Abstract
Using self-mixing interferometry (SMI) with a periodical modulated injection current, high resolution displacement sensing can be achieved by retrieving the initial phase of an SMI signal at each modulation period. However, the existing initial-phase-based detection methods can only obtain a single point measurement of displacement within each single modulation period. Thus, they are only effective when the target is subject to slow movement, or the injection current is modulated by a signal of very high frequency, which are not practical in many applications. In this work, a new method is proposed to tackle the problem. Firstly, a reference signal is obtained by setting the target still. Then Fast Fourier Transform and its inverse (FFT/IFFT) are applied to the reference signal and the SMI signal, leading to a formulation to obtain the SMI signal phase, which enables the SMI system to retrieve the time varying displacement in each modulation period. As the proposed method is able to measure displacement at multiple discrete time instances (dependent on the number of samples for FFT), the measurement resolution is significantly improved over existing method. Hence, the measurement capability of the SMI system is enhanced greatly. Both simulation and experiments are conducted and the results are presented to verify the proposed algorithm.
Highlights
When a fraction of external optical feedback re-enters the cavity of a laser diode (LD), the laser intensity and optical frequency will alter. Such a laser diode system is often called as self-mixing interferometry (SMI), the modulated laser intensity is called an SMI signal
In this paper, we propose a new method, where the phase of an SMI signal caused by displacement within each modulation period is considered to be time varying
The laser intensity of the SMI system with a fixed target is used as a reference signal
Summary
When a fraction of external optical feedback re-enters the cavity of a laser diode (LD), the laser intensity and optical frequency will alter. This will require a long initial distance between the LD and the target and high modulation magnitude To relax these restrictions, in this paper, we propose a new method, where the phase of an SMI signal caused by displacement within each modulation period is considered to be time varying. For the case of moving target with modulated injection current, the laser intensity after subtracting A(t) is called as the SMI signal and can be expressed as: I1(t) = B1 cos(2π fct + φ0 + φ(t)),. We choose 512-point FFT applying to half period of the modulation signal, and the sampling frequency should be Fs = 102.4 kHz. As the sampling frequency is about 100 times higher than the carrier frequency, the Nyquist condition should be met for both the reference signal and the SMI signal. When applying sinusoidal vibration on the target, the maximum vibration frequency ft max of the PZT is limited by the formula ft max
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