This chapter describes the functional principles of single-photon counting in silicon achieved by using single-photon counting avalanche diode (SPAD) technology. It explains the different readout modes of single SPADs on the one side, and of arrays of SPADs forming silicon photomultipliers (SiPM) with analog output, SiPMs with a digital output, or SPAD arrays that can be read out in form of frames that form SPAD-based imagers, on the other. This silicon-based technology is compared to traditionally used photomultiplier tube, multichannel plate, or image intensifier technologies in applications requiring near single-photon counting and time responses in a nanosecond or subnanosecond regions. This chapter also discusses the fabrication issues of SPAD devices as well as figures of merit used for their characterization. Finally, the chapter explains how SPAD arrays are used in time-of-flight-based ranging and/or 3D imaging applications.

A one-dimensional analytical model of charge transfer in charge-coupled devices, which describes the spatial–temporal behavior of the charge carrier density in a potential well, is presented. The general solution of this model considers the transfer dynamics in terms of the electric drift field, i.e., self-induced drift and fringing-field drift, and yields an analytical solution for the total number of charge carriers. A comparison of the transfer efficiency for various electric drift fields is presented. The modulation transfer function in dependence on the transfer efficiency is analyzed, aiming especially at time-delay integration (TDI) applications. Finally, the results of this model are concluded and discussed in detail.

This paper presents an investigation of the responsivity of a time-delay integration (TDI) charge-coupled device that employs anti-blooming clocking and uses a varying number of TDI stages. The influence of charge blooming caused by unused TDI stages in a TDI deployed selection scheme is shown experimentally, and an anti-blooming clocking mechanism is analyzed. The impact of blooming on sensor characteristics, such as the responsivity, the conversion gain, and the signal-to-noise ratio, is investigated. A comparison of the measurements with and without this anti-blooming clocking mechanism is presented and discussed in detail.

Single-Photon Avalanche Diode (SPAD)-based 'Light Detection And Ranging' (LiDAR) systems often use the first photon measurement principle to acquire ranging information. While those systems provide accurate distance measurements, they can easily saturate in high background scenarios. Recent improvements in SPAD quenching circuit technology open up the opportunity for SPAD LiDAR systems to detect multiple photons while measuring with a single laser pulse, partially circumventing this challenge. The theoretical framework for the distribution of higher order single photon detections is presented and discussed how the sensor's typical quenching times influence it. Measurements with a SPAD circuitry capable of detecting multiple events in a single measurement are presented. Differences to first-photon and continuous detection implementations are discussed and advantages in high background light scenarios are shown.

LiDAR is a key sensor technology for future driving. For autonomous vehicles a fast and reliable three dimensional monitoring of the environment is essential for managing a wide variety of common traffic situations. Since these kinds of systems use typically light in the near infrared range, ambient light of the sun is a serious problem due to its high intensity compared to the laser source. Therefore, reducing the influence of ambient light on the distance measurement is very important. In this paper we present a 2 x 192 pixel SPAD-based direct time-of-flight line sensor for flash LiDAR applications with high ambient light rejection integrated in standard CMOS technology. Two commercially available 905 nm laser diodes emitting short pulses are employed for scene illumination For time measurement an in-pixel time-to-digital-converter with a resolution of 312.5 ps and full range of 1.28 mu s has been implemented. Each pixel uses four vertically arranged single SPADs for background light rejection based on the detection of temporal correlated photons. This technique allows the discrimination of the received laser pulse buried in the superimposed background light and, hence, to improve the measurement quality. Additionally, different parameters of the coincidence detection circuit, such as coincidence depth and time, can be varied during operation to enable a real time adjustment to the present ambient light condition, which is measured between each laser shot by operating the sensor in photon counting mode. By using this technique the sensor allows a reliable distance measurement at various ambient and target conditions.

In this contribution, we present the concept of a 4×128 pixel line sensor for direct time-of-flight measurement based on single-photon avalanche diodes (SPAD) fabricated in a high-voltage automotive 0.35 μm CMOS process. An in-pixel time-to-digital converter with a resolution of 312.5 ps determines the arrival of photons reflected from targets in the area of view. Since we are employing a so-called first photon approach, there are no dead-time effects. In addition, our approach uses a variable photon coincidence detection to suppress effects of ambient illumination. As a test vehicle we have implemented a 1×80 pixel CMOS SPAD line sensor and characterized it.

Indirect time-of-flight measurement with SPADs is performed by counting incident photons in several time windows. Since SPADs exhibit dead time not all incident photons can be counted within a given time window. This affects the expected values and, hence, the variance of the distance measurement. For photon detection rates close to the inverse of the dead time, which defines the maximum count rate of a SPAD, the probability of photon detection cannot be assumed constant within the window anymore. In this paper the effects of dead time on the photon counts are analyzed by employing statistical calculations. Based on these a model to correct such effects can be derived.

This communication addresses the range accuracy of SPAD-based time-of-flight (TOF) sensors that employ laser pulse modulation. Two basic approaches are considered: indirect and direct TOF. We investigate confidence intervals and derive formulas for standard errors of the relative distance error for both approaches based on photon statistics.

Indirect time-of-flight (TOF) measurement with single-photon avalanche diodes (SPADs) is performed by counting incident photons in several time windows. Since SPADs exhibit dead time not all incident photons can be counted within a given time window. This affects the expected values and, hence, the variance of the distance measurement. For photon detection rates close to the inverse of the dead time, which defines the maximum count rate of a SPAD, the probability of photon detection cannot be assumed constant within the window anymore. In this paper, the effects of the dead time on the photon counts as well as the corresponding variances are analyzed by employing statistical calculations. Based on these a model which can be used to correct systematic error is derived. In addition, the detailed analysis of the variance is useful to estimate the performance of an indirect TOF system in the design phase.

We present a 1×80 pixel line sensor for direct time-of-flight measurement based on single-photon avalanche diodes fabricated in a high-voltage 0.35 pm CMOS process. An in-pixel time-to-digital-converter with a resolution of 312.5 ps determines the arrival time of the first-photon for each emitted laser pulse from a flash illumination source for all pixels in parallel. Distance determination is performed by collecting the time stamps over multiple pulses in a histogram and applying proper software algorithms. Ambient light suppression is achieved by detection of photon coincidences from four single SPADs in each pixel. By adjusting the time and depth of the coincidence detection a good result in varying ambient conditions is achieved.

For applications like autonomous driving a fast and reliable monitoring of the vehicle's environment is essential. With the possibility of fabricating single-photon avalanche diodes in standard CMOS processes, small and cost-efficient time-of-flight sensors can be realized. To estimate the performance of such a sensor a general theoretical model taking into account the properties of the light source, the sensor, and the environment is of key importance. In this paper we will present a model to predict the performance parameters like achievable range and precision of different time-of-flight measurement techniques.

High ambient illumination reduces the range and target detection reliability in light-based 3D sensors. Raising the optical power of the artificial illumination source to overcome the influence of high ambient light is often not possible for systems with flash illumination due to eye safety constraints. The high timing resolution of single-photon avalanche diodes enables the search for photon concurrences in incident photon streams. In this paper a theoretical analysis of coincidence and its benefits for 3D sensors with single-photon avalanche diodes is presented.

The integration of silicon photomultiplier (SiPM) and frontend electronics in a suitable optoelectronic CMOS process is a promising approach to increase the versatility of single-photon avalanche diode (SPAD)-based single photon detectors. By integrating readout amplifiers, the device output capacitance can be reduced to minimize the waveform tail, which is especially important for large area detectors (> 10 x 10 mm(2)). Possible architectures include a single readout amplifier for the whole detector, which reduces the output capacitance to 1.1 pF at minimal reduction in detector active area. On the other hand, including a readout amplifier in every SiPM cell would greatly improve the total output capacitance by minimizing the influence of metal routing parasitic capacitance, but requiring a prohibitive amount of detector area. As tradeoff, the proposed detector features one readout amplifier for each column of the detector matrix to allow for a moderate reduction in output capacitance while allowing the electronics to be placed in the periphery of the active detector area. The presented detector with a total size of 1.7 x 1.0 mm(2) features 400 cells with a 50 mu m pitch, where the signal of each column of 20 SiPM cells is summed in a readout channel. The 20 readout channels are subsequently summed into one output channel, to allow the device to be used as a drop-in replacement for commonly used analog SiPMs.

Conversely to the continuous wave indirect time-of-flight (CW-iToF) imaging scheme, pulsed modulation ToF (PM-iToF) imaging is a promising depth measurement technique for operation at high ambient illumination. It is known that non-linearity and finite charge-transfer speed impact trueness and precision of ToF systems.(1-3) As pulses are no Eigenfunctions to the shutter system, this issue is especially pronounced in pulsed modulation.(2,3) Despite these effects, it is possible to find analytical expressions founded on physical observations that map scenery parameters such as depth information, reflectance and ambient light level to sensor output.(3,4) In the application, the inverse of this map has to be evaluated. In PM-iToF, an inverse function cannot be yielded in a direct manner, as models proposed in the literature were transcendental.(3,4) For a limited range an approximating linearization can be performed to yield depth information.(5) To extend the usable range, recently, an alternative approach that indirectly approximates the inverse function was presented.(6) This method was founded on ID doping concentration profiles, which, however, are typically not made available to end users. Also, limitations of the ID approximation as well as stability are yet to be explored. This work presents a calibration methodology that copes with detector insufficiencies such as finite charge transfer speed. Contrarily to the state of the art, no prior knowledge on details of the underlying devices is required. The work covers measurement setup, a benchmark of various calibration schemes and deals with issues such as overfitting or defect pixels.

In this article a model is introduced that describes the charge transfer in pixels of an image sensor. The model is suitable for image sensors where lateral drift field photo detectors were implemented and considers the effects of thermal diffusion, drift due to the built-in potential gradient, and self-induced drift.The analytical result is compared with a numerical solution and confirmed by measurements. With this model it is possible to predict the amount of collected charge at the sense node for very short integration times in comparatively long pixel structures. This is particularly important for indirect time-of-flight applications with CMOS image sensors.This approach enables the optimization of the pixel layout as well as an advanced calibration that might possibly enhance the distance precision. The model can also be applied to image sensors featuring pinned photodiodes. (C) 2016 Elsevier Ltd. All rights reserved.

With the possibility of fabricating single-photon avalanche diodes in standard CMOS processes, arrays for range imaging applications have been developed. Proper operation in high ambient illumination environments is one of the major issues of scannerless sensors published so far. In this paper a theoretical study of the direct and indirect working principle regarding high ambient illumination is shown. Further, new concepts based on these principles to reduce the sensitivity to ambient light are presented.

In recent years, various developments have advanced the field of optical sensors based on single-photon avalanche diodes. In this contribution we present two sensors that were designed in 0.35μm CMOS technology. A silicon photomultiplier achieves a fill factor of 68 % at 50 μm pixel pitch and allows improved functionality by cointegration of application-specific readout electronics. A time-gated line sensor with gating times down to 1.5ns and serial digital output was designed based on optimized pixel geometry suitable for spectroscopy applications. Planned further improvements of sensors based on single-photon avalanche diode technology, including on-chip temperature compensation, are presented.

This work is dedicated to efficient optimization of pulse-modulated (PM) indirect time-of-flight (iToF) through analytical modeling. Measurements that verify the validity of the model for two generations of CMOS iToF imagers are presented. As convexity is not guaranteed and e.g. eye-safety constraints have points of non-differentiability, the feasibility of Evolutionary Strategy (ES) optimizers was investigated. Compared to alternative non-differentiating global optimizers this has the advantage of offering systematic and random progress capability without the need for phenotype-genotype mapping. A MATLAB implementation is presented that demonstrates convergence of a problem with 6 degrees of freedom (DOF) in less than 100 iterations. Compared to the brute force approach this is an improvement by several orders of magnitude, as there computation time scales exponentially with the number of DOF.

This contribution describes the modeling of CMOS image sensors employed in time-of-flight (ToF) sensor systems for 3D ranging applications. Our model relies on the theoretical description of photo-generation, charge transfer including diffusion, fringing field, and self-induced drift (SID). This method makes it possible to calculate the time-dependent charge carrier generation, transfer, and distribution.The employed approach allows elimination not only of irradiance-dependent charge transfer, but also of undesired reflectance effects, and the influence of ambient light through an in-pixel background measurement. Since the sensor is operated with very short integration times it is crucial to accomplish a fast transfer of the generated charge from the photodetector to the sense node, and speedy conversion into an electrical signal at its output. In our case, we employed a lateral drift field photodetector (LDPD), which is basically a pinned photodiode with a built-in drift field formed by a doping gradient.A novel pixel structure is presented which is optimized for a fast charge transfer by the appliance of the shown model. Numerical calculations predict a two times faster charge collection.