Light detection in lidar imaging systems usually accounts for five different types of detectors: PIN diodes, avalanche photodiodes (APD), single-photon avalanche photodiodes (SPAD), multi-pixel photon counters (MPPC) and, eventually, photomultiplier tubes (PMT). Each one may be built from the material which addresses the wavelength of interest. The most used single-detector are PIN photodiodes, which may be very fast detecting events in light if they have enough sensitivity for the application, but do not provide any gain inside of their media, so in optimal efficiency conditions, each photon creates a single photoelectron. For applications that need moderate to high sensitivity and can tolerate bandwidths just below the GHz regime typical of PIN diodes, avalanche photodiodes (APDs) are the most useful receivers, since their structure provides a certain level of multiplication of the current generated by the incident light. APDs are able to internally increase the current generated by the photons incident in the sensitive area, providing a level of gain, usually around two orders of magnitude. In fact, their gain is proportional to the reverse bias applied, so they are linear devices with adjustable gain which provide a current output proportional to the optical power received. Single-photon avalanche diodes (SPAD) are essentially APDs biased beyond the breakdown voltage, and with their internal structure arranged to repetitively withstand large avalanche events. Whereas in an APD a single photon can produce in the order of tens to few hundredths of electrons, in a SPAD a single photon produces a large electron avalanche of thousands of electrons which results in detectable photocurrents. An interesting arrangement of SPADs has been proposed recently with MPPC, which are pixelated devices formed by an array of SPADs where all pixel outputs are added together in a single analog output, effectively enabling photon-counting through the measurement of the fired intensity [
45,
120,
121,
122]. Finally, PMTs are based on the external photoelectric effect and the emission of electrons within a vacuum tube which brings them to collision with cascaded dynodes, resulting in a true avalanche of electrons. Although they are not solid-state, they still provide the largest gains available for single-photon detection and are sensitive to UV, which may make them useful in very specific applications. Their use in autonomous vehicles is rare, but they have been the historical detector of reference in atmospheric or remote sensing lidar, so we include them here for completeness.
3.2.1. Gain and Noise
As described above, the gain is a critical ability of a photodetector in low SNR conditions as it enables us to increase the available signal from an equivalent input. Gain increases the power or amplitude of a signal from the input (in lidar, the initial number of photoelectrons generated by the incoming photons which are absorbed) to the output (the final number of photoelectrons sent to digitization) by adding energy to the signal. It is usually defined as the mean ratio of the output power to the input signal, so a gain greater than 1 indicates amplification. On the other hand, noise includes all the unwanted, irregular fluctuations introduced by the signal itself, the detector and the associated electronics which accompany the signal and perturb its detection by obscuring it. Photodetection noise may be due to different parameters well described in [
127].
Gain is a relevant feature of any photodetector in low SNR applications. Conventionally, a photon striking the detector surface has some probability of producing a photoelectron, which in turn produces a current within the detector which usually is converted to voltage and digitized after some amplification circuitry. The gain of the photodetector dictates how many electrons are produced by each photon that is successfully converted into a useful signal. The effect of these detectors in the signal-to-noise ratio of the system is to add a gain factor G to both the signal and certain noise terms, which may also be amplified by the gain.
Noise is, in fact, a deviation of the response to the ideal signal; so, it is represented by a standard deviation (
). A combination of independent noise sources is then the accumulation of its standard deviations, which means that a dominant noise term is likely to appear:
Thermal noise and shot noise are considered fixed system noise sources. The first is due to the thermal motion of the electrons inside the semiconductor, which adds electrons to the output current which are not related to the incident optical power. Shot noise is related to the statistical fluctuations in the optical signal itself and the statistical interaction process with the detector. Shot noise is relevant only in very low light applications, where the statistics of photon arrival become observable. Other noise sources are considered as external, such as background noise , readout noise , or speckle noise . They respectively appear as a consequence of the existence of background illumination in the same wavelength of the laser pulses, fluctuations in the generation of photoelectrons or its amplification, or the presence of speckle fluctuations in the received laser signal. While fixed system noise will not be affected by the gain of the detector, background, readout and speckle noise will also be amplified by the gain, which may become counter-productive for detection. When either thermal or shot noise are the dominant noise source, we are said to be in the thermal or shot noise regimes of a detector, and the existence of gain significantly improves the SNR value.
The SNR for a detector with gain may then be written as:
where
is the number of photoelectrons generated by real incoming photons. Equation (
9) shows the advantage to work in thermal or shot regime regarding gain.
3.2.2. Photodetectors in Lidar Imaging Systems
(a) PIN photodiodes
A PIN photodiode is a diode with a wide, undoped intrinsic semiconductor region between a p- and a n-doped regions. When used as a photodetector, the PIN diode is reverse-biased. Under this condition the diode is not a conductor, but when a photon with enough energy enters the depletion region it creates an electron-hole pair. The field of the reverse bias then sweeps the carriers out of the region creating a current proportional to the number of incoming photons. This gives rise to a photocurrent sent to an external amplification circuit. The depletion region stays completely within the intrinsic region, and it is much larger than in a PN diode and almost constant-sized, regardless of the reverse bias applied to the diode.
When using PIN diodes as receivers, most of photons are absorbed in the I-region, and carriers generated therein can efficiently contribute to the photocurrent. They can be manufactured with multiple different materials including Si, InGaAs, CdTe,… yielding wide options regarding their spectral response, although the most usual single-element detectors used are based on Si and InGaAs. PIN photodiodes do not have any gain (G = 1) (
Figure 12), but may present very large bandwidths (up to 100 GHz, depending on its size and capacitance), dimensions of millimeters, low cost, low bias and large QE. However, due to their features their sensitivity is not enough for low light applications. In lidar imaging systems, they are typically used as detectors in pulsed lidars to raise the start signal for the time-to-digital converter at the exit of the laser pulse.
(b) Avalanche photodiodes
An avalanche photodiode (APD) is a diode-based photodetector with an internal gain mechanism operated with a relatively high reverse bias voltage (typically tens or even hundredths of volts), sometimes just below the breakdown of the device, which happens when a too-large reverse bias is applied. As with a conventional photodiode detector, the absorption of incident photons generates a limited number of electron-hole pairs. While under high bias voltage, a strong internal electric field is created which accelerates the carriers generated and creates additional secondary electrons, in this case by impact ionization. The resulting electron avalanche process, which takes place over a distance of only a few micrometers, can produce gain factors up to a few hundredths but is still directly proportional to the incoming optical power and to the reverse bias. The amplification factor of the APD dictates the number of photoelectrons that are created with the successful detection of each photon, and, thus, the effective responsivity of the receiver. Gain may vary from device to device and strongly depends on the reverse voltage applied. However, if the reverse voltage is increased further, a voltage drop occurs due to the current flowing through the device load resistance. This means that the value of the maximum gain has a dependence on the photocurrent. Although there is a large linear region of operation where the output photocurrent presents gain proportional to the power of the incoming light, when the APD is operated near its maximum gain (and thus close to the breakdown voltage) the APD response is not linear anymore, and then the APD is said to operate in Geiger mode. The level of gain required to obtain the optimal SNR value will often be dependent on the amount of incident light (
Figure 12). Several excellent reviews of APDs in detail are available, e.g., [
128].
APDs are very sensitive detectors. However, the avalanche process itself creates fluctuations in the generated current and thus noise, which can offset the advantage of gain in the SNR. The noise associated with the statistical fluctuations in the gain process is called excess noise. Its amount depends on several factors: the magnitude of the reverse voltage, the properties of the material (in particular, the ionization coefficient ratio), and the device design. Generally speaking, when fixed system noise is the limiting noise factor the performance of APDs is much better than devices with ordinary PIN photodiodes. However, increasing gain also increases the excess noise factor, so there exists an optimal operating gain for each operating condition, usually well below the actual maximum gain, where the maximum SNR performance can be obtained.
Linear-mode APDs (in contrast to Geiger-mode APDs or SPADs, described next) present output signals amplified by a gain and proportional to the incoming light. Compared to PIN photodiodes, they have comparable bandwidth, but can measure lower light levels, and thus may be used in a variety of applications requiring high sensitivity such as long-distance communications, optical distance measurements, and obviously for lidar. However, they are not sensitive enough for single-photon detection. They are a mature and widely available technology, so APDs are also available in array form, in multiple sizes, in either 1D or 2D arrays, with photosensitive areas up to mm, especially in Si. Large InGaAs arrays, on the contrary, are hard to find and prohibitively priced at present.
(c) Single-photon avalanche photodiodes
APDs working in Geiger-mode are known as single-photon avalanche diodes (SPADs). SPADs are operated slightly above the breakdown threshold voltage (
Figure 12), the electric field being so high that a single electron–hole pair injected into the depletion layer can trigger a strong, self-sustained avalanche. The current rises swiftly to a macroscopic steady level and it keeps flowing until the avalanche can be
, meaning it is stopped and the SPAD is operative again. Under these circumstances, the photocurrent is not linearly amplified, but rather a standard final current value is reached regardless if it has been triggered by only one or by several incident photons. The design of the device architecture needs to be prepared for repeated avalanches without compromising the response of the detector. The structure of SPADs is different from those of linear mode APDs in order to withstand repeated avalanches and have efficient and fast quenching mechanisms.
For effective Geiger-mode operation, the avalanche process must be stopped and the photodetector must be brought back into its original quiescent state. This is the role of the quenching circuit. Once the photocurrent is triggered, the quenching circuit reduces the voltage at the photodiode below the breakdown voltage for a short time, so the avalanche is stopped. After some recovery time, the detector restores its sensitivity and is ready for the reception of further photons. Such a dead-time constitutes a substantial limitation of these devices, as it limits the count rate and leaves the device useless for times in the 100 ns scale, severely limiting its bandwidth. This is being tackled through improved quenching circuits. Currently, two types of quenching are in use: passive, in which avalanche is interrupted by lowering the bias voltage below breakdown using a high-value resistor; and active, based on active current feedback loops. Active quenching was specifically devoted to overcoming the slow recovery times characteristic of passive quenching. The rise of the avalanche is sensed through a low impedance and a reaction back on the device is triggered by controlling the bias voltage using active components (pulse generators or fast active switches) that force the quenching and reset transitions in shorter times [
129]. Currently, active quenching is a very active research line, due to its relevance in low light detection in several imaging applications [
130].
The macroscopic current generated due to the avalanche is discernible using electronic threshold detection. Since threshold detection is digital, it is essentially noiseless, although there exist different mechanisms that can also fire the avalanche process generating noise. The main sources of false counts in SPADs are thermally-generated carriers and afterpulsing [
131]. The first case is due to the generation-recombination processes within the semiconductor as a result of thermal fluctuations, which may induce the avalanche and produce a false alarm. In the second case, during the avalanche, some carriers are captured by deep energy levels in the junction depletion layer and subsequently released with a statistically fluctuating delay. Released delayed carriers can retrigger the avalanche generating these after-pulses, an effect that increases with the delay of avalanche quenching and with the current intensity.
SPADs are, however, extremely efficient in low light detection, and can be used when an extremely high sensitivity at the single-photon detection level is required. Devices with optimized amplifier electronics are also available in the CMOS integrated form, even as large detector arrays, in applications from quantum optics to low-light biomedical imaging. The intensity of the signal may be obtained by repeated illumination cycles counting the number of output pulses received within a measurement time slot. Statistical measurements of the time-dependent waveform of the signal may be obtained by measuring the time distribution of the received pulses, using the time-correlated single-photon counting (TCSPC) technique [
21]. SPADs are used in a number of lidar applications and products, taking advantage of its extreme sensitivity, and may be found individually, or in 1D or 2D arrays. Their main drawback is their sensitivity to large back reflections which may saturate the detector and leave it inoperative for short periods, an event easily found in real life where large retroreflective signs are present almost everywhere on the road as traffic signs, as discussed in
Section 2.2.2.a when speaking of flash imagers.
(d) Multipixel photon counters
SPADs are very efficient in the detection of single photons, as they provide a digital output in the presence of one or more photons. The signal obtained when detecting one or several photons is thus equivalent, which is a drawback in several applications. Multipixel photon counters (MPPCs), also known as silicon photomultipliers (SiPMs), are essentially SPAD arrays with cells of variable size that recombine the output signal of each individual SPAD into a joint analog signal [
132,
133]. In such a fashion, the analog signal is proportional to the number of SPADs triggered, enabling photon-counting beyond the digital on/off photon detection capability presented by SPADs.
Each microcell in an MPPC consists of a SPAD sensor with its own quenching circuit. When a microcell triggers in response to an absorbed photon, the Geiger avalanche causes a photocurrent to flow through the microcell. The avalanche is confined to the single-pixel where it was initiated while all other microcells remain fully charged and ready to detect photons. When a photon is detected, the receiving unit in the array outputs a single pulse with a fixed amplitude that does not vary with the number of photons entering the unit at the same time. The output amplitude is equal for each of the pixels. Although the device works in digital mode pixel by pixel, MPPCs become analog devices as all the microcells are read in parallel and each of the pulses generated by multiple units is superimposed onto each other to obtain the final photocurrent. As a drawback, linearity gets worse as more photons are incident on the device, because the probability for more than one photon hitting the same microcell increases. Further, as an array, the potential for crosstalk and afterpulsing between cells may be significant depending on the application [
134]. Optical crosstalk occurs when a primary avalanche in a microcell triggers secondary discharges in one or more adjacent microcells, i.e., the unit that actually detects photons affects other pixels making them produce pulses that make the output signal higher than that implied by the amount of the incident light. Its probability depends on fixed factors (like the size of the microcell and the layered architecture) and on variable ones (like the difference between the bias voltage being applied and the breakdown voltage).
A typical MPPC has microcell densities of between 100 and several 1000 per mm, depending upon the size of the unit. Its characteristics are greatly connected with the operating voltage and ambient temperature. In general, raising the reverse voltage increases the electric field inside the device and so, improves the gain, photon detection efficiency and time resolution. On the other hand, it also increases undesired components that lower the SNR, such as false triggers due to thermal noise and afterpulsing. Thus, the operating voltage must be carefully set in order to obtain the desired characteristics.
Despite these practicalities, MPPCs have many attractive features including very high gains (about ), analog photon-counting capabilities, a wide number of available commercial sizes (they are even modular so they can be attached next to each other), and lower operation voltage and power consumption values than the ones required for conventional PMTs. Due to its characteristics, it is a useful device for most low light applications, in particular for lidar or in any single photon application where solid-state detectors are an advantage related to PMTs.
(e) Photomultiplier tubes
As a final detector in the series, photomultiplier tubes (PMTs) have played, and still play, a relevant role in several applications, including atmospheric lidar for remote sensing. They have been compared to MPPC detectors in atmospheric lidar showing comparable performance [
135].
PMTs are based on the external photoelectric effect. A photon incident onto a photosensitive area within a vacuum tube that extracts a photoelectron from the material. Such a photoelectron is accelerated to impact onto a cascaded series of electrodes named dynodes, where more electrons are generated by ionization at each impact creating a cascaded secondary emission. Each photoelectron generated is multiplied in cascade enabling again single-photon detection. It is possible to obtain gains up to
at MHz rate [
136]. They have dominated the single-photon detection scene for many years, especially in scientific and medical applications. They are still the only photodetectors with a decent response and gain in the UV region, present unrivaled gain at all wavelengths and their rise times are in the ns scale, so their bandwidth is very large (>1 GHz). However, PMTs are bulky, fragile devices which are not solid-state, and which are affected by magnetic fields, which strongly limits their applicability in autonomous vehicles. Other disadvantages include the requirement for a high-voltage supply, the high cost and, in some cases, their low quantum efficiency.
Table 4 presents a brief summary of the main features of the photodetectors we have just described.