A method to measure sub nanometric amplitude displacements based on optical feedback interferometry

Abstract

Optical feedback interferometry is a well known technique that can be used to build non-contact, cost effective, high resolution sensors. In the case of displacement measurement, different research groups have shown interest in increasing the resolution of the sensors based on this type of interferometry. Such efforts have shown that it is possible to reach better resolutions by introducing external elements such as electro-optic modulators, or by using complex signal processing algorithms. Even though the resolution of the technique has been increased, it is still not possible to characterize displacements with total amplitudes under λ/2. In this work, we propose a technique capable of measuring true nanometre amplitude displacements based on optical feedback interferometry. The system is composed by two laser diodes which are calibrated within the moderate feedback regime. Both lasers are subjected to a vibration reference and only one of them is aimed to the measurement target. The optical output power signals obtained from the lasers are spatially compared and the displacement information is retrieved. The theory and simulations described further on show that sub-nanometre resolution may be reached for displacements with amplitudes lower than λ/2. Expected limitations due to the measurement environment will also be discussed in this paper.

Differential self-mixing interferometry for micro-cantilever motion sensing

“…Once the fringes have been detected1, the velocity and respective displacement are calculated using the equations described in Ref. 19,20 which for small displacements are equivalent to Eq.(3). only the person in charge of the measurement is at the room to limit the appearance of unknown bias in the measurement.…”

“…As it is shown in Fig.1 where the sub-index r is used for the reference signal and m for the measurement signal, the fringe intervals in the measurement OOP will be modified according to the displacement. 19,20 Thus, for a small displacement ∆d, the resolution of the technique can be calculated by:…”

Differential optical feedback interferometry for the measurement of nanometric displacements

“…Because of mechanical constraints, as well as to avoid speckle effect over the OFI signal, the ramp-like displacement, described before, is substituted in practice by a periodic triangular motion of limited amplitude (typically lower or equal to 38 m). Taking into account that each transition happens whenever a displacement is reached, it is possible to define the sampling frequency [12] as:…”

“…This results in a small time difference in the transition intervals of the signals, which is proportional to the difference of the LD wavelengths. To avoid this bias, it is possible to compare the velocity of the reference stage rather than the direct measurement of DSMI displacement as described in [12].…”

“…More recently [11,12], we proposed a differential method capable of reaching theoretical resolutions in the order of . In this paper we present some of the experimental results obtained with the proposed method.…”