4.1.

Sensitivity

The laser-beam shape, the transmit-pulse energy, and the propagation path of the light factor into what is received; atmospheric absorption and scattering attenuate the laser beam as it propagates, and turbulence can cause broadening, defocusing, and deflection. The target orientation, surface texture, and reflectivity properties also affect performance; for example, the geometric complexity of the surface and the Lambertian and specular components of the target's reflectivity determine how much energy is reflected back to the receiver's aperture, and the orientation of the target relative to the angle of incidence can lengthen the pulse and modulate its shape. Finally, the optical efficiency, the detector optical-to-electrical conversion efficiency, and the photoreceiver gain-bandwidth and sensitivity properties significantly influence system performance.

The amount of laser energy returned from multifaceted targets can be estimated as¹³

Equation (1) is useful for establishing a photon budget for use in performing system-design trade studies; the received signal power can easily be converted to photons for a given laser pulse duration, knowing the energy per photon. Figure 2 shows the photons expected from 30% reflective targets at various ranges, calculated for several laser pulse energies. Here, a 0.5-mrad laser divergence and a 30-mm diameter receiver with 70% optical efficiency are assumed.

Fig. 2

Modeled photon returns for the lidar receiver for 1, 10, and 100 nJ, and $\text{1-}\mu \mathrm{J}$ pulse energies, assuming a 30-mm aperture, a 30% reflective target, and a 0.5-mrad divergent laser.

One of the first parameters to choose when designing a lidar sensor is its threshold value (for instance, in voltage: $V_{\mathrm{th}}$) given the noise level of the photoreceiver (${\sigma }_{v,n}$), which must be computed from the specification on the probability of false alarm (PFA), i.e., the probability that a signal will be larger than the threshold in the absence of the target. The PFA and the FAR are related to each other by the fact that the number of false alarms over some time duration is the product of the false alarm rate per individual sample (PFA) by the number of samples being made during that time, as follows:

As shown in Table 1, a $1.5\text{-}\mu \mathrm{s}$ time-of-flight is required for 220-m range. For this scenario, a 60-Hz FAR implies that one in every 11,363 range samples will be corrupted by a false positive. For the lidar sensor specified in Table 1, this is roughly once per frame. Similarly, for a flash lidar configuration, if there are total pixels of $N_{\text{pixels}}$ in an array, each characterized by the same FAR (in Hz), then Poisson statistics can be applied to find

Rice^14,15 relates the single-pixel FAR to the bandwidth (BW, in Hz) of the analog signal into the comparator, the detection threshold ($n_{\mathrm{th}}$, in electrons), and the magnitude of the noise on the signal into the comparator ($n_{\text{noise}}$, in electrons), as follows:

Note that, physically speaking, both the detection threshold and the noisy signal into the pixel comparator are voltage quantities; for convenience of comparing signal levels, both quantities have been referred to the input node of the amplifier chain and expressed in units of electrons.

To find the condition restricting $n_{\mathrm{th}}$, Eqs. (3) and (4) can be combined as follows:

The approximations generally hold true for photodiodes and large photon numbers, in which both the detector and amplification noise processed can be approximated as normal distributions. In these cases, the PFA is a rapidly decreasing function of the ratio, $v_{\mathrm{th}}/{\sigma }_{v,n}$, between the threshold value and the standard deviation of the photoreceiver’s dark noise.

However, the treatment of Eq. (5) is not adequate for avalanche photodiodes (APDs). All APDs generate excess noise due to the statistical nature of the avalanche process. The excess-noise factor ($F$) is the ratio of the mean square gain to the square of the mean gain; it is also the ratio by which the spectral intensity of shot noise on an APD's current exceeds that would be expected from a noiseless multiplier on the basis of Poisson statistics alone.

The excess-noise factor is a function of both the gain ($M$) and the APD's effective ionization coefficient ratio ($k$). The first-order statistics of the excess-noise factor are normally calculated using a formula derived by Mclntyre¹⁶ which is based on the assumption of an avalanche medium with uniform characteristics and an impact-ionization process that is independent of carrier history, expressed as

The excess shot noise of an APD at a given gain depends on its effective ionization coefficient ratio, according to Eq. (6). The values of the effective ionization coefficient ratio are significant because they correspond to different APD device technologies that are compatible with near-infrared-sensitive InGaAs absorbers. The most common InGaAs APDs have bulk InP multipliers characterized by $k=0.4$. InGaAs APDs with thin InAlAs multipliers are characterized by $k\text{\hspace{0.17em}<\hspace{0.17em}}0.2$, and Voxtel, Inc., has developed InGaAs APDs with multiple gain stages that can operate with $k~0.02$¹⁷

Most InGaAs APDs generate the majority of their primary dark current in their absorber, alongside the primary photocurrent generated by the optical signal and the background signals. In that case, dark carriers from primary dark current can be grouped with the background, as follows:

It is often overlooked that, for APD photoreceivers, normal statistical methods cannot be used to calculate PFA. The dark current signals from an APD photoreceiver resemble the pulse-height distribution of the multiplication process to the carriers; after avalanche multiplication, each primary carrier injected into an APD’s multiplier may yield a different number of secondary carriers. For most linear-mode APDs, the statistical distribution of $n$ output carriers resulting from an input of $a$ primary carriers is that derived by McIntyre¹⁸

The McIntyre distribution has a pronounced positive skew. The importance of the value of $k$ on the shape of the distribution and the resulting lidar receiver sensitivity is shown in Fig. 3. Figure 3 shows the dark count rates measured on an APD photoreceiver for the cases of APDs with $k=0.2$ and $k=0.02$, as a function of the threshold level. As shown in Fig. 3, top, at a gain of about 6, the high-gain events from the distribution of the $k=0.2$ APD will start to dominate the FAR, limiting the threshold values for this particular receiver to greater than 0.53V for operation at 30-Hz FAR. However, in the case of the $k=0.02$ APD (Fig. 3, bottom), even at gains of $M=11$, the APD photoreceiver distribution is closer to Gaussian, and—for this particular receiver—the 30-Hz FAR can be achieved closer to 0.49 V.

Fig. 3

Dark-output distribution of photoreceivers for the cases of (a) a $k=0.2\mathrm{APD}$ and (b) a $k=0.02\mathrm{APD}$, showing the tails of the distribution due to the McIntyre-distribution function cause a significant increase in false counts, even at modest gain—much more than the Gaussian assumption.

At this voltage threshold level, the photon equivalent threshold level ($n_{\mathrm{t}\mathrm{h}}$) can be calculated using the measured conversion gain of the receiver. The curves of Fig. 3 can be modeled for each APD bias by convolving the gain distribution with the amplifier noise to find the value of $n_{\mathrm{t}\mathrm{h}}$ for the target FAR.

Using a pulse time ($\tau$), the product of noise current and integration time, scaled by the elementary charge, can be recognized as the total charge noise ($n_{Q,\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{k}}$). These operations can be applied to find the FAR, as follows:

To find the probability of laser-pulse detection, $P_{\mathrm{DE}}$, the detection threshold to achieve a given FAR can be combined with the average signal strength, based on the complementary cumulative distribution function of the convolution of the signal and noise distributions, as

4.2.

Time Resolution

To capture the TOF, the detector elements must include circuitry to timestamps of the laser-pulse echoes. Achieving 5-cm range resolution requires timestamps with $\sim 333\text{-}\mathrm{ps}$ resolution. Timestamps can be generated using either: a time-to-analog converter, which records the timestamp by sampling a time-variable voltage ramp; or a time-to-digital converter, which—upon the return of the pulse—latches the digital value of a counter, often with a vernier scale, developed from gate-delay elements, used for the least significant bits. Jitter, walk, and drift are the three major factors limiting time resolution.

In the absence of noise and amplitude variations, the leading-edge discriminator would mark the arrival time of each analog pulse with precision and consistency. However, practical systems include a non-negligible level of electronic noise, and this noise causes an uncertainty—or “jitter”—when the analog pulse crosses the discriminator threshold. If ${\sigma }_n$ is the voltage amplitude of the noise superimposed on the analog pulse, and $dV/dt$ is the slope of the signal when its leading edge crosses the discriminator threshold, the contribution of the noise to the timing jitter is

As shown in Fig. 4, from Eq. (11), the relationship is immediately apparent between the signal amplitude, detector gain, and amplifier transimpedance gain on the timing accuracy. If the noise cannot be reduced, the minimum timing jitter is obtained by setting the discriminator threshold for the point of maximum slope on the analog pulse. Thus, preserving the fastest possible rise time from the signal source is a clear benefit.

Fig. 4

Illustration of the time walk effect, including a time-over-threshold discriminator signal and a jitter effect.

“Time walk” is the systematic dependence of the timing on the amplitude of the input pulse. As shown in Fig. 4, with a leading-edge timing discriminator, smaller pulses produce an output from the discriminator later than larger pulses, leading to variable timing in response to the variations in the input pulse amplitudes. Obviously, when a wide range of pulse amplitudes must be processed, time walk can seriously degrade the time resolution. To ensure precise timing, time walk must be minimized or eliminated. The recommended techniques to minimize time walk include amplitude-compensated measurements implemented using pulse amplitude or time-over-threshold compensation, or by implementing a constant-fraction-discrimination circuit.

5.1.

Infrared Transmitter

The available SWIR transmitter sources include edge-emitting pulsed semiconductor laser diodes, erbium-doped fiber lasers, and erbium-doped glass diode-pumped solid-state (DPSS) lasers, with the latter two choices best suited for long-range lidar. Fiber lasers allow the combination of short pulse durations with repetition rates up to $\sim 1\text{million shots}/\mathrm{s}$, at a practical upper pulse energy of $\sim 1\mu \mathrm{J}$, whereas erbium-doped glass lasers can be configured for higher peak power, albeit generally with low repetition frequencies.

Figure 5 shows a prototype of a new compact, low-cost 1535-nm DPSS laser from Voxtel. We custom-developed this cost-effective $20\text{-}\mu \mathrm{J}$ pulse energy, 400-kHz pulse-rate laser for autonomous navigation lidar. This allows for an array to be stepped or scanned across the FOR. For example, when the $20\text{-}\mu \mathrm{J}$ pulses are matched to 200 detector elements, roughly 100 nJ per pulse, such that 220-m range can be achieved (see Fig. 2), $\sim 80\text{million}$ angle-angle-range vectors per second can be obtained—$\sim 1/9$ which is required to meet the full FOR specified in Table 1.

Fig. 5

Picture of Voxtel’s miniature 1535-nm DPSS laser, which has a beam quality of $M^2<1.1*\mathrm{DL}$ (diffraction limit) and operates at $20\mu \mathrm{J}$ at up to 400-kHz repetition rates.

5.2.

Lidar Photoreceivers

As the photoreceiver sets the system sensitivity, its performance can obviously have dramatic effects on the required average laser power. Lidar photoreceivers typically comprise a photodetector, transimpedance amplifier (TIA), and pulse-detection circuit. At the 905-nm wavelength, the two primary solid-state photodetector options are silicon PIN photodiodes and silicon avalanche detectors. While, when compared to silicon, both InGaAs and germanium (Ge) detectors offer the potential for improved temporal response to 905-nm optical radiation, both detector types are more commonly operated at wavelengths beyond $1\mu \mathrm{m}$, where silicon does not respond. For $1.5\text{-}\mu \mathrm{m}$ operation, InGaAs photodiodes have higher bandwidth and less noise than Ge detectors.

To reduce the laser pulse energy requirements, APDs may be used. An APD is a special type of photodiode that amplifies photocurrent via an electron avalanche process. APDs can be operated in either linear mode or Geiger mode (GM). In GM operation, the APD is momentarily biased beyond its breakdown voltage, such that it may enter avalanche breakdown in response to signals as weak as a single photon. The penalty for the extreme sensitivity of GM is that GM APDs cannot measure the amplitude of multiphoton pulse returns, and they must be reset after firing before rearming. The dead time of a GM APD can span a few nanoseconds for silicon GM APDs to a few microseconds for InGaAs GM APDs. In 3-D-imaging applications, the dead time prevents single-laser-shot reception of multiple target returns from objects closely spaced in range and makes GM APDs susceptible to blinding by atmospheric backscattering or optical solar clutter. This hindrance limits the practical utility of GM APDs for practical commercial lidar applications, especially for InGaAs GM APDs.^19,20

In linear-mode operation, the average output of the APD is proportional to the strength of the optical signal, and the detector can operate continuously. Common SWIR-sensitive linear-mode APDs operate with average avalanche gain of $\sim M<50$, more typically at $M=10$ to 20. Dark current is greater for the larger-diameter photodetectors typically used in scanned lidar systems, and the excess-noise contribution to the shot noise limits the benefits of high avalanche gain.²¹

The FAR of an APD is often dominated by the excess noise of the dark-current contribution and the background-signal contributions. Furthermore, as introduced above, the distribution of the gain—not just its average value—has an impact on sensitivity.²² Conventional InGaAs/InP APDs typically have bulk InP multiplication layers characterized by an ionization coefficient ratio of $k\sim 0.4$, which parameterizes the McIntyre excess-noise equation.²¹ Voxtel has developed a multistage APD, the single-carrier-multiplication APD, which has gains exceeding 50 with excess noise characterized by $k\sim 0.02$. Figure 3 shows the possibilities of improved sensitivity that can be achieved in such APDs by allowing for lower threshold settings with lower FAR.

5.2.1.

Scanned lidar single-element InGaAs APD photoreceivers

When the FOV of the lidar photoreceiver is matched to the laser, background noise and susceptibility to multiple scattering factors are reduced, and long-range detection is achieved. Figure 6 shows a picture of one of Voxtel’s ROX™ InGaAs APD-based lidar photoreceivers, which integrates an InGaAs APD detector, an amplification and pulse-processing application-specific integrated circuit, and temperature-compensating biasing circuits, within the hermetic TO-8 package.²³ In these photoreceivers, the TIA bandwidth is much smaller than that of the photodiode (typically, a few gigahertz), and it defines the noise bandwidth. Examples of the sensitivity calculations for a Voxtel single-element InGaAs $250\text{-}\mu \mathrm{m}$ collection area APD detector as a function of pulse width are shown in Fig. 7; the noise-equivalent input (NEI) is $\sim 25\text{photons}$, about eight times lower than the 210-photon threshold sensitivity (30 Hz FAR).

Fig. 6

Our Voxtel ROX APD laser-ranging photoreceiver includes in package temperature compensation and calibration.

Fig. 7

Measured sensitivity of an InGaAs APD photoreceiver shown as a function of pulse width. Here the higher conversion efficiency of the readout IC (ROIC) increases sensitivity for shorter pulse returns. The threshold sensitivity for 60-Hz FAR (red line; top) is $\sim 6\times$ the NEI (shown for reference; blue line; bottom).

5.2.2.

Staring lidar and step-stare lidar two-dimensional InGaAs photoreceiver focal plane array

APDs of this type can also be made in arrays. Figure 8 shows a picture of Voxtel’s VX-806 lidar $128\times 128$-element FPA, which captures the time and amplitude of three pulse returns in each pixel. The input-referred noise of $36{\mathrm{e}}^{-}$ is made possible by the high conversion gain of the in-pixel amplifiers and the low capacitance of the linear-mode-APD InGaAs detector elements. With an 80% quantum efficiency, the APDs, when operated at a gain of $M=20$, allow for an NEI level of below 3 photons [$36/(80\%\times 20)=2.25\text{photons}$] to be possible. The plot of per-pixel NEI and sensitivity (for 30 Hz and 10 kHz FAR across the entire array) is shown in Fig. 9, as a function of gain. As can be seen, due to the increased excess-shot noise of the dark current, there is an upper limit to useful APD gain. At higher operating gain, the positive skew of the pulse distribution of the avalanche gain process leads to an increase in excess noise. These effects can be mitigated by using a lower threshold setting and using multipulse processing to enhance receiver sensitivity.

Fig. 8

InGaAs lidar FPA with $128\times 128$ elements capable of capturing three timestamps with 200-ps time resolution.

Fig. 9

NEI as a function of gain for various laser-pulse widths for Voxtel’s VX-806 InGaAs APD ROIC.

5.3.

Mechanical and Nonmechanical Scanners

Rotating-mirror systems are high performance and, to date, have provided the primary test bed and development platform for the use of lidar in autonomous vehicles.³ To transition from systems like these to low-cost, compact lidar systems that can fit within the body panels of vehicles, developers are considering a number of alternatives.

Traditional laser beam-steering systems (or scanners) are bulky, power-hungry, and vibration-prone mechanical systems, and new devices—with ultralow size, weight, and power—for electro-optic laser beam steering are needed. The ability to incorporate high mechanical stability and minimal hardware to steer a laser beam from its source to its target quickly, efficiently, and precisely will allow laser scanning—both in transmit and receive modes—to be used almost anywhere.

Alternative solutions to mechanical beam steering that have been explored include microlens arrays, microelectro-mechanical systems,^24,25 liquid-crystal polarization gratings,²⁶ holographic glasses, and birefringent prisms. All of these approaches suffer from one or more of the following limitations: low throughput, scattering, small steering angle/aperture, high fabrication cost, and large size/weight.

5.4.

Calibration and Clutter Rejection

To enable processors to perform the split-second decision making required for assisted-driver and self-driving cars, the sensor package must provide accurate 3-D data. This requires compensation for optical distortions, scanner pointing errors, mounting alignment, detector nonunformity, nonlinearity due to signal amplitude as a function of range, target reflectance, and angle, as well as georeferencing errors.