Applying the phase difference property of polarization angle for measuring the concentration of solutions

This paper proposes a simple method for measuring the concentration of solutions based on the phase difference of internal reflection polarization angle and circularly polarized heterodyne interferometry. For a circularly polarized heterodyne light beam incident on the boundary surface between a hemispherical prism and a test solution, the reflected light passes through a properly oriented analyzer for interference. The phase difference between s- and p-polarized light is sensitive to the solution concentration when the incident angle equals the internal reflection polarization angle. Based on these effects, the resulting phase difference makes it possible to analyze the concentration of solution through heterodyne interferometry. The experiments in this study confirm the feasibility of this method, which provides the advantages of simple installation, ease of operation, and high accuracy.     

Measurement of small displacement based on surface plasmon resonance heterodyne interferometry

This paper proposes an optical method for measuring small displacements using the surface plasmon resonance (SPR) heterodyne interferometry. A heterodyne light beam reflected by a mirror passes through a hemisphere glass and then enters into a surface plasmon resonance apparatus at the resonant angle. A small displacement of the mirror will introduce a phase-difference variation between p- and s-polarizations of the light emerging from the SPR apparatus. The phase-difference variation can be precisely measured with the heterodyne interferometric technique, and the associated displacement can be estimated. The feasibility of this method was verified by experiment, and the displacement measurement resolution of about 1.4 nm over a traveling range of 6 μm was achieved. Our method of measurement has the merits of both common-path interferometry and heterodyne interferometry.     

Measuring small wavelength differences by heterodyne interferometry and optical activity of chiral crystal

The optical activity of a chiral crystal and common-path heterodyne interferometry are used in a simple measurement technique that was developed to measure small wavelength differences. When circularly polarized heterodyne light passes through a chiral crystal, the plane of polarization rotates. The phase difference between the right- and left-circular lights is directly proportional to the angle of rotation. The rotation angle depends strongly on the wavelength. The phase difference can be accurately detected and substituted into specially derived equations to estimate wavelength variations. The feasibility of this method was demonstrated and the wavelength sensitivity was about 0.00812 nm. This method provides the advantages of a simple structure, ease of operations, a large wavelength measurement range and high sensitivity.     

Non-contact method for measuring solution concentration using surface plasmon resonance apparatus and heterodyne interferometry

A simple non-contact method is proposed for measuring the concentration of solutions. Using the significant phase difference between p- and s-polarizations of the reflected light of a surface plasmon resonance apparatus, the variation in the phase difference, which is caused by a variation in the concentration of a test solution, can be accurately measured by common path heterodyne interferometry. Then, by substituting the corresponding variation in the incident angle of light at the base of the SPR prism in a specially derived equation, the concentration of the test solution can be determined. The validity of this method was demonstrated experimentally. This method is characterized by the advantages of the device having a simple non-contact structure; it being easy to operate; and its high accuracy, stability, and resolution.     

Applying the optical activity of cholesteric liquid crystal for measuring small wavelength differences

This work proposes a simple measurement technique based on the optical activity of cholesteric liquid crystal (CLC) and circular common-path heterodyne interferometry for measuring small wavelength differences. A circularly polarized heterodyne light passes through a CLC cell and an analyzer, generating an interference signal. When the CLC cell is properly chosen with a circular regime, it has strong optical activity. Accordingly, the phase difference between the left and right circular light of the interference signal depends strongly on the wavelength. As the wavelength changes, variations of the phase difference can be accurately detected by heterodyne interferometry. Substituting the variation of phase difference into specially derived equations, the wavelength variations can be estimated accurately. The feasibility of this method, which is applicable when the wavelength is larger than the product of the pitch and the refractive index of the CLC cell, was demonstrated; it provides the advantages of simple installation, ease of operation, and high accuracy.     

A method for measuring the complex refractive index and thickness of a thin metal film

A circularly polarized heterodyne light beam is incident on a thin metal film, causing successive reflections and refractions to occur at the two sides of the thin film. The phase difference between p- and s-polarizations of the multiple-beam interference signal can be measured accurately with an analyzer and heterodyne interferometry. The phase difference depends on the azimuth angle of the analyzer, the complex refractive index and the thickness of the thin metal film. The measured values of the phase differences under three different azimuth angles of the analyzer can be substituted into the special equations derived from Fresnels equations and multiple-beam interference. Hence, the complex refractive index and the thickness of the thin metal film can be estimated by using a personal computer with a numerical analysis technique. Because of its common-path optical configuration and its heterodyne interferometric phase measurement, this method has many merits, such as high stability against surrounding vibrations, high resolution and easy operation. PACS 78.66.Bz; 78.20.Ci; 07.60.Cy     

Measurement of small differences in refractive indices of solutions with interferometric optical method

Based on the principles of both surface plasmon resonance (SPR) and heterodyne interferometry, an optical method for measuring small differences in refractive indices of solutions was proposed. On a specially designed probe, two light beams are incident on both reference and test solutions. The phase differences between the p- and s-polarizations of each reflected light under SPR condition are measured simultaneously with heterodyne interferometric technique. The phase values are substituted into special equations derived from Fresnel's equations. Finally, the difference between the refractive indices of these two solutions can be estimated. The feasibility of this method was demonstrated and the measurement sensitivity of refractive index can reach a value of at least 8.57×10⁻⁷. This method should bear the merits of a simple structure, easy operation, high sensitivity and rapid measurement.     

共路外差法分析牛顿望远镜偏振特性

应用共路外差干涉法分析了牛顿望远镜的偏振特性。根据菲涅耳定律求出了入射光s-偏光和p-偏光入射到望远镜各点的反射率公式。给出了共路外差干涉法测量牛顿望远镜偏振特性的实验装置原理图。采用632.8nm的外差光源,分析了牛顿望远镜对s-偏光和p-偏光反射系数、相位差以及对入射光偏振度的影响,根据入射角度的不同绘制了相应的变化曲线。结果表明：镀有铝膜的牛顿望远镜对入射光偏振特性影响较小,s-偏光和p-偏光反射系数相差不到0.01,偏振度变化不超过0.07,适用于激光遥感偏振成像的接收系统。     

频差偏差对全视场外差测量精度的影响

根据全视场外差测量的相关理论,推导了频差偏差与仪器测量精度的相互关系.分析了频差大小、频差偏差、采集初始时间、初始相位、采样频率和采样周期数等相关参数对测量精度的影响.研究结果可以作为全视场外差测量设备设计、参数选取的理论依据;并给出了通过合理选择采样时间和采样帧数提高测量精度的一种方法.     

U-shaped optical fiber sensor based on multiple total internal reflections in heterodyne interferometry

In this paper, an optical fiber sensor based on multiple total internal reflections (MTIRs) in heterodyne interferometry is proposed. With the optical fiber sensor the phase shift difference due to the multiple total internal reflections effect between the p- and s-polarizations is measured by using heterodyne interferometry. Substituting the phase shift difference into Fresnel's equations, the refractive index for the tested medium can be calculated. The resolution of the sensor can reach 1.6×10^?6 refractive index unit (RIU). The optical fiber sensor could be valuable for chemical, biological and biochemical sensing. It has some merits, such as, high resolution and stability, high sensitivity, high resolution and real-time measurement.     

Surface profile measurement using laser-scanning angle deviation microscopy

Laser-scanning angular deviation microscopy based on the small angle measurement using surface plasmon resonance (SPR) phase detection technique is proposed. The phase shift coming from a SPR sensor is measured by a common-path heterodyne interferometry. This phase deviation is proportional to the beam converging or diverging angle, due to the specimen departing from the focal plane of objective lens. Using the phase deviations, one can calculate the surface profile by use of numerical method. The specimen could be scanned in real-time and the axial-resolution could be better than 1 nm. PACS 07.79-v; 68.37.-d; 73.20.Mf; 42.30.Wb; 42.62.Eh     

Investigation of glass panels thickness profile by all-fiber digital heterodyne interferometry

All-fiber digital heterodyne interferometry is a laser metrology technique employing pseudo-random codes phase modulated onto an optical carrier signal. In this heterodyne interferometer system, the optical signal includes signal reflected and transmitted from the sample, respectively. Compared with the conventional heterodyne interferometry, this enhanced optical system has much higher measurement sensitivity, and can distinguish the signal which reflected from the front and the rear surface of the sample. Analysis and simulation for the digital heterodyne interferometry are presented. It takes approximately 4 s to scan the whole surface with the diameter of 300 mm. The thickness profile of the sample is obtained in the experiment. The discussion about the experiment is given finally.     

孔径透射率调制对外差探测的影响

信号光与本地光的夹角是影响探测器输出外差信号强度的主要因素。当夹角过大时,甚至不能检测到外差信号。通过分析提出,外差信号的振幅实际上是接收孔径透射率函数的傅里叶变换,以此为依据提出一种降低失配角对外差信号影响的方法,即在接收孔径处放置透射率分布满足一定函数形式的透过型元件,使其傅里叶频谱满足预定的要求,这种情况下两光束夹角增大时,探测器输出的外差信号强度能得到增强,从而降低了对探测系统瞄准精度的要求。     

A phase sensitive optical rotation measurement in a scattered chiral medium using a Zeeman laser

A novel circular polarized optical heterodyne interferometer using a Zeeman laser to measure optical rotation both in nonscattered and scattered chiral medium is proposed. A pair of correlated orthogonal circular polarized light waves of different temporal frequency propagating in the chiral medium at different speed is studied. This results in phase retardation between circular polarized light waves of which the phase difference is proportional to the optical rotation angle of a linear polarized light in a chiral medium. In the mean time, two orthogonal circular polarized light waves can be treated as a circular polarized photon pair that is able to reduce the scattering effect in a scattered chiral medium. Then the optical rotation angle can be measured in the scattering medium. In addition, a common-path configuration with respect to circular polarized light waves immune the background noise. This further improves the sensitivity on optical rotation measurement based on phase difference detection.     

The separation of out-of-plane displacement from in-plane components by fringe carrier method based on large image-shearing ESPI

A fringe carrier method for separating out-of-plane displacement from in-plane components based on large image-shearing electronic speckle pattern interferometry (ESPI) is presented. If the test object is respectively illuminated by two expanded symmetric illuminations in large image-shearing ESPI, two interferometers are formed. Carrier fringe patterns can be introduced by tilting reference surface a small angle. The carrier fringe patterns are demodulated after deformation of the object. Two phase maps, which include out-of-plane and in-plane displacement, can be obtained by using Fourier transform. Then out-of-plane displacement can be easily separated from in-plane displacement by simple operation between two unwrapped phase distributions. The principle of spatial carrier frequency modulation in large image-shearing ESPI is discussed. A typical three-point-bending experiment is completed. Experimental results are offered. The results show that the method offers high visibility of carrier fringes. And the system presented does not need a special beam as a reference light and has simple optical setup.     

Temporal heterodyne shearing speckle pattern interferometry

Shearing speckle pattern interferometry is a full-field speckle interferometric technique used to determine surface displacement derivatives. In this paper, a new measurement system of real-time heterodyne shearography interferometry is presented. This system combined with heterodyne measurement, shearography interferometry and time domain signal processing technology can dynamically detect the out-of-plane displacement gradient. The principles and system arrangement are described. Using the Jones matrix, the mathematical expression of light intensity distribution passing through this system is deduced. A preliminary experiment was performed to demonstrate the performance of this new device, and simulations were conducted using the finite element method. Comparison of results shows that quantitative measurement of the displacement derivative has been achieved.     

Recent developments in laser-diode interferometry

Laser-diode (LD) interferometry based on heterodyne techniques is described. The developments covered include: sinusoidal phase- modulating, distance-measuring feedback and phase-shifting interferometry. The wavelength is controlled by the laser injection current and is continuously or stepwise changed to introduce a time-varying phase difference between the two beams of an interferometer with unbalanced optical path lengths. A feedback interferometer is described with electronics to stabilize the phase shift and to lock the interferometer on a preset phase condition by controlling the injection current of the LD. An automated phase-measuring interferometric system is developed in which the laser current is changed to synchronize intensity data acquisition with the clocks of a charge-coupled device. A typical experimental result shows measurements of the profile of a diamond- turned Al surface.     

二维光栅角度信号响应函数研究

本文在平行相干光照明条件下,推导出了二维光栅剪切成像系统的角度信号响应函数,并描绘出了角度响应函数二维曲面.虽然光栅剪切成像系统常用的分束光栅有四种,分析光栅有三种,分析光栅和分束光栅之间还存在多种不同组合,但是产生的角度信号响应函数曲面却只有三种,即峰型位移曲面、谷型位移曲面和峰谷对称型位移曲面.其中峰型位移曲面和谷型位移曲面之间具有数值互补关系,由此还可以把峰型位移曲面和谷型位移曲面归纳为一种,最终只需要考虑两种位移曲面.这个理论结果无疑显著简化了人们对二维光栅剪切成像的认识,将对今后讨论定量提取二维角度信号的工作奠定基础.     

Spectral heterodyne tomography

A novel method of optical coherent tomography—spectral heterodyne tomography—is proposed. Spectral heterodyne tomography is based on parallel heterodyne detection of a multitude of frequencies of the light backscattered by an object under study. The result of this detection is a spectral distribution of the amplitude and phase of the scattered radiation. Subsequent numerical processing allows one to find the distribution of scattering centers over the depth corresponding to the point of entrance of the incident light. The proposed method is potentially characterized by a higher efficiency as compared with the most successful approach to optical coherence tomography, based on heterodyne scanning interferometry.     

Method of making mosaic gratings by using a two-color heterodyne interferometer containing a reference grating

We propose and demonstrate a two-color heterodyne interferometric method for making a perfect mosaic of two planar gratings that can substitute for a single and larger grating without introducing wavefront aberration at any wavelength. The lateral and longitudinal phase errors are separated and eliminated by use of two wavelengths in the interferometry. The accuracy of the phase difference measurement is improved by this heterodyne scheme. The method ensures that the lateral gap between the two subaperture gratings is an integer multiple of the grating period. For a pair of 0.72 microm period gratings we experimentally achieved a lateral alignment error of less than 1% of the grating period.