Methods for the calibration of vibration pick-ups by laser interferometry: I. Theoretical analysis

Abstract

A regression analysis method is applied for data transforming and error evaluation in the sine-approximation method (SAM) for the calibration of vibration pick-ups by laser interferometry. A new simple algorithm for phase unwrapping in the SAM is also proposed. To make a more valuable comparison of this modified SAM with other techniques, i.e. the fringe counting method (FCM) and the minimum point method (MPM), the resolution of the measuring system is increased by using a double optical path difference homodyne interferometer. Additionally the uncertainty of the FCM is suppressed by implementing the procedure of fringe phase analysis in the turning points of the vibration cycle. This paper presents a theoretical analysis of the above mentioned problems.

High resolution, molecular-specific, reflectance imaging in optically dense tissue phantoms with structured-illumination

“…The algorithm used for optical-section image reconstruction is based on the sine approximation method. 8,9 The structured-illumination pattern, which is in the form of a sinusoidal amplitude grating, is projected on to the image plane to be reconstructed. Light remitted from the total sample is imaged onto an array of photodetectors.…”

“…It should be noted that the least-squares estimate returns a vector b with minimum errors for any source of an additive noise. A detailed analysis of this problem was given by Dobosz et al 8,9 Finally, the signal amplitude at this pixel is recovered by means of ( )…”

“…Therefore, to overcome these problems we undertook two actions: (1) we applied the sine approximation algorithm for image reconstruction and (2) we used targeted reflectance contrast agents to provide a molecularspecific source of increased signal from cells overexpressing cancer-related biomarkers. The sine approximation algorithm applied here in the context of structured-illumination has been previously used to monitor vibrations 8,9 and to measure shape 10 ; however, in the context of image processing, this is a new approach. We find the algorithm to be very robust and, most importantly, that the sine approximation algorithm works correctly for significantly smaller dynamic range than is required by conventional structured-illumination imaging techniques.…”

<title>Current status of measurement standards for vibration and shock in NRLM</title>

“…dx?i4t (4) aitLf2x (5) Usually the zero point of the Bessel function of the first order is adopted. Comparing the output of the accelerometer measured by the rms voltmeter with the acceleration amplitude a derived from equation(S), the sensitivity of the accelerometer at that vibration frequency is determined.…”

Optimization of displacement-measuring quadrature interferometers considering the real properties of optical components

“…After the raw signals are obtained, the data are processed offline. The processing algorithm first determines and effectively corrects the common nonlinearities [11][12][13] and then unwraps the phase to obtain the displacement [14]. The extremes are either read from the 2 kHz-low-pass filtered raw voltage signals as their maximum and minimum values or obtained from the retrieved free coefficients of the fit.…”