白光相移干涉中频谱对测量精度的影响

在相移干涉中有时采用白光干涉来扩大深度测量范围,白光光源的使用,缩短了光束的相干长度,降低了测量精度。本文从干涉理论出发推导了白光相移干涉法测量三维表面形貌的计算公式,通过数值积分的方法分析了干涉光频谱对测量精度的影响。分析表明,在白光相移干涉测量中表面形貌的测量精度与中心波长和频谱宽度有关,白光频谱越宽,测量精度越低,中心波长越大,测量精度越高。     

Phase shift calibration in speckle photography—a first step to practical real-time analysis of speckle correlation fringes

Abstract

The paper is focused on the implemention of phase shift calibration in speckle photography with a view to introducing the possibility of realtime analysis of displacement data obtained by the method. Phase reversal is accomplished by varying pressure within an air-filled quartz cell inserted in the pump beam in a conventional two-beam coupling arrangement. It is shown that phase reversal is achieved when a π-shifted speckle pattern overlaps on an unshifted speckle pattern at the observation plane. This phenomenon is exploited for calibration of the phase shift. Experimental results show good agreement with the theory.     

Theoretical analysis of fluorescence light shifts in optically pumped cesium beam frequency standards

Shirley's analysis (1985) is generalized to calculate the fluorescence light shifts in various optically pumped Cs beam standards, especially in the two-beam type frequency standard that enables a real-time correction of an end-to-end cavity phase shift. Using tables of light shift coefficients and mean fluorescence photon numbers per atom, fluorescence light shifts in one- and two-beam type optically pumped Cs beam frequency standards using noncycling detection and cycling detection, are evaluated. Results obtained are useful to correct the fluorescence light shifts in optically pumped Cs beam frequency standards.     

Analysis tools for the accurate evaluation of a small frequency standard

The short, optically pumped cesium beam tube developed at Laboratoire de l'Horloge Atomique has been carefully evaluated. For that purpose, we have developed a digital servo system that controls three parameters: the frequency of the ultra stable oscillator (USO), the microwave power of the signal experienced by the cesium atoms, and the static magnetic field applied to the atoms. The frequency standard shows a very satisfactory level of short- and medium-term frequency stabilities. A relative frequency offset, measured to be 4.10(-12 ), results mainly from the residual phase difference between the oscillatory fields in the two interaction regions, which is due to imperfection in cavity symmetry. We present two different means of analyzing the causes of this spurious frequency offset using theoretical and experimental considerations. First, a numerical simulation of the beam tube response is performed as a function of the microwave field amplitude for different values of the residual phase difference DeltaPhi. Results include the cavity-pulling effect. Compared with the measured frequency offset, the numerical simulation leads to a second-order Doppler shift of -3.3 mHz and a residual phase difference, DeltaPhi, between the fields interacting with the atoms in the second and first regions of the Ramsey cavity, amounting to +150 murad. Second, an experimental method of measurement of DeltaPhi without beam reversal is implemented. The latter yields DeltaPhi=155+/-17 murad. Finally, the clock accuracy is determined. It is equal to +/-14.10(-13).     

A beam reversal experiment for the estimation of microwave powershifts in an optically pumped Cs beam frequency standard

The characteristics of microwave-power-dependent frequency shifts of an optically pumped Cs frequency standard are reported. The general features of the shifts are in good agreement with simple theoretical predictions. The shift is quite symmetrical in beam reversal, and the standard deviation of the difference between the observed and predicted shift is about 6×10-14     

Total internal reflection of pulsed light beam upon ideal non-absorbing plasma

Total internal reflection (TIR) of a pulsed light beam from vacuum incident upon an ideal non-absorbing plasma was investigated theoretically using the Fourier transform method. Because of the Goos–Hänchen effect, the reflected pulsed beam undergoes distortions such as carrier frequency shift and chirp. The distortions are magnified on condition that the pulsed beam is TM-polarized and illuminates the interface at large angle of incidence, which should be avoided for reflection of pulsed beam upon optical mirrors with metal film. Meanwhile, it is shown that the Goos–Hänchen shift and time delay of this TIR can be both positive and negative, which is consistent with the results obtained from stationary phase theory.     

Total internal reflection for precision small-angle measurement

A method for precision small-angle measurement is proposed. This method is based on the total-internal-reflection effect of a light beam at a pair of glass prisms. Angular displacement of the light beam is measured when the intensity change of the reflected beam is detected as a result of the relative phase shift between the s- and the p-polarized beams. An initial phase shift between the s- and the p-polarized components is introduced to increase measurement sensitivity. For increased measurement linearity and reduced effect of laser power fluctuation on the output, a differential method is used in which the light beam is split equally into two beams, each reflected at a prism and detected by a photodiode. The output is obtained as the difference of the two detected intensities divided by their sum. A prototype device was built, which demonstrated a nonlinearity error of 1.3% in a measurement range of ?0.6 degrees or 0.4% in ?0.3 degrees . The peak-to-peak noise level was found to be at approximately 0.5 arc sec. This noise level can be reduced further and resolution increased by a reduction of the measurement range.     

Light shifts in an optically pumped Cs beam frequency standard

Frequency shifts caused by light, which are called light shifts in an optically pumped Cs beam frequency standard, were estimated. Frequency shifts due to monolithic light were measured by introducing laser light along the Cs beam. The relative dependence of the shift on the laser frequency agreed very well with the theory, but the absolute shift was between one and two times that of the theory. The light shifts due to the optical pumping and optical detection in the standard are estimated to be less than 2×10^-15 and 1×10^-16, respectively, and both are negligible at the present state of development     

Measurement of dynamic end-to-end cavity phase shifts in cesium-fountain frequency standards

We have measured a previously unobserved systematic frequency shift in our cesium-fountain frequency standard, NIST-F1. This shift, predicted theoretically previously, mimics the well-known end-to-end phase shift in atomic beam standards when synchronous thermal transients are present. Detuning the microwave cavity several megahertz from resonance reduces this effect to the deltaf/f = 1o(-16) level.     

Optical method for measuring optical rotation angle and refractive index of chiral solution

Based on the phenomena of Brewster's angle and the principles of common-path heterodyne interferometry, we present an optical method for measuring the optical rotation angle and the refractive index of a chiral solution simultaneously in one optical configuration. A heterodyne light beam and a circularly polarized heterodyne light beam are separately guided to project onto the interface of a semicircle glass and a chiral solution. One of the beams is transmitted through the solution, and the other is reflected near Brewster's angle at the interface. Then the two beams pass through polarization components respectively for interference. The phase differences of the two interference signals used to determine the rotation angle and the refractive index become very high with the proper azimuth angles of some polarization components, hence achieving an accurate rotational angle and a refractive index. The feasibility of the measuring method was demonstrated by our experimental results. This method should bear the merits of high accuracy, short sample medium length, and simpler operational endeavor.     

Interferometric analysis of nanostructured surface profiles: correcting material-dependent phase shifts

We present a technique to correct interferometry for the material-dependent phase shift that accompanies reflection. Such corrections are needed for nanometer accuracy of surfaces that are not of homogeneous composition. We adapt the general theory of reflection from surfaces in which there are irregular and unresolved areas of several materials to treat the specific case in which only two materials are present, as is the case for many practical applications. We show, for the approximation of a large numerical aperture that collects all reflected light, how measurements of three quantities, together with known values of the optical constants, allow determination of the material-dependent phase shift at each position on the surface. We demonstrate with numerical simulation, appropriate to measuring a surface of alumina in which optically unresolved titanium carbide granules are embedded, that our approach also succeeds, with nanometer accuracy, when the numerical aperture is small. The method is discussed for use with a miniature interferometric phase sensor, but it has application to any interferometer.     

Optical manipulation of multiple stable states in photorefractive four-wave mixing

Abstract

We propose an approach to manipulate the convergence in multiple solutions of phase conjugate reflectivity in photorefractive four-wave mixing. Although a method forcibly adding a π-phase shift to an incident beam has been already proposed to control the reflectivity, some restrictions have been required in the boundary conditions for the successful operation. Here, we control the reflectivity with the boundary conditions in which the phase shift operation is ineffective by itself. In our method, the phase shift operation is combined with the procedure of turning an incident beam on and off. With a numerical analysis of four-wave mixing, we show that our new approach brings drastic change in the spatial distribution of the index grating and leads the phase conjugate reflectivity which was not manipulated previously.     

Far-field scattering of an axisymmetric laser beam of arbitrary profile by an on-axis spherical particle

Experimental laser beam profiles often deviate somewhat from the ideal Gaussian shape of the TEM(00) laser mode. In order to take these deviations into account when calculating light scattering, we propose a method for approximating the beam shape coefficients in the partial wave expansion of an experimental laser beam. We then compute scattering by a single dielectric spherical particle placed on the beam's axis using this method and compare our results to laboratory data. Our model calculations fit the laboratory data well.     

Quantum-well enhancement of the Goos-Hänchen shift for p-polarized beams in a two-prism configuration

It is predicted that the Goos-H?nchen effect can be resonantly enhanced by placing a metallic quantum well (ultrathin film) at the dielectric-vacuum (air) interface. We study the enhancement of the phenomenon, as it appears in frustrated total internal reflection with p-polarized light, both theoretically and numerically. Starting from boundary conditions for the electromagnetic field, which in a self-consistent manner take into account the quantum-well dynamics, we derive new expressions for the amplitude reflection and transmission coefficients of light, and from these the stationary phase approximation to the Goos-H?nchen shifts is obtained. It is shown that large peaks appear in the Goos-H?nchen shift below the critical angle in reflection, and these are located at the minima for the energy reflection coefficient. Both positive and negative shifts may occur, and the number of peaks depends on the gap width. To determine the accuracy of the simple stationary phase approximation, we carry out a rigorous stationary energy-transport calculation of the Goos-H?nchen shift. Although the overall agreement between the two approaches is good, the stationary phase approach mostly overestimates the peak heights. For a Gaussian incident beam, the resonance displacement of the reflected beam can be as large as the Gaussian width parameter. It is suggested that the possible relation between the Goos-H?nchen effect and the optical tunneling phenomenon in the two-prism configuration should be reinvestigated by depositing quantum wells on the glass-vacuum interfaces to obtain a better spatial photon localization.     

Implementation of the beam reversal technique on compact cesiumclocks: towards an improvement in accuracy

Reports the evaluation of the residual phase difference ▵φ in a short (18 cm) Ramsey cavity by implementing the beam reversal technique in an optically pumped cesium beam clock. ▵φ is measured to be 21 ±1.5 μrad, allowing a more accurate evaluation of the frequency performance of this small cesium clock. Finally, the clock accuracy is equal to 1.1·10^-13     

Optical Kerr coefficient measurement in coiled high-birefringent fibers

The optical Kerr effect in coiled high-birefringent fibers was measured based on a double-beam polarimetric method. A Q-switched Nd:YAG laser, operating at 1.064 mum (FWHM of 80 ns at 1 kHz), was used as the pump beam and a cw 0.633-mum He-Ne laser was used as the probe beam with its polarization fixed at 45 degrees with respect to the birefringent axis whereas orientation of the linearly polarized pump light varied. The phase shifts induced by an intense pump beam in a short bow-tie high-birefringent fiber were determined for different fiber lengths coiled into 15- and 30-cm-diameter drums. It was found that the induced phase shift changes drastically with the state of polarization of the pump light. A strong dependence of the phase shift on orientations of linear pump polarization is attributed to differential losses of eigenmodes peculiar to birefringent axes. Therefore, optical Kerr coefficients remain unchanged regardless of the dependence of the nonlinear response of the coiled high-birefringent fibers on pump polarization.     

Effects of Arbitrary Phase Shift on the Higher-order Self-diffraction in Absorptive Photorefractive Medium

Abstract

Interactions between optical beams incident upon and two higher-order self-diffracted beams generated within an absorptive photorefractive material are investigated by solving a set of coupled differential equations. The medium is assumed to be free of linear and circular birefringence. Arbitrary phase shift between the light grating and the refractive index grating is considered. It is shown that under favourable conditions, a significant amount of power may be transferred to the newly generated waves. Investigated are the effects of phase shift, thickness and absorption of the crystal, coupling constant and off-Bragg parameter on energy transfer to the higher-order diffracted beams. It is shown that in the case of phase-shift other than π/2, higher-order self-diffracted beams can be generated on both sides of the input beams. Coupled wave equations are solved numerically by a fourth-order Runge-Kutta method and results are presented in graphical form. This analysis is valid for the near collinear interacting beam geometry, i.e. in the case of large grating spacing.     

An interferometric method for simultaneously determination the phase retardation and fast-axis azimuth angle of a wave plate

In this study, an interferometric method was proposed for the simultaneous measurement of phase retardation and fast-axis azimuth angle of a wave plate by using a Mach–Zehnder interferometer. The wave plate to be tested is placed in one of the light passages in the interferometer, and two analyzers with transmission axes at horizontal and vertical orientations are arranged at the two output regions. When a linearly polarized laser light beam is passed through the interferometer, two interference light beams are simultaneously generated. Through an analysis of the intensities of the two light beams, the phase retardation and fast-axis azimuth angle of the tested wave plate can be simultaneously determined using specially derived equations. The feasibility of the proposed method was demonstrated using measurements of zero-order half-wave and zero-order quarter-wave plates. The proposed method is easy to operate, enables rapid measurement, and has high stability and accuracy.     

Edge location by use of optical phase variation

Traditional optical methods for locating an edge are based on light intensity variation with respect to a reference triggering level. Since the intensity variation is subject to stray light, the intensity variation of the light source, and the triggering level variation, the exact position of the edge cannot be determined. We describe a method for edge location that uses a phase variation in a modified differential interferometer. The maximal point of the slope of the phase variation across an edge is determined exactly by the relative position between the focused beam spot and the detected edge if the initial intensity ratio of the two single-frequency interference beams is kept unchanged. Therefore the phase variation can be used to locate the edge with high resolution and accuracy. To make practical use of the phase variation, the second derivative of the phase was used as a monotonic zero-crossing signal across the edge. The theoretical and the experimental verification have been conducted in detail. The results of the experiment show the feasibility of edge location when phase variation is used. The scheme is not affected by stray light and the intensity variation of the light source.     

位相测量轮廓术的仿真研究：系统结构参数的影响

在一个结构光三维传感器的计算机仿真系统上，研究了由观察光场重建三维面形的过程，以及系统主要结构参对位相测量轮廓术的影响，提出了根据对标准平面的测量结果对参数进行修正的方法，为实际系统的结构调整和参数校正提供了一种新的途径。