Developing self‐mixing interferometry for instrumentation and measurements

Abstract

In this review, self-mixing interferometry (SMI), a new configuration of interferometry, is discussed. SMI has practical advantages compared to standard interferometry, for example SMI does not require any optical part external to the laser chip and can be employed in a variety of measurements. Applications range from the traditional measurements related to optical pathlength -like displacement, small-amplitude vibrations, velocityto sensing of weak optical echoes -for return loss and isolation factor measurements, CD readout and scroll sensing -and also, a special feature because of the interaction with the medium, measurements of physical parameters, like the laser linewidth, coherence length, and the alfa factor. Because it is also a coherent detection scheme, the SMI works close to the quantum limit of the received field, typically 90 dBm, so that minimum detectable amplitudes of 100 pm/ Hz are currently achieved upon operation on diffusive targets, whereas a corner cube allows half-wavelength counting mode -or 0.5 μm resolution -on a dynamic range up to 2 m and more. With its compact setup, the SMI is easy to deploy in the field and can interface a variety of experiments -from MEMS testing to rotating machines vibration testing to pickup of biological motility. The illustration shows a double-channel, differential SMI incorporated in a thermomechanical test equipment to trace the mechanical hysteresis cycle of the beads of a motor-engine brake. : Self-mixing interferometry Figure 2 (online color at: www.lpr-journal.org) Self-coupling interaction can be represented by a rotating-vector addition, with a small returned component a E 0 exp iϕ dynamically added to the cavity field E 0 : the in-phase component cos ϕ generates AM modulation, whereas the in-quadrature component sin ϕ is responsible for FM.2ks (k = wavevector, s = distance) external to the perturbed laser. This is the case studied by Spencer and Lamb in [2]. In applications, we will readily take advantage of weak coupling in self-coupled systems by making out of it very sensitive echo sensors and interferometers.Before proceeding, let us explain the self-mixing modulations as the result of rotating-vector addition [5] as in Fig. 2. Let E 0 be the unperturbed cavity field, and aE 0 expi2ks the field back from the target, a being the attenuation and 2ks the phase delay of propagation. As is well known from communication theory, rotating vector addition generates an AM modulation driven by the in-phase component of the modulating term, that is aE 0 cos 2ks, and an FM by the in-quadrature component, or aE 0 sin 2ks.In applications, while the AM is readily available from the intensity (or power) detected by a photodiode, FM is difficult to retrieve because is impressed onto the optical frequency (it requires frequency downconversion, see Sect. 3.2.3).Also in the weak regime of mutual-coupling we find AM and FM in each of the two interacting lasers, and the driving terms are now the ratio of amplitudes and the frequency difference of the two waves [6]. The...

All Analog Processing of Speckle Affected Self-Mixing Interferometric Signals

“…3. Strong feedback regime: It exists for C > 4.6, characterized by a chaotic SM signal [2]. Each fringe in the SMI signal represents a target displacement of λ/2.…”

“…Using simple fringe counting, a sensor would then ensure λ/2 resolution by detecting all the fringes. In the absence of speckle, P(t) or SMI signal can be processed by the phase unwrapping methods [9], [12,13] as per (1)(2)(3), to provide corresponding D(t) with much better accuracy. In the absence of speckle, SMI fringes can be easily detected, especially in case of moderate feedback regime [9], [23].…”

“…The underlying reason is the two-fold impact of speckle on SMI signals: variations in 1) peak to peak amplitude of SMI signal and 2) optical feedback coupling causing a change in SMI operating regime [1,2]. Both effects can be observed in an experimentally acquired speckle affected SMI signal shown in Fig.…”

“…ELF mixing interferometry (SMI) or optical feedback interferometry [1,2] is a promising and inherently simple sensing scheme in which the employed laser diode simultaneously acts as a source, detector, as well as microinterferometer. Use of SMI has been demonstrated for imaging [3], distance [4], flow [5], biomedical [6], embedded [7] and mechatronics [8] applications etc.…”

Infrasound detection by laser diode self-mixing interferometry

“…For target distances L 0 < 10 m and LD linewidth below 10 MHz, the shot noise dominates over the phase noise. The ultimate sensitivity for vibration measurement is set by the quantum noise associated with the detected photocurrent signal [10,25] . This value can be expressed in terms of noise equivalent vibration as noise equivalent displacement (NED)=[(λ/2π(S/R)]/RV , where S/R is the SNR of the amplitude photocurrent measurement.…”