Surface slope profile is commonly used to evaluate X-ray reflective optics, which is used in synchrotron radiation beam. Moreover, the measurement result of measuring instrument for X-ray reflective optics is usually the surface slope profile rather than the surface height profile. To avoid the conversion error, the slope-based figuring model is introduced introduced by processing the X-ray reflective optics based on surface height-based model. However, the pulse iteration method, which can quickly obtain the dell time solution of the traditional height-based figuring model, is not applied to the slope-based figuring model because property of the slope removal function have both positive and negative values and complex asymmetric structure. To overcome this problem, we established the optimal mathematical model for the dwell time solution, By introducing the upper and lower limits of the dwell time and the time gradient constraint. Then we used the constrained least squares algorithm to solve the dwell time in slope-based figuring model. To validate the proposed algorithm, simulations and experiments are conducted. A flat mirror with effective aperture of 80 mm is polished on the ion beam machine. After iterative polishing three times, the surface slope profile error of the workpiece is converged from RMS 5.65 μrad to RMS 1.12 μrad.
We achieve a surprisingly exact agreement between the simulation results and the experimental observations (J. C.
Travers et al. Opt. Express 16, 14435-14447(2008)) of visible supercontinuum (SC) generation pumped by a 400W
single mode continuous wave (CW) fiber laser. The propagation of CW field in photonic crystal fibers (PCF) is
numerically simulated by solving the generalized nonlinear Schrödinger equation with the adaptive split-step Fourier
method for high accuracy; moreover, we apply the method of averaging the generated spectra in many simulations to
approach the experimental results. Our simulations confirm that the extension of SC toward short wavelengths is due
to the trapping of dispersive waves by redshifted solitons.
This paper introduces the algorithm and the basic theory of Independent Component Analysis (ICA), and discusses how to choose the proper ICA model of the data by the characteristics of the underlying signals to be estimated. The Spatial ICA (SICA) is applied to model and analysis of the data in the experiment when the signals and noises are spatially dependent. The data acquired from the intrinsic optical signals which are caused by electricity stimulation to sciatic nerve of rat are analyzed by SICA. In the result, the active-related component of the signals and its time course can be separate, and the signals of heartbeat and respiration also can be separated.
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