Chapter 2. Pulsed time-of-flight laser rangefinding
- Table of Contents
- 2.1. Leading edge discrimination
- 2.2. High-pass timing discrimination
Laser rangefinders can be divided into several categories in terms of their operation principle. This work concentrates on a technique in which the distance is measured as a direct product of the propagation delay of a laser beam, i.e. the time-of-flight method, and still more precisely, in which a pulse wave is used as the laser beam, i.e. pulsed time-of-flight laser rangefinding.
Time-of-flight laser radars are used in wide variety of industrial, customer and military applications, including absolute distance measurements, profiling, automotive safety, vibration and proximity measurements, velocimetry, positioning, vehicle guidance and 3-D vision (Araki & Yoshida 1996, Kaisto et al. 1993, Kawashima et al. 1995, Määttä et al. 1993). Absence of physical contact and short measurement times with optically visible targets are distinguishing characteristics for all these types of measurement. Typical measurement distances are up to several ten metres, or even several kilometres in military applications in particular. The accuracy needed varies accordingly, from mm-level to a few metres. The most important performance parameters are precision, accuracy, measurement range and measurement time.
A pulsed time-of-flight laser rangefinding device typically consists of a laser pulse transmitter, the necessary optics, two receiver channels and a time-to-digital converter, as shown in Fig. 2. The laser pulse transmitter emits a short optical pulse (typically 2 to 20 ns) to an optically visible target and the transmission event is defined either optically, by detecting a fraction of the pulse, or electrically, from the drive signal of the laser diode. The start pulse is then processed in a receiver channel, which generates a logic-level start pulse for a TDC. In the same way the optical pulse reflected from the target and collected by the photodetector of the stop receiver channel is processed and a logic-level stop pulse is generated for the TDC. The TDC uses its time base to convert the time interval to a digital word which represents the distance from the target.
The amplitude of the received stop signal varies over a wide range depending on the measurement distance and the reflectivity and angle of the target. The dynamic range of the signal depends on the application, and may be 1:1000 or even more. As the length of the laser beam is much longer than the accuracy usually needed (2 metres vs. a few millimetres or centimetres), a specific point in the pulse has to be defined, and consequently a logic-level pulse for the TDC has to be produced. The timing event should not change when the level of the signal varies, as it will directly affect the measurement result, with 6.7 ps corresponding to 1 mm.
The function of the receiver is to produce accurately timed logic-level pulses from optical input pulses of varying amplitude. Since the timing discriminator plays an important role in this process, solutions for this component are described in more detail here.
The timing event can be generated either from the edge of the pulse which is allowed to saturate in the receiver channel or by linear signal processing, in which gain control structures are usually needed, due to the wide dynamics of the input signal and the limited dynamic range of the receiver channel. The simplest way of defining the timing point is the former one, a leading edge discrimination technique in which a comparator with a constant threshold voltage is used to trigger the leading edge of the received pulse. The drawback of the technique is that if the amplitude of the pulse changes, the timing point also changes and generates a walk error Δt, as shown in Fig. 3a. Thus the walk error represents the change that takes place in the timing event when the amplitude of the pulse varies. The principle of operation of the leading edge timing discriminator and its walk error are presented in more detail in section 2.1.
In order to reduce the walk error, more sophisticated techniques has been developed in which the signal is processed in a linear manner. One technique of this kind is the well known constant fraction discriminator (CFD), where the timing point is generated by comparing an attenuated pulse and a delayed pulse, so that their crossing point defines a constant fraction of the pulse (Gedge & McDonald 1968). In this technique the timing point (crossing point) is insensitive to variation in the amplitude of the signal. If the shape of the rising edge does not vary, the method can be used for amplitude and rise time-compensated (ARC) timing, given proper selection of the delay (Paulus 1985). The CFD is well suited for applications in which the signal has a fast rising edge and a long tail (e.g. scintillation detector/PMT measurements in nuclear physics), because the discriminator utilises only rising edge and peak amplitude information regarding the pulse. CFDs constructed with discrete components usually require delay lines, whereas an exact delay of a few nanoseconds is difficult to realise in integrated circuits without degradation in the slope and amplitude of the signal. The CFD is nevertheless integrable by means of operations such as attenuation, a C-R differentiator, an R-C low-pass filter or a distributed R-C delay line (Jackson et al. 1997).
A pulse signal which also has a fast falling edge (i.e. no long tail) can be generated using a PIN or APD as the photodetector. Here constant fraction detection can be implemented by identifying the crossing point between the falling edge of a pulse and the rising edge of a delayed pulse (Kostamovaara & Myllylä 1985). In integrated solutions, however, the technique again calls for an exact delay of some nanoseconds.
A simple C-R high-pass filter was used successfully here to discriminate the timing point of the pulse. This filter generates from the unipolar input pulse a bipolar output pulse in which the zero crossing point is insensitive to amplitude variations, as shown in Fig. 3b. The operation of the technique and the walk error originating from detection of the zero crossing point are presented in more detail in section 2.2.
Figure 3. a) Walk error with a leading edge discriminator, and b) the bipolar pulse used in the high-pass timing discrimination technique.
2.1. Leading edge discrimination
A leading edge discriminator is the simplest way to detect the arrival of a pulse. A comparator with a constant threshold voltage is used to define the timing mark for the TDC. The threshold voltage has to be so high that noise will not cause false triggerings. The walk error in the leading edge discrimination arises from the amplitude variation and shape of the input pulse, the bandwidth and dynamics of the receiver channel and the level of the threshold. The error consists of three sources: a geometrical timing error which occurs even with an ideal receiver, error caused by the finite bandwidth, slew-rate and dynamic range of the receiver and a change in the propagation delay of the timing comparator. The last-mentioned is usually negligible relative to the previous ones.
The walk error can be estimated by means of a simple piecewise linear model of the rising edge of the input pulse Vin, as shown in Fig. 4b, fed to an amplitude-limiting circuit followed by a bandwidth limiting circuit, as shown in Fig. 4a (van de Plassche 1994). Using the notation in Fig. 4b, the delay in the timing point from the beginning of the rising edge tp at the output to the amplitude limiting circuit is
where Vth is the threshold voltage and vp and tr are the peak amplitude and the rise time of the pulse before amplitude limitation. The delay variation represents the walk error of an ideal receiver channel (geometrical walk error). If, for example, the rise time of the pulse is 1.6 ns and the threshold is 50 mV, an amplitude variation from 100 mV to 2 V will results in a timing point variation from 0.8 ns to 40 ps and thus generate a walk error of 760 ps. In real applications, however, the maximum amplitude of the input pulse is much greater, so that the geometrical variation in the timing point in this case can be estimated to be 0.8 ns.
Figure 4. a) A simple model of the receiver channel and input and output signals of the bandwidth limiting circuit with b) small and c) large signal amplitudes.
This model neglects slew-rate limitation and models the delay change caused by the finite bandwidth of the receiver by feeding the amplitude-limited signal into a single pole bandwidth limiting circuit. The largest input signal of the bandwidth limiting circuit can be estimated to be a step with an amplitude equal to the maximum linear amplitude of the amplifier channel Vmax, as shown in Fig. 4c. This leads to an output signal waveform vout of
where RC is the time constant of the bandwidth limiting circuit. The delay of the threshold crossing point, calculated using an RC of 640 ps (corresponding to a bandwidth of 250 MHz), Vth of 50 mV and Vmax of 2 V, is 16 ps, which represents the shortest delay. The longest delay appears with the smallest input signal, and if the slew rates of the input signal and the output signal of the bandwidth limiting circuit are equal at the threshold level, as shown in Fig. 4b, the delay is simply RC, corresponding to 640 ps. The bandwidth limitation thus generates a walk error of 624 ps, which is considerable in relation to the walk error of 800 ps achieved with an ideal receiver channel (infinite bandwidth).
The walk error can be compensated for using a correction table in the range where the amplitude of the signal can be measured and the signal is not saturated. This calls for an accurate peak detector, because the compensation is very sensitive to amplitude changes at low signal levels (Ruotsalainen 1999a).
The walk error was simulated numerically using the Matlab program and the simulation model described above, but improved in the sense that the single pole of the bandwidth limiting circuit was replaced by three identical poles (a low-pass filter with a –60 dB/decade roll-off) so that the resulting –3 dB frequency was equal to 250 MHz. The delay in the timing point as a function of the input signal level is shown in Fig. 5. The curves show the geometrical walk error, the error caused by the finite bandwidth and the sum of these. The x-axis shows the ratio between the peak amplitude of the signal and the threshold level. The rise time of the input signal is assumed to be 1.6 ns and the maximum linear amplitude to be 40 times the threshold level (corresponding to Vth = 50 mV and Vmax = 2 V), which means that the signal begins to saturate in the receiver after a value of 40 on the x-axis.
Figure 5. Delay in the timing point of the leading edge discriminator as a function of signal level.
The walk error is 1.6 ns when the amplitude of the input signal varies from 2 times to 10 000 times the threshold level (1:5000) and saturates at that level. The error in the range from 2 to 40 which is the linear range of the receiver channel, can be compensated for by means of correction table obtained by measuring the amplitude of the pulse. This compensation would reduce the walk error by 1.2 ns, so that the uncompensatable walk error is 400 ps, corresponding to a distance of 60 mm (±30 mm). The residual walk error is small enough for some applications, but a more accurate timing discriminator has to be used in short range applications in particular. The benefits of the leading edge discrimination method are its simplicity, the wide dynamic range of the input signal and the possibility to perform the measurement with a single pulse without any gain adjustments or information about the level of the incoming pulse. The walk error can be reduced by increasing the bandwidth of the receiver and shortening the rise time of the optical pulse.
Another important parameter for timing discriminators is jitter, which defines the statistical error in the timing point. The timing jitter σt, representing the standard deviation of the distribution of the measurements, can be calculated using the triangle rule (Bertolini 1968)
where σv is the noise power at the timing point tp and v(t) is the input signal of the timing comparator. The noise in the equation usually originates from the noise of the receiver channel electronics. The jitter is largest with the smallest input signals, but is still smaller than the walk error in the leading edge detection method. A rise time of 1.6 ns, for example, and a peak signal amplitude to rms-noise level ratio (SNR) of 10, which represents the smallest usable signal level, will results in a precision of about 160 ps (24 mm, σ-value). This can be improved by averaging single measurements, which results in an improvement of √N, where N is the number of averaged asynchronous measurements (Hewlett-Packard AN 162-1).