Blind identification of occurrence of multi-modality in laser-feedback-based self-mixing sensor Download: 637次
Self-mixing interferometry (SMI) or optical feedback (OF) interferometry[1,2] is actively researched for vibration, angle[3], frequency[4], size[5], range-finding[6], topography[7], and seismic applications[8] due to the simple, low-cost, and miniaturized nature of self-mixing (SM) sensors. In order to design low-cost SM sensors, usually commercial off the shelf (COTS) laser diodes (LDs) are preferred. However, due to OF inside the active laser cavity, such low-cost mono-modal LDs are prone to mode switching (as a function of operating conditions[911" target="_self" style="display: inline;">–
Fig. 1. Experimental (a), (b) multi- and (c) mono-modal SM signals acquired under different OF coupling and operating current conditions based on the HL6501MG LD ( ) with of (a), (c) 78 mA and (b) 82 mA.
The objective of this Letter is to robustly identify the occurrence of multi-modal SM signals so that an alert can be raised to appropriately interpret SM fringe count and/or SM operating conditions that can be changed (e.g., by changing the LD current[13] or amount of OF[14]) to revert back to mono-modal SM operation[12,15], for which algorithms exist yielding high accuracy measurements[16
SM-based multi-modality is reported to occur due to variation in parameters such as LD-to-target distance[21,22], temperature[9], or LD current[10,13]. Measurement of laser emission spectra confirmed the existence of multiple laser modes undergoing an SM signal[9,13,23] for different laser sources such as Fabry–Perot LD[21], quantum cascade laser[23], and vertical-cavity surface-emitting laser (VCSEL)[10].
Recently, a method based on an artificial neural network was proposed to classify mono- and multi-modal SM signals with a success rate of 98.75%[24]. However, this neural-network-based approach requires hand-crafted feature engineering. Pertinent features (based on temporal and spatial characteristics of SM fringes) are extracted only after performing correct SM fringe detection, a task which is difficult to achieve for noisy, experimental SM signals even when only one mode undergoes SMI, as attested by the use of advanced detection methods based on Hilbert transform[25], customized wavelet transform[26], double-derivative[27] and signal envelope tracking[28], etc. However, in this Letter, the multi-modality of the SM signal is identified without using robust fringe detection by evaluating four different SM signal statistics under different noise, OF strength, amplitude of target vibration, and laser modality conditions. Use of majority vote among the four techniques has provided 100% identification success rate.
Various mono- and multi-modal SM signals were acquired by using two different LDs, L637P5 by Oclaro® and HL6501MG by Hitachi®, one at a time. A polished metallic ring (mounted on a mechanical shaker, SF-9324 by PASCO®) was used as the remote vibrating target. The L637P5 LD has an operating wavelength
Each of the proposed four different techniques for identification of SM multi-modality is detailed below.
The variance-based technique (VBT) is based on the parameter
However, to perform VBT on normalized SM signals, two main phases are required: (1) customized local maxima detection and (2) estimation and analysis of
VBT second phase steps (see Fig.
The kurtosis-based technique (KBT) is based on the statistical parameter of kurtosis, which is indicative of a signal’s irregularity. Usually, the amplitude of multi-modal SM signals is more irregular as compared to that of mono-modal SM signals. Thus, the kurtosis value of an SM signal, denoted by
Here,
Fig. 4. Steps of the kurtosis-based technique (KBT), skewness-based technique (SBT), and skewness–kurtosis-based technique (SKBT).
The skewness-based technique (SBT) uses the statistical parameter of skewness, which is a measure of asymmetry of the SM data around the sample mean. Conventionally, mono-modal SM signals are evenly distributed around the mean value. However, most commonly encountered multi-modal signals are not even around the mean value. Thus, the skewness parameter of an SM signal (denoted by
Thus,
The skewness–kurtosis-based technique (SKBT) is based on the ratio (
Fig. 5. Evolution of parameters with respect to and target vibration amplitude for noiseless mono-modal signal (a) , (b) , (c) , and (d) .
Let us now discuss how the various threshold values, used in each of the four presented techniques, were set by performing simulations for a representative sample of SM signals by using the SM model[12] under different OF coupling (such as the frequently encountered weak and moderate OF regime[1,2]), amplitude of target vibration in terms of
Furthermore, to ascertain the impact of additive noise on the chosen parameters, simulations for the weak feedback regime (
Fig. 6. Simulated mono-modal SM signals with SNRs of 10 dB and 40 dB in the case of (a) weak feedback regime ( ) and (b) moderate feedback regime ( ).
Table 1. Values of Statistical Parameters of Simulated Normalized Mono-Modal SM Signals for Varying SNR under Weak-Feedback Regime for C=0.1 and Amplitude of 5λ0
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Table 2. Values of Statistical Parameters of Simulated Normalized Mono-Modal SM Signals for Varying SNRs under Moderate-Feedback Regime (C=4) and Amplitude of 5λ0
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It can be observed from Table
Conducting these simulations under different levels of noise, amplitude of target vibration, and OF coupling provides information about the expected range and worst-case value of the proposed parameters, resulting in extraction of different threshold values (see Table
Table 3. Extracted Threshold Values of Proposed Statistical Parameters Based on Simulations on Mono-Modal SM Signals under Varying Optical Feedback, Vibration Amplitude, and Signal to Noise Ratio
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In order to determine the performance of the proposed techniques, the experimental dataset was tested to identify the modality of these SM signals by using the threshold values of Table
Table 4. Performance of Proposed Techniques by Testing Experimentally Acquired Dataset of 60 SM Signals
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An analysis of misidentified signals led to the observation that misidentification by the proposed techniques occurred for different SM signals. So, majority voting (MV) based on results of the four techniques was undertaken (for each tested signal), resulting in a 100% success rate. If a lower number of parameters are used for the sake of reducing the complexity of the blind identification, then
To conclude, an OF-based LD can provide a multi-modal SM signal in place of the usually encountered mono-modal SM signal because of mode-hopping caused by a change in operating conditions, such as LD-to-target distance. This can cause misinterpretation of the SM fringe count, resulting in a drastic increase in metric measurement error. To avoid this error, a continuous monitoring of the SM signal is necessary, so that, as the SM signal becomes multi-modal, it could be detected immediately and possibly reverted back to mono-modal behavior (e.g., by changing the LD current or OF strength). In this Letter, different techniques based on SM signal statistics are evaluated for future continuous monitoring of emission modality of low-cost LD-based SM sensors. These proposed techniques have been successfully tested on experimentally acquired mono- and multi-modal SM signals with success rates of 85% (VBT), 75% (KBT), 91% (SBT), and 93% (SKBT). Importantly, use of MV among the four proposed techniques has provided 100% success rate of SM modality identification.
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Muhammad Usman, Usman Zabit, Olivier D. Bernal, Gulistan Raja. Blind identification of occurrence of multi-modality in laser-feedback-based self-mixing sensor[J]. Chinese Optics Letters, 2020, 18(1): 011201.