Minimum detectable phase shift in spectrum-analysis techniques of optical interferometric vibration detection

Abstract

The minimum detectable phase shift indicated in recent experimental reports of new linear spectrumanalysis techniques of optical interferometric vibration detection is established as the direct consequence of the 1/f noise voltage in the system components. The dynamic range and inaccuracy predicted by the simple theoretical model presented is in good agreement with experimental measurements. The conclusions of the analysis are compared with experimental reports of heterodyne shot-noise-limited optical systems. With this effective tool the generic class of spectrum-analysis techniques can be analyzed and relatively weighed to assess the effect of noise. This analysis is applicable to optical interferometry in general, although the experiments specifically involved fiber-optic modulators.

Wide dynamic range homodyne interferometry method and its application for piezoactuator displacement measurements

“…Furthermore, the method has a resolution limit, which is the minimum finite modulation index x that can be measured, which depends on the random noise. In order to consider the effect of electronic noise on the photodetected signal, a deterministic formulation proposed in [27] will be followed, which is valid for noise voltages that vary with frequency f according to 1∕f m , where m is a positive integer that depends on the noise type. Using this approach, the noise-free voltage components in Eqs.…”

“…For the particular value of m 1 used in [27], the noise is generated by semiconductor junctions in optical and electronic components (laser, photodetector, amplifier, acquisition system, etc.). This kind of noise will be employed in this paper only for comparison with other authors, once the experimental measurements show, in the frequency bands explored in this work, that white noise (m 0) predominates.…”

“…In this work, the dynamic range is defined as in [19,27]; it is lower-limited by the minimum detectable phase shift (MDPS) and upper-limited when the error exceeds 0.05 rad. The MDPS was defined in order to estimate the resolution of the method in the presence of noise and is the value of x when the absolute error satisfies Δx jx 0 − xj x in the presence of noise.…”

A simplified and higher dynamic range version of the J1…J4 method for optical phase measurements

“…It is important to stress that the use of the J 1 … J 4 technique requires that the fundamental and first three harmonics magnitudes should be larger than the noise floor at their respective frequencies. As a result, phase modulation indexes greater than 0.175 rad are needed for a typical interferometric setup [14, 15]. On the other hand, when x = 5.2 rad there are large errors because J 1 = − J 3 , and both the numerator ( J 2 = 0) and the denominator in (3) become zero.…”

“…This kind of noise depends on the characteristics of the laser source and the specific photodetector, electronic amplifier, acquisition system, and detection bandwidth used. In the presence of 1/f noise, the factor f 13 in (4 a) must be corrected to [15] where K = Δ V 1 /4 AF , and Δ V 1 is the noise voltage at the fundamental frequency. The factor K can be accurately determined from experiments from the magnitude spectrum of I ( t ) [14, 15].…”