KEYWORDS: Signal attenuation, Phonons, Acoustics, Sensors, Single mode fibers, Signal processing, Signal to noise ratio, Phase modulation, Polarization
For the pump-probe stimulated Brillouin scattering with probe pulse of a few nanoseconds duration and with a finite DC level, the acoustic wave relaxation time varies with the pump power and DC level. For the pump power of 1- 6mW, the acoustic wave relaxation changes between 9 to 90 ns for polarization maintained fiber (PMF) at temperature of -45°C for 2 ns pulse width. When pulse to DC ratio of the probe varies from 10 to 20dB, the acoustic relaxation time changes between 24 to 45ns for single mode fiber (SMF) at 25°C. This induced a power increment spectral feature in detected AC pump signal in the Brillouin loss spectrum of two temperature or strain sections, where both spectral components appeared at the positions much longer than natural phonon relaxation time (~10ns) equivalent length. This can cause problem for the distributed sensor in determining the strain/temperature boundary, and central Brillouin peak fitting due to the multiple peak convolution, and it affects temperature and strain accuracy. We propose the 2nd order partial derivative of Stokes signal with respect to frequency and position giving a maximum or minimum at the boundary between two different strained sections. This allows finding the true stress or temperature corresponded section.
We introduce a phenomenological model, based on steady state analytical solution adapted to transient regime through modification of the Brillouin spectrum with the pulse spectrum. This model can accurately de-convolve the strain profiles from measured spectra. The model includes experimental parameters such as the electro-optic modulator Extinction Ratio, the pulse width, pulse and pump powers, position and sensing fibre length. The pulse base is treated as pure steady state contribution. A systematic numerical analysis has been carried out and the results are qualitatively matched with our experimental results. The experimental results have been used to validate the model and evaluate its limitations. Within this context, the approach has been applied to experimental data obtained under well-controlled laboratory conditions. The agreement is good and reflects the Brillouin frequency and then the strain distribution along the fibre. The approach is also successful when used to deconvolve the main strain contributions of a pipe subjected to a compression stress. The strength of the model lies in its simplicity of implementation because it is quasi-analytical and is not restricted to short fibre lengths.
The strain and temperature dependence of the Brillouin gain/loss spectrum has been studied in terms of Brillouin frequency, power and bandwidth for panda, bow-tie and tiger polarization maintaining (PM) fibers using our Brillouin gain/loss based distributed sensor system for the first time. The PM fibers are stressed at various temperature to measure the power, bandwidth and Brillouin frequency coefficients at the spatial resolution of 20 cm. Using our measured coefficients with various combinations Brillouin power and bandwidth and Brillouin frequency, we realized three groups of simultaneous temperature and strain sensing, for Brillouin frequency combined with bandwidth, strain/temperature resolutions are 39με/2°C (panda), 126με/3°C (bow-tie), 598με/16°C (tiger); for the Brillouin frequency combined with power, strain/temperature resolutions are 153με/8°C (panda), 237με/4°C (bow-tie); for the bandwidth combined with power, strain/temperature resolutions are 135με/38°C (panda), 195με/38°C (bow-tie).
Three-dimensional microscopy by computational deconvolution methods requires accurate knowledge of the point spread function (PSF) that characterizes the microscope. Experimental PSF's can only be measured over small regions about focus because the small objects necessary for PSF measurement are dim. Theoretical computation of the PSF requires accurate knowledge of all the experimental setup parameters. Some parameters may be difficult or impossible to measure. In blind deconvolution, the PSF and the specimen are estimated simultaneously, an under-determined problem with non-unique solutions. Most existing approaches to blind deconvolution rely on enforcing constraints on the specimen function and PSF, sometimes in ad-hoc ways. We derived a parametric blind deconvolution method by assuming that the PSF follows a mathematical expression with unknown parameters. The parameters are then estimated together with the specimen function. Preliminary results presented here show that this algorithm rapidly estimates the correct PSF.
KEYWORDS: Confocal microscopy, Expectation maximization algorithms, Microscopes, Image restoration, Image resolution, Optical transfer functions, Image processing, 3D image processing, Point spread functions, Signal to noise ratio
Three-dimensional (3-D) microscopy with a non-confocal microscope is fundamentally limited because the optical transfer function (OTF) is zero over a cone-shaped region of the spatial frequency domain and thus the image has a missing cone of optical information that potentially results in artifacts. The strictly confocal scanning microscope (i.e. one with only one pinhole-aperture that is infinitesimally small) does not suffer from this missing cone and thus images are not artifactual. However the pinhole aperture has very low light collection efficiency and images have low signal-to-noise ratio (SNR). Because of this low light-collection efficiency the scanning microscope is commonly operated in a partially confocal regime either by using a larger confocal aperture, multiple confocal apertures working in parallel, or a combination of both. With a larger aperture more out-of-focus fluorescence is collected, with multiple apertures more out-of-focus excitation is produced. In either case the optical axis resolution is degraded relative to that of the ideal confocal microscope. Fortunately neither approach suffers form a missing cone. Frequency components are attenuated relative to the strictly confocal case, but they are no completely missing. We present results that show that applying image restoration methods to partially confocal images it is possible to obtain artifact free images with the same or better resolution than with a strictly confocal microscope.
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