Power-efficient Fourier domain optical coherence tomography setup for selection in the optical path difference sign using Talbot bands

A power-efficient Fourier domain optical coherence tomography fiber system is presented free of mirror terms. The object and reference beams from the interferometer are spatially separated to illuminate different parts of the diffraction grating in the spectrometer according to a method inspired from the use of Talbot bands. In this way, the system is made sensitive to only one sign of the optical path difference in the interferometer.     

Analysis of period and visibility of dual phase grating interferometer

Dual phase grating interferometer may simultaneously achieve large field of view and high x-ray dose efficiency. Here, we develop a simple theoretical method to better understand the imaging process of the dual phase grating interferometer. The derivation process of fringe period and the optimal visibility conditions of the dual phase grating interferometer are given in detail. Then, we theoretically prove that the fringe period and optimal visibility conditions of the dual phase grating interferometer include that of the Talbot interferometer. By comparing our experimental results with those of other researchers, we find that when the positions of phase gratings are far away from the positions where the fringe visibility is optimal, the fringe period of the dual π -phase grating interferometer is twice the theoretical results under the illumination of polychromatic x-ray. This conclusion may explain the contradictory research results of dual phase grating interferometer among different researchers.     

Simple phase-shifting lateral shearing interferometer

A phase-shifting electronic speckle pattern shearing interferometer with a very simple shearing device is proposed. Two partially reflective glass plates are used to introduce the shear in this new interferometer. The reflection coefficients of the coatings on the two plates are 0.3 and 0.7. The distance between the two glass plates controls the size of the shear. The proposed new interferometric system is simple, flexible, and low cost.     

Multi-directional lateral shearing interferometer based on rotatable prism pairs

The common camera lens usually includes the spherical glass/plastic lens and aspheric glass/plastic lens. However, spherical/aspheric shape measurement is still a key problem in the process of optical lens fabrication. At present, the in-process measurement of spherical/aspheric shape is conducted mainly by the probe-contacting method. But after a long time, its probe could be scratched severely and cause some big errors. Laser shearing interferometry is a good substitute to some degree. Nevertheless, it is not convenient for general shearing interferometer to carry out the in-process measurement because it is only suitable for certain kind of spherical/aspheric with respect to aperture or asperity. Here a new lateral shearing interferometer is proposed to solve the described problems. It is based on two Jamin plates and rotatable prism pairs which are used not only for shearing displacement and direction, but also for fringe period and tilt degree, in order to meet requirements of various spherical/aspheric shapes or asperities. The new interferometer features a simple optical structure and two symmetric light paths, which makes its system with minimal error. The relation between shearing displacement, fringe period and prism angle of rotation is given in this paper. And the error source is primarily from the manufacture errors of prisms and plates. The final experiments show that one can achieve good-quality fringe patterns according to the requirement of measurement, concerning the shearing direction, shearing displacement, fringe period, tilt degree, etc.     

Collimation method using fourier imaging and moire techniques

Two techniques are proposed for beam collimation with the Talbot interferometer. One is called the mismatch method in which two gratings with slightly different periods are used. In the other method (called the grating shift method), one of two gratings of the same period is shifted in its plane in the direction perpendicular to the grating lines.     

部分相干光栅衍射效应和干涉术

本文提出一种新的部分相干照明的光栅衍射干涉仪.先分析了光栅的介于Talbot和Lan效应之间的部分相干衍射效应.部分相干干涉图的特点是条纹由频率成倍的两种光栅状载波所表征.调整光源狭缝,系统在两相干性极端分别转成Talbot和Lau干涉仪.理论分析采用了模糊函数方法.最后给出了实验.     

改变写入Bragg波长的干涉条纹运动的扫描式Talbot干涉仪

一种干涉条纹运动的扫描式Talbot干涉仪被用于改变光纤Bragg光栅的写入Bragg波长。在系统中,光纤光栅是由来自相位掩模的±1级衍射光经平面镜反射后在远场形成紫外干涉条纹写入的,其中,相位掩模被用作±1级衍射光的分束器。值得注意的是通过干涉条纹的运动来扫描写入光纤光栅,有效降低了Talbot干涉仪对写入光源相干性的要求。     

利用一块相位掩模和两块棱镜改变光纤光栅的写入Bragg波长

一种相位掩模干涉仪被用于写入不同的Bragg波长的。在该系统中,光纤光栅是由来自两可旋转棱镜所形成的紫外干涉条纹写入的,其中,相位掩模被用作&;#61617;1级衍射光的分束器。并且,当两块顶角由相位掩模的&;#61617;1级衍射角和棱镜折射率确定的棱镜的底部相互平行放置时,该相位掩模给出了Bragg波长的参考值。当Bragg波长的移位为1 nm时,棱镜最大的旋转角为1 degree,最小的旋转角是~2.4 minute。与Talbot干涉仪中平面镜的旋转角~23 second/nm相比,该相位干涉仪中棱镜的旋转精度降低了2~3个数量级。替代了许多具有不同光栅周期的相位掩模,该可调谐相位掩模干涉仪仅用一块相位掩模和两块旋转棱镜就实现了写入具有不同Bragg波长的光栅。     

Changing photo-written Bragg wavelengths of fiber gratings via one phase mask and four mirrors

A phase mask interferometer is developed to photo-write long gratings with arbitrary Bragg wavelengths. In this system, the fiber Bragg grating is photo-written by UV interference stripes of 193 nm reflected from two rotatable mirrors and two fixed mirrors, where the phase mask is not only used as a beam splitter, but also initialized the reference quantity of Bragg wavelength; the fixed mirrors are used for reducing the incident angle; the rotatable mirrors are used for adjusting the corresponding photo-written Bragg wavelength. It is worth noting that the photo-written length is fourfold as high as the length in the Talbot interferometer with the same mirror size.     

Step index fibre using laser interferometer

A model is suggested to describe the fringe shift which occurs due to the phase variations of cladded glass fibre introduced between the two plates of the liquid wedge interferometer illuminated with a He–Ne laser. The fringe shift of the phase object which appears in the denominator of the Airy distribution formula of the multiple beam interference is represented in the harmonic term. An experiment is conducted using liquid wedge interferometer where the step index glass fibre of a nearly quadratic thickness variation is introduced between the two plates of the interferometer. The obtained fringe shift shows a good agreement with the proposed quadratic model. The Matlab code is written to plot the interferometer fringes comprising the shift of the step index fibre. Secondly, recognition of elliptical fibres is outlined using tomographic imaging. Finally, results and concluding remarks are given.     

用四台阶相位板产生涡旋光束

涡旋光束的产生与应用是当前光学领域的研究热点. 利用傅里叶级数展开法分析了四台阶相位板的相位结构, 发现四台阶相位板可看作是由一系列不同拓扑荷数的螺旋相位板所组成, 用线偏振光直接照射相位板时, 将产生多级衍射光波, 各级衍射光均为不同拓扑荷数的涡旋光波, 由于多级衍射光波间的干涉导致光强分布偏离轴对称分布, 因而与涡旋光波有一定差距. 在此基础上, 提出了用四台阶相位板产生涡旋光束的新方案, 借助于Mach-Zehnder 干涉仪光路, 两块四台阶相位板产生的衍射光干涉叠加, 通过调节干涉仪光路的相位差, 使一部分衍射级干涉相消, 另一部分衍射级干涉相长, 相互加强, 从而把线偏振光转换为涡旋光束. 数值模拟计算了几种周期数不同的四台阶相位板衍射光强和角动量分布, 并与螺旋相位板进行比较, 证明用简单的四台阶相位板不仅能够获得与用螺旋相位板相同的涡旋光束, 而且可以用周期数较小的四台阶相位板产生具有大拓扑荷数的涡旋光束, 降低了制作相位板的难度.     

双棱镜改变写入Bragg波长的相位掩模技术

将一种可旋转的双棱镜引入到相位掩模技术中以改变光栅的写入Bragg波长.在该系统中,光纤光栅是由来自可旋转双棱镜所形成的波长为248 nm的紫外干涉条纹写入的,其中,相位掩模被用作 1级衍射光的分束器,通过双棱镜的旋转可改变两写入光束的交叉角.为了初始化Bragg波长的参考值,双光栅的顶角由相位掩模的 1级衍射角和双棱镜的折射率确定.因为在～100 nm范围内两光束的非对称旋转对光栅周期的改变是5×10~(-4) nm,双棱镜引入的光栅的闪耀可忽略.当Bragg波长的移位为1 nm时,棱镜最大的旋转角为～1 degree,最小的旋转角是～2.4 min.与Talbot干涉仪中平面镜的旋转角～23 s/nm相比,该相位干涉仪中棱镜的旋转精度降低了2～3个数量级.     

用于制作光纤光栅的Talbot干涉仪的分析与建模

对用于制作光纤光栅的Talbot干涉仪进行了分析.当考虑准分子激光器的空间相干性和时间相干性时,几何光学中的光线法并不能给出Talbot干涉仪干涉场的真实强度分布情况,而通过光的电磁理论,则可以提供对干涉场的详细描述.基于电磁理论,建立了一个Talbot干涉仪干涉场计算模型,并首次将Talbot干涉仪的反射镜转角作为模型计算参数加以考虑,随后进行了一系列的计算.计算结果显示了干涉场的分布,同时表明空间相干性对Talbot干涉仪的近场干涉和远场干涉影响都很大,其中远场干涉对空间相干性的要求更严格,且对于远场干涉,反射镜转角的影响不可忽视.     

In-plane ESPI using an achromatic interferometer with low-coherence laser source

The use of an achromatic interferometer is explored as a means of doing in-plane ESPI measurements using a laser diode as the light source. This interferometer type, which uses a diffraction grating in place of the conventional beamsplitter, has two features that make it suitable for making ESPI measurements over extended areas, even when using a low-coherence laser diode source. First, the parallelogram optical geometry of the interferometer causes all rays passing through to have the same optical path lengths. Second, the interferometer is achromatic, whereby the piezo-actuated mirror that steps the illumination light does so by the same phase angle, independent of wavelength. This latter feature accommodates the spectral impurity of a laser diode source. A periodic variation of fringe visibility is observed in experiments, where narrow ranges of high visibility occur at regular spatial intervals. This behavior derives from the clustered discrete spectral character of laser diode light output. A method to “tune” the interferometer by slightly rotating the diffraction grating is described so as to achieve consistent high fringe visibility throughout the measured images.     

Modeling of the fringe shift in multiple beam interference for glass fibers

A quadratic model is suggested to describe the fringe shift occurred due to the phase variations of uncladded glass fiber introduced between the two plates of the liquid wedge interferometer. The fringe shift of the phase object is represented in the harmonic term which appears in the denominator of the Airy distribution formula of Fabry-Perot’s interferometer. A computer program is written to plot the computed fringe shifts of the described model. An experiment is conducted using liquid wedge interferometer where the fiber of a nearly quadratic thickness variation is introduced between the two plates of the interferometer. The obtained fringe shift shows a good agreement with the proposed quadratic model. Also, it is compared with the previous theoretical shift based on ray optics of semi-circular shape.      

Inscription and Visualization of Tilted Fiber Bragg Gratings

Tilted fiber Bragg gratings with different tilt angles have been inscribed in single-mode isotropic optical fiber with an increased photorefractivity using Talbot interferometer and KrF-excimer laser system. Their spectra are studied. Using a confocal laser scanning luminescent microscope the images of gratings in transmitted light were obtained. The calculated dependence of the slope angle of the grating recorded in the Talbot interferometer on the angle between the strokes of the interference pattern created in the interferometer and the transverse section of the optical fiber is experimentally verified.     

Talbot interferometry with a vibrating phase object

We describe a Talbot interferometer for measuring a vibrating phase object. The time-average fringes are moiré patterns modulated by the zeroth-order Bessel function. They provide information about the tilt at every point of a vibrating plate, for example. The Talbot interferometer is robust (common path) and cheap (printers grids as beam-splitters). The experiments can be performed with laser illumination or with a collimated beam of white light. Some experimental results are shown.     

Variable Wavelengths Fiber Bragg Gratings Written with A Phase Mask and Four Prisms

Using only one diffractive element, the Talbot interferometer provides a robust and inherently stable method for reproducing fiber Bragg gratings with variable wavelengths, and reduces the complexity of the fiber grating fabrication system. However, the usable length of the grating is limited by the practical length of the mirrors. This paper presents a phase mask with two fixed prisms and two rotational prisms to inscribe fiber Bragg gratings with variable Bragg wavelengths. In this system, the fiber Bragg grating is inscribed by UV interference stripes of 193 nm derived from two rotational prisms and two fixed prisms, where phase mask is used as a beam splitter of ±1 order diffraction light. It is noteworthy that the tunable phase mask interferometer decreases the demand of the length of prism evidently.     

ON THE APPLICATION OF THE HILCER PRISM INTERFEROMETER TO THE RESOLUTION OF SPECTRAL LINES

An interference pattern of two systems of fringes has been obtained by vising two radiations in a Hilger prism interferometer A system of white bands with equal spacing which are always parallel to the refracting, edge of the prisin is the result of the intersection of the two systems of fringes. The white bauds travel as one of the reflecting mirror in the interferometer makes a parallel displacement. Let d be the displacement of mirror when the white bauds travel one spacing, we have 1/λ₂-1/λ₁=1/2d. Two yellow doublets in sodium and mercury lamps were used. The values found for 1/λ₂-1/λ₁ were 17.22cm^-1 and 63.29cm^-1 respectively. A comparison of this method with the visibility corve by Michelson interfero-ineter has been discussed.     

Variable Wavelengths Fiber Bragg Gratings Written with A Phase Mask and Four Prisms

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