光源,改变入射到等厚干涉腔中的光束倾 角,从而实现点源移位移相干涉。但是,该方案仅适 用于反射式、有一定腔长的等厚干涉光路[17],无法应 用于传统的等光程马赫-曾德尔干涉仪。 本文提出了一种变倾角移相马赫-曾德尔干涉仪 方案。以反射镜为移相器,调制入射到马赫-曾德尔干 涉模块中准直光束的倾角;以小口径激光棒作为待测 件,增加等光程马赫-曾德尔干涉仪中参考光与测试光 的光程差。当入射到干涉模块的光束倾角发生变化时, 两路光的光程差随之变化。该方法避免了一般泰曼型 或斐索型干涉仪在测量激光棒透射波前时产生的多次 干涉现象,改善了光束两次透过激光棒的边缘衍射效 应,突出了马赫-曾德尔干涉仪单次透过待测小口径激 光棒的结构优势。采集到系列移相干涉图后,根据随 机移相算法[18]解算相位。 190254-3  2 理论推导 2.1 变倾角移相原理 图 1(a)为变倾角移相原理光路图,平行光束入射 到马赫-曾德尔干涉腔中,形成一对相干光。其中一路 光经反射镜折转形成参考光,另一路光经反射镜折转 后入射到激光棒中,形成测试光;图 1(b)为光束经过 待测激光棒的等效光路图,当平行光束垂直入射到激 光棒中,即光束倾角 θ为 0时,参考光与测试光的传 播方向相同,此时这两路光之间存在光程差为 0 ( 1)L n= −Δ , (1) 式中:L 和 n 分别表示激光棒的厚度和折射率,可理 解为透射式的等倾干涉。 改变移相反射镜的倾角,使得经该反射镜折转后 入射到干涉腔中的平行光束与光轴的夹角为 θ,倾斜 光束经过图 1(b)后,此时参考光与测试光的光程差为 2 2[ (sin ) cos ]nAC CD AB L n θ θ= + − = − −Δ 。(2) 由式(2)可知,参考光与测试光的光程差Δ随入射 到干涉腔中平行光束的倾角 θ而变,每幅干涉图中相 应的相位量ϕθ与倾角 θ的关系可以表示为 2( 1) [ ( 1) / 2 ]θφ kL n kL n n θ≈ − + − , (3) 其中每幅干涉图中对应的移相量为 2[ ( 1) / 2 ]θδ kL n n θ≈ − , (4) 式中:k=2π/λ为波数,λ为入射光的波长。由式(4)可 知,改变入射到干涉腔中的光束倾角,可以在干涉图 中引入不同的移相量,实现了移相干涉测量。 综上,移相反射镜实现了光束变倾角,待测激光 棒增加了参考光与测试光的光程差,两者作为关键元 件,使得马赫-曾德尔干涉系统中相干光之间的光程差 发生变化,从而实现了变倾角移相干涉测量。 2.2 随机移相算法 采集到系列移相干涉图后,利用随机移相算法进 行待测激光棒的相位恢复,该算法主要是采用最小二 乘方法求解线性回归模型的迭代算法[18]。变倾角时间 移相干涉图的背景和调制度可认为是时间不变量,此 时测量得到的干涉条纹光强可表示为 ( , , ) ( , ) ( , )cos ( , ) ( , , )I x y t A x y B x y φ x y x y t= + +⎡ ⎤⎣ ⎦Δ , (5) 式中:A(x, y),B(x, y)分别是干涉图的背景光强和调制 度,φ(x, y)是待测相位,Δ(x, y, t)=δ(t)+α(t)x+β(t)y,α(t) 和 β(t)分别为 x和 y方向的倾斜系数,δ(t)为移相量。 最小二乘法求解线性回归模型的迭代算法主要包括以 下计算步骤:首先对干涉图背景、调制度和待测相位 进行初始估计,初始估计不要求有较高的精度;接着 对式(5)中的时间相关量即移相量和倾斜系数进行线 性一阶近似,得到干涉光强的迭代值与实际测量值之 间的误差,运用最小二乘法,得到迭代更新后的移相 量及倾斜系数;然后根据计算结果,进一步更新迭代 后的干涉图光强,并计算优值函数: 2 m k 1 1( ) [ ( , ) ( , )]/ ( ) 2 N i i i i χ t I r t I r t B r N = = −⎡ ⎤⎣ ⎦∑ 。 (6) 当优值函数满足 χ(t) ε时,终止迭代。其中 ε为 迭代精度,一般设定为一个小量;最后根据收敛后的 计算结果求解出精确的相位分布,进而计算出待测激 光棒的透射波前质量。具体的计算流程如图 2所示。 3 实验结果 图 3 为变倾角时间移相马赫-曾德尔干涉仪的系 统光路图。其中,光源采用中心波长为λ=632.8 nm的 He-Ne 激光器,激光束经光纤耦合后形成点光源,点 光源发出的扩散光经物镜准直后形成口径为 Ф25....

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  • ...格昂贵,难以用于现场检测的一体化结构干涉仪中。 偏振移相技术也是马赫-曾德尔干涉仪中常用的 时域移相方法。Santa等[14]在测量双折射材料的幅值和 方向时,通过旋转偏振片引入相移;Tania等[15]采用偏...

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Journal ArticleDOI
15 Feb 2021
Abstract: In this paper, we study the relationship of local birefringence and stress oriented inhomogeneous elasticity of a sample from the spatial frequency response of focused surface plasmon (FSP). The birefringence of the sample varies the propagation constant of surface plasmon with regard to its direction and produces an elliptic absorption pattern in the reflected spatial frequency distribution. Birefringence is calculated from the ratio of the propagation constant along the fast to slow axis of the sample. The change in eccentricity was proportional to the applied stress on cellophane film. A strong correlation (0.94∼0.97) exists between FSP and phase shifting interferometry results.

2 citations


Cites background from "Measurement of birefringence using ..."

  • ...However, determination of spatially varying retardance calls for special techniques [18,19,20]....

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Journal ArticleDOI
Abstract: A temporal 4-step polarization phase-shifting technique for digital speckle pattern interferometry (DSPI) with one fixed and two rotatable polarizers is proposed. The fixed polarizer is used to filter out the reflected object beam in one polarization direction, and the two rotatable polarizers are used to perform the 4 times phase shifts. The Jones derivation illustrates the object surface phase distribution can be derived from the 4 speckle pattern interferograms, which are bright, gloomy, bright, and gloomy successively. The experiment shows that the proposed temporal polarization phase-shifting technique is able to extract the phase change caused by a tiny out-of-plane displacement. Unlike the PZT-driven phase-shifting, the polarization phase-shifting in this method is stable and accurate in the long term.

1 citations

Journal ArticleDOI
TL;DR: The experimental results show the feasibility and high precision of this dynamic Mach-Zehnder interferometer, and the phase distribution can be retrieved exactly, thereby realizing dynamic measurement.
Abstract: A dynamic Mach-Zehnder interferometer based on lateral displacement of a point source array is proposed. The point source array is generated by a point source and a phase grating, where four point sources are of identical intensity. The lateral displacement of each point source can be adjusted to introduce π/2 phase steps in the interferograms. With a specially designed lens array in the spatial split imaging system, four separated and clear imaging interferograms can be captured in a single shot. Using a four-bucket algorithm, the phase distribution can be retrieved exactly, thereby realizing dynamic measurement. The experimental results show the feasibility and high precision of this dynamic Mach-Zehnder interferometer.

References
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Journal ArticleDOI
Abstract: Using a low-coherence Michelson interferometer, we measure two-dimensional images of optical birefringence in bovine tendon as a function of depth. Polarization-sensitive detection of the signal formed by interference of backscattered light from the sample and a mirror in the reference arm give the optical phase delay between light that is propagating along the fast and slow axes of the birefringent tendon. Images showing the change in birefringence in response to laser irradiation are presented. The technique permits rapid noncontact investigation of tissue structural properties through two-dimensional imaging of birefringence.

928 citations

Journal ArticleDOI
TL;DR: Scanning laser polarimetry provides quantitative measurements that correspond to known properties of the retinal nerve fiber layer in normal and glaucomatous eyes.
Abstract: Purpose To determine whether retardation (change in polarization) measurements of healthy subjects and glaucoma patients obtained by using a confocal scanning laser polarimeter correspond to known properties of the nerve fiber layer. Methods A polarimeter, an optical device used to measure the change in linear polarization of light (retardation), was interfaced with a scanning laser ophthalmoscope to obtain retardation data at 65,536 locations (256 × 256 pixels) in a study of normal subjects and patients with primary open-angle glaucoma. To validate the instrument, we compared our measurements with known properties of the human retinal nerve fiber layer in 105 normal subjects. Additionally, we compared retardation measurements in eyes of 64 normal subjects and 64 age-matched glaucoma patients treated in a referral practice. Results In normal eyes, mean (± S.D.) peripapillary retardation was highest in the superior and inferior arcuate regions and lowest in the temporal and nasal regions, 12.0 ± 1.9, 13.1 ± 2.0, 7.0 ± 1.8, and 7.0 ± 1.6 degrees, respectively. Retardation decreased toward the periphery and was lower over blood vessels. In normal eyes, retardation decreased with increasing age in the superior and inferior regions. Mean retardation was statistically significantly higher among normal eyes than glaucoma eyes in the inferior and superior regions but not in the temporal or nasal areas. Conclusions Scanning laser polarimetry provides quantitative measurements that correspond to known properties of the retinal nerve fiber layer in normal and glaucomatous eyes.

473 citations


"Measurement of birefringence using ..." refers methods in this paper

  • ...EQ-TARGET;temp:intralink-;e011;326;741 ðδx þ δyÞ 1⁄4 ðδ1 − δ2Þ þ ðζx − ζyÞ i:e:; δ 1⁄4 ðδx þ δyÞ − ðζx − ζyÞ; (11)...

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  • ...54(11) Optical Engineering 54(11), 113112 (November 2015)...

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  • ...54(11) Sircar and Bhattacharya: Measurement of birefringence using polarization phase-shifting Mach–Zehnder interferometer...

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Journal ArticleDOI
TL;DR: Quantitating retinal nerve fiber layer thickness may enhance discrimination between glaucomatous and normal eyes earlier than is currently available by anatomic and functional approaches.
Abstract: • We describe a new technique for the measurement of retinal nerve fiber layer thickness and compare its results with histopathologic measurements in the same eyes. For these studies, two fixed monkey eyes were incised and placed on a pedestal in a plastic viewing dish. The eyes were perfused to maintain a pressure between 10 and 20 mm Hg. An ellipsometer, an optical device used to measure the change in polarization of light (retardation), was implemented in a laser tomographic scanner to obtain polarization data from the two monkey retinas. For the 15 measured locations, retardation ranged between a mean (± SD) of 0.9° ± 1.8° and 23.7° ± 0.3°. Subsequently, retinal nerve fiber layer thickness was measured at the imaged points in epoxy resin-embedded sections by an observer masked to the ellipsometry data. These values ranged between 20.4 μm and 213.9 μm. There was an excellent correlation (R =.83) between retardation and the histopathologic measurement of retinal nerve fiber layer thickness. Quantitating retinal nerve fiber layer thickness may enhance discrimination between glaucomatous and normal eyes earlier than is currently available by anatomic and functional approaches.

472 citations


Additional excerpts

  • ...EQ-TARGET;temp:intralink-;e010;63;151δy 1⁄4 −ðδ2 þ ψ þ ζyÞ; (10)...

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Journal ArticleDOI
TL;DR: A measuring system for determining the state of polarization of a beam of light in terms of its Stokes parameters which can be fully automated incorporates a monochromator and single photon counting detection and can be applied over a large wavelength range for very weak optical signals.
Abstract: We describe a measuring system for determining the state of polarization of a beam of light in terms of its Stokes parameters. The technique which can be fully automated incorporates a monochromator and single photon counting detection and can thus be applied over a large wavelength range for very weak optical signals. Fourier transformation of the data by an on-line minicomputer allows immediate calculation of the Stokes parameters. We discuss special applications to light emitted from excited atomic systems with and without cylindrical symmetry.

253 citations

Journal ArticleDOI
TL;DR: P polarization-sensitive optical coherence tomography (OCT) images of human skin in vivo are presented, demonstrating the ability of the technique to visualize and quantify the birefringent properties of skin.
Abstract: Optical coherence tomography enables cross-sectional imaging of tissue structure to depths of around 1.5 mm, at high-resolution and in real time. Incorporation of polarization sensitivity (PS) provides an additional contrast mechanism which is complementary to images mapping backscattered intensity only. We present here polarization-sensitive optical coherence tomography (OCT) images of human skin in vivo, demonstrating the ability of the technique to visualize and quantify the birefringent properties of skin. Variation in normal skin birefringence according to anatomical location is demonstrated, and discussed in relation to collagen distribution at each location. From measurements on a sample of five human volunteers, mean double-pass phase retardation rates of 0.340+/-0.143, 0.250+/-0.076, and 0.592+/-0.142 deg/microm were obtained for the dorsal hand, temple, and lower back regions, respectively. We demonstrate how averaging the Stokes parameters of backscattered light over a range of axial and lateral dimensions results in a reduction of speckle-induced noise. Examples of PS-OCT images from skin sites following wound healing and repair are also presented and discussed.

225 citations


Additional excerpts

  • ...EQ-TARGET;temp:intralink-;e008;63;376 tan δx − tan δy 1⁄4 1⁄2tanðδ∕2Þ 1⁄22 cosð2φÞ i:e:; δ 1⁄4 2 tan−1 ðtan δx − tan δyÞ 2 cosð2φÞ : (8)...

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