Determining large step heights using zero-order interference fringe identification and an external cavity diode laser

Zero-order interference fringe identification is a powerful tool for measuring large step heights. In contrast to white light scanning interferometry, this study utilizes an external cavity diode laser as the light source. The zero-path difference point can be accurately identified by combining wavelength scanning interferometry, in which the laser wavelength is continuously changed, with single wavelength interferometry, in which the laser wavelength is fixed. The experimental apparatus is a two-arm interferometer containing the sample in the measurement arm. The step height denotes the distance between two locations of a zero-order interference fringe, which are obtained by continuously varying the length of the reference arm. The accuracy of a sample of 10 mm step height was found to be 0.33 μm.     

Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals

We report on processing the spectral interference signals by a new method based on a windowed Fourier transform applied in the wavelength domain. First, the numerical simulations are performed to demonstrate high precision of the phase retrieval from the spectral signal. Second, the feasibility of the method is confirmed in processing experimental data from a dispersive Michelson interferometer comprising a cube beamsplitter made of BK7 glass. From the retrieved spectral phase difference, the effective thickness of the beamsplitter is determined precisely.     

A new method to measure the wavelength of single-mode pulsed lasers with a scanning Michelson interferometer

We report on the possibility to measure the wave-lengths of pulsed single-mode lasers by means of a two-beam Michelson interferometer in motion [1,2]. The corner reflector moves with a nearly constant speed creating a path differenceL so thatL/C 1/, being the spectral width of the laser to be measured. The reference laser is a stabilized He-Ne (Spectra-Physics, model 117 A) to a precision of the order of two parts in 10⁹. The fringe pattern of the two beams (reference beam and measured beam) is sampled simultaneously with a repetition rate of 40 ms. With this new method, the frequency doubled injection-seeded Nd: YAG laser wavelength has been measured with an accuracy of the order of 1.5 in 10⁸3 × 10^–4 cm^–1 at 532nm.     

Inspection of a micro-cantilever’s opened and concealed profile using integrated vertical scanning interferometry

In this paper, we describe a method based on the proposed vertical scanning interferometry (VSI) for the measurement of both surface profile of the micro-cantilever and corresponding etching sacrificial layer beneath the cantilever by only one scanning. A white light source illuminates a micro-cantilever at a certain incident angle through a Mirau interference objective. With this arrangement the top surface of the cantilever and a normally obstructed surface profile beneath the cantilever can be assessed in the same system. A digital filtering technique based on Fourier transform and a Gaussian fit are implemented to simultaneously retrieve an envelope of two series of interferograms at the top surface of a cantilever and as well as area of interest underneath the cantilever. The retrieved envelope peaks, which represent the height information of points on the test surface, are plotted to show whole field surface contour and demonstrate its effectiveness as a means for micro-electro-mechanical systems (MEMS) dual/multi-layer inspection. Results obtained agree well with those of a commercial instrument and show that the proposed method is simple and accurate.     

Organic modification of TEOS based silica aerogels using hexadecyltrimethoxysilane as a hydrophobic reagent

The experimental results on the synthesis and characterization of tetraethoxysilane (TEOS) based hydrophobic silica aerogels using hexadecyltrimethoxysilane (HDTMS) as a hydrophobic reagent by two step sol-gel process, are described. The molar ratio of tetraethoxysilane (TEOS), methanol (MeOH), acidic water (0.001 M, oxalic acid) and basic water (10 M, NH₄OH) was kept constant at 1:55:3.25:1.25 and the molar ratio of HDTMS/TEOS (M) was varied from 0 to 28.5 × 10⁻². The organic modification was confirmed by infrared spectroscopic studies, and the hydrophobicity of the aerogels was tested by the contact angle measurements. The maximum contact angle of 152° was obtained for M = 22.8 × 10⁻². The aerogels retained the hydrophobicity up to a temperature of 240 °C and above this temperature the aerogels became hydrophilic. The aerogels were characterized by the thermal conductivity, density, contact angle measurements, optical transmission and scanning electron micrographs.     

Micro Extrinsic Fiber-Optic Fabry-Perot Interferometric Sensor Based on Erbium- and Boron-Doped Fibers

Micro extrinsic Fabry-Perot interferometers （MEFPIs）, with cavity lengths of up to ~ 9 μm and maximum fringe contrast of ~19 dB, are fabricated by chemically etching Er- and B-doped optical fibers and then splicing the etched fiber to a single-mode fiber, for the first time to the best of our knowledge. The strain and temperature responses of the MEFPI sensors are investigated experimentally. Good linearity and high sensitivity are achieved. Such a type of MEFPI sensor is cost-effective and suitable for mass production, indicating its great potential for a wide range of applications.     

Consideration and compensation of calibration falloff for optical flying height measurement

In sub-10 nm low flying height (FH) region, system calibration is a significant challenge to achieve precise FH measurement. Unloading calibration mechanism is utilized for every FH measurement using three-wavelength interferometry. Our experiment has shown that the cutoff frequency of photodetectors and the bandwidth of optical filters induce calibration falloff during the calibration process. As a result, the FH measured is underestimated, i.e., the FH measured is lower than its true value. In this paper, mathematical models are proposed to eliminate the side effects due to the bandwidth of optical filters and the cutoff frequency of photodetectors. Results indicate that the proposed compensation schemes are effective in terms of improving the calibration accuracy.     

Berry phase in a bipartite system with general subsystem–subsystem couplings

The Berry phase in a bipartite system described by the XXZ model is studied in this Letter. We calculate the Berry phase acquired by the bipartite system as well as the geometric phase gained by each subsystem. The results show that as the coupling constants tend to infinity all geometric phases go to zero, this confirms the prediction given by us previously [X.X. Yi, L.C. Wang, T.Y. Zheng, Phys. Rev. Lett. 92 (2004) 150406] for bipartite systems with a specific subsystem–subsystem coupling.     

Analysis of a loss-compensated recirculating delayed self-heterodyne interferometer for laser linewidth measurement

A loss-compensated recirculating delayed self-heterodyne interferometer (LC-RDSHI) for laser linewidth measurement is theoretically analyzed. An analytical result for the output spectrum of the LC-RDSHI is obtained. It is found that the spectrum from a LC-RDSHI is equivalent to a spectrum from a conventional delayed self-heterodyne interferometer with equivalent time delay and frequency shift, but modified by a periodical function, which could significantly influence the laser linewidth measurement. The parameters of a LC-RDSHI must be optimized to permit an accurate and direct measurement of laser linewidth from the output spectrum.     

Direct laser ablation of sub-100 nm line structures into polyimide

Periodic line structures with a period of 167 nm and linewidths varying from 30 to 100 nm have been produced in polyimide by direct ablation with a KrF laser using an interferometric technique. The characteristics of this interferometer as it applies to the ablation of these line structures, including linewidth and alignment sensitivity, are analyzed. The ability to control the linewidth by varying the average incident fluence is described theoretically and demonstrated experimentally. This externally generated period of 167 nm also prevents the spontaneous growth of laser induced periodic surface structures (LIPSS).     

Mean-Field Dynamics of a Two-Mode Bose-Einstein Condensate Subject to Decoherence

We discuss the dynamics of Bose-Einstein condensates in a double-well potential subject to decoherenee （or particle loss）. Starting from the full many-body dynamics described by the master equation, an effective Gross- Pitaevskii-like equation is derived in the mean-field approximation. By numerically solving the GP equation, we find that macroscopic quantum self-trapping disappears for strong decoherence, while generalized self-trapping occurs under weak decoherence. The fixed points have been calculated, and we find that an abrupt change from elliptic to an attractor and a repeller occurs, reflecting the metastable behavior of the system around these points.     

Single-element interferometer

A very simple and stable interferometer using a single optical element - a beam-splitter cube - is presented. The device resembles a two-arm interferometer in which the arms are together in one collimated beam, and the two beam halves interfere with the help of the beam-splitter cube. The proposed device produces simultaneously two interferograms with a relative phase-shift of π (rad). Since the period of straight interference fringes can be stably controlled, the device has potential application in spatial-carrier interferometry and for flexible writing of fiber Bragg gratings.     

A longitudinal stern-gerlach atomic interferometer

A new magnetic field configuration has been used in the mixing and elongating regions of the longitudinal Stern-Gerlach interferometer. This configuration has proven to considerably improve the performances of the interferometer. An analysis in terms of the vector model of a spin 1 particle is presented.Laboratoire associé au CNRS, URA 282     

Generation and Modulation of Phase Difference of Output Intensities in a Feedback Nd:YAG Laser with an Extracavity Waveplate Rotated

External anisotropic feedback effects on the phase difference behaviour of output intensities in a microchip Nd：YAG laser are presented. By rotating a quarter wave plate placed in the external cavity, the angle between laser initial polarization direction and o-axis of the wave plate is tuned from -45°to 45°, which results in variable extra-cavity birefringence along two orthogonal detection directions. With only one optical path and one wave plate, laser intensities of the two orthogonal directions, both modulated by the external cavity length, are output with a tunable phase difference, which can be continuously changed from zero to twice as large as that of the waveplate. Experimental results as well as a theoretical analysis based on Fabry-Perot cavity equivalent model and the refractive index ellipsoid, are presented. The potential applications of this phenomenon are also discussed.     

Optical-to-microwave frequency chain utilizing a two-laser-based optical parametric oscillator network

A method for building an optical-to-microwave frequency chain and for measuring optical frequencies relative to the cesium primary frequency standard is described. Based on optical frequency division via parametric oscillators, the concept is to generate two known ratios (1/2 and 4/9) of an optical calibration frequencyf ₁ whose frequency difference is measured relative to the cesium clock. The (1/2) ratio is obtained by either a 2:1 frequency division off ₁ or second-harmonic generation of (l/2)f ₁. The (4/9) ratio off ₁ can be generated with a 3:1 frequency divider driven by a second laser atf ₂ that is chosen to be near (2/3)f ₁, which in turn is obtained with af ₁-pumped 3:1 frequency divider. A set of auxiliary Optical Parametric Oscillators (OPOs) with outputs centered at (1/2)f ₁ is used to facilitate the difference-frequency measurement between the two ratios. A practical configuration utilizing a YAG and a Ti: Al₂O₃ laser and its application to a number of precision measurements of interest are presented.     

Experimental Investigation on a Fibre-Optic Hydrophone with a Cylindrical Helmholtz Resonator

A novel mechanical anti-aliasing filtering fibre-optic hydrophone with a cylindrical Helmholtz resonator is con- structed and tested. The experimental results show that the hydrophone has a function of low-pass filtering. The low frequency acoustic sensitivity is about -160 dB （1 rad/#Pa）, and the response curve has a resonance deter- mined by the Helmholtz resonator. Theoretical and experimental results both show that the resonant frequency moves towards high frequency with the increasing orifice diameters. The sensitivity attenuation of high frequency is larger than lOdB. This new fibre-optic hydrophone is a prototype device for a class of sensors used to eliminate the aliasing in future sonar systems.     

Instantaneous velocity measurement of dynamic deformation by digital holographic interferometry

A novel method for the instantaneous velocity measurement of dynamic deformation by digital holographic interferometry is proposed. During dynamic deformation, a series of digital holograms is recorded by a high-speed camera. At each pixel of the phase difference maps, phase and amplitude information are combined as complex phasor (CP). Each pixel can be then considered as an independent sensor and a sequence of complex phasors of such a sensor is analyzed by short time Fourier transform (STFT) along the time axis. A fast iterative algorithm is developed for the computation of instantaneous velocity. The displacement of each pixel can also be obtained by integration of the instantaneous velocity over time and phase unwrapping process is thus avoided. The performance of the proposed CP method is compared experimentally with the commonly used digital phase subtraction method.     

New theoretical and experimental results in fresnel optics with applications to matter-wave and X-ray interferometry

We present new methods and formulae for calculating the image amplitude and image spatial power spectral density produced by monochromatic point-source illumination of a finite (and/or infinite) periodic complex transmission grating. At specific finite-width resonances the image amplitude is seen to display periodic complex amplitude self-imaging of the grating, with interlaced alias images. The finite width grating resonances (as a function of spatial frequency) are broadened (from zero width) and displaced in frequency relative to those produced by an infinite grating, although the finite resonance width relative to illumination wavelength variation persists with infinite gratings. In the Fresnel domain the self images are generalizations of the Talbot and von Lau effects, while in the Fraunhofer to Fresnel transition domain, our formulae demonstrate the formation of these structures from Fraunhofer diffraction order side-lobes. Using these results, design criteria are provided for constructing lens-free three-grating interferometers with spatially diffuse illumination and detection. Such interferometers have a wide variety of applications for both X-rays and matter-waves, including a phase sensitive imaging device and/or narrow-band interference filter. For wavelengths in the Ångstrom to sub-Ångstrom range they feature high throughput and ease of fabrication. Experimental results using light with such an interferometer are presented. Our results conclusively demonstrate interference and image aliasing in such a device with spatially diffuse illumination and detection. The experiment is readily reproducible in any undergraduate physics laboratory.Work supported by ONR Grant N00014-90-J-1475, by the firm J. F. Clauser & Assoc., and (MWR) by a U.S. Dept. of Education Fellowship     

The effect of errors and detector noise on sensitive detection of chirp and pulse asymmetry of ultrashort laser pulses from interferometric autocorrelation signals

We have studied the effect of various types of systematic and non-systematic errors on unbalanced spectrally modified interferometric autocorrelation signals for detection of pulse chirp and asymmetry of ultrashort laser pulses. The effect of systematic errors arising due to limited number of data points per fringe, scan rate etc, and non-systematic errors due to phase noise, additive noise, multiplicative noise and quantization of interferometric autocorrelation (IAC) signals is illustrated using a linearly chirped asymmetric laser pulse. It is seen that the spectrally modified IAC signals based on difference of normalized envelope functions corresponding to different frequencies are not much sensitive to various noises, permitting their use for sensitive detection of pulse chirp and asymmetry. The analysis is supported by experimentally recorded IAC signals under different conditions.     

Modified temporal-phase-unwrapping method for measuring in real time the out-of-plane displacements of the tympanic membrane of Mongolian Gerbil

A technique for measuring in real-time continuous out-of-plane displacements of delicate objects is proposed, and demonstrated on the tympanic membrane of Mongolian Gerbil. The technique is based on the combination of two methods: the spatial phase shifting (SPS) and the modified temporal phase unwrapping (TPU). The combination allows to obtain, in several steps, the phase values of the points that undergo out-of-plane displacement as the object is deformed. The technique reduces the frame acquisition time of the standard TPU used in moiré interferometry by a factor of 4, which is important to diminish post-mortem artifacts during in-vitro experiments and to reduce motion artifacts in in-vivo tests. The proposed technique is robust against problems associated with the temporal phase-shifting method, such as nonlinear phase shift and noise. The advantages and disadvantages are discussed.