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Abstract
In the pulsed light time-of-flight (ToF) measurement, the timing point generated in the receiver channel is very important to the measurement accuracy. Therefore, a differential hysteresis timing discrimination method is proposed to generate timing points of the receiver channel. This method is based on utilizing the unbalanced characteristics of the fully differential operational amplifier circuit as well as introducing extra hysteresis levels to achieve the stable generation of timing points. With this method, fewer circuit components are consumed and the dynamic range of the receiver channel is not limited by its linear range. The experiments demonstrate that a receiver channel applying the proposed discrimination reaches better single shot accuracy compared to that using leading-edge timing discrimination. This method is also suitable for the timing walk error compensation by means of pulse width. Finally, these results verify the effectiveness of the proposed method in pulsed light ToF measurement.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The pulsed light time-of-flight principle is based on measuring time interval between start pulse and stop pulse. The technology using this principle has been widely applied in various fields. The advantages of the pulsed ToF technique are the capability to capture a measurement event at a higher speed and to achieve nanosecond accuracy even with a single measurement shot [1,2]. In time interval measurement systems, pulsed light can be generated either by a light source or by a luminous event. In applications where pulsed lights are generated by light sources, distance detections by measuring the transit time of a laser pulse to the target and back to the receiver are the typical and widely used applications, which are known as LIDAR. They are extensively used for mapping, surveying, on board of ground vehicles, aircraft, spacecraft, satellites, geodesy, forestry and for civil as well as military purposes [3–5]. More recently, range sensors of various kinds such as depth cameras and range scanners by measuring the depths of scene points have been used in computer graphics and computer vision for 3D object modeling, which is shown in Fig. 1 [4]. In applications where pulsed lights are generated by luminous events, time-of-flight positron emission tomography (ToF-PET) is a representative application and has become a major trend of PET instrumentation in medical imaging. A pair of gamma rays (photons) is produced as a result of positron and electron annihilation reactions. ToF-PET uses the time difference Δt in the detection of the photon pair, which travels in the opposite direction, and correlates it to position Δx of the point of annihilation, as also shown in Fig. 1 [6]. Furthermore, this technique can also be used in fluorescence lifetime measurement and imaging [7,8].
In time interval measurements, the timing receiver channel is indispensable. Its function is first to convert the received optical signal into an electric pulse signal by photodetectors such as avalanche photodiode (APD), Geiger-mode APD (Gm-APD) or photodiode array, then amplify it by a transimpedance amplifier (TIA) and finally generate a timing point (or a timing stop signal) by a timing discriminator. The timing discrimination point is very important because it directly affects the accuracy of time measurement due to the jitter error and walk error. Generally, it is generated by two main methods of timing discrimination. [9]. The first is constant fraction discrimination (CFD). Through this method, the timing point is generated by comparing the delay signal and the attenuated signal of the original pulse. It should be noted that the method of CFD is used typically only in a limited dynamic range of less than 1:100 or less [10]. Therefore, electrical gain control or auto gain control (AGC) structure are usually introduced in the design of receiver channel [11–14]. Though the dynamic range of the receiver channels is extended (e.g. 1:600), they are incapable of handling the dynamic range of the received optical signals (>1:10000) [2]. Leading-edge discrimination is another widely used method. The leading edge of the received pulse is detected as the signal crosses a certain threshold. It is amplitude independent, therefore, it works even when the pulse shape is saturation distortion and it is suitable for fast signal processing. However, the large walk error caused by varying amplitude is typically introduced and therefore compensations are needed to be performed [2,9]. To the best of the author's knowledge, some other methods have also been reported to improve the accuracy. Kurtti et al. proposed a unipolar to bipolar based timing discriminator and then performed zero-crossing detection for time discrimination [15]. Cao et al. presented the differential time domain method (DTDM) based on peak discrimination to improve the accuracy [16].
Inspired by these methods, in this paper, differential hysteresis timing discrimination is proposed to extract the timing point in the receiver channel. This method requires a simple circuit structure and a low component count, i.e. just using a fully differential operational amplifier (op amp) and a timing comparator at the output of the receiver channel. The main advantages of this timing discrimination method are the wide dynamic range of the input signal and the possibility to perform the measurement with a single pulse without any gain controls, which make the receiver channel possible for compact and array applications.
The remaining sections of the paper are organized as follows. In Sec. 2, circuit description of the entire receiver channel is first presented. The principle of how it generates the stable timing point is also analyzed in detail. The entire noise of the receiver channel is described in Sec. 3, along with its effect on the important parameter in the design and the overall timing jitter error. In Sec. 4, a prototype circuit is first designed, then compare with leading edge timing discrimination, experiments are performed to verify the effectiveness of the proposed method. Finally, Sec. 5 presents the conclusions.
2. Circuit description of the receiver channel
In a pulsed light ToF measurement system, designs of high dynamic range, wide bandwidth, and low noise receiver channel are beneficial for the system ability. In this design, a simplified block diagram of the receiver channel is shown in Fig. 2, including a photodiode, transimpedance preamplifier, post amplifier and timing discriminator.
The received optical signal is first converted to a pulsed current signal ${i_p}$ by a linear APD (First Sensor, AD500-9). Then, ${i_p}$ is amplified and converted into a voltage signal by the preamplifier, in which the op amp (LTC6268-10) with FET input is selected. Phase compensation is introduced in this stage so that the 45-degree phase margin can be guaranteed and −3 dB bandwidth can be optimized when ${C_F}$ satisfies [17,18]
where ${C_{IN}}$ is the total input capacitance, ${R_F}$ is the transimpedance gain, ${f_c}$ is the unity gain bandwidth frequency of the amplifier. Further, a fully differential op amp (LTC6409) is adopted in the post amplifier circuit to expand the amplification capability and enhance anti-interference ability. In this stage, ${R_{a1}}$ and ${R_{a2}}$ are set slightly different, ${R_p}$ is used to balance the effect of preamplifier output resistance. Finally, the timing comparator (LT1711) with rail-to-rail complementary outputs generates a logic-level timing pulse as a timing stop signal and sends it to time-to-digital converter (TDC) or other time computing units.2.1. Analysis of the unbalanced post amplifier
In this design, we present a differential hysteresis timing discrimination method, which requires the cooperation of unbalanced post amplifier and comparator. Generally, problems will occur if the balanced differential post amplifier is directly connected to the comparator. As illustrated in Fig. 3(a), the balanced op amp converts single-ended signals from preamplifier into differential signals ${v_{op}} = {v_{ocm}} + {v_{od}}/2$ and ${v_{on}} = {v_{ocm}} - {v_{od}}/2$, where ${v_{ocm}}$ and ${v_{od}}$ are the output common-mode (CM) and differential-mode (DM) voltages, respectively. First, when ${v_{od}} = 0$ (i.e. in the stage of no pulsed light received), then ${v_{op}} = {v_{on}} = {v_{ocm}}$. In this case, the comparator is in a critical state and unable to output the correct logic level. Furthermore, the comparator is more susceptible to the noise on the output pair of the post amplifier, and it will usually output the switching oscillations as also shown in Fig. 3(a). This will cause a large false alarm to the time measurement and lead to invalid measurement results.
Fig. 3. (a) Principle of the timing comparator switching oscillations when the balanced fully differential op amp is directly connected to the timing comparator and (b) a conservative solution by adding an extra stage after the fully differential op amp. The input source of A2 can be regarded as a voltage source ${v_{o1}}$ in series with the source resistance ${R_s}$.
A conservative solution as shown in Fig. 3(b) is to convert differential signals into a single-ended signal, then connect it to the comparator, and set the appropriate threshold voltage through an external circuit to ensure the correct comparator output. The logic level output is obtained by the leading-edge timing discrimination method. This is a feasible solution but it consumes extra circuits.
Different from Fig. 3(b), this paper utilizes unbalanced characteristics of the fully differential op amp and introduces extra comparator hysteresis to achieve the stability and timing discrimination. In practice, every fully differential circuit is somewhat imbalanced, due to mismatches introduced by imperfect fabrication [19]. When mismatches are included, the models and analysis of the post amplifier circuit become more complicated because the mismatches introduce interaction between the CM and DM signals. To illustrate the effect of resistor pair mismatch, as shown in Fig. 4(a), assume the op amp is balanced, has infinite input impedance, zero output impedance and ignore the input source resistance (For simplicity, ${R_p}$ and ${R_s}$ are regarded as part of ${R_{a1}}$ and ${R_{a2}}$, respectively). And let the resistor pair of ${R_{a1}}$ and ${R_{a2}}$ in the feedback network be the only mismatch in the circuit.
Fig. 4. (a) Simplified post amplifier inverting gain circuit with resistor pair mismatch and coupled (b1) differential mode and (b2) common mode half-circuits models for the circuit.
In addition, ${v_{s1}}$ and ${v_{s2}}$ are the input signals, where ${v_{sd}} = {v_{s1}} - {v_{s2}}$ and ${v_{sc}} = ({{v_{s1}} + {v_{s2}}} )/2$ represent the DM and CM part of the input source, respectively. Then the circuit can be analyzed by its coupled DM and CM half-circuits models as shown in Figs. 4(b1) and (b2) [19]. In this figure, ${a_{dm}}$ is the open loop DM gain; $a_{cm}^{\prime}$ is the equivalent CM gain including the effect of the common mode feedback (CMFB) loop; ${v_{cmc0}}$ can be seen as constant reference voltage of CMFB, which is related to ${v_{ocm}}$ pin; ${i_{Ra\_d}}$ and ${i_{Ra\_c}}$ are the input DM and CM currents, respectively. Also, define $\Delta {R_a} = {R_{a1}} - {R_{a2}}$, and ${R_a} = ({{R_{a1}} + {R_{a2}}} )/2$. For simplicity, when $\Delta {R_a} = 0$, ${i_{Ra\_c}}$ can be estimated in Fig. 4(b2) as
2.2. Analysis of the differential hysteresis timing discriminator
In addition to utilizing unbalanced characteristics of the differential op amp, extra levels of hysteresis are increased to further guarantee the stability of the timing comparator which is realized by adding feedback to the comparator as demonstrated in Fig. 5.
In this figure, ${R_c}$, ${R_d}$ are external resistors and the timing comparator has rail-to-rail complementary outputs. On the one hand, when ${v_{op}}$ is sufficiently smaller than ${v_{on}}$, then the comparator non-inverting output meets the condition of ${v_{o + }} = {V_{OL}} = 0$, while the inverting output meets ${v_{o - }} = {V_{OH}} = {v_{cc}}$, where ${v_{cc}}$ is the comparator supply voltage, ${V_{OL}}$ and ${V_{OH}}$ are the comparator output low and high, respectively. In this case, ${v_{o + }}$ switches from ${V_{OL}}$ to ${V_{OH}}$ in the condition of ${v_{op}} - {v_{on}} = \alpha {v_{cc}}$, where $\alpha = {R_c}/{R_d}$. On the other hand, ${v_{o + }}$ switches from ${V_{OH}}$ to ${V_{OL}}$ in the condition of ${v_{on}} - {v_{op}} = \alpha {v_{cc}}$. Therefore, the extra hysteresis voltage width ${v_{wd}} = 2\alpha {v_{cc}}$ is provided to enhance the timing comparator stability. For the DM signal ${v_{od}}$, let $|{{v_{odif0}}} |> \alpha {v_{cc}}$, then the equivalent upper threshold voltage of the timing point is ${v_{eq\_th1}} = |{{v_{odif0}}} |+ \alpha {v_{cc}}$. Correspondingly, the equivalent lower threshold voltage is ${v_{eq\_th2}} = |{{v_{odif0}}} |- \alpha {v_{cc}}$. Therefore, the comparator switching threshold voltage can be adjusted indirectly by utilizing the imbalance of the post amplifier and extra hysteresis of the comparator. And the timing point can be generated either from edge of the linear signal pulse or edge of the saturated large signal pulse, which means the linear range of the receiver channel does not limit the dynamic range.
3. Noise analysis
3.1. Overall noise of the receiver channel
In this design, noise performance is very important because it affects the setting of ${v_{odif0}}$ and the output timing jitter. In the receiver channel, there are five primary sources of noise: shot noise, photodiode thermal (Johnson) noise, amplifier current noise, resistance thermal noise, and amplifier voltage noise [13,18,21]. Among them, the first two terms are related to the photodiode and both will be amplified by the signal gain along with the useful signal. In this paper, the noise of the photodiode is not considered because the noise of different photodiodes is slightly different.
Firstly, in the preamplifier, as illustrated in Fig. 6, the spectral density of the noise voltage directly contributed by the feedback resistor ${R_F}$ is ${e_{no1\_{R_F}}} = \sqrt {4kT{R_F}} $, where k is Boltzmann’s constant and T is the absolute temperature in Kevin. ${i_{ni1}}$ and ${e_{ni1}}$ are the input current and voltage noise spectral density of A1, respectively, which both include pink ($1/f$) noise and white noise. The noise current flows directly through the feedback resistor, producing a noise voltage ${e_{n\_{R_F}i1}} = {i_{ni1}}{R_F}$. Like the noise voltage of ${R_F}$ itself, this noise voltage transfers to the output with unity gain and the contributed output spectral density component is ${e_{no1\_i}} = {e_{n\_{R_F}i1}}$ [17]. Generally, the noise voltage result from ${e_{ni1}}$ is the dominant noise of the preamplifier which can be expressed as ${e_{no1\_e}} = {e_{ni1}}/\beta $, where $1/\beta $ is the noise gain [17,18]. Hence, the change trend of preamplifier total output noise spectral density ${e_{no1}} = \sqrt {{e_{no1\_e}}^2 + {e_{no1\_{R_F}}}^2 + {e_{no1\_i}}^2} $ is similar to that of ${e_{no1\_e}}$.
Fig. 6. Noise equivalent model for the preamplifier and SPICE simulated output noise spectral densities at three different ${C_F}$ values.
As shown by the green curve, in the low frequency band, ${e_{no1}}$ shows a downward trend of $1/f$ due to pink noise in ${e_{ni1}}$ and ${i_{ni1}}$. In the middle frequency band up to ${f_{zf}}$, it remains at the noise floor level ${e_{nif}}$, where ${f_{zf}}$ is the dominant zero of the noise gain [18]. In the high frequency band, the curve peak emerges because ${f_{zf}}$ causes ${e_{no1}}$ to rise, and then the bandwidth limitation of A1 causes ${e_{no1}}$ to fall. Moreover, the added phase compensation capacitor will affect the noise gain peak. For comparison, it can also be seen from the figure that a small value of ${C_F}$ (e.g. ${C_F} < {C_{Fi}}$) will increase the peak and lead to a large ${e_{no1}}$, where ${C_{Fi}}$ satisfies Eq. (1). Although a large value of ${C_F}$ (e.g. ${C_F} > {C_{Fi}}$) can reduce the total output noise, excessively large ${C_F}$ will greatly reduce the system bandwidth [17]. In this case, the ‘wasted’ extra bandwidth of the op amp is used by the noise gain and serves to amplify noise. Therefore, choosing ${C_F} = {C_{Fi}}$ can maximize the use of op amp bandwidth and is moderate for noise performance.
Secondly, in the unbalanced post amplifier, the main noise of the post amplifier is input source noise (i.e. preamplifier output noise ${e_{no1}}$) and inherent noise, which includes resistance thermal noise, input current noise ${i_{ni2}}$ and differential input voltage noise ${e_{ni2}}$ of fully differential op amp. The noise equivalent model of post amplifier with all noise sources is shown in Fig. 7, where preamplifier output noise ${e_{no1}}$ and ${e_{no1\_{R_s}}} = \sqrt {4kT{R_s}} $ represent input source noise. And the output noise spectral density generated by the input source can be written as
Fig. 7. Noise equivalent model for post-amplifier with all noise sources and SPICE simulated total output noise spectral density (excluding ${e_{no2\_cm}}$).
The resistance thermal noise of ${e_{ni2\_{R_{a1}}}}$, ${e_{ni2\_{R_{a2}}}}$, ${e_{ni2\_{R_b}}}$ and ${e_{ni2\_{R_p}}}$ all obey the form of $\sqrt {4kTR} $, where R is the corresponding resistance. By multiplying the respective noise gain of the noise source, the output noise density contributed by circuit inherent noise satisfies the expression of
As also shown in Fig. 7, the input source noise ${e_{no2\_s}}$ contributes the most to the total output noise. In order to reduce this noise, it can also be achieved by reducing its gain ${R_b}/({R_s} + {R_{a2}})$ appropriately.
Thirdly, in the timing discriminator, the total input noise of the comparator is expressed as
where ${e_{ni3\_{R_c}}}$ is the thermal noise of ${R_c}$, ${e_{ni3\_e}}$ is the input voltage noise of comparator. And, ${e_{no2}}$ is the dominant noise in ${e_{ni3}}$. Due to the introduction of the hysteresis loop, the thermal noise of ${R_d}$ and the contribution of comparator input current noise $2{i_{ni3}}{R_d}$ will be directly transferred to its output, but usually this effect is much smaller than that of ${e_{ni3}}$.3.2. Effect of noise on ${v_{odif0}}$
As can be seen from Eqs. (6) and (7), a larger $|{{v_{odif0}}} |$ means less risk of oscillation. Properly increasing ${v_{ocm}}$ by output pin can help increase $|{{v_{odif0}}} |$ without affecting ${K_{CMCR}}$, but ${v_{ocm}}$ is usually limited to the maximum output swing. Moreover, increasing $|{{v_{odif0}}} |$ by introducing a larger $\Delta {R_a}$ and smaller ${R_a}$ or ${R_b}$ is beneficial to achieve a smaller oscillation probability and better stability, assuming the gain of the post amplifier (i.e. ${R_b}/{R_a}$) is fixed. Nevertheless, this will also cause more loss of ${K_{CMCR}}$. To make a trade-off between the two aspects, the circuit should be carefully designed when utilizing the mismatch feature. In the case of no switching oscillations, the degree of mismatch should be set as small as possible to ensure the largest CM conversion rejection capability. The absolute value of the minimum mismatch voltage ${|{{v_{odif0}}} |_{min}}$ is determined by the total noise on the differential output pair.
Broadly speaking, the distribution of ${e_{no2}}$ in the time domain is approximately Gaussian. Thereby, according to the Gaussian distribution characteristics, the peak to peak noise on differential output pair ${v_{no2\_pp}} = 6.6{v_{no2\_RMS}}$ covers a 99.9% ${v_{no2}}$ occurrence probability, where ${v_{no2}}$ is the instantaneous value of noise, ${v_{no2\_RMS}}$ is the RMS noise. Therefore, as illustrated in Fig. 5, according to the principle of noise superposition, the minimum mismatch voltage can be expressed as
This means when the above formula is satisfied, the timing comparator will have a 99.9% probability that it will not oscillate or generate false alarm.3.3. Effect of noise on the overall timing jitter
In the receiver channel, the timing jitter error caused by noise will affect the time measurement accuracy. As demonstrated in Fig. 8, the jitter of the timing point affected by noise can be estimated as [2,22]
where ${\sigma _n}(t )$ is noise power at the timing point, $v(t )$ is the input signal at the input of the timing comparator. Single shot precision which is an important indicator in time measurement will be reduced by the jitter error. It can be seen from Eq. (14) that the larger the noise is, the more severe the jitter is and the lower single shot precision the measurement reaches.In the timing receiver channel, the input noise of the comparator ${e_{ni3}}$ is the main source of the entire timing jitter. Compared with the circuit solution in Fig. 3(b), the receiver channel with the proposed discrimination method generally has lower comparator input noise and thus higher single shot accuracy. The reasons are given as follows. First, in Fig. 3(b), in addition to the output noise of the balanced differential op amp ${e_{no2}}$ being directly transferred to the input node of the comparator A5 through the additional stage, the input current and voltage noise of A4 as well as resistance thermal noise will also be transferred by multiplying their respective noise gains. Second, the threshold voltage is set by the resistor divider. This structure causes the noise of the supplied voltage source to be directly passed to the negative input node of A5, which increases the input total noise of A5. Third, due to the limited power supply rejection ratio of the op amp, adding an additional stage will always increase the risk of power supply noise coupling into the signal path.
In addition, through proper design of the proposed circuit, not only the good differential characteristics of the post amplifier can still be maintained, but also the differential comparison of the timing discriminator can be achieved, which may also reduce the timing jitter error.
4. Experiments
The experiments were carried out to evaluate the performance of pulsed light time-of-flight measurement based on the proposed differential hysteresis timing discrimination. The prototype circuit in Fig. 2 was designed and tested. In the receiver channel, the linear APD was biased at −150$V$. Hence, it has a lower parasitic capacitance ${C_D} \approx 1.2pF$, and a 905 nm bandpass filter is also integrated in it to reduce the influence of ambient light. The FET input op amp LTC6268-10 was chosen in the preamplifier with extremely low input bias current and low input capacitance (∼0.45 $pF$). The transimpedance gain of preamplifier was ${R_F} = 25k\Omega $. It is noted that no additional ${C_F}$ was set because the stray or parasitic capacitance of the gain resistor (∼0.1 $pF$) on the actual circuit board is sufficient for ${C_F}$ according to Eq. (1). Second-order RC low-pass filter was also employed to reduce the noise effect of bias voltage source. In the post amplifier, fully differential op amp LTC6409 was chosen and powered by a single 5 $V$ power supply, where ${R_{a1}} = 26.4\Omega $, ${R_{a2}} = 23.6\Omega $ (i.e.$\Delta {R_a}$=2.8 $\Omega $, ${R_a} = 25\Omega $) and the post amplification was set to ${R_b}/{R_a}$=32. Therefore, the CM to DM conversion rejection ratio ${K_{CMCR}}$ reaches about 50$dB$. In addition, the output CM voltage ${v_{ocm}}$ was set to 2$V$ through an external voltage source. The comparator LT1711 was chosen and the extra hysteresis voltage $\alpha {v_{cc}}$ was set to 20$mV$ by adjusting ${R_d}/{R_c}$.
Figure 9 shows the ${v_{op}} - {v_{on}}$ waveform of differential output pair acquired by the differential probe (TDP1500) on the oscilloscope (Tektronix, MSO54). By detecting the rise time of the linear signal, the total bandwidth of the receiver channel was estimated to be 70$MHz$, with total transimpedance gain about 800 $k\Omega $, as shown in Fig. 9(a). In Fig. 9(b), it could be seen that $\sqrt 2 {v_{no\_pp}}$ was 221.93$mV$ and ${v_{odif0}}$ was ∼230$mV$. And the maximum signal-to-noise ratio (SNR) was 90. The proposed timing discrimination method can process linear signals and saturated large signals without being affected by the linear range of the receiving channel. Therefore, the designed prototype circuit is reasonable and stable to perform time interval measurement.
Fig. 9. Linear (a) and saturated large signal (b) of ${v_{op}} - {v_{on}}$ waveform captured by the differential probe.
To verify the time measurement performance, an experimental platform like ranging system was set up as shown in Fig. 10. In the experiment, the laser pulse was generated by a 905 nm near-infrared laser emitting module (LASER COMPONENTS, L-CUBE-9-40/200-30/100), and the pulse trigger signal was generated by FPGA. In order to simulate the effect of different light intensities on the time measurement, a polarizer (Thorlabs, LPNIRE200-B) was placed in front of the light source to attenuate its intensity, as the pulsed laser can be considered as linearly polarized. And the intensity of the modulated laser follows Malus’ Law
where ${I_0}$ is the original emitted light intensity, $\theta $ is the polarization angle between laser and polarizer. Two objects with different reflectivity (white paper and green cloth) were used to reflect the pulsed light to further expand the range of light intensity variation. Then, the receiver channel converted the optical signal into an electrical signal and ultimately, the timing discrimination logic signal was generated. In this paper, a time measurement event is regarded as the delay between the trigger signal of the laser pulse and the timing discrimination signal. The events were detected and recorded by the oscilloscope with a sampling rate of 6.25GS/s.First, the timing jitter error was measured. Figure 11(a) shows the time interval measurements and single shot distributions acquired by the oscilloscope. In the figure, the blue curve was the trigger signal and the red curve was the timing discrimination signal. The oscilloscope recorded a total distribution of 8036 points, and the measured timing jitter was about 291.382ps. For comparison, we also designed the receiver channel with circuit structure in Fig. 3(b). Under the condition that other parameters were the same, its timing point was generated by the leading-edge timing discriminator. Under the same experimental environment, the oscilloscope also recorded 8025 points, and the single point distribution was shown in Fig. 11(b). And the timing jitter was about 411.837ps. By comparison, the timing jitter in Fig. 11(a) was smaller, indicating that receiver channel with the proposed discrimination method had higher single shot precision.
Fig. 11. Measured time interval and single shot distributions of receiver channel with (a) differential hysteresis timing discrimination and (b) leading-edge timing discrimination.
Moreover, walk error will also affect the accuracy of time measurement which consists of two parts. The first part is called geometrical error which is caused by the finite rise time of the pulse. The second part results from the electronic delay in the receiver channel [2,23]. Like leading-edge timing discrimination, although large dynamic range can be realized by the proposed discrimination, the timing point will also change and the relatively large walk error emerges with the amplitude of the pulse changes. To reduce its influence, it has been reported that walk error can be compensated in the time domain, if its relation to the pulse width is known [10]. This compensation method by measuring the pulse length is also suitable for the receiver channel in this paper and is therefore adopted. Because the pulse width of the timing discrimination logic level was also obtained, while measuring the time interval.
Figure 12 demonstrated the measured compensation relation between pulse width and walk error. The dynamic range of the simulated light intensity was about 1:2000. It showed that the wider the pulse length was, the smaller walk error was. By utilizing compensation curve, the time measurement accuracy is improved, and the time accuracy after pulse width correction can reach ∼350ps.
5. Summary
In the pulsed light ToF measurement system, we proposed a differential hysteresis timing discrimination method which was used to generate a timing point in the receiver channel. This method was achieved by utilizing the unbalanced characteristics of the circuit as well as adding extra hysteresis levels, which required the cooperation of a fully differential op amp and a complementary outputs comparator. In addition, this method needs less circuitry components and dose not limit dynamic range of the channel. This paper first presented circuit description of the entire receiver channel. The principle of the proposed method and how the circuit generated the stable timing point were analyzed in detail. Second, noise performance of the receiver channel was analyzed and simulated. In the design, the setting of ${v_{odif0}}$ and the output timing jitter will be affected by noise. Under the premise of ensuring the stability of the system, ${v_{odif0}}$ which was limited by the output RMS noise of the post amplifier should be kept as small as possible to obtain a large CM to DM conversion rejection ratio and ${|{{v_{odif0}}} |_{min}}$ was set to about $9.3{v_{no2\_RMS}}$. The overall timing jitter error that affects the single shot accuracy in time measurement is mainly caused by the total input noise of the comparator. The receiver channel with the proposed discrimination method can avoid excess noise sources compared to the receiver channel in Fig. 3(b). In the experimental test, we designed the prototype circuit of receiver channel with 70$MHz$ total bandwidth and 800 $k\Omega $ transimpedance gain. Compare with leading-edge timing discrimination in Fig. 3(b), the proposed method has been verified by the ToF measurement results, indicating that it has better single shot accuracy. Walk error could also be compensated by using pulse width over a dynamic range of 1:2000 when applying this method. Finally, results confirm the feasibility and effectiveness of the method in pulsed light ToF measurement.
Funding
Fundamental Research Funds for the Central Universities (30917011321); National Natural Science Foundation of China (61675099, 61701233).
Disclosures
The authors declare no conflicts of interest.
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