3.1.

Self-Mixing Signal Dependence on Distance

The experimental setup for measurement of the dependence of self-mixing signal on distance is presented in Figure 2. A Philips 1550-nm GaInAsP LD CQF 58 with monomode fiber with a 1-m length was used in our experiments. There is a special potentiometer P for precise adjustments of the laser pump current. A special low-noise two-channel amplifier used for the signals from the PD and from the resistor in the laser current chain, correspondingly. Light consists of nine longitudinal modes, and the shift between them was 1.11 nm (Figure 3). The frequency difference between the longitudinal modes of laser active cavity was Δf=1.25×10¹¹ Hz, the equivalent optical (taking into account the refractive index) longitudinal size of the cavity was about 1.2 mm.

Figure 2

Schematic experimental arrangement with amplifiers for PD and LD output signals and with LD current regulation. Used laser package from Philips CQF 58, which contain an optical fiber of 1 m length: PD, photodiode (integral), and LD, laser diode.

Figure 3

Spectrum of LD CQF 58 passport data.

The measured dependence of the self-mixing interference on the distance between laser and target is presented in Figure 4 (first five maximums and others). The distance between minimum and maximum on the self-mixing modulation function curve was 0.89 mm.

Figure 4

Dependence of self-mixing interference on the distance: left, first five maximums, and right, all maximums. Here horizontal axis represents the distance between optical fiber output and target, and the vertical axis, the signal amplitude in arbitrary units.

We used a reflective surface attached to a loudspeaker cone driven by a signal generator as a target, to provide phase variations of the external optical feedback. The diode laser package incorporates a PD accommodated in the rear facet to monitor the laser power. This characteristic of the device is particularly well suited to observing the self-mixing interference and it provides a convenient internal detector. A typical output signal obtained in this case is shown in Figure 5. The feedback was less than 10 in all experiments. The upper trace in Figure 5 is the signal applied to achieve the periodic target movement, and the resultant intensity modulation (middle trace) is the self-mixing signal observed. Another structure of the same device was also observed. For signal separation and capturing, there is an additional resistor (R=50 Ω) with intermittent potential in the laser pump current chain. In the same figure (lower trace) the self-mixing signal is presented.

Figure 5

Typical signals observed from self-mixing: upper trace, signal applied to achieve the periodic target movement; middle and lower traces, self-mixing signals from the PD and the resistor in the laser current chain. Here the horizontal axis represents time, and the vertical axis, the signal amplitude in arbitrary units.

The theoretical value for distances between the positions of two maximums on the self-mixing modulation function curve is about 1.2 mm. The difference between theoretical estimation of distance between maximums and the measured real value of 0.89 mm (Figure 4) would be explained by slightly different length of laser cavity used in theoretical estimation. This length was derived from passport data of light spectrum of the diode laser (Figure 3).

The dependence of the self-mixing signal amplitude maximums on distance can be explained by the characteristics of spatial broadening of laser light beam as well as by its limited longitudinal coherence. The spatial broadening of the beam from the optical fiber was measured by the method applied in Ref. 21. The radiation angle of the fiber was 40 deg at a 90 level and the intensity dependence on distance from the fiber r was typical for spherical wave 1/r². The decrease of the measured maximums (Figure 4) with increased distance fit well with this dependence.

The longitudinal coherence is determined by the width of the radiated light spectrum. If the round-trip time of the light in the external cavity τ _ext =2L/c is within the coherence time, the interference between the backscattered field and field inside the laser active cavity is strongest. If the round-trip time is larger than the laser light coherence time, the phase changes between the intracavity and backscattered light cause a strong reduction of the interference and consequently the self-mixing signal. Introducing the longitudinal coherence length through the width of the spectrum of the radiated light l _coh =c/Δf the relative reducing of the self-mixing signal is proportional to the ratio¹⁶

In our experiments, a multimode laser was used and its spectrum consists of a series of narrow lines (Figure 3). In this case, there are two different coherence scales. One is determined by the width of single longitudinal mode. On the other hand, the whole spectrum includes N modes separated by ΔF=c/2l, where l is length of the laser cavity. The total intensity is obtained as a sum of N uncorrelated spectrum lines and the longitudinal coherence length I _coh =2l has its minimal value 2.4 mm. The real length of the external cavity L consists of two parts: the length of the optical fiber l_f=1 m and distance from the fiber r and L=l_f+r, which is much longer than the coherence length. The relatively small changes in distance L caused by variances of r (Figure 4) cannot affect the condition L≫l _coh . Calculated by Eq. (3), the dependence of the self-mixing signal on distance r from the fiber is not significant. In this case, the measured dependence of maximums amplitude on distance (Figure 4) was caused by the decrease of light intensity with distance caused by the beam broadening only.

3.2.

Self-Mixing Signal Dependence on Laser Current and Sensitivity of the Method

First, we measured the self-mixed signal amplitude as a function of the laser pump current. The pump current was adjusted precisely with a potentiometer and the output signals of both channels were recorded simultaneously. These characteristics are similar and one of them shown is in Figure 6. As we can see in both cases, the self-mixed signal dependence on the laser pump current as inversely proportional, and the maximum value of the signal corresponds to the pump current near threshold.

Figure 6

Mixed signal amplitude dependent on laser current: the used laser was QF 4142 with a threshold current I _th =24 mA. Here the horizontal axis is laser current in milliamperes and the vertical axis, the signal amplitude in arbitrary units.

Second, we measured the sensitivity of self-mixing as a method. We registered a maximum distance L _max =42 mm (distance from optical fiber output to target) when the self-mixed signal amplitude in the amplifier output is equal to the noise (SNR is 1). This situation corresponds to the minimum reflected signal that we were able to measure without additional signal processing. Thereafter, we geometrically calculated the amount of a radiation reflected from the target to the optical fiber input in the case of L _max . The measured optical radiation distribution from the optical fiber in different directions is the same on both plane surfaces and the calculated spatial angle for 90 of radiation is 10 deg. The calculated geometrical laser spot surface of reflected radiation on the plane surface of the optical fiber input S=πr²=π(2L tan φ)²=168 mm ².

We calculated geometrically minimum optical power P _min (SNR=1), reflected back to a laser cavity, without considering losses from the refracting of different surfaces, losses from matching, and losses from mixing in the case of an optical fiber core diameter of 9 μm and a laser output optical power P=0.05 mW (near threshold). As a result, P _min =S _fiber /S×P=19 pW, which gives a satisfactory sensitivity for this method.

3.3.

Application of Method for Flow Detection

The experimental scheme used to investigate the flow effects of self-mixing with a pigtail diode laser is shown on Figure 7. The pigtail laser package consists of an LD, which is kept at constant temperature by Peltier element, and a PD. The matched monomode optical fiber is 1 m long with a core diameter of 9 μm and without any lens, which means that the SNR of output signal can be improved by having a collecting lens in the fiber output end. In this scheme, the light from the pigtail heterojunction InGaAs LD (Philips CQF 58) with a wavelength of 1550 nm and with an output optical power 1.0 mW is emitted from the fiber output and reflected back into the laser cavity via the same fiber. The liquid used is an aqueous suspension of polymer microspheres with a sphere diameters of 7.0 μm, a polymer density of 1.05 g/cm³, a refractive index of 1.59, a concentration approx. 10⁷ spheres/ml, produced by Duke Scientific Corporation. The rotating speed of the vessel containing liquid can be adjusted in range of 0.1 to 0.7 turns/s. The end of the fiber is fixed at under 45 deg near to the liquid surface. The distance from the fiber end to the liquid surface is 1 mm and distance from the rotation center is 4 mm. The speed of rotating vessel was increased in five equal steps and the self-mixing signal power spectrum was recorded. As we can see from the Figure 8, the spectrum maximum corresponds to the particle flow rate, which increases proportionally to the rotation speed of the turning vessel.

Figure 7

Experimental arrangement for flow detection.

Figure 8

Recorded power spectrums at five different flow velocities of the liquid.

A PC with a data acquisition card (PCI-MIO-16E-1) was used to record the output signal. The data acquisition resolution is 12 bits and frequency of discretization in our case is 50 kHz. After discretization, the signal was filtered by a high-pass filter (HPF) to reduce the low-frequency noise level. The third order filter was used in that case. The HPF filtering limits the theoretical minimum velocity that can be detected (1.6 mm/s); the upper frequency limit is set by the Nyquist criteria (19 mm/s). After filtering, the signal was windowed and the power spectral density was calculated inside 2048 sample frames. To obtain a reasonable SNR, the power spectrum was averaged over 40 frames, the frames were 50 overlapped. The length of the signal that was processed was 2048×40×0.5×0.2×10⁻⁴ s≅0.8 s, which means that the first measurement result can be obtained in less than a second, and for continuous measurements, the time resolution is limited by the frame size and discretization frequency 2048×0.2×10⁻⁴ s≅0.04 s. A sliding window additionally smoothed the calculated power spectrum; the window size was 200 points. Thereafter, the frequency with the maximum amplitude was detected and the frequency-to-velocity transform was performed. National Instruments graphical programming software LabView was used to record and for signal-processing purposes.

3.4.

Application of Method for Pulse Profile Measurement

The pulse profile registration was performed using the same setup and equipment as represented in Figure 2. The probing ray was led via the optical fiber to the skin surface (arm artery). At the end of the fiber, a special clamp was attached to minimize the interfering signal due to involuntary tremors of the body (the position of the fiber tip relative to the arm was fixed).

The signals were recorded with a sampling rate of 10 kHz, which gave a bandwidth of 0 to 5000 Hz, the duration of the recording was 10 s. The recorded signal was preprocessed using a sliding window, the length of the Hanning windowed signal was 128 points, and power spectrum was calculated after every 8 points (resolution 0.8 ms) using the fast Fourier transform (FFT) algorithm. For every calculated power spectrum segment the frequency with maximum amplitude was detected, which gave us the time-dependent Doppler frequency (pulse profile). See the sliding processing part of the upper channel in Figure 12 in Sec. 3.5. We used the National Instruments data acquisition board (DAQ) AT-M10-16E-10 to digitize the signals locally and transmit the digital data to the PC with a resolution of 12 bits.

As we can see in the frame of the recorded pulse profile signal in Figure 9, the shape of each pulsation has more peaks, including a major peak and a secondary peak immediately following the major peak. The reasons for this are the reflections of the blood pressure wave, but the output signal of our system represents the absolute value of the skin vibrations, because we can not distinguish movement toward or away from the probing ray. In this figure, time t₂ corresponds to the maximum velocity of vessel extension, and time t₄ to the maximum velocity of vessel restriction. We have the maximum diameter of the vessel at time t₃ and the normal diameter at t₁ and t₅, respectively.

Figure 9

Frame of recorded pulse profile signal.

3.5.

Application of Method for Pulse Wave Delay Time Measurement

Pulse wave delay time is measured as a time interval between the electrocardiogram (ECG) signal and the skin vibration signal near different arteries of the human body. We used a four-lead system with the standard ECG clinical device Mingograf-4 produced by Siemens-Elema for ECG recordings. The setup for measurement is represented in Figure 10. Six different measurement points Mp1 to Mp6 were used to measure the pulse wave in different arteries. Both of the signals were recorded with a sampling rate of 10 kHz, and the duration of the recording was 10 s. The recorded signals are shown in Figure 11. The first signal (upper curve) is the ECG used as a reference signal for the time measurement, the second curve is a processed laser Doppler signal (pulse profile), and the third curve is a signal from the LD used as an input signal (without processing).

Figure 10

Experimental arrangement for pulse wave delay time measurement.

Figure 11

Recorded pulse profile, processed pulse profile, and ECG signals.

The recorded laser Doppler signal was preprocessed (Figure 12) using a sliding window, the length of the Hanning windowed signal was 128 points and the power spectrum was calculated after every 8 points (resolution 0.8 ms) using the FFT algorithm. For every calculated power spectrum the frequency with the maximum amplitude was detected. The maximum of every pulse profile t₂ (Figure 9) was detected using the adaptive level peak detector, after which the pulse vibration starting point t₁ was determined. The calculated time-dependent frequency (pulse profile) never goes exactly to the zero because of the noise, and that makes it difficult to determine the exact starting point of the pulse vibration. In this paper, the starting point of the pulse wave was fixed to the time point where tangent of the maximum value of the first derivative of current pulse profile and the zero frequency converge. The discretization frequency of the ECG was reduced to 335 Hz, because there is no relevant information above 100 Hz. Thereafter, the ventricular electrical activation starting point R peak (Figure 11) in the ECG was located by the adaptive level peak detector. The pulse delay was calculated as a time difference between the R peak of the ECG and the following pulse starting point of the laser Doppler signal.

Figure 12

Block diagram of digital signal processing algorithm for pulse delay measurements.

The results of the pulse delay measurements are presented in Table 1. One recording (10 s) contains about 12 to 13 pulses. The mean delay of the pulses was calculated without the maximum and minimum values of every data series. The heart rate mean values are calculated in the same way. The values of the heart rate are different for different points of the human body because these measurements are made at different time moments.

Table 1