Optimisation of the Nelder-Mead Simplex Method for Its Implementation in A Self-Mixing Laser Displacement Sensor
A laser diode self-mixing sensor enabling us to perform displacement measurements under moderate feedback has been designed with a resolution up to 32 nm. In this paper, we focus on the signal processing required to reach such a resolution and notably on
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Abstract A laser diode self-mixing sensor enabling us to perform displacement measurements under moderate feedback has been designed with a resolution up to 32 nm. In this paper, we focus on the signal processing required to reach such a resolution and notably on the Nelder-Mead simplex method we used for the joint estimation of parameters like the linewidth enhancement factor and feedback level described by the coupling factor. Further more, influence of initial step size λ of Nelder Mead method on the reduction in the convergence time as well as on the possibilities of introducing parallelism in the algorithm have been studied for implementation in a future integrated sensor. This analysis leads to optimize the number of optical power samples necessary for joint estimation, the adaptations of Nelder-Mead method and its parameter λ on our application, all of which result in the consequent reduction in computing time necessary for convergence to the optimum values. Keywords Optical sensors · optical feedback · laser interferometry · signal processing · displacement measurement · Nelder-Mead method
1 Introduction Optical feedback interferometry (OFI), the so-called self-mixing effect, has been widely studied for the last two decades. As a matter of fact, spectral characteristics of a laser diode (LD) are strongly affected by optical feedback, leading to the degradation of the LD performances for applications like DVD readers. However, this optical feedback can also be of practical use for sensing applications like Usman Zabit Universit´e de Toulouse, LOSE, INPT, ENSEEIHT, Toulouse, France Francis Bony Universit´e de Toulouse, LOSE, INPT, ENSEEIHT, Toulouse, France Thierry Bosch Universit´e de Toulouse, LOSE, INPT, ENSEEIHT, Toulouse, France, e-mail: [email protected]
S.C. Mukhopadhyay, G.S. Gupta (eds.), Smart Sensors and Sensing Technology, c Springer-Verlag Berlin Heidelberg 2008
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displacement, vibration, distance, velocity (of both solid targets and fluids) and correlated measurements [1]. The physical principle of our displacement sensor is thus based on moderate feedback occurring when the optical beam reflected by a remote target at a distance D(t) is coupled back into the LD active cavity. The re-injected laser beam is then self-mixed with the light-wave inside the LD cavity, causing strong variations of the Optical Output Power (OOP) when the optical path length varies, i.e. when the target is moving and/or the injection current of the LD is modulated. The OOP is then monitored by means of a photodiode enclosed in the typical LD package, an OOP variation occurring for each half-wavelength (λ0 /2) displacement of the target, where λ0 represents the laser wavelength under free running conditions. The feasibility of this OFI sensor has previously been reported, displacements being measured with a resolution up to λ0 /20, i.e. around 40 nm [2]. In this paper, the operating principle is introduced. The signal processing developed for a self-mixing signal under moderate feedba
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