Estimation of the degree of asphericity of a glass sphere using a vectorial shearing interferometer

The degree of asphericity is estimated by determining the average radius of curvature in different sections, at various points on the surface of a sphere, and the deviation from it. We employ the vectorial shearing interferometer (VSI) as the instrument to determine the radius of curvature from two subapertures of the transparent glass sphere. We incorporate the sphere as a thick lens into the interferometric setup, illuminating it with an expanded beam. The spherical aberration, introduced by the sphere in the wave front, depends on the local sphere radius, on the refraction index of the glass, and on the cone angle of the source. The wave front aberrated by the sphere impinges on the VSI. Here, the wave front is divided in two in amplitude, it is sheared vectorially, and it is superimposed with itself. The fringe pattern is formed in the intersection of the wave fronts. The shape of the resulting fringe pattern is directly related to spherical aberration. We estimate qualitatively the degree of asphericity, comparing the phase gradients in different sections of the sphere. Here, we report on the experimental setup to test the asphericity, the results with different vectorial shearing (magnitude and direction). Finally, we perform a comparison with the theoretical predictions.     

Lens Sag Measurement of Microlens Array Using Optical Interferometric Microscope

This study attempted to develop a detection system for lens sag of the microlens array in real time using an optical automatic inspection framework to link with the computer through a camera. An image processing technique was applied to detect the spherical microlens array, and then, the results were compared.The system light source used laser light and applied CCD to collocate with the microscope array to form an automatic optical detection system for an optical interferometric microscope. It applied the principle of the Fizeau interferometer, illuminated the surface of microlens array, and formed the phase difference required by the interference of two lights through the laser light reflected by the reference plane and the surface of the microlens array, thus, forming an interference fringe.When the sag of the microlens was much longer than the wave length of the detection light source, the fringe would be densely distributed, thus, only a few central fringes were clear in the microscopic image. An image processing method was used to search the center of the interference fringe and a creative algorithm was utilized to obtain the lens sag of the microlens. As proved by the experiment, lens sag of 4 microlens arrays were detected in real time, with a minimum detection error of 0.08 μm, and a maximum detection error of 4 μm (error value 1 ~ 9%), according to different sample processes. This system featured a simple structure and is applicable to non-contact detection and detection of different-sized microlens arrays.     

非球面检测中最佳入射球面波和最佳参考球面波的确定

为了能够对非球面光学元件面型进行高精度的干涉检测,提出了一种确定最佳入射球面波和最佳参考球面波的新方法。该方法通过计算分析入射球面波与非球面反射波干涉条纹密度,确定最佳入射球面波的波源位置;通过计算分析在干涉图记录平面CCD上干涉条纹的密度,确定非球面检测时参考球面波波源的最佳位置。应用该理论与方法,不仅可明确非球面检测时CCD等光路元件选型的具体策略,而且可用于指导非球面检测调试过程,并能够通过对干涉图的深入分析,获得更多被测非球面的信息。     

Measuring optical properties of an eye lens using magnetic resonance imaging

We compare the focal lengths of porcine lenses measured optically and by using a novel MRI technique. The geometric properties of the lenses were also measured and compared. The MRI technique exploits the dependence of both the lens refractive index and relaxation rates on the local protein concentration. By measuring the refractive index and corresponding values of R2 (=1/T2) for samples of lens homogenates with different protein concentrations, the dependence of refractive index on R2 was determined empirically. R2 maps, constructed from monoexponential fits to multiecho images of a slice through the lens containing the optical axis, were converted to refractive index maps using this relationship. A simulated ray trace through the refractive index map provided an estimate of lens focal length that was compared to a direct optical measurement of focal length using a laser ray-tracing method. It was found that the mean focal lengths estimated from the two techniques agreed within experimental uncertainty. The refractive index profile along the optical axis was found to be well described by a simple function of the form n=n0 + n1 x ra where r is the (normalized) lens radius.     

毛细管干涉仪的理论分析

从几何光学出发,推导了毛细管干涉仪的从柱面透镜到接收屏的光线的光程．对光线追迹模拟,结果表明毛细管干涉仪的干涉条纹的形成可用双光束的干涉来解释．从柱面不同位置入射的两条光线可能具有相同的光程,而且从柱面透镜不同位置出发的两条光线可能到达接收屏的同一点,当它们满足相干条件时,就会形成干涉条纹．建立了干涉条纹的计算机模拟程序, 模拟了毛细管中液体折射率、毛细管内径、外径对干涉条纹的影响. 结果表明实验中应使用薄壁毛细管, 由于干涉条纹对柱面透镜到毛细管之间的距离非常敏感, 为提高精度, 建议在实验中用已知折射率的标样来确定这一距离.     

Flow visualization by an improved double exposure method in holography

Some optical differential interferometric techniques were investigated in order to measure the density distribution in the air jet flow of a small scale flow cell while excluding the effects of the optical distortion of its glass windows. A technique using moiré fringe formation by rotating the reference wave in one exposure of the double exposure method was found to be most suitable for this purpose. High contrast and multiplication of moiré fringes can be obtained by a moiré fringe sharpening and multiplication method.     

二次波面干涉的剪切散斑干涉计量术

提出了一种新的剪切散斑干涉方法─—二次波面干涉的剪切散斑干涉计量术．这一方法将被测物体变形前后波面的第一次干涉信息分别储存在两张全息干板上，通过光学信息处理实现波面的第二次干涉．两次波面干涉分别消除了位移和位移的一阶导数场对波面位相的影响，得到仅反映位移二阶导数场的条纹图．     

Measurement of properties of silver telluride thin films using holography

Holography is an interferometric method of recording the light waves diffracted by a subject illuminated with coherent light. Holographic interferometry (H.I.) is one of the most important applications of holography. It is concerned with the formation and interpretation of fringe patterns, which appears when a wave generated at some earlier time and stored in a hologram is later reconstructed by interfering with comparison wave. We report a technique, which uses double exposure holographic interferometry together with simple mathematical interpretation, which allow immediate finding of stress and thickness of thin film. We tested the same for different normalities of solutions. It was further noticed that the fringe spacing changes with solution concentration as well as time of deposition. The thin films are prepared using electrodeposition technique. It’s structural, morphological and optical study carried out by XRD, SEM, and UV-Vis-NIR spectrophotometer.     

Surface plasmon interferometric microscopy for three-dimensional imaging of dynamic processes

A method, which we named surface plasmon interferometric microscopy, for real-time displaying of the dynamic evolution of the refractive index (RI) of a sample in three-dimensions is demonstrated experimentally. The Fourier fringe analysis technique is employed to get the phase variations of the samples by demodulating the interference patterns captured by a CCD camera, and the 3D RI distribution can be obtained through numerical interpolation from the relation between the phase and the RI of the samples. Our method may provide an interesting way to monitor fast dynamics of physical, biological, and chemical processes in real time.     

Highly sensitive interferometric system for optical surface contouring

In the present work we demonstrate a highly sensitive system for optical surface contouring constructed by combining phase conjugation and digital phase shifting interferometry. The phase conjugating mirror in the modified phase conjugate Michelson interferometer is based on degenerate four wave mixing in a photorefractive BTO crystal. Digital phase shifting interferometry is used to decode the interference fringe pattern. An increase in sensitivity and high measurement accuracy are achieved through this new combination due to the interferometric scheme and the phase shifting. Experimental results are presented. The interferometric system is flexible and undergoes further improvement.     

Comparative study between interferometric and Z-scan techniques for thermal lensing characterization

This work presents an original, comparative study between two optical techniques for the analysis of thermal lensing induced by a low-power, cw laser beam focused onto a sample cell containing a weak absorbing medium. It deals with an interferometric technique and a Z-scan technique in real time. The interferometric method permits the determination of the spatial profile of the thermal lens. The development of the work puts in evidence the high sensitivity of both techniques for the detection and measurement of low absorption coefficients and refractive index changes in dye solutions at very low concentrations. Improvements in the sensitivity of both methods can make possible the measurement of very small phase shift distortions of the wavefront. One shows also the mutual complementary character of two techniques for the characterization and measurement of linear and nonlinear properties of materials.     

Measurement of three components of a displacement vector using heterodyne holographic interferometry

A new method for measuring a displacement vector using a single hologram is discussed. The method realizes the measurement by observing the object through three or more points on the hologram using a single lens and by using a heterodyne technique to detect accurate phase differences. In order to establish the optimum optical system of this method, it is necessary to estimate the measuring errors caused by fringe reading error and optical setting error. These two errors are calculated for a typical optical system. On the basis of the results of the analysis, an experimental result was evaluated.     

超视力人眼模型的研究

超视力人眼模型对充分发掘人眼视力达到“鹰视”具有重要意义。用Zernike多项式描述角膜前表面，用渐变折射率描述晶状体的折射率分布，同时考虑人眼视轴和光轴的夹角对成像的影响，利用光学设计软件Zemax建立了人眼超视力模型。将Zernike条纹矢高面应用到人眼模型中，能有效改变视轴方向(即5°视场)的成像质量，提高点扩散函数（PSF）值。采用晶状体渐变折射率符合人眼的实际解剖结构，可有效减小人眼像差。通过分析人眼极限分辨能力和人眼模型波像差，得出当空间频率为60周期/度时，该模型对目标高频细节感知的调制度可达到0.55。     

A high‐accuracy complex‐phase method of simulating X‐ray propagation through a multi‐lens system

The propagation of X‐ray waves through an optical system consisting of many X‐ray refractive lenses is considered. For solving the problem for an electromagnetic wave, a finite‐difference method is applied. The error of simulation is analytically estimated and investigated. It was found that a very detailed difference grid is required for reliable and accurate calculations of the propagation of X‐ray waves through a multi‐lens system. The reasons for using a very detailed difference grid are investigated. It was shown that the wave phase becomes a function, very quickly increasing with increasing distance from the optical axis, after the wave has passed through the multi‐lens system. If the phase is a quickly increasing function of the coordinates perpendicular to the optical axis, then the electric field of the wave is a quickly oscillating function of these coordinates, and thus a very detailed difference grid becomes necessary to describe such a wavefield. To avoid this difficulty, an equation for the phase function is proposed as an alternative to the equation of the electric field. This allows reliable and accurate simulations to be carried out when using the multi‐lens system. An equation for the phase function is derived and used for accurate simulations. The numerical error of the suggested method is estimated. It is shown that the equation for the phase function allows efficient simulations to be fulfilled for the multi‐lens system.     

Critical ray-like propagation modes along graded-index planar optical waveguides

Graded-index planar optical waveguides and surface compression layers were formed simultaneously in the surface layer of glass plates by ion exchange. A change in the refractometer patterns was observed. Before ion exchange, only a critical ray fringe was observed, but with ion exchange a guided wave fringe appeared on the high effective refractive index side of the ‘critical ray’ fringe, and the number of guided wave fringes increased. The guided wave fringe or fringes were birefringent, whereas the ‘critical ray’ fringe was kept nonbirefringent. It was concluded that the ‘critical ray’ propagated along the bottom of a waveguide, ie at the foot of the refractive index distribution.     

Refractive index profiling of a GRIN optical fiber using a modulated speckled sheet of light

A method for calculating the refractive index of GRIN optical fiber from its transverse interference pattern is presented.In this method the transverse interference fringe pattern through an optical fiber using a sheet of light is applied to get the refractive index profile of it. The optical fiber is not immersed in a matching liquid as used in different techniques [Barakat N, El-Hennawi HA, El-Zaiat SY, Hassan R. Pure Appl Opt 1996;5:27].In this method a sheet of He–Ne laser light is allowed to illuminate the fiber. The light sheet is divided into two parts, the first is refracted through the fiber while the second is used as a reference beam. Interference pattern will be obtained between these two rays displaying the refractive index variation along the fiber radius.The fringe shift of such interference pattern has been measured and used to calculate the deflection angle of light refracted by the fiber and the cladding. An equation is derived to calculate the refractive index profile difference ratio δn at different positions across the fiber cross section in terms of the corresponding deflection angle and is verified experimentally.The optical path difference between these two rays (refracted and reference beam divided by the fiber) has been derived and the fringe shift obtained has been used to calculate the refractive index profile of the fiber.Introducing a ground glass screen on the passage of the two light beams (refracted and reference beam divided by the fiber), two superimposed identical speckle patterns are formed leading to the formation of a third speckle pattern modulated by a grid structure displaying the optical thickness of the fiber.     

Automatic refractive index profiling of fibers by phase analysis method using Fourier transform

Automatic fringe pattern analysis is a powerful and inexpensive digital image-processing technique. It is used to analyze the fringe pattern obtained by different optical techniques, such as multiple-beam Fizeau fringes. To perform accurate and fast automatic measurement of fiber refractive index profile, phase analysis method has been used with the Fourier transform technique. In this paper, the refractive index profiles of polyethylene fibers with different draw ratios are presented by two methods, fringe shift method and phase analysis method. A comparison between the results obtained is presented.     

Direct measurement of group dispersion of optical components using white-light spectral interferometry

We present a simple white-light spectral interferometric technique employing a low-resolution spectrometer for a direct measurement of the group dispersion of optical components over a wide wavelength range. The technique utilizes an unbalanced Mach-Zehnder interferometer with a component under test inserted in one arm and the other arm with adjustable path length. We record a series of spectral interferograms to measure the equalization wavelength as a function of the path length difference. We measure the absolute group refractive index as a function of wavelength for a quartz crystal of known thickness and the relative one for optical fiber. In the latter case we use a microscope objective in front and a lens behind the fiber and subtract their group dispersion, which is measured by a technique of tandem interferometry including also a Michelson interferometer.     

The use of a plane parallel glass plate for determining the lens' parameters

The present article reports a shearing interferometric technique for determining the various lens' parameters, namely, the focal length, refractive index, radii of curvatures etc. The wave aberrations have also been investigated for the different values of the focal length of the same lens by immersing it in various liquids. The lens itself acts both as autocollimator and decollimator. Modified criteria for evaluating the correct position of the focal length have been adopted. The defocusing involved is observed in terms of the interference fringes. The plane parallel glass plate acts as a double shearing interferometer. The location of the point source is confirmed by testing the wavefront parallelism. A graph (refractive index versus lens' power) with various liquids has been plotted which gives the desired parameters.     

Recording and optical processing of images of projected fringes in the study of objects with a periodic surface texture

Specific features of application of the fringe projection method to the study of objects with a periodic surface texture are analyzed. It is shown that a moire pattern is formed in the image recording process. It is caused by the superposition of two periodic structures, namely, the image of the texture of the surface under study and the system of projected fringes. The bending of moire fringes in the pattern is determined by the summary effect of two functions, which describe the bending of the images of surface texture and the system of projected fringes, because of the deviation of the relief shape from the comparison plane. A method for the optical processing of a photographic image by two coherent light beams is described, which makes possible a separate interferometric visualization of the aforementioned functions. Results of experimental studies are presented.