Measuring Two Vibrations Using Dual-external-cavity Structure In A Self-mixing System

Measuring based on Laser self-mixing interference(SMI)has been widely used because of simple structure,easy collimation and low cost.After a part of the light emitted by the laser is reflected or scattered by an external object,the feedback light will mix with the light in the laser resonator.And the coupled light will affect the change process of output power and output frequency,thus producing the laser SMI.For measuring vibration,we need to process SMI signal which carries the external vibration.In recent years,researchers have proposed many data processing method for vibration measurement based on SMI,but the studies are based on the single channel measurement.If we need dual channel or multidimensional measurement,it should repeat twice in the same measure,which is complicated in structure and processing method.To solve this problem,a dual-external-cavity structure in SMI system is proposed in this paper.We also use the improved algorithm for dominant harmonic order based on the structure to measure the vibration information of two objects,which has the advantages of simple structure and strong anti-interference ability.Firstly,according to the theory of traditional SMI,we analyze the dual-external-cavity structure in SMI system theoretically and derive the mathematical formula by the three-mirror cavity model and the equivalent substitution method,and finally the power and frequency equations are obtained.By comparing the power equation of traditional SMI and SMI with dual-external-cavity structure,we can conclude that the mixed signal of SMI with dual-external-cavity structure is the sum of two independent SMI signals under weak feedback.Secondly,we validated SMI with dual-external-cavity structure in the time-and frequency-domain.After Fourier transforming to SMI with dual-external-cavity structure,the vibration information of two objects can be obtained in the spectrum.And when the frequency difference between two vibration values is large enough,the vibration frequency values of two objects can be clearly searched in the spectrum.And the accuracy of the conclusion is verified by numerical simulation and construction experiments.Then,this paper proposes an improved algorithm for dominant harmonic order in order to measure the vibration information of two vibrating objects at the same time.The algorithm gets the vibration frequency by searching the main frequency in spectrum and the vibration amplitude by the properties of a class of Bessel function.Compared with the traditional algorithm for dominant harmonic order,the improved algorithm has not only widely applicable scope and better robustness.It can be effectively used in SMI with dual-external-cavity structure.Finally,based on SMI with dual-external-cavity structure,we can measure two vibrations in the same time using the improved algorithm for dominant harmonic order.We also can conclude that we can measure the vibration information of two objects simultaneously with only one semiconductor laser and one photo detector through numerical simulation and construction experiments.