Performance analyses of an infrared single-mode all-fiber-optic Fourier-transform spectrometer

Stretching one of a pair of fiber arms can be done to realize optical phase modulation for an IR single-mode all-fiber-optic Fourier-transform spectrometer (FTS). But this operation will inevitably limit the physical performance of a FTS. We study these limits theoretically and experimentally. The optical path difference (OPD) will be dispersive. At the first-order approximation, this OPD dispersion will result in a shift in the recovered spectra. The spectral resolution and the sampling distance will also be dispersive. Linear birefringence introduced when a curved fiber is stretched will affect the final spectra. This effect can be eliminated by real-time compensation and (or) by system design. Errors encountered uniquely in the all-fiber-optic FTS in the optical phase domain, such as the fiber-parameter errors, nonlinearity of the piezoelectric cylinder, and their effects on the spectra are analyzed, from which we deduce the requirements for calibration. Finally, calibration methods for optical phase modulation are discussed.     

Chromatic Dispersion Effects on Infrared Single-mode All-fibre Optic Double Fourier Interferometric Imaging

Abstract

In an infrared (IR) single-mode fibre-linked optical telescope array, not only the spatial but also the spectral resolution of a star can be simultaneously obtained as long as the fibre arms are stretched to generate the optical path difference (OPD) modulation. This imaging technique is called IR single-mode (SM) all-fibre optic (AFO) double Fourier interferometry (DFI). The fibre-stretching operation will inevitably introduce a chromatic dispersion problem and make the OPD wavelength dependent. In this paper, a point source response expression for the IR SM AFO DFI is first established. Accordingly, the recovered mutual spectral density (MSD) is deduced. One of the dispersion effects on MSD is a wavenumber shift; this and other effects on MSD are discussed. Then, we establish the final map expression for a point source and discuss the dispersion effects on it. One of these effects is a shift of the image position. Finally, we discuss the effects of the first-order approximation of the OPD. To reduce these effects, a method of dividing the whole spectral band into subbands is pointed out and discussed.     

Measuring intermodal dispersion in optical fibres using white-light spectral interferometry with the compensated michelson interferometer

Abstract

Employing a low-resolution miniature fibre-optic spectrometer, it is demonstrated that the spectral interference fringes are resolved at the output of a tandem configuration of the compensated (non-dispersive) Michelson interferometer and a two-mode optical fibre only in the vicinity of two different equalization wavelengths. Namely, the overall equalization wavelength at which the optical path difference (OPD) in the interferometer is the same as the group OPD between modes, and the fibre equalization wavelength at which the group OPD between modes is zero. Moreover it is shown that the OPD adjusted in the interferometer and measured as a function of the overall equalization wavelength gives directly the spectral dependence of the intermodal group OPD in an optical fibre. Thus the new technique of white-light spectral interferometry is used to measure intermodal dispersion in two different two-mode optical fibres in the spectral range approximately from 620 to 850 nm.     

Spatial beam shaping of ultrashort laser pulses: theory and experiment

We studied the spatial intensity profile of an ultrashort laser pulse passing through a laser beam shaping system, which uses diffractive optical elements to reshape a Gaussian beam profile into a flat-topped distribution. Both dispersion and nonlinear self-phase modulation are included in the theoretical model. Our calculation shows that this system works well for ultrashort pulses (approximately 100 fs) when the pulse peak intensity is less than 5 x 10(11) W/cm2. Experimental results are presented for 136 fs pulses at 800 nm wavelength from a Ti:sapphire laser with a 6 nJ pulse energy. We also studied the effects of lateral misalignment, beam-size deviation, and defocusing on the energy fluence profile.     

Simulation of Error in Digital Photoelasticity by Jones Calculus

Abstract: The accuracy of parameter evaluation by automated photoelastic techniques depends on both their theoretical formulation and experimental procedure. The sensitivity of techniques such as phase shifting and load stepping to error in optical misalignment and quarter-wave plate mismatch would be of interest. A generic approach to simulation of error in digital photoelasticity is presented. The simulation has showed how to associate the errors in the phase map to the misalignment of optical elements.     

THE EFFECT OF UNDERCUT, MISALIGNMENT AND RESIDUAL STRESSES ON THE FATIGUE BEHAVIOUR OF BUTT WELDED JOINTS

Abstract— A mathematical model is developed to predict the effect of weld toe undercut, misalignment and residual stresses on the fatigue behaviour of butt welded joints subjected to zero-to-tensile loading. Linear Elastic Fracture Mechanics (LEFM), Finite Element Analysis (FEA) and superposition approaches have been used for the modelling. It has been found that an undercut at the toes of welded joints is one of the most important weld geometry parameters. The reduction of fatigue strength of welded joints with a weld toe undercut is at least twice that of joints without an undercut in comparison with flush-ground welded plate. A misalignment of 5% of plate thickness and an undercut of 2% of plate thickness are fairly representative for the lower boundary of S-N curves of butt joints. The improvement of fatigue limits by means of surface treatments is shown to be effective for both undercut and misaligned joints. This approach is practical for a "Fitness-for-Purpose" assessment of welded joints subject to fatigue conditions.     

Programmable ultrashort optical pulse delay using an acousto-optic deflector

We present an optical pulse delay (OPD) for delaying ultrashort optical pulses that uses an acousto-optic deflector as an active component. The OPD is designed to correct for chromatic dispersion caused by the significant color spectrum of ultrashort pulses. It is intended to be used as one of the components in a three-dimensional memory system based on pulse-collision addressing in two-photon materials. Calculations show that the OPD should be able to provide 65 arbitrary delays with a random access time of ? 1 μs for 100-fs pulses. The power efficiency of the OPD can be as high as 85% and hence permits two units to be cascaded to provide more than 4000 distinct delays. The number of delays and the access time can be optimized such that a fewer number of delays are obtained with a shorter access time, which favors high-speed operations. We provide experimental results that use a Michelson interferometer to measure three different delays, approximately 1 mm apart (equivalent to ?3-ps time delay), obtained with 130-fs pulses. In addition we include an analysis of the performance of acousto-optic devices for both monochromatic light and ultrashort pulsed lasers. Finally, we provide the design of the optical pulse-delay system for a three-dimensional memory application.     

Digital Hilbert transformation for separation measurement of thicknesses and refractive indices of layered objects by use of a wavelength-scanning heterodyne interference confocal microscope

A wavelength-scanning heterodyne interference confocal microscope quickly accomplishes the simultaneous measurement of the thickness and the refractive index of a sample by detection of the amplitude and the phase of the interference signal during a sample scan. However, the measurement range of the optical path difference (OPD) that is obtained from the phase changes is limited by the time response of the phase-locked loop circuit in the FM demodulator. To overcome this limitation and to improve the accuracy of the separation measurement, we propose an OPD detection using digital signal processing with a Hilbert transform. The measurement range is extended approximately five times, and the resolution of the OPD is improved to 5.5 from 9 microm without the electrical noise of the FM demodulator circuit. By applying this method for simultaneous measurement of thickness and the refractive index, we can measure samples 20-30-microm thick with refractive indices between 1 and 1.5.     

Modeling the instrument line shape of Fourier-transform spectrometers within the framework of partial coherence

The instrument line shape (ILS) of Fourier-transform spectrometers is modeled within a framework that enables us to take into account the partial coherence of optical fields. The cross spectral density and the angular coherence functions are used to develop a global ILS model including all possible geometric defects that can be introduced by a realistic two-beam interferometer. Tilt and shear no longer only reduce the modulation efficiency but are presented as contributors to the ILS. The case of an incoherent secondary planar source is covered and agrees with previously known results. However, it shows a coupling among tilt, shear, and optical path difference (OPD). A quasi-coherent source is also studied. Differences between the incoherent and the quasi-coherent cases are highlighted. The relative localization of the reference laser beam in the interferometer is shown to be of significance to provide a sampling scale that minimizes the OPD, or phase, induced by angular misalignment.     

Étude spectroscopique des films minces deposés à l'interface par excitation optique des plasmons de surface

Surface plasmons (SPs) are collective charge density waves which are confined to the interfacial region between an active medium (e.g. silver) and a dielectric (electrolyte). They can be excited by light under the attenuated total reflection condition. We used the focused attenuated total reflection method in which SP excitation is recognized as a dark line in the p-polarized reflected light cone. The presence of an adsorbent or a film leads to modifications in the dispersion curve from which the optical properties of the film can be derived.In this paper we present both theoretical and experimental investigations of thin dielectric films with an optical absorption band. The results show clearly the correlation between the structures which appear in the dispersion curve and the optical properties of the film.In a previous investigation we have studied the pyridine-Ag system and we found that the activation cycle for silver (usually used in surface-enhanced Raman spectroscopy) in a chloride-containing electrolyte and in the presence of pyridine leads to the formation of a surface complex which exhibits an absorption band in the near-IR, a region in which pyridine itself does not absorb. We present here some preliminary results for rhodamine B adsoption on silver in order to correlate quantitatively the optical properties of this well-known dye and the anomalous structures which induces on the SP dispersion curve for silver.     

Interferometric verification for the polarization imaging spectrometer

The optical throughput is usually attenuated by the use of two linear polarizers in a polarization imaging spectrometer. To avoid such attenuation, in some special cases to be determined, one may remove a polarizer. Theoretical formulae for different cases are derived by using the matrix representation of the polarizers, Savart plate, and random unpolarized electromagnetic beam. The theoretical and experimental results comply with the Fresnel–Arago polarization interference laws. The normal case, without removing a polarizer, adapted itself to general applications, and the abnormal case, with the fore polarizer removed, was only adapted to polarized scenes.     

Wavelength-scanning interferometry of a transparent parallel plate with refractive-index dispersion

Testing for flatness of an optical parallel plate in a Fizeau interferometer suffers from problems caused by multiple-beam interference noise. Each internal-reflection component can be separated from the signal by its modulation frequency in a wavelength-scanned interferometer; however, the frequency depends on the thickness and the refractive-index dispersion of the test plate and on the nonlinearity of the scanning source. With a new 19-sample wavelength-scanning algorithm we demonstrate the elimination of the reflection noise, the effect of the dispersion up to the second order of the reflectance of the test plate, and as the nonlinearity of the source. The algorithm permits large tolerance in the air-gap distance, thus making it somewhat independent of the thickness of the test plate. The minimum residual reflection noise with this algorithm for testing a glass plate is approximately lambda/600. Experimental results show that the front surface of the test plate was measured within 1 nm rms of its true shape over a 230-mm-diameter aperture.     

Simultaneous measurement of surface shape and variation in optical thickness of a transparent parallel plate in wavelength-scanning Fizeau interferometer

Wavelength-scanning interferometry permits the simultaneous measurement of variations in surface shape and optical thickness of a nearly parallel plate. Interference signals from both surfaces of the test plate can be separated in frequency space; however, these frequencies are shifted from the expected frequency by the refractive-index dispersion of the test plate and any nonlinearity that is due to wavelength scanning. Conventional Fourier analysis is sensitive to this detuning of the signal frequency and suffers from multiple-beam interference noise. We propose new wavelength-scanning algorithms that permit a large tolerance for dispersion of the test plate and nonlinearity of scanning. Two 19-sample algorithms that suppress multiple-interference noise up to the second order of the reflectance of the test plate are presented. Experimental results show that the variation in surface shape and optical thickness of a glass parallel plate of 250-mm diameter was measured with a resolution of 1-2 nm rms.     

High-accuracy thickness measurement of a transparent plate with the heterodyne central fringe identification technique

In a modified Twyman-Green interferometer, the optical path variation is measured with the heterodyne central fringe identification technique, as the light beam is focused by a displaced microscopic objective on the front/rear surface of the test transparent plate. The optical path length variation is then measured similarly after the test plate is removed. The geometrical thickness of the test plate can be calculated under the consideration of dispersion effect. This method has a wide measurable range and a high accuracy in the measurable range.     

Optical performance of a diffraction-limited molded-glass biaspheric lens

Optical performance results are reported for a molded-glass biaspheric lens. The 6-mm optical diam lens is intended for use in a laser-based optical disk application. The design with fabrication tolerances has an expected on-axis transmitted wave-front performance of 0.06-wave rms optical path difference (OPD) when tested at 0.6328 ,4m and a numerical aperture of 0.45. Transmitted wave-front aberrations were measured on actual molded lenses using a heterodyne interferometer. Typical performance was 0.05-0.08-wave rms- OPD. Experimental results involving mold rotation indicate that lens performance is primarily limited by a surface figure accuracy of one of the molds.     

Wave propagation and transient response of a FGM plate under a point impact load based on higher-order shear deformation theory

In this paper, the wave propagation and transient response of an infinite functionally graded plate under a point impact load are presented. The effective material properties of functionally graded materials (FGMs) for the plate are assumed to vary continuously through the plate thickness and be distributed according to a volume fraction power law along the plate thickness. Based on the higher-order shear deformation theory and considering the effect of the rotary inertia, the governing equations of the wave propagation in the functionally graded plate are derived by using the Hamilton’s principle. The analytic dispersion relation of the functionally graded plate is obtained by means of integral transforms and a complete discussion of dispersion for the functionally graded plate is given. Then, using the dispersion relation and integral transforms, exact integral solutions for the functionally graded plate under a point impact load are obtained. The transient response curves of the functionally graded plates are plotted and the influence of volume fraction distributions on transient response of functionally graded plates is analyzed. Finally, the solutions of the higher-order shear deformation theory and the first-order shear deformation theory are studied.     

兰姆波频散方程的理论求解及实验研究

为了得到板内各声波模态的理论传播速度,利用牛顿切线法求解Lamb频散方程。求解相速度时,保持了频率和板厚在计算中的独立性;求解群速度时利用隐函数求偏导的方法。克服了编程求解中频率厚度不能分离的困难。随后在钢板上进行了实验验证。声速采用声发射定位技术进行测量,并把实验数据进行拟合。研究发现薄板上的实验数据和理论值吻合,厚板上的扩展波理论群速度比实验群速度高400 m/s。     

Determination of lamb wave dispersion data in lossy anisotropic plates using time domain finite element analysis. Part I: theory and experimental verification

A theoretical and experimental approach for extraction of guided wave dispersion data in plate structures is described. Finite element modeling is used to calculate the surface displacement data (in-plane and out-of-plane) when the plate is subject to either symmetrical or antisymmetrical impulsive force stimulation at one or both of the parallel faces. Fourier transformation of the resultant space-time displacement histories is then employed to obtain phase velocity as a function of frequency. Experimental verification in the case of antisymmetrical stimulation is provided by means of a high-power Q-switched laser source that is used to excite guided waves in the plate. The subsequent out-of-plane displacement data were then obtained by means of a scanning laser vibrometer, and good agreement between theory and experiment is demonstrated. Examples of dispersion data are provided for aluminum, and excellent correlation between the data sets and conventional Rayleigh-Lamb theory for plate structures was obtained. This was then extended to lossy polymeric plates, in addition to both unpolarized and polarized piezoelectric ceramic plates, again with good agreement between the finite element modeling and optical experiments. The last set of results prepares the way for a detailed investigation of the nonhomogeneous piezoelectric composite waveguides described in a companion paper (Part II).     

Analysis of the film thickness dependence of a single-phase unidirectional transducer using the coupling-of-modes theory and the finite-element method

A coupling-of-modes (COM) analysis is given for the film thickness dependence of a single-phase undirectional transducer (SPUDT), while the finite-element method (FEM) is employed for evaluating all the coefficients of COM equations. The relationship between the directivity and dispersion curves of the transducer is discussed. The theoretical analysis shows that when the electrode finger thickness increases through a threshold value, a mode conversion phenomenon occurs and the value of the reflection phase changes from the positive to the negative. This result predicts that the forward direction of a film thickness difference type SPUDT will move conversely when the electrode film thickness increases through the threshold thickness. A prototype step-type SPUDT, fabricated on 128 degrees Y-X LiNbO(3) substrate, showed a directivity of 10 dB/transducer at 481.5 MHz, and a low-loss surface acoustic wave (SAW) filter showed a minimum insertion loss of 3.8 dB.