In our earlier work, we introduced and demonstrated continuous wave frequency modulated differential optical feedback to measure low-frequency vibrations with displacements lower than half of emission wavelength of the laser. Using modulated optical feedback interferometry on perturbations whose amplitude was smaller than half the emission wavelength of the laser, the proposed sensor-enabled nanometric scale amplitude measurements from the shift in fringes that appear in a vibrating target by comparing them with the fringes on the stationary target. We extend the application of the technique to noncontact measurement of surface perturbations generated by acoustic beams. First, the displacement of the acoustically perturbed membrane of the transducer at a frequency of 26 kHz with an amplitude of 101 nm (λ / 10) is performed using a single laser diode in a point-and-measure fashion. Once the acoustic waveform has been characterized, the instantaneous surface displacement of a remote aluminum plate due to acoustic pressure is measured using the same setup, yielding a value of 75 nm. As a consequence, an application of a very cost-effective, noncontact, and high accuracy sensor based on the laser diode under optical feedback has been presented.
The nonlinear dynamics of a semiconductor laser with optical feedback (OF) combined with direct current modulation of the laser is demonstrated to suffice for the measurement of subwavelength changes in the position of a vibrating object. So far, classical Optical Feedback Interferometry (OFI) has been used to measure the vibration of an object given its amplitude is greater than half the wavelength of emission, and the resolution of the measurement limited to some tenths of the wavelength after processing. We present here a methodology which takes advantage of the combination of two different phenomena: continuous wave frequency modulation (CWFM), induced by direct modulation of the laser, and non-linear dynamics inside of the laser cavity subject to optical self-injection (OSI). The methodology we propose shows how to detect vibration amplitudes smaller than half the emission wavelength with resolutions way beyond λ/2, extending the typical performance of OFI setups to very small amplitudes. A detailed mathematical model and simulation results are presented to support the proposed methodology, showing its ability to perform such displacement measurements of frequencies in the MHz range, depending upon the modulation frequency. Such approach makes the technique a suitable candidate, among other applications, to economic laser-based ultrasound measurements, with applications in nondestructive testing of materials (thickness, flaws, density, stresses), among others. The results of simulations of the proposed approach confirm the merit of the figures as detection of amplitudes of vibration below λ/2) with resolutions in the nanometer range.
Force sensing is a common practice used for the characterization of matter properties and in particular of bio-materials. Different optical methods have been used in the past to allow high resolution force measurements while avoiding uncertainties induced by external loading of contact sensors. In this paper, we propose the use of differential self-mixing interferometry, a self-aligned, cost effective and compact technique that allows the measurement of displacements with a theoretical resolution in the order of λ/2000 and a practical resolution in the order of λ/200 in practical applications. The DSMI sensor is used to detect the motion of a rectangular cross section cantilever placed on a piezoelectric stage. The measurements were compared with the signal received from the internal piezo stage capacitive sensor, which has a nominal resolution of 2nm. Results show that the DSMI sensor is able to follow accurately the cantilever displacement. A discussion of the potentials, limitations and required further developments of the method will also be presented.
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.