2.1.

Configuration

The sensor configuration and the photo of the optics are shown in Figs. 1 and 2, respectively. First, we describe the conceptual explanation for this sensor. The receiver is scanless and, additionally, has both a large receiving aperture and a wide FOV with only a single receiver (i.e., not arrayed). This is realized by the photodiode (PD), which has a high-aspect ratio receiving area (“high-aspect ratio PD”). This PD exists behind the receiving optics in Fig. 2, and its photo is also shown in the same figure. As with the TOF measurement method, the sinusoidal wave intensity modulation and phase difference detection are used. By using this modulation method, the problem encountered in using the high-aspect ratio PD can be prevented. The explanation for this effect is shown in detail later.

The operation of this sensor is described here. The laser beam is intensity modulated with sinusoidal wave. The modulated beam is transmitted to the target (here, the vehicle and the road), and the beam is scanned using a MEMS scanner in the FOV of a scanless receiver. The backscattered light is optical-to-electrical converted by the high-aspect ratio PD through the receiving optics, and current-to-voltage converted by the trans-impedance amplifier (TIA) as the received signal. The phase difference between the modulation signal and the received one is measured by the digital phase detector. The phase detector is a type of lock-in detection. Therefore, the phase detector also acts as a notch filter for noise reduction. In the signal processor, the distance to the target ($m$) is measured from the phase difference and is obtained by

where $f_m$ is the modulation frequency (Hz), $c$ is the light speed ($\mathrm{m}/\mathrm{s}$), and $d\phi$ (rad) is the phase difference between the modulation signal and the received signal. The measured data are plotted in the laser scanning area using the measured distance and the corresponding angle information. The SNR is derived from the received intensity, and the root-mean-square (RMS) error of the measured distance is predicted as The description of the above equation is shown in the Appendix. Note that the SNR is defined as the intensity ratio in the electrical signal domain. By using this predicted RMS error, bad measured data are screened. After this screening, the processing for the vehicle detection and axle counting is carried out. The algorithm of this processing is explained later.

The sensor parameters are shown in the following. We selected a wavelength region of $1.48\mu \mathrm{m}$ by considering the eye-safety. The laser diode is the one typically used as a pumping light source for an erbium-doped fiber amplifier. The laser is directly intensity modulated by a laser driver. The output average power is about 250 mW, and the modulation frequency is about 10 MHz, which corresponds to a distance ambiguity of 15 m. This ambiguity is enough for measuring a distance of up to 10 m, which is the required measurement distance in the ITS application of vehicle detection and axle counting. The output of the laser diode is coupled to a single-mode optical fiber, and the output of the fiber is collimated by transmitting optics. The diameter of the output beam is 2 mm, and the half-angle beam divergence is about 0.36 mrad. The MEMS scanner with an electromagnetic drive type is used. The laser scanning full-angle is 30 deg and the resonant frequency is 550 Hz. This corresponds to the high-speed scanning of $0.9\mathrm{ms}/\text{line}$. This realizes a spatial resolution of 25 mm for the vehicle moving direction when the vehicle speed is $100\mathrm{km}/\mathrm{h}$. The sampling frequency of the phase detector (i.e., the TOF measurement interval) is about 600 kHz. This means 500 distance measurements per each line scan. It is obvious that the sensor configuration of this paper is much simpler than the arrayed receiver configuration with an element number of 550. The aperture of the receiving optics is 26.3 mm, and its focal length is 25 mm. The size of the receiving area of the device is $13\mathrm{mm}(\text{length})\times 50\mu \mathrm{m}(\text{width})$. The width is determined in order to make the FOV wider than the beam divergence. The length is determined to keep the sufficient frequency response at the modulation frequency of 10 MHz. The cutoff frequency of this PD itself is 30 MHz. Owing to this size, an FOV of 30 deg, which matches the laser scanning angle, is realized for the scanning direction.

The sensitivity of the high-aspect PD is $1.1\mathrm{A}/\mathrm{W}$. The dark current is 5 nA and is larger than the values for smaller size PDs (note that the dark current is proportional to the size). However, the dark current shot noise does not impact the noise characteristic at the output of the TIA, which is shown in Sec. 2.2.

2.2.

Key-Device: High-Aspect Ratio Photodiode

The high-aspect ratio PD is the key device which we have recently developed. The schematic of the cross section of this device is shown in Fig. 3. We select the indium gallium arsenide (InGaAs) as the material of the device to utilize in the eye-safe wavelength region. The InGaAs absorbing layer and indium phosphorus (InP) window layer are grown on an n-type InP substrate by the metal organic chemical vapor deposition. The top surface is coated with a passivating film, which acts as an antireflection coating.

We also add a contrivance to the TIA to make use of the advantage of the high-aspect ratio PD. The PN junction capacitance, which corresponds to the capacitance between the Zn diffusion layer and the n-InP substrate layer, increases if the received area of the PD becomes larger. This increasing of the PN junction capacitance increases the noise level of the TIA. To prevent this problem, we applied an LC-resonant method for noise suppression. The schematic of the TIA with the LC-resonant method is shown in Fig. 4. The equivalent input noise current density $i_{\mathrm{eq}}$ is expressed as

where $i_n$ is the input noise current density of the amplifier ($\mathrm{A}/{\mathrm{Hz}}^{1/2}$), $k$ is the Boltzmann constant, $T$ is the temperature of the amplifier (K), $e_n$ is the input noise voltage density ($\mathrm{V}/{\mathrm{Hz}}^{1/2}$), $R_F$ is the feedback resistance (ohm), and $Z_{\text{in}}$ is the input impedance of the amplifier (ohm).

The input impedance of the amplifier $Z_{\text{in}}$ in Eq. (3) is written as

where $\omega =2\pi f$, $f$ is the signal frequency, $C_P$ is the PN junction capacitance of the detector (F), $C_M$ is the common-mode capacitance of the amplifier (F), $C_D$ is the differential input capacitance of the amplifier (F), $C_S$ is the stray capacitance of the circuit (F), and $L$ is the inductance (H). Without the inductor, the input impedance of the amplifier $Z_{\text{in}}$ decreases with the increasing of the PN junction capacitance $C_P$, and the equivalent input noise current density $i_{\mathrm{eq}}$ increases. On the other hand, the input impedance becomes large at the LC-resonant frequency and the noise level can be reduced around the LC-resonant frequency. The resonant frequency is shown as follows: With the developed high-aspect ratio PD, the PN junction capacitance $C_P$ is 72 pF. The commercial available operational amplifier is used; the common-mode capacitance is 4.5 pF, the differential input capacitance is 0.7 pF, and the stray capacitance is 10 pF. To set the resonant frequency on about 10 MHz, an inductance of $3.3\mu \mathrm{H}$ was used.

Figure 5 shows the noise spectrum of the TIA, the amplifier connected with the high-aspect ratio PD without an LC-resonant circuit, and the amplifier connected with a high-aspect ratio PD with the resonant circuit. The increase in noise level of the amplifier without LC-resonant method is confirmed, but with the LC-resonant method, the reduction of the noise level is realized around 10 MHz. This noise reduction works only around the resonant frequency. This means that this noise reduction does not work if the pulsed method is used for TOF measurement since the pulsed method generally needs a wide receiving bandwidth. This is the reason why sinusoidal wave modulation is used here. By using this modulation, the receiving frequency can be unified, and the noise in the other frequency is filtered out by the phase detector. Therefore, the effect of the above-mentioned noise reduction appears distinct. The trans-impedance gain is $78\mathrm{kV}/\mathrm{A}$ and the input noise current density of the TIA is $3.7\mathrm{pA}/{\mathrm{Hz}}^{1/2}$ within a 1.2-MHz bandwidth around the modulation frequency. The noise power at the output of the post amplifier is $-66\mathrm{dBm}$ with a bandwidth of 1.2 MHz. In Fig. 5, it is obvious that the noise levels before and after the connection to the LC resonant to the high-aspect ratio PD are almost same around 10 MHz. This means the dark current shot noise does not impact the noise characteristic.

2.3.

Key-Device: Phase Detector

The high dynamic range of the phase detector is required because there is the some target reflectance. In the case of the target reflectance is 1 and $1\times {10}^{-3}$, which corresponds to the white and black color, the order of the received electric power is 1 and $1\times {10}^{-6}$ because the received optical power is changed to the current by the photodetector.

The phase detector was produced by using a field-programmable gate array because the noise characteristics with the digital phase detector are better than those of an analog phase detector circuit, and a highly accurate measurement of the phase difference was realized. In addition, a high dynamic range by high- and low-input channels was developed for detecting high- and low-reflection targets such as white colored and black colored vehicles.

Figure 6(a) shows the block diagram. The input signal is divided two ways. One is the high channel at low gain and the other is the low channel at high gain. The clock in the phase detector is used for sampling of the analog-to-digital converter (ADC), and the transmitter signal whose frequency is multiplied from the clock frequency. The amplitude and RMS phase error characteristics of the phase detector are shown in Fig. 6(b). The vertical axis is a decimal number of 16 bit, and the horizontal axis is the electric input power. The range of input power is $-24$ to $-60\mathrm{dBm}$ for the high channel, and is 16 dBm to $-45\mathrm{dBm}$ for the low channel.

The calculated phase error is derived from Eq. (2) and the noise level, which is denoted in Sec. 2.2. The results are shown in Fig. 6(b). The figure shows that there is a difference of the phase error under the 100 (decimal number) between the measured and theoretical results. This difference is caused by additional error in the digital processing of the phase detector.

The RMS error of the measured distance in digital value $\mathrm{\Delta }{z}^{\prime }$ is written as

where $c$ is the light speed ($\mathrm{m}/\mathrm{s}$), $\mathrm{\Delta }{\phi }^{\prime }$ is the phase error in a digital value (decimal number), and $n$ is the bit number of the ADC. In this system, a 16 bit AD converter is used. For example, the amplitude is 1000 (decimal number) and the phase error is 45 (decimal number) at the high channel when the received power is $-20\mathrm{dBm}$. In this case, the RMS error of the measured distance is 1.03 cm from Eq. (6).