MINIMIZING THE WALK ERROR IN PULSEDTOF- LASER DISTANCE MEASUREMENT Ari Kilpel, Juha Ylitalo, Juha Kostamovaara University of Oulu / Electronics Laboratory / Finland

1. INTRODUCTION In TOF (time-of-flight) laser distance meters the terms resolution and accuracy are usually used for determining the performance of the device. Resolution means the amount of random changes in the measurement result and it depends on the changes in the timing moment, which in turn depends on the ratio between noise and slew rate of the measurement pulse. If it is assumed that the distance is measured n times and the noise in the measurement process is randomly distributed, the resolution is improved by factor 1 / n compared to the single measurement result. In practice, when the measurement takes a long time, the drift of the measurement result (caused for example by changes in the temperature) limits the longest measurement time, which is reasonable to use. The term inaccuracy includes the nonlinearity of the device, the error in the automatic gain control (AGC), the long-time and temperature drifts of the measurement result and so called walk error. The walk error means changes in the measured distance as a function of the shape and power of the measurement signal reflected and collected from the target. The walk error is created in the time pickoff circuit, which converts the analog measurement pulses to logic level pulses so that only those pulses are accepted which are bigger than a certain reference value, which is usually selected to be a little bit higher than the noise level. The time-pickoff circuit is a essential component, not only in TOF laser radars, but also more generally in time spectroscopy, which is used for example in nuclear science measurements /Gedcke68, Paulus85/. The purpose is to get a logic output pulse that is precisely related in time to the occurence of an event. The performance of the time-pickoff circuit is measured with three parameters: drift, timing jitter and walk error. Drift means the long-term timing error as a function of component aging and temperature variations in the timing circuitry. Long-term drift can often be calibrated to a level small enough. Timing jitter, which is expressed with the term resolution, is caused by statistical fluctuation of the shapes of the measurement pulses and noise in the measurement system. The value of the walk error depends on the shape and amplitude of the measurement pulses. In principle both the power and shape may change in the measurement process. The propagation delay dispersion of the fibers and the limited slew rate of the amplifiers may affect to the shape of the measurement pulse. With a careful design and selection of the optics, fibers and post amplifiers we may omit the effect of the fiber dispersion and limited slew rate to the shape of the pulses. There is also some fluctuation between the shapes of successive pulses from the laser. However if the averaged shape of the pulses remain the same, we may include the effect of the shape fluctuation in the term of resolution.

In this work the reasons for the walk error in laser radars and methods to reduce it were examined. Measurements were done both with two channel and one channel laser radars. The term "two channel radar" means that both START- and STOP-pulses have their own amplifiers and time-pickoff circuits. The prototype distance meter used was a two channel laser radar, which was same type as mentioned in /Mtt93/. That type of laser radar is used in steel industry for measuring the thickness of the lining in a steel converter. The single channel laser radar used in the measurements was a commercially manufactured laser radar, which is used in ship yards for measuring shapes of the ship blocks in distances 2 - 30 m /Kaisto93/. The origin of the reason of the walk error is the same in both one and two-channel laser radars.

2. THE PRINCIPAL TYPES OF TIME-PICKOFF TECHNIQUES AND THE REASONS FOR WALK ERROR

The time-pickoff circuit creates a logic level timing pulse, when two signals become equal. These signals can be either two pulses or a pulse and a reference level. In several time-pickoff circuits a bipolar pulse is formed from the input pulse. The bipolar pulse crosses the reference level, which is usually zero level. The crossing time of the voltages is detected with a time discriminator. The discriminator used can be for example a comparator /Maier74/, /Cable88/ or a tunnel diode /Leskovar76/. There can be two origins for the walk error: either changing of the timing moment or because the slew rate of the input pulse affects to the operation of the time discriminator. In an ideal case the timing moment in the input of the time discriminator does not depend on the shape or amplitude of the input pulses. If the time discriminator is a comparator, the limited gain-bandwidth of the comparator product affects to the propagation delay, when the slew rate of the input pulses change. The higher the slew rate of the input pulse is, the smaller is the propagation delay of the comparator. If the slew rate of the input pulse is kept constant and the amplitude of the input pulses are changed, the propagation delay remains also unchanged, provided that the amplitude of the input pulses exceeds some minimum level /Binkley88/. The timing jitter of the measurement result depends on slew rate and noise of the input pulse:2 t =

2 n2 ( dV / dt ) V = D

(1),

where n is the r.m.s. noise of the input of the time-pickoff circuit and ( dV / dt ) V = D is the slew rate of the signal in the timing moment /Bertolini68/. Eq. 1 is derived for timing, where the input pulse crosses a reference level. From (1) it can be noted that the timing moment should be chosen as a point in which the value of noise is minimized and the value of the slew rate is maximized. There are many sources of noise in TOF laser radars: the signal-induced noise, the noise from avalanche photodiode and amplifiers and the noise from the background. The origin of almost all these noise

signals is current flowing in pn junctions, so their character is shot noise. In the reference /Mtt93/ it has been measured with a similar type TOF laser radar as used in this work, that at + 760 C background temperature the noises from the background and receiver electronics have equal values, about 7 pA Hz . When the temperature of the background is decreased to room temperature, the effect of the background noise can be neglected. The shot noise from the signal current created in the avalanche photodiode varies in the range 10 pA Hz 33 pA Hz , when the signal level varies in the normal operating range. So, in normal room temperature and at small signal levels both the noise from the electronics and the signal-induced noise must be taken into account. The higher the timing moment is chosen in the rising or trailing edge, the stronger the signal-induced noise is at the timing moment. In account to this the slew rate is small and the relaxation oscillations may cause instability in the top of the laser output pulse. For these reasons the timing moment should not be chosen near the peak of the pulse. The time-pickoff circuits can be divided roughly to two groups, constant fraction discriminators and leading edge discriminators. A leading edge discriminator produces an output pulse, when the leading edge of the input pulse crosses a fixed threshold level. In leading edge timing the time of occurence of the output pulse is a function of the amplitude and rise time of the input signal. Also, because the timing moment changes, the resolution does not remain in optimum level, when the amplitudes of the input pulses change. In order to decrease the walk error the reference level can be changed according to the amplitude of the input pulses. In the constant fraction timing the input signal is divided to two parts. The other part of the signal is delayed and a fraction of the undelayed signal is subtracted from it. The timing moment is the point where the two signals have equal amplitudes. This happens, when the combined bipolar pulse crosses zero level. The optimum fractional point and the value of the delay are selected so, that walk error and resolution are minimized /Gedcke67/. The delay action is usually implemented with a delay cable and the attenuating with a resistor divider. Pulse inverting is possible to realize with a pulse transformer or with a shorted delay cable. If the time discriminator used is a comparator, the delayed and undelayed pulses can be fed to the different input nodes and subtraction of the pulses from each other is not needed. The most popular CFD types are so called true-constant-fraction (TCF) and amplitude-and-rise-timecompensated (ARC) discriminators. The pulse diagrams of the two methods are presented in figures 1a and 1b. From the figures it can be seen that the delay of the latter pulse and the slew rate of the bipolar pulse are smaller in ARC techniques than in TCF techniques. For this reason the resolution of the ARC techniques is worse than in TCF techniques, provided that the noise in the leading edge is equally big in both methods. The advantage of the ARC method is that the timing moment remains stable, even if the rise time of the input pulse changes. The main principle of the CFD used in this research work was presented first in the reference /Kostamovaara85/. In this method the input pulse is divided to two parts. The other pulse is delayed, but the non-delayed pulse is not attenuated like in TCF and ARC methods. The time discrimintator used is a fast comparator with ECL logic outputs and the delayed and non-delayed signals are fed to different input nodes of the comparator. The value of the delay cable is selected so, that the two pulse levels cross each other at the trailing edge of the first pulse and at the same time the leading edge of the latter pulse. The timing moment is usually selected to be at a 30 % - 50 % level of the maximum

amplitude. The pulse diagram is presented in the figure 2a. With this method the advantage is that the resolution value is small, because the summed slew-rate value of the two input pulses is higher than in other CF techniques. In a CFD timing process the walk error is introduced by three reasons even if the timing is otherwise ideal: the limited gain-bandwidth product of the comparator, offset voltage between the input nodes of the comparator and possible crosstalk between the input node of the comparator and some other part in the circuit. The comparator used should have as high gain-bandwidth product as possible in order to get small walk error. The offset voltage between the input nodes may introduce walk error, but the offset voltage may be also used for cancelling the walk error, which is caused by the limited speed of the comparator. The effect of the offset voltage can be seen from the figures 2a and 2b. In fig. 2a the input pulses of the CFD are presented without offset voltage between the input nodes. It can be seen, that when the amplitude of the input pulse changes, the timing moment remains in the same point. If a positive offset voltage is added to the delayed pulse, the smaller the input pulse is, the earlier the timing moment moves. The third reason for the walk error may be some crosstalk in the circuit. It can be reduced by careful design of the circuit.

3. THE STRUCTURE OF A TOF LASER RADAR

The structures of the laser radars used in this work are presented in figure 1. The measurement system consists of a transmitter, two receiver channels, two constant fraction discriminators and a time measuring unit. In addition to that the system may include also an optical attenuator and a microprocessor unit, which measures the power of the received signal and controls the operation of the optical attenuator. The laser transmitter has its own oscillator and it sends optical pulses in 4 kHz frequency. The start-pulses are taken directly from the outgoing radiation from diffuse reflection. In a single channel laser radar the whole receiver channel is common to start- and stop-pulses, which are separated after the CFD to their own channels with logic gates. The transmitter includes a semiconductor laser, either a SH- or multiheterostructure MOCVD-type, the pulse power of which is in a range of 5 W - 50 W. The FWHM of the measurement pulses in the channel are in a range of 6-8 ns. The receiver channel consists of a silicon PIN- or avalanche photodiode and a transimpedance amplifier with a transimpedance of 7 k. The voltage amplification of the post amplifiers is about 20 (= 26 dB). The bandwidth of the whole receiver channel is 100 kHz - 100 MHz. The CFD converts the analog measurement pulses to ECL logic pulses, which are feeded to the TDC (time-to-amplitudeconverter). The TDC measures the time difference between the start- and stop-pulses. It consists of a 100 MHz oscillator and counters which roughly digitize the time interval to be measured. The time fractions between the start ans stop pulses and their respective next clock pulse but one are digitized with an interpolation circuit based on analog time-to-amplitude conversion /Kostamovaara85/. The distance value can be read from the output of the TDC as a 16 bit word with a PC or a microcomputer card. The simplified schematic diagram of the time discriminator is presented in figure 4. The threshold level of the noise comparator is adjusted according to the background noise. The noise level in the receiver channel after the postamplifiers is about 11 mVRMS in normal room lights and temperature. Then the amplitudes of the largest noise pulses are approx. 60 - 70 mV and the threshold level of the

noise comparator is adjusted for example to 100 mV - 150 mV. The output pulse of the noise comparator goes through ECL-flip-flop n:o 1 (type 10H131) to the data input of the flip-flop N2. So the output of the flip-flop N2, which is at the same time the output of the discriminator, can change its state only when the amplitude of the input pulse of the discriminator exceeds the threshold level adjusted to the noise comparator. The real timing pulse comes from the timing comparator to the clock input of the flip-flop N2. The flip-flop N1 has two purposes: it extends the the data input pulse of the flip-flop N2 and it latches the output nodes of the noise comparator as long time as the output of the flip-flop N2 resets the state of the flip-flop N1. The latter function is important, because if the output nodes of the noise comparator change, it may happen at the same time as the input pulses to the timing comparator cross each other. Then the output pulse of the noise comparator can be coupled to the input nodes of the timing comparator through the parasitical capacitances between the bonding wires in a dual comparator circuit. The strenght of the measurement signal can be estimated on the basis of the amplitude of the measurement pulses in the electrical channel, after the postamplifiers. The impedance of the channel is 50 ohms and the amplitude may usually vary in a range of 0.2 V - 2.0 V. In this range the single shot resolution of the device is in a range of 70 - 330 ps, when the device is located in normal room lights and temperature. Then the resolution of 10 000 measurements may vary in a range of 0.7 - 3.3 ps. In the laser radars used in this work the saturation level of the pulses coming out from the postamplifiers is approx. 2.7 V.

4. THE MEASUREMENTS

Three different comparator types were tested as time discriminators. The types were Analog Devices AD 96687 and Signal Processing Technology HCMP 96870A and SPT 9689. The walk error of the distance meter was measured with several offset voltages with all three comparator types. All the comparators tested are pin-compatible with each other. Some differences can be found in input resistance, connections of unused LATCH-inputs, propagation delay and the dispersion of propagation delay as a function of overdrive and slew-rate of the input signal. In all comparators the input capacitance depend on type of the case and it is approx. 1 pF with LCC-case and 2-3 pF with cerdipcase. In all measurements a double channel laser radar was used, except in the walk error measurement presented in figure 7d, which is measured with a single channel laser radar. The semiconductor laser used in double channel radar was a pigtailed MOCVD laser diode CVD-193F (manufactured by Laser Diode Inc.), the pulse power of which was 18 W measured from the end of the fiber. The rise and fall times (between 10 % and 90 %) of the channel pulse were 4.5 ns and 4.7 ns, respectively, and the FWHM was 7.9 ns measured with a oscilloscope Tektronix DSA602A, which has a bandwidth of 1 GHz. The shape of the channel pulse is presented in figure 5. In a single channel laser radar a smaller laser, type CVD-93F, was used. It had a pulse power of 5 W, rise time of 3.3 ns, fall time of 4.3 ns and FWHM of 6.8 ns. The delay cable in the constant fraction discriminator was 190 cm long in the measurements presented in figures 6 - 7d.. With that cable the cross point of the undelayed and delayed pulses was about at 38 % of the maximum height of the pulse, when the FWHM of the measurement pulse was 7.9 ns. The walk error measurements with zero offset voltage are presented in figure 6. The zero offset voltages were adjusted so, that the comparators oscillated at 50 % duty cycle, when no signal was fed to the input nodes and the output of the postamplifier was disconnected from the input of the CFD. Then the external offset voltage has compensated the internal offset voltage of the comparator. It could be noticed that the dependence of the propagation delay on the ovedrive and the slew rate of the input signal was clearly largest with the AD 96687 -comparator and smallest with the SPT 9689 -comparator. The walk error measurements with different offset voltages are presented in figures 7a-7d. The measurements have been done with a double channel laser radar using three different comparator types and with a single channel laser radar using only one comparator type, the SPT 9689. For all comparators the walk error curves have been measured with several values of offset voltage. Smallest walk error, +/- 1mm with input amplitude range 0.2 V - 2.0 V, was reached with the SPT 9689. The walk errors measured with single and double channel laser radars don't differ significantly from each other. The effect of the timing of the crossing point in the input of the timing comparator was studied by measuring the resolution and walk error values with several delay cable lenghts (figures 8a-8b). In all tests the comparator type was AD96687 and the offset voltage was 33 mV. Figure 8a presents the single-shot resolution of the laser radar with different cable lengths. From the figure it can be seen, that the single-shot resolution varies in a range of 8 mm - 39 mm in a amplitude range of 0.2 V - 2.0 V

in the best case, with 190 cm long delay cable. With larger input amplitudes than 1.3 V the resolution values were slightly better with longer delay cables than 190 cm, but with smaller input amplitudes than 1.3 V the resolution values were clearly best with 190 cm long delay cable. The resolution is in principle best with longest delay cables, because then the timing point takes place at a low point of the pulse, where the pulse power and at the same time the signal-induced noise are lowest. However with large offset voltages the timing point may move to a slowly rising point in the beginning of the input pulse, when the input amplitude is low and the delay cable is long. The result is deterioration of the resolution value.

5. EVALUATION OF THE VALUE OF THE WALK ERROR

In the evaluation of the value of the walk error theoretically several things must be taken into account: the dependence of the propagation delay on the slew rate of the input pulses and the offset voltage in the input nodes of the comparator. In all the calculations below it has been assumed that the internal offset voltage of the comparator circuit is zero. A simplified model of the propagation delay of a comparator has been intoduced on /Arbel80/. The internal capacitances of the comparator create the propagation delay. Let's suppose simply that the comparator is an amplifier, which has single pole and we operate in small signal range and the shape of the input pulses remains the same. The open loop gain in s-domain is:

U0 ( s ) e s D A( 0 ) = F(s) = Ui ( s ) 1 + sA( 0 ) 0

(2),

where A(0) is the open loop gain in zero frequency and 0 = 1 0 is the time constant corresponding to the upper -3 dB frequency limit of the unit gain. The term e s D means that there is a limit D in the minimum propagation delay. If the input signal is a linear ramp ui ( t ) = SR t , where the slew rate of the linear ramp is SR, then:

SR Ui ( s ) = 2 sThe Laplace transform of the output signal is:

(3)

SR e s D A( 0 ) U 0 ( s ) = F ( s )Ui ( s ) = 2 1 + sA( 0 ) 0 s

(4)

Now we may assume that D t