1. Introduction

Lidar has advantages in comparison to radar due in part to the diffraction characteristics of light. For instance, lidar has a greater ability to obtain fine spatial and range resolution at long stand-off distances. It is desirable for a lidar system to operate in the 1550 nm band typically employed for telecommunication, since this band has compatibility with a vast optical infrastructure, enhanced eye safety, and reduced solar background noise. Coherent detection has previously been used to enable sensitive range measurements at 1550 nm [1–3]. However the complexity of coherent systems is a deterrent to their use.

An alternative to complex coherent detection is the use of single photon detectors (SPDs) to realize sensitive time-of-flight (TOF) lidar. The most practical 1550 nm sensitive SPD is the single photon avalanche diode (SPAD) [4]. Due to their relatively poor noise and after-pulsing characteristics in comparison to their cousin the Silicon SPAD, 1550 nm sensitive SPADs have traditionally been gated such that they are sensitive to single photons only during a short (typically ns-scale) electrical gate. With proper precautions, gated SPADs can be used for long range (km scale) lidar [5].

Recent advances have led to free-running SPADs that could in principle replace their gated counterparts, but the free-running devices tend to require a long (μs) recovery time after a detection [6,7] thus slowing down measurement times. Another option is the use of high speed (GHz) detector gating, which acts to reduce the break-down current through the SPAD and has been shown to improve the APD recovery times [8]. Recently a GHz gated APD was used in a lidar system to emulate an un-gated detector by using an optical pulse repetition rate that is unsynchronized with respect to the gate rate [9]. A histogram of the time delay between the transmitted laser pulse and received photon detection event can be recorded using a time-to-digital converter, where the temporal peak of the histogram reveals the object distance.

A range measurement (r_measured) from a TOF lidar system is ambiguous to some integer number of unambiguous ranges (R_unambiguous), where r_measured = r_actual (mod R_unambiguous). If R_unambiguous is longer than the furthest object to be measured, or for imaging applications longer than the extent of an object to be imaged, then the ambiguity is resolved. Various techniques have been developed to enable long unambiguous ranges. The most obvious method is to use a low optical pulse repetition rate such that only one pulse is in flight at a time, but this technique slows down the measurement rate and can have other undesirable effects especially when using optical amplifiers. High measurement-speed compatible techniques have been developed including correlating a high rate transmit and receive pulse sequence [10] or the use of multiple optical pulse frequencies [11].

We describe here a lidar system with a synchronized but unequal gate and pulse repetition rate. The rates are chosen so that after processing the detection events a stationary object produces a histogram where the location of the histogram peak reveals the distance to the object. The range to the object is determined from the temporal shift of the histogram peak using the equation δτ = 2·δd/c, where c is the speed of light, δd is the object displacement, and δt is the temporal shift. The histogram is generated by choosing the optical pulse frequency f_light and detector gate frequency f_gate to satisfy f_light = f_gate·N/D, where N and D are relatively prime numbers (integers with no common factor other than 1) and D is the number of bins in the histogram. The time-gated detection efficiency essentially under-samples the return optical pulse generating a measurement of the overall system detection temporal response function. The histogram bins can then be viewed as equivalent time (similar to a sampling oscilloscope), with the histogram bins separated by a temporal resolution of 1/(D·f_light) and achieving R_unambiguous = 0.5·c/f_light. We thus refer to the method as gated equivalent time (GET) lidar. The method localizes the temporal position of a detection event to roughly the half-width of the gated detection efficiency (~140 ps in our case). This detection efficiency half-width is typically smaller than the natural detector jitter, where jitter is what limits a more traditional photon counting measurement that use time-to-digital converters [9,10]. The histogram is generated using only the binary output of the detector at the gate rate. The measurement method removes some typical electronic rate bottlenecks and may help to improve measurement rates of high resolution lidar. We have previously demonstrated a similar lidar system for measuring velocity [12].

The unambiguous measurement range can be extended by using multiple optical pulse rates simultaneously by judiciously choosing the N and D values of each rate. By evaluating the same detected data using multiple histograms having a different number of bins (different D values), the unambiguous range can be extended considerably. The optical pulse rates are strategically chosen so that a histogram of a particular D value generates a single histogram peak from one of the optical pulse frequencies, while the counts from the other optical pulse frequencies are roughly equally distributed over the remaining histogram bins. In this way a single detector can simultaneously isolate any of the optical pulse frequencies for evaluation simply by post-processing the data using the desired number of histogram bins. We demonstrate this range extension method using a single laser and detector by appropriately modulating the laser output.

Using purely repetitive pulse frequencies as demonstrated here may allow for simpler equipment to be employed, such as gain-switched DFB lasers driven by sinusoidal waveforms. Additionally, the total number of detector counts required for resolving the range ambiguity can be kept to small levels thus speeding up measurement times. We note that very recently another group has demonstrated the use of multiple optical pulse frequencies for extending the unambiguous measurement range [11]. The prior work used a gate frequency unlocked to the optical pulse rates, thus requiring time-tagging electronics and producing jitter-limited performance.

2. Operating principle

The optical pulse and detector gate frequencies for the GET lidar system are chosen to satisfy f_light/f_gate = N/D where N and D are relatively prime numbers. D corresponds to the number of bins in the histogram formed by collecting the aggregate photon counts of every D^th gate over some histogram measurement interval t_hist. The raw histogram is re-ordered such that the re-ordered histogram is related to an equivalent time representation. The bin reordering uses the mapping bin_i = mod(b·N,D) where b is the original bin number (b is in the set {0,(D-1)}) and i is the re-ordered bin number in the set {0,(D-1)}. The histogram bins can then be viewed as equivalent time, with the histogram bins separated by a temporal resolution of 1/(D·f_light). The number of counts in each bin is related to the light intensity detected at that equivalent time. The location of the peak corresponds to the distance of the object within some unknown number of unambiguous ranges. The convolution of the gate width and the optical pulse width is chosen so that at least 3 bins have elevated counts which allows the location of the peak of the histogram to be determined to a much higher resolution than the bin spacing by using curve fitting or correlation techniques. The achievable resolution is typically limited by the number of counts in the count-elevated bins due to Poisson-like noise statistics.

When using a single optical pulse rate the unambiguous range is R_unambiguous = 0.5·c/f_light. Of course this range can be extended by reducing the optical pulse rate, but higher pulse rates are desirable for fast measurement times and for other practical reasons such as the gain dynamics in Erbium-doped optical amplifiers. Two or more optical pulse frequencies can be used to extend R_unambiguous. For instance, we can use a first optical pulse frequency f_pulse,1 = f_gate·N₁/D₁ from which we determine the object range r to r_1$\approx$mod(r, R₁), where R₁ is the unambiguous range associated with f_pulse,1 and the approximately equal sign accounts for measurement noise. A second pulse frequency of f_pulse,2 = f_gate·N₂/D₂ can also be used which determines the object distance to r_2$\approx$mod(r, R₂). The actual range to the object should be consistent with both pulse frequencies simultaneously so that M₁·R₁ + r₁–e₁ = M₂·R₂ + r₂–e₂ where M_1,2 are integers to be solved for, and e_1,2 represent measurement errors. There are multiple solutions to this equation, and they occur periodically. For example, when r₁ = r₂ = e₁ = e₂ = 0, the solutions are M₁ = N₁·D₂·K/G and M₂ = N₂·D₁·K/G, where G = gcd(N₁·D₂, N₂·D₁) and K is any integer. So given r₁ and r₂, we restrict 0≤ M₁< N₁·D₂/G and 0≤ M₂< N₂·D₁/G so there is only one solution for the most likely M₁ and M₂ which can be found using any of various well-known methods such as the backwards Euclidean algorithm. This extends the measured unambiguous range (R_1,2) to

3. Experiment

A basic test to determine ranging resolution as a function of received power is depicted in Fig. 1 (Top). The range resolution is defined by measuring the standard deviation of the difference between the set and measured range values over a large number of set-range values. The set-range values are deliberately chosen so that the peak of the optical pulse may fall within a large number (>20) of places within the histogram bins so as to fairly emulate measurements of an unknown distance. Instead of changing the range directly, we control the time delay between the optical pulse and the gate by changing the phase of a clock generator (CG: SRS CG-636) that controls the timing of the optical pulses. This scheme is easily automated which allowed the large number of measurements required to be conveniently acquired.

 

Fig. 1 (a) Block diagram of GET lidar system configured for measuring ranging resolution vs. optical power. (b) Re-ordered histograms of 80 bins (black open squares) and 85 bins (blue filled diamonds). Dotted lines connect the points to guide the eye.

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The CG is set to 500 MHz. A 1.25 GHz f_gate is produced using a frequency generator (FG₃: Gigatronics 1026) that is locked to the CG via the CG’s 10 MHz reference (REF) output. The CG output is down-counted in a divide-by-16 circuit which feeds two additional frequency generators (FG_1,2: Analog Devices ADF4350) that are configured to generate f₁ = f_gate·6/85 and f₂ = f_gate·7/80, or about 88.2 and 109.4 MHz respectively. These frequencies feed pulse generator (PG) electronics which generate ~150 ps pulses at the respective input frequency. The two pulses are summed in a combiner, filtered in a low pass filter (1.9 GHz LPF), and amplified in a driver amplifier to create the RF modulation signal into a Mach-Zehnder Interferometer (MZI) optical modulator. The MZI carves optical pulses of ~200 ps width from a CW laser. The optical signal is amplified in an Erbium doped fiber amplifier (EDFA), filtered by an optical band pass filter (O-BPF), attenuated by a computer-controlled variable attenuator, monitored with an in-line power monitor (P_mon), and further attenuated by a fixed optical attenuator before being sent to the SPD (NuCrypt CPDS-2000). The CG has a phase resolution of 1° and a phase range of ± 700°, which translates to a time shift resolution of 5.56 ps and time range of 7.78 ns. We analyzed the temporal control this system gave us by observing a generated pulse on an Agilent 86100a DCA triggered using the 1.25 GHz clock and found a systematic equivalent range error of ~5 mm peak-to-peak that is periodic every 360° of applied phase shift. This systematic error was subtracted out so that the measurements have <1 mm of remaining systematic error which was adequate for our purposes.

The raw detector count events are recorded in memory and post-processed into histograms. In order to observe the return pulse at the 109.4 MHz or 88.2 MHz pulse frequency the data is parsed into histograms of 80 or 85 bins, respectively. Figure 1 (Bottom) shows the re-ordered histograms for a given measurement after parsing it into 80 or 85 bins. It is clear that for either histogram length one of the pulses is isolated and the other is roughly evenly distributed throughout the histogram bins, thus allowing the desired pulse to be observed. R_unambiguous is 1.7 m and 1.37 m for the two pulse frequencies independently, but extends to 163.2 m when the conditions of Section 2 for extending R_unambiguous are obeyed. These conditions require that the sum of the errors of the two range measurements are under about 7 mm, otherwise there will be a failure in the calculation leading to large errors.

The bias and threshold values for the SPD are kept constant for each measurement set and lead to an unsaturated CW detection efficiency of ~3% and dark count rate of ~10⁻⁴. The corresponding RMS range error for a 1 ms measurement time is plotted for both frequencies when analyzed independently in Fig. 2 (Left). In this data set, each point represents the standard deviation of 21 measurements with a 0.70486 mm intended set-range step size. We employ an after-pulse masking feature in the SPD that ignores 47 gates after a detection event to help control after-pulsing. In order to account for the after-pulse masking feature the histograms were scaled from raw counts to probabilities by dividing the number of counts by the number of valid gates during a measurement interval. This step allowed for improved performance at higher received powers.

 

Fig. 2 (a) Resolution as a function of received power for 109 MHz (open squares) and 88 MHz (filled diamonds) pulses. The dotted line shows the expected trend for count-statistics limited performance (see text). (b) Corresponding failure probability for the extended range calculation.

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The peaks of the histograms are determined via a Gaussian curve fitting, although essentially the same results can be obtained with a (computationally faster) correlation based technique. Also shown in the figure is a plot of the expected range resolution as a function of power if the detector jitter t_jitter is assumed to be 130 ps and the timing resolution scales as t_jitter/counts, where counts are defined as the number of detection events expected in the three largest bins of the 109 MHz histogram. There is about a 20 dB power range over which the measured resolution follows the expected range resolution due to counting statistics. At very low powers (corresponding to <10⁻² photons/pulse and <20 counts) the resolution degrades quickly due to insufficient count statistics while at very high powers the resolution degrades due to saturation effects in the SPD. It is likely the saturation effects in the SPD could be mitigated via appropriate post-processing. Nevertheless, we note that <3 mm of resolution is possible over a >40 dB instantaneous dynamic range. Figure 2 (Right) shows the failure rate for the unambiguous range extension procedure, which operates reliably over a ~40 dB range. We note we also analyzed the data over a 100 μs measurement interval and as expect obtained similar curves with ~10 dB higher power required for a given range resolution.

We then performed an actual ranging/imaging experiment to corroborate the emulated results. The distance to a moving curved plastic fan blade located 3 meters away was measured using a 6 (18) mm diameter transmit (receive) lens coupled to single mode fiber. Figure 3 (Left) shows the results with a 500 μs measurement time/point at ~-75 dBm of received power. An image of the passing blade is clearly observed. We determine a “reference” shape for the blade by fitting the points to a 2nd order polynomial. The measurement time was chosen as a balance between the higher range precision of longer measurement times and the desire for many independent points to accurately measure the blade shape. The reference shape has a ~0.6 mm standard deviation with respect to the 500 μs measurement time/point data. This reference shape is used as the assumed actual fan profile for a series of measurements made using a reduced 100 μs measurement time with an additional 0 dB, 5 dB, or 10 dB of optical attenuation. The measured standard deviations with respect to the reference shape are 1.1, 1.7, and 3.3 mm, respectively. An example data set shown in Fig. 3 (Right) corresponds to 5 dB additional attenuation. Although the data is more noisy due to fewer counts, the same underlying curve is obtained. The data corroborates the ability to perform sub-mm ranging on sub-ms time-scales.

 

Fig. 3 Range measurements to a moving curved fan blade as a function of time. (a) 500 μs per point, about −75 dBm power. The curve is a best 2nd order polynomial line. (b) 100 μs per point, −80 dBm power with the same fitting curve.

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4. Conclusion

We demonstrate a novel lidar system that exploits the high temporal resolution and fast measurement times afforded by GHz rate gating of a single photon detector in order to obtain high resolution ranging measurements at high speeds. The scheme uses optical pulse rates that are locked but unequal to the detector gate rate. We characterize the performance of the system as a function of power, including the use of multiple pulse rates to extend the unambiguous measurement range. We further demonstrate imaging of a moving fan blade and obtain results consistent with sub-mm resolution on a sub-ms time scale. The technique is expected to be valuable for high speed ranging at long distances.