A principal component approach to space-based gravitational wave astronomy

The current approach to data analysis for the Laser Interferometry Space Antenna (LISA) depends on the time delay interferometry observables (TDI) which have to be generated before any weak signal detection can be performed. These are linear combinations of the raw data with appropriate time shifts that lead to the cancellation of the laser frequency noises. This is possible because of the multiple occurrences of the same noises in the different raw data. Originally, these observables were manually generated starting with LISA as a simple stationary array and then adjusted to incorporate the antenna's motions. However, none of the observables survived the flexing of the arms in that they did not lead to cancellation with the same structure. The principal component approach is another way of handling these noises that was presented by Romano and Woan which simplified the data analysis by removing the need to create them before the analysis. This method also depends on the multiple occurrences of the same noises but, instead of using them for cancellation, it takes advantage of the correlations that they produce between the different readings. These correlations can be expressed in a noise (data) covariance matrix which occurs in the Bayesian likelihood function when the noises are assumed be Gaussian. Romano and Woan showed that performing an eigendecomposition of this matrix produced two distinct sets of eigenvalues that can be distinguished by the absence of laser frequency noise from one set. The transformation of the raw data using the corresponding eigenvectors also produced data that was free from the laser frequency noises. This result led to the idea that the principal components may actually be time delay interferometry observables since they produced the same outcome, that is, data that are free from laser frequency noise. The aims here were (i) to investigate the connection between the principal components and these observables, (ii) to prove that the data analysis using them is equivalent to that using the traditional observables and (ii) to determine how this method adapts to real LISA especially the flexing of the antenna. For testing the connection between the principal components and the TDI observables a 10x 10 covariance matrix containing integer values was used in order to obtain an algebraic solution for the eigendecomposition. The matrix was generated using fixed unequal arm lengths and stationary noises with equal variances for each noise type. Results confirm that all four Sagnac observables can be generated from the eigenvectors of the principal components. The observables obtained from this method however, are tied to the length of the data and are not general expressions like the traditional observables, for example, the Sagnac observables for two different time stamps were generated from different sets of eigenvectors. It was also possible to generate the frequency domain optimal AET observables from the principal components obtained from the power spectral density matrix. These results indicate that this method is another way of producing the observables therefore analysis using principal components should give the same results as that using the traditional observables. This was proven by fact that the same relative likelihoods (within 0.3%) were obtained from the Bayesian estimates of the signal amplitude of a simple sinusoidal gravitational wave using the principal components and the optimal AET observables. This method fails if the eigenvalues that are free from laser frequency noises are not generated. These are obtained from the covariance matrix and the properties of LISA that are required for its computation are the phase-locking, arm lengths and noise variances. Preliminary results of the effects of these properties on the principal components indicate that only the absence of phase-locking prevented their production. The flexing of the antenna results in time varying arm lengths which will appear in the covariance matrix and, from our toy model investigations, this did not prevent the occurrence of the principal components. The difficulty with flexing, and also non-stationary noises, is that the Toeplitz structure of the matrix will be destroyed which will affect any computation methods that take advantage of this structure. In terms of separating the two sets of data for the analysis, this was not necessary because the laser frequency noises are very large compared to the photodetector noises which resulted in a significant reduction in the data containing them after the matrix inversion. In the frequency domain the power spectral density matrices were block diagonals which simplified the computation of the eigenvalues by allowing them to be done separately for each block. The results in general showed a lack of principal components in the absence of phase-locking except for the zero bin. The major difference with the power spectral density matrix is that the time varying arm lengths and non-stationarity do not show up because of the summation in the Fourier transform.

High speed digital holographic interferometry for hypersonic flow visualization

Optical imaging techniques have played a major role in understanding the flow dynamics of varieties of fluid flows, particularly in the study of hypersonic flows. Schlieren and shadowgraph techniques have been the flow diagnostic tools for the investigation of compressible flows since more than a century. However these techniques provide only the qualitative information about the flow field. Other optical techniques such as holographic interferometry and laser induced fluorescence (LIF) have been used extensively for extracting quantitative information about the high speed flows. In this paper we present the application of digital holographic interferometry (DHI) technique integrated with short duration hypersonic shock tunnel facility having 1 ms test time, for quantitative flow visualization. Dynamics of the flow fields in hypersonic/supersonic speeds around different test models is visualized with DHI using a high-speed digital camera (0.2 million fps). These visualization results are compared with schlieren visualization and CFD simulation results. Fringe analysis is carried out to estimate the density of the flow field.

A study on stratification of concentration in crystal-growth of alpha-liio3 by holographic-interferometry

A new thermoplastic-photoconductor laser holographic recording system has been used for real-time and in situ observation of alpha-LiIO3 crystal growth. The influence of crystallization-driven convection on the concentration stratification in solution has been studied under gravity field. It is found that the stratification is closely related to the seed orientation of alpha-LiIO3 crystal. When the optical axis of crystal seed C is parallel to the gravity vector g, the velocity of the concentration stratification is two times larger than that in the case of C perpendicular-to g. It needs 40 h for the crystalline system of alpha-LiIO3 to reach stable concentration distribution (expressed as tau) at 47.6-degrees-C. The time tau is not sensitive to the seed orientation. Our results provide valuable data for designing the crystal growth experiments ia space.

Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air

By employing pump-probe back longitudinal diffractometry, the electron density and decay dynamics of a weak plasma channel created by a 1-KHz fs laser in air has been investigated. With ultrashort laser pulses of 50 fs and low energy of 0.6 mJ, we observe weak plasma channels with a length similar to 2 cm in air. An analytical reconstruction method of electron density has been analyzed, which is sensitive to the phase shift and channel size. The electron density in the weak plasma channel is extracted to be about 4x10(16) cm(-3). The diameters of the plasma channel and the filament are about 50 and 150 mu m, respectively, and the measurable electron density can be extended to less than 10(15) cm(-3). Moreover, a different time-frequency technique called linearly chirped longitudinal diffractometry is proposed to time-resolved investigate ultrafast ionization dynamics of laser-irradiated gas, laser interaction with cluster beam, etc.

Sinusoidal phase-modulating laser diode interferometer for measuring angular displacement

We propose a sinusoidal phase-modulating laser diode interferometer for measuring small angular displacement. The interferometer is based on a Fabry-Perot plate. It has a simple structure and is insensitive to external disturbance. Sinusoidal phase-modulating interferometry is used for improving the measurement accuracy. A charge-coupled device (CCD) image sensor is used for measuring the distance between the reflected beams from two faces of the Fabry-Perot plate. From the distance, the initial angle of incidence is calculated. Compared with Michelson interferometers and autocollimators, this interferometer has the advantage of compact size and simple structure. The numerical calculation and experimental results verify the usefulness of this novel interferometer. (C) 2004 Society of Photo-Optical Instrumentation Engineers.

Real-time micro-vibration measurement in sinusoidal phase-modulating interferometry

As there exist some problems with the previous laser diode (LD) real-time microvibration measurement interferometers, such as low accuracy, correction before every use, etc., in this paper, we propose a new technique to realize the real-time microvibration measurement by using the LD sinusoidal phase-modulating interferometer, analyze the measurement theory and error, and simulate the measurement accuracy. This interferometer utilizes a circuit to process the interference signal in order to obtain the vibration frequency and amplitude of the detective signal, and a computer is not necessary in it. The influence of the varying light intensity and light path difference on the measurement result can be eliminated. This technique is real-time, convenient, fast, and can enhance the measurement accuracy too. Experiments show that the repeatable measurement accuracy is less than 3.37 nm, and this interferometer can be applied to real-time microvibration measurement of the MEMS. (C) 2007 Elsevier GmbH. All rights reserved.

Study on eight-pass dual-frequency laser interferometer with nanometer precision

A new dual-frequency laser displacement measurement interferometer with nanometer precision has been developed. An eight-pass optical subdivision technology is proposed to improve resolution based on commercial interferometers. A static positioning error measuring method has been used to examine the precision and repeatability of the laser interferometer. An optical resolution of 1.24 nm and an accuracy of nanometer scale have been achieved.

Group delay dispersion measurement of Yb : Gd2SiO5, Yb : GdYSiO5 and Yb : LuYSiO5 crystal with white-light interferometry

We report the measured group delay dispersion (GDD) of new crystals Yb:Gd2SiO5 (Yb:GSO), Yb:GdYSiO5 (Yb:GYSO) and Yb:LuYSiO5 (Yb:LYSO) over wavelengths from 1000nm to 1200nm, with a white-light interferometer. Those GDD data should be useful for the dispersion compensation for femtosecond pulse generation in the lasers with these new crystals as the gain media. (C) 2007 Optical Society of America

Electron number density measurements in magnesium laser produced plumes

Interferometry has been used to investigate the spatio-temporal evolution of electron number density following 248 nm laser ablation of a magnesium target. Fringe shifts were measured as a function of laser power density for a circular spot obtained using a random phase plate. Line averaged electron number densities were obtained at delay times up to ∼100 ns after the laser pulse. Density profiles normal to the target surface were recorded for power densities on target in the range 125–300 MW cm−2.

Production of ultracollimated bunches of multi-MeV electrons by 35 fs laser pulses propagating in exploding-foil plasmas

Very collimated bunches of high energy electrons have been produced by focusing super-intense femtosecond laser pulses in submillimeter under-dense plasmas. The density of the plasma, preformed with the laser exploding-foil technique, was mapped using Nomarski interferometry. The electron beam was fully characterized: up to 10(9) electrons per shot were accelerated, most of which in a beam of aperture below 10(-3) sterad, with energies up to 40 MeV. These measurements, which are well modeled by three-dimensional numerical simulations, validate a reliable method to generate ultrashort and ultracollimated electron bunches. (C) 2002 American Institute of Physics.

Characterization of laser plasmas for interaction studies: Progress in time-resolved density mapping

Time-resolved probe interferometry was used to obtain complete density mapping of laser produced plasmas. The plasma was produced by symmetrical irradiation of thin targets, to be used for short pulse delayed interaction experiments. The progress in the plasma characterization due to the use of a picosecond pulse probe is reported, and the relative merits of different target designs are also discussed. The two-dimensional density maps obtained appear to be in substantial agreement with two-dimensional hydrodynamic code predictions.

Megagauss magnetic field generation and plasma jet formation on solid targets irradiated by an ultraintense picosecond laser pulse

The spatial and temporal evolution of spontaneous megagauss magnetic fields, generated during the interaction of a picosecond pulse with solid targets at irradiances above 5 x 10(18) W/cm(2) have been measured using Faraday rotation with picosecond resolution. A high density plasma jet has been observed simultaneously with the magnetic fields by interferometry and optical emission. Two-dimensional magnetohydrodynamic simulations reproduced the main features of the experiment and showed that the jet formation is due to pinching by the magnetic fields.

Experimental investigation of hole boring and light sail regimes of RPA by varying laser and target parameters

Temporal evolution of plasma jets from micrometre-scale thick foils following the interaction of intense (3 × 10 W cm ) laser pulses is studied systematically by time resolved optical interferometry. The fluid velocity in the plasma jets is determined by comparing the data with 2D hydrodynamic simulation, which agrees with the expected hole-boring (HB) velocity due to the laser radiation pressure. The homogeneity of the plasma density across the jets has been found to be improved substantially when irradiating the laser at circular polarization compared to linear polarization. While overdense plasma jets were formed efficiently for micrometre thick targets, decreasing the target areal density and/or increasing the irradiance on the target have provided indication of transition from the 'HB' to the 'light sail (LS)' regime of RPA, characterized by the appearance of narrow-band spectral features at several MeV/nucleon in proton and carbon spectra.

Modeling target bulk heating resulting from ultra-intense short pulse laser irradiation of solid density targets

Isochoric heating of solid-density matter up to a few tens of eV is of interest for investigating astrophysical or inertial fusion scenarios. Such ultra-fast heating can be achieved via the energy deposition of short-pulse laser generated electrons. Here, we report on experimental measurements of this process by means of time-and space-resolved optical interferometry. Our results are found in reasonable agreement with a simple numerical model of fast electron-induced heating. (C) 2013 AIP Publishing LLC.