Path-length distribution and path-length-resolved Doppler measurements of multiply scattered photons by use of low-coherence interferometry

We report first results of measurements by low-coherence Doppler interferometry of the path-length distribution of photons undergoing multiple scattering in a highly turbid medium. We use a Mach-Zehnder interferometer with multimode graded-index fibers and a superluminescent diode as the light source. The path-length distribution is obtained by recording of the heterodyne fluctuations that arise from the Brownian motion of particles in an Intralipid suspension as a function of the optical path length. The experimental path-length distribution is in good agreement with predictions of Monte Carlo simulations. In the heterodyne spectrum, an increase of the mean Doppler frequency with path length is observed.     

MEMS profilometry by low coherence phase shifting interferometry: Effect of the light spectrum for high precision measurements

A white light interferometer can be used to measure profiles of a few nanometers and is therefore particularly well adapted for micro electro mechanical systems characterization. We present theoretical and experimental results on the profile precision as a function of the light source spectrum. We demonstrate that even if a broadband source is used in the phase shifting mode, the knowledge of the light spectrum allows to calculate a correction factor. This factor determines the local effective wavelength and can be used in order to increase the measurement precision of sample profiles.     

Determination of path length difference by low coherence interference spectrum

Path length difference is the key parameter in two-beam interferometer, especially in low coherence interferometer. It determines the visibility of the interference fringes. In this study, we present a method to determine the path length difference between two arms of a fiber optic Mach–Zehnder interferometer by evaluating the peaks of power distribution of the interference spectrum with a wide band light source. The experimental results are in close agreement with the theoretical calculations.     

Doppler effect's contribution to ultrasonic modulation of multiply scattered coherent light: Monte Carlo modeling

Modulation of light by ultrasound in turbid media is investigated by modified public domain software based on the Monte Carlo algorithm. Apart from the recognized modulation mechanisms, originating in scatterers' displacements and refractive index modulation, an additional mechanism, evolving from Doppler shift during photon scattering, is considered. Comparison of the relative contributions from all three mechanisms to light modulation by ultrasound is performed for different medium scattering properties and ultrasound frequencies. Refractive index modulation remains the strongest mechanism for light modulation by ultrasound, but for high ultrasound frequencies and for large scattering coefficients the Doppler effect can become dominant.     

Mechanisms of ultrasonic modulation of multiply scattered incoherent light based on diffusion theory

An analytic equation interpreting the intensity of ultrasound-modulated scattering light is derived,based on diffusion theory and previous explanations of the intensity modulation mechanism.Furthermore,an experiment of ultrasonic modulation of incoherent light in a scattering medium is developed.This analytical model agrees well with experimental results,which confirms the validity of the proposed intensity modulation mechanism.The model supplements the existing research on the ultrasonic modulation mechanism of scattering light.     

Efficient phase matching algorithm for measurements of ultrathin indium tin oxide film thickness in white light interferometry

Optical Review - A novel method is proposed to measure the thickness of the indium tin oxide (ITO) film, which is less than 20 nm, using valid Fourier’s phase information of white...     

Measurement of wedge angle of a transparent parallel plate using quasi-monochromatic light source and phase shifting interferometry

A new technique (to our knowledge), for the measurement of residual wedge angle (RWA) of high optical quality transparent nearly parallel plate (PP), using a quasi-monochromatic light source, is presented. Advantages and drawbacks of the technique and the results obtained for a PP, using a filtered white light source, is discussed. A slightly modified optical setup for accurate determination of RWA, using phase shifting interferometry (PSI), has been described. Results obtained, applying PSI, for a validation experiment and for the determination of RWA of a quasi-PP is presented. The PSI based technique does not suffer from any measurement ambiguities due to limitation in effective beam aperture. Hence the technique is suitable for high accuracy measurement of RWA of PP. In both the optical setups, presented in this paper, the respective interfering beams travel the same optical circuit and are thus subject to same perturbation in optical path, due to external mechanical vibration, which finally cancels out. Thus the measurements are much less affected by external vibrations. Since the respective interfering beams undergo identical reflections and transmissions, the visibility or contrast of the interference fringes is very good.     

Depolarization of multiply scattered light in transmission through a turbid medium with large particles

An approximate analytical method for solving the vector radiative transfer equation is proposed. The method is based on the assumption that single scattering of light by large-scale inhomogeneities occurs predominantly through small angles. The method is applied to calculate the polarization state of multiply scattered light. The results obtained are discussed for various turbid media.     

Measurement of optical constants of thin polymer films using spectrally resolved white light interferometry

Using the spectrally resolved white light interferometry we present our experimental results on the measurement of the optical constants of thin polymer films coated on a transparent substrate. As an extension to our previous work (J. Opt. Soc. Am. B12, 1559 (1995)) on thick glass plates, we have shown here that this technique can be effectively applied to very thin polymer films also. We have improved the accuracy of our results by using the Sellmeier dispersion formula for fitting the data. From the width and position of the zero-order fringe and the frequency of modulations in the white light spectrum, the refractive indexn(λ) and thicknesst of the thin polymer films are calculated. To study the accuracies involved in the technique, PVA, PMMA and PS films of varied thicknesses are coated on glass plates and the measured values are compared with ellipsometer studies.     

Simultaneous measurement of flow velocity and Doppler angle by the use of Doppler optical coherence tomography

Monitoring blood flow velocity could have great value for biomedical research and clinical diagnostics. One of current restrictions to determine flow velocity by the use of Doppler optical coherence tomography (Doppler OCT) is that the Doppler angle should be predefined. However, from a practical point of view, it is not easy to predetermine Doppler angle for a flow beneath the tissue surface. In this work, a novel method for measuring both flow velocity and Doppler angle simultaneously by the use of Doppler OCT is proposed and demonstrated. Based on Doppler spectrum analysis, this technique measures both longitudinal and transverse components of flow velocity by detecting its Doppler shift and Doppler bandwidth to determine velocity and Doppler angle simultaneously. Such a technique extends flow velocity measurement into a broadening practical use of Doppler OCT where Doppler angle would not need to be predefined, for example, blood flow beneath the tissue surface. Therefore, with this technique, Doppler OCT could be applied to more practical diagnoses of microcirculation.     

Nonlinear interferometry and phase measurements for surface second-harmonic generation in a dispersive geometry

Direct measurement of the phase of the surface nonlinear susceptibility is based on the interference of nonlinear optical signals. Up to now, this has not been possible for Second-Harmonic Generation (SHG) in geometries such as Total Internal Reflection (TIR) due to the refractive dispersion of harmonic and fundamental light created in TIR. We demonstrate two schemes which enable us to overcome this dispersion, leading to interference between two second-harmonic signals generated consecutively by the same laser. The advantages and limitations of the two approaches are discussed. We use this technique to check the theoretical predictions for the nonlinear Fresnel factors for SHG in the TIR geometry.Paper presented at the 129th HE-Heraeus-Seminar on Surface Studies by Nonlinear Laser Spectroscopies, Kassel, Germany, May 30 to June 1, 1994     

Full-field measurement of the phase retardation for birefringent elements by using common path heterodyne interferometry

A collimated heterodyne light passes through the tested material and an analyzer, full-field interference signals are taken by a fast CMOS camera. The series of interference intensities recorded at any pixel are the sampling points of a sinusoidal signal. From those points, the associated argument of that pixel can be derived by a least-square sine fitting algorithm on IEEE 1241 Standards. Subtracting the average argument of the reference signal, the phase retardation of that pixel can be obtained. The phase retardations of other pixels can be obtained similarly. Its validity is demonstrated.     

Evaluation of spectral phase in spectrally resolved white-light interferometry: Comparative study of single-frame techniques

Spectral phase in a white-light interferogram contains information about the absolute optical path difference (OPD) in the interferometer. Evaluation of spectral phase is therefore important in applications such as profilometry with white light. In spectrally resolved white-light interferometry (SRWLI) the white-light interferogram is spectrally decomposed by a spectrometer in order to determine this phase. Several single-frame techniques in SRWLI have been proposed for the evaluation of the phase including Fourier transform, Hilbert transform, spatial phase shifting, windowed Fourier transform and wavelet transform. In this paper we present a comparative study of these techniques in this application in relation to the temporal phase-shifting technique which is a multi- frame method. Further, we also propose a modified method to remove the influence of source spectrum modulation in Hilbert transform procedure.     

System for coincidence measurements of the ions desorbed and projectiles scattered from noble gas solid surfaces by slow multiply charged ion impacts

We have developed a new experimental apparatus for performing coincidence measurements of the ions desorbed and projectiles scattered from the surfaces of noble gas solids by slow multiply charged ion impacts at grazing incidence angles. This simultaneously measures the desorbed ions' flight times and the scattered projectiles' charge states. We also conduct experiments on 6 keV Ar⁶⁺ impacts onto a solid Ne surface using the device.     

Optimum quantum state of light for gravitational-wave interferometry

The laser interferometric gravitational-wave detectors are sensitive to the quantum state of light employed in the dark port of interferometric system. In this paper a general quantum state for the dark input port is assumed. The quantum state of light is expanded versus the Fock states. The quantum noise of interferometric system is computed as a function of the quantum state of light. The variational method and the genetic algorithm are employed to determine the coefficients of the dark input port and the laser input power for the minimization of the quantum noise. Calculation shows that the optimum quantum state for the dark input port is very close to the vacuum squeezed state. For this optimum quantum state the quantum noise and optimum laser power reduces one order of magnitude relative to the conventional interferometer.     

用于干涉测量的短相干固体激光器光谱纵模特性

对固体激光器的光谱纵模特性与复相干度的关系进行了理论分析,推导出了在任意纵模数下的光程差与复相干度的关系式。通过比较窄谱宽激光器与谱宽较宽的测量用普通固体激光器在不同纵模数下的复相干度特性,发现固体激光器谱宽较宽,复相干度衰减较快,不同纵模数下的衰减速度和周期不同,纵模数越多复相干度震荡衰减越快,不会出现周期性的高相干区域。根据理论分析搭建了一台用于干涉测量的短相干多纵模固体激光器,并对其光谱纵模特性和相干长度进行了测量,实验结果与计算结果一致。     

辐射场的起伏对囚禁离子的量子相干性的影响

研究了囚禁离子与一随机相位的驻波场相互作用时的量子动力学行为,讨论了辐射场的起伏对囚禁离子的量子崩塌-回复特性的影响.对于相位扩散模型获得了这个问题的解析解.     

Space-time resolved reflectivity measurements of picosecond laser-pulse induced phase transitions in (111) silicon surface layers

The changes in reflectivity of a silicon surface, irradiated by a green picosecond pulse, are probed during and following that pulse with a spatial resolution of 10 m. The data indicate the development of a liquid phase, and a resolidification either into a single crystal or an amorphous phase. The latter has a characteristic ring-type pattern, and occurs only at locations where the incident picosecond laser fluence lies between 0.2 and 0.26 J/cm². The reflectivity data appear to be in good quantitative agreement with a simple heating model, in which the electrons and phonons maintain a local thermodynamic equilibrium on a picosecond time scale.On leave from Philips Research Laboratories, D-2000 Hamburg 54, F. R. Germany     

Measurements of phase retardation and principal axis angle using an electro-optic modulated Mach–Zehnder interferometer

This paper presents an electro-optic modulated circular heterodyne modified Mach–Zehnder interferometer and a convenient two-phase signal-processing algorithm for the measurement of variations in the magnitude of phase retardation and the angle of principal axis in optical materials. The developed method solves the problems of normalized intensity jump and limited phase retardation measurement range associated with the circular heterodyne interferometer proposed previously. The present method uses a saw-tooth wave signal to drive an electro-optic (EO) modulator, and employs a lock-in amplifier to demodulate the principal axis angle and the phase retardation. Specifically, this paper considers two main sources of measurement errors, namely the misorientation of the EO modulator and the reflection phase retardation of the beam splitter. Furthermore, the study develops calibration procedures and identifies a means to minimize measurement errors induced by the reflection phase retardation of the beam splitter.     

Signal processing method of phase correction for laser heterodyne interferometry

A novel signal processing method of movement direction identification and phase correction is presented for laser heterodyne interferometry. Based on the reference signal, four intervals with phase difference of 90° each other are set up. The real-time movement direction identification and the integer fringe counting are realized by detecting the times that the rising-edge of the measurement signal crosses the intervals. The phase correction approach is proposed in detail to solve the fraction phase compensation when the initial phase difference is not equal to the zero phase difference. Three experiments of the stability test, the nanometer and micrometer displacement tests on bi-directional movement were performed to demonstrate the usefulness and feasibility of the presented signal processing method.