Patent Publication Number: US-2021165083-A1

Title: Configurable array of single-photon detectors

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of U.S. Provisional Patent Application 62/942,761, filed Dec. 3, 2019, which is incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to systems and methods for depth mapping, and particularly to sensor arrays used in time-of-flight sensing. 
     BACKGROUND 
     Time-of-flight (TOF) imaging techniques are used in many depth mapping systems (also referred to as 3D mapping or 3D imaging). In direct TOF techniques, a light source, such as a pulsed laser, directs pulses of optical radiation toward the scene that is to be mapped, and a high-speed detector senses the time of arrival of the radiation reflected from the scene. The depth value at each pixel in the depth map is derived from the difference between the emission time of the outgoing pulse and the arrival time of the reflected radiation from the corresponding point in the scene, which is referred to as the “time of flight” of the optical pulses. 
     Single-photon avalanche diodes (SPADs), also known as Geiger-mode avalanche photodiodes (GAPDs), are detectors capable of capturing individual photons with very high time-of-arrival resolution, of the order of a few tens of picoseconds. They may be fabricated in dedicated semiconductor processes or in standard CMOS technologies. Arrays of SPAD sensors, fabricated on a single chip, have been used experimentally in 3D imaging cameras. 
     U.S. Patent Application Publication 2017/0052065, whose disclosure is incorporated herein by reference, describes a sensing device that includes a first array of sensing elements, which output a signal indicative of a time of incidence of a single photon on the sensing element. A second array of processing circuits are coupled respectively to the sensing elements and comprise a gating generator, which variably sets a start time of the gating interval for each sensing element within each acquisition period, and a memory, which records the time of incidence of the single photon on each sensing element in each acquisition period. A controller controls the gating generator during a first sequence of the acquisition periods so as to sweep the gating interval over the acquisition periods and to identify a respective detection window for the sensing element, and during a second sequence of the acquisition periods, to fix the gating interval for each sensing element to coincide with the respective detection window. 
     SUMMARY 
     Embodiments of the present invention that are described hereinbelow provide improved apparatus and methods for optical sensing. 
     There is therefore provided, in accordance with an embodiment of the invention, optical sensing apparatus, including at least one semiconductor substrate and a first array of single-photon detectors, which are disposed on the at least one semiconductor substrate and are configured to output electrical pulses in response to photons that are incident thereon. A second array of counters are disposed on the at least one semiconductor substrate and are configured to count the electrical pulses output by the single-photon detectors. Routing and aggregation logic is configured, in response to a control signal, to connect the single-photon detectors to the counters in a first mode in which each of at least some of the counters aggregates and counts the electrical pulses output by a respective first group of one or more of the single-photon detectors, and in a second mode in which each of the at least some of the counters aggregates and counts the electrical pulses output by a respective second group of two or more of the single-photon detectors. 
     In a disclosed embodiment, the single-photon detectors includes single-photon avalanche diodes (SPADs). 
     In some embodiments, the control signal includes a gating signal, and the counters are configured to aggregate and count the electrical pulses over respective periods indicated by the gating signal. Typically, the gating signal causes different ones of the counters to aggregate and count the electrical pulses over different, respective gating intervals, so that the second array of counters outputs a histogram of the electrical pulses output by the single-photon detectors with bins defined responsively to the gating intervals. In disclosed embodiments, the apparatus includes a radiation source, which is configured to direct a series of optical pulses toward a target scene, and the single-photon detectors are configured to receive optical radiation that is reflected from the target scene, and the counters are configured to aggregate and count the electrical pulses while the gating intervals are synchronized with the optical pulses with a delay between the optical pulses and the gating intervals that is swept over a sequence of different delay times during the series of the optical pulses. In one embodiment, the counters are configured to aggregate and count the electrical pulses in first and second bins of the histogram while the gating intervals are swept over the sequence of different delay times, and the apparatus includes a processor, which is configured to compute a time of flight of the optical pulses by comparing respective first and second counts accumulated in the first and second bins. 
     Additionally or alternatively, in the first mode, each of the counters counts the electrical pulses that are output by a single, respective one of single-photon detectors. In some embodiments, in the second mode, each of the at least some of the counters aggregates and counts the electrical pulses output by at least four of the single-photon detectors that are mutually adjacent in the first array. In disclosed embodiments, the control signal includes a gating signal, which causes the counters to aggregate and count the electrical pulses over respective gating intervals, and the apparatus includes a radiation source, which is configured to direct a series of optical pulses toward a target scene, wherein the single-photon detectors are configured to receive optical radiation that is reflected from the target scene, and a processor, which is configured to compute a time of flight of the optical pulses responsively to counts of the electrical pulses that are output by the counters over different gating intervals while operating in the second mode, and to apply the computed time of flight in setting a gating interval for the counters in the first mode. In one embodiment, the processor is configured to generate a three-dimensional (3D) map of the target scene responsively to the time of flight computed in the second mode, to identify an object of interest in the 3D map, and to set the gating interval for the counters in the first mode responsively to a depth of the object of interest in the 3D map so as to acquire a two-dimensional (2D) image of the object of interest. 
     There is also provided, in accordance with an embodiment of the invention, a method for optical sensing, which includes providing, on at least one semiconductor substrate, a first array of single-photon detectors, which are configured to output electrical pulses in response to photons that are incident on the single-photon detectors, and a second array of counters, which are configured to count the electrical pulses output by the single-photon detectors. In response to a control signal, the single-photon detectors are connected to the counters in a first mode in which each of at least some of the counters aggregates and counts the electrical pulses output by a respective first group of one or more of the single-photon detectors, and in a second mode in which each of the at least some of the counters aggregates and counts the electrical pulses output by a respective second group of two or more of the single-photon detectors. 
     There is additionally provided, in accordance with an embodiment of the invention, a method for optical sensing, which includes directing a series of optical pulses toward a target scene and imaging optical radiation that is reflected from the target scene onto an array of single-photon detectors, which output electrical pulses in response to photons that are incident thereon. The electrical pulses output by the single photon detectors are counted in multiple different gating intervals that are synchronized with each of the optical pulses, including at least first and second gating intervals at different, respective delays relative to the optical pulses, while the delays are swept over a sequence of different delay times during the series of the optical pulses. A time of flight of the optical pulses is computed by comparing respective first and second counts of the electrical pulses that were accumulated in the first and second gating intervals over the series of the optical pulses. 
     In some embodiments, counting the electrical pulses includes aggregating the pulses over groups of mutually-adjacent single-photon detectors in the array. 
     Additionally or alternatively, the first and second gating intervals are synchronized at respective first and second delays relative to the optical pulses, such that a difference between the first and second delays remains fixed while the first and second delays are swept over the sequence of different delay times during the series of the optical pulses. In one embodiment, the second gating interval begins upon termination of the first gating interval. Alternatively, an initial part of the second gating interval overlaps with the first gating interval. Additionally or alternatively, the first and second gating intervals have a common, predefined duration, and the sequence of the different delay times spans the predefined duration. 
     In a disclosed embodiment, the gating intervals are selected responsively to a range of the target scene so that the photons in the series of the optical pulses that are reflected from the target scene are incident on the array of single-photon detectors only during the first and second gating intervals. 
     In some embodiments, the multiple different gating intervals include at least a third gating interval, such that the electrical pulses counted during the third gating interval are indicative of a background component of the optical radiation that is incident on the array of single-photon detectors, and computing the time of flight includes compensating for the background component in comparing the first and second counts. In one embodiment, the third gating interval is synchronized with the optical pulses so as to measure stray photons in the optical pulses that are incident on the array of single-photon detectors without having reflected from the target scene. Alternatively or additionally, the electrical pulses counted during the third gating interval are indicative of an ambient component of the optical radiation that is incident on the array of single-photon detectors. In a disclosed embodiment, computing the time of flight includes calculating a ratio of the first and second counts after subtraction of the background component counted during at least the third gating interval. 
     There is further provided, in accordance with an embodiment of the invention, apparatus for optical sensing, including a radiation source, which is configured to direct a series of optical pulses toward a target scene, and a first array of single-photon detectors, which are configured to receive optical radiation that is reflected from the target scene and to output electrical pulses in response to photons that are incident thereon. A second array of counters are configured to count the electrical pulses output by the single photon detectors in multiple different gating intervals that are synchronized with each of the optical pulses, including at least first and second gating intervals at different, respective delays relative to the optical pulses, while the delays are swept over a sequence of different delay times during the series of the optical pulses. A processor is configured to compute a time of flight of the optical pulses by comparing respective first and second counts of the electrical pulses that were accumulated in the first and second gating intervals over the series of the optical pulses. 
     The present invention will be more fully understood from the following detailed description of the embodiments thereof, taken together with the drawings in which: 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic side view of depth mapping apparatus, in accordance with an embodiment of the invention; 
         FIG. 2  is a block diagram showing detectors and processing circuits making up a super-pixel in a sensing array, in accordance with an embodiment of the invention; 
         FIG. 3  is a block diagram showing details of routing and aggregation logic in a sensing array, in accordance with an embodiment of the invention; 
         FIG. 4  is a block diagram that schematically illustrates an operating configuration of a super-pixel in an aggregation mode, in accordance with an embodiment of the invention; and 
         FIGS. 5-7  are timing diagram that schematically illustrates methods for measuring TOF to a target scene, in accordance with embodiments of the invention. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Overview 
     The speed and sensitivity of single-photon detectors, such as SPADs, makes them a good choice for TOF imaging. SPAD arrays with integrated control logic and memory, such as those described above in the Background section, are starting to become commercially available. These integrated array devices, however, are still limited by the tradeoff of array pitch and power consumption against the spatial and depth resolution that they are capable of achieving. 
     Embodiments of the present invention that are described herein provide optical sensing apparatus and methods that address this tradeoff, and achieve more versatile SPAD array operation and more accurate depth mapping for a given array size and pitch. 
     Some embodiments provide optical sensing apparatus in which an array of single-photon detectors, such as SPADs, are disposed on a semiconductor substrate and output electrical pulses in response to incident photons. An array of counters, also disposed on the semiconductor substrate, count the electrical pulses output by the single-photon detectors. Routing and aggregation logic on the substrate is able to vary the configuration of the counters, relative to the detectors, in response to external control signals, and specifically to connect different groups of the single-photon detectors to different counters. 
     For example, in a first mode, each of the counters (or at least each of at least some of the counters) aggregates and counts the electrical pulses output by a respective first group of the single-photon detectors, which may even include only a single detector—meaning that each counter is connected to its own detector. In this mode it is also possible to create a two-dimensional (2D) image of a scene, in which the pixel values are given by the number of counts accumulated from each detector. 
     In a second mode, on the other hand, each of these counters aggregates and counts the electrical pulses output by a respective second group, which includes two or more of the detectors. Each counter can be gated to count the pulses it receives during a respective gating interval. In this manner, two or more counters with different gating intervals can be used together to construct a histogram of photon arrival times over the corresponding group of detectors. The gating intervals can be synchronized with optical pulses emitted by a radiation source in order to measure the times of flight of photons reflected from a target scene, and thus create a three-dimensional (3D) map of the scene. 
     If an object of interest (for example, a human face) is identified in such a 3D map, the gating interval for the counters in the first mode described above can then be set, relative to the optical pulses emitted toward the object, based on the depth of the object of interest in the 3D map. The detector array will thus acquire a 2D or 3D image of the object of interest with enhanced rejection of background radiation on account of the short, targeted gating interval that is applied. 
     In this sort of gated 3D acquisition, the gating intervals can made shorter, within the range of interest, thus narrowing the histogram bins and enhancing the depth resolution of the apparatus. Yet another benefit of the range-gating capabilities of the apparatus is the elimination of interference due to multi-path reflections, which propagate over a longer range and thus will reach the detector after the gate has closed. (In the absence of range gating, both direct and multi-path reflections will be detected in the histogram.) When the range to the target scene is known, the intensity of the radiation source can also be controlled as a function of the range, to avoid saturation of the detectors at short range and compensate for weaker signals at long range. 
     Other embodiments provide novel methods for TOF measurement using an array of single-photon detectors. These methods may be implemented advantageously using the aggregation and gated counting capabilities of the apparatus described above; but the methods may alternatively be performed using other sorts of single-photon detector arrays and gated counting logic. 
     In one of these embodiments, a series of optical pulses is directed toward a target scene, and optical radiation that is reflected from the target scene is imaged onto an array of single-photon detectors. Logic circuits associated with the array (such as the array of counters described above) count the electrical pulses output by the single photon detectors in multiple different gating intervals that are synchronized with each of the optical pulses, with each gating interval at a different, respective delay relative to the optical pulses. The delays of the gating intervals relative to the optical pulses are swept over a sequence of different delay times during the series of the optical pulses, and each counter accumulates the electrical pulses from the respective gating interval over the sequence of different delays. A processor computes the times of flight of the optical pulses simply by comparing the respective counts of the electrical pulses that were accumulated in two of the gating intervals over the series of the optical pulses. 
     As will be explained further hereinbelow, this approach is able to achieve high resolution in time of flight using only a small number of different gating intervals, due to the modulation of the delays between the optical pulses and the gating intervals. In fact, only two such gating intervals are required, although additional gating intervals can advantageously be used in order to measure and subtract out background components of the optical radiation that is incident on the detector array, for example due to stray photons and ambient radiation, as well as to enhance the temporal resolution. 
     System Description 
       FIG. 1  is a schematic side view of depth mapping apparatus  20 , in accordance with an embodiment of the invention. In the pictured embodiment, apparatus  20  is used to generate depth maps of an object  22 , for example a part of the body of a user of the apparatus. To generate the depth map, an illumination assembly  24  directs pulses of light toward object  22 , and an imaging assembly  26  captures the photons reflected from the object. (The term “light,” as used in the present description and in the claims, refers to optical radiation, which may be in any of the visible, infrared, and ultraviolet ranges; and pulses of light are equivalently referred to as “optical pulses.”) 
     Illumination assembly  24  typically comprises at least one pulsed laser  28 , which emits short pulses of light, with pulse duration in the picosecond to nanosecond range and high repetition frequency, for example 100 MHz or more. Collection optics  30  direct the light toward object  22 . Alternatively, other source configurations, pulse durations and repetition frequencies may be used, depending on application requirements. For example, illumination assembly may emit multiple pulsed beams of light along different, respective axes, so as to form a pattern of spots on object  22 . In this case, although the spatial resolution of apparatus  20  in the transverse plane may be reduced, the depth resolution can be enhanced by concentrating the histogram capture and processing resources of imaging assembly  26  in the areas of the spots. 
     Imaging assembly  26  comprises objective optics  32 , which image object  22  onto a sensing array  34 , so that photons emitted by illumination assembly  24  and reflected from object  22  are incident on the sensing array. In the pictured embodiment, sensing array  34  comprises sensing circuits  36  and ancillary circuits  38 . Sensing circuits  36  comprises an array of single-photon detectors  40 , such as SPADs, each of which outputs electrical pulses indicative of a time of incidence of a single photon that is incident on the sensing element. Ancillary circuits  38  comprises an array of processing circuits  42 , which are coupled respectively to the sensing elements. 
     Circuits  36  and  38  are disposed on a semiconductor substrate, which may comprise a single chip or two or more separate chips, which are then coupled together, for example using chip stacking techniques that are known in the art. Circuits  36  and  38  may be formed on one or more silicon wafers using well-known CMOS fabrication processes, based on SPAD sensor designs that are known in the art, along with accompanying counters and logic as described hereinbelow. Alternatively, the designs and principles of detection that are described herein may be implemented, mutatis mutandis, using other materials and processes. All such alternative implementations are considered to be within the scope of the present invention. 
     Imaging device  20  is timed to capture TOF information continually over a series of image frames, for example at a rate of thirty frames/sec. In each frame, processing circuits  42  count photons that are incident on detectors  40  in one or more gating intervals and store the respective counts in histogram bins corresponding to the gating intervals. A system controller  44  reads out the individual counter values, computes the times of flight of the optical pulses responsively to the counter values, and generates an output depth map, comprising the measured TOF—or equivalently, the measured depth value—at each pixel. The depth map is typically conveyed to a receiving device  46 , such as a display or a computer or other processor, which segments and extracts high-level information from the depth map. Controller  44  may also set imaging device to capture two-dimensional images, as is described further hereinbelow. 
     System controller  44  typically comprises a programmable processor, such as a microprocessor or embedded microcontroller, which is programmed in software or firmware to carry out the functions that are described herein. This software or firmware may be stored in tangible, non-transitory computer-readable media, such as optical, magnetic, or electronic memory media. 
     Alternatively or additionally, at least some of the processing functions of controller  44  may be carried out by hard-wired or programmable digital logic circuits. 
     Structure and Operation of the Sensing Array 
     Reference is now made to  FIGS. 2 and 3 , which are block diagrams showing details of detectors  40  and processing circuits  42 , in accordance with an embodiment of the invention.  FIG. 2  shows a super-pixel  50 , which comprises a group of detectors  40  that share certain processing circuits, as described below. Sensing array  34  typically comprises a matrix of many super-pixels of this sort. In the pictured example, super-pixel  50  comprises sixteen detectors  40 , which are mutually adjacent in array  34 ; but alternatively, array  34  may be divided into super-pixels comprising larger or smaller numbers of detectors.  FIG. 3  shows routing and aggregation logic, including a counter  58 , that is included in each processing circuit  42 . 
     As shown in  FIG. 3 , the electrical pulses output by each detector  40  are both input to a respective multiplexer and output via an aggregation line to the other processing circuits  42  in super-pixel  50 . Multiplexer  54  receives control signals (not shown) from routing and aggregation logic  52  ( FIG. 2 ), which control the aggregation mode of processing circuit  42 . For example, the aggregation lines and multiplexers in super-pixel  50  may operate in a first aggregation mode in which each counter  58  (or at least some of the counters) aggregates and counts the electrical pulses output by a respective first group of detectors  40 ; and this first group may be limited to the single, respective detector  40  that is coupled directly to processing circuit  42 . In a second aggregation mode, each counter  58  aggregates and counts the electrical pulses output by a second group of two or more of detectors  40 , typically including at least four detectors, and possibly all of the detectors in super-pixel  50 . 
     Routing and control logic  52  also receives and decodes gating instructions from system controller  44 , and accordingly outputs a gating signal to an AND gate  56  in each processing circuit  42 . The gating signal controls the periods, i.e., the gating intervals, during which each counter  58  aggregates and counts the electrical pulses that are output from detectors  40  via multiplexer  54 . System controller  44  typically synchronizes the gating intervals with the optical pulses emitted by illumination assembly  24 . In a particular embodiment that is described below, with reference to  FIGS. 5-7 , the gating intervals are synchronized with the optical pulses with a delay between the optical pulses and the gating intervals that is swept over a sequence of different delay times during a series of the optical pulses. 
     In some operating configurations, and particularly when operating in the second aggregation mode mentioned above, the gating signals cause different counters  58  in super-pixel  50  to aggregate and count the electrical pulses over different, respective gating intervals. As a result, the array of counters  58  will effectively output a histogram of the electrical pulses output by detectors  40  in super-pixel  50 , with each bin of the histogram defined by a corresponding gating interval. Thus, in the present example, routing and control logic  52  may configure the histogram to have anywhere from two to sixteen bins. Alternatively, the gating signals may be set (particularly in the first aggregation mode) so that all of counters  58  share the same gating interval. 
       FIG. 4  is a block diagram that schematically illustrates an operating configuration of super-pixel  50  in the second aggregation mode, in accordance with an embodiment of the invention. In this case, routing and control logic  52  has configured super-pixel  50  to generate a four-bin histogram: The outputs of all of detectors  40  in super-pixel  50  (labeled collectively as “SPAD events”) are aggregated and input to AND gates  56 , which are triggered by routing and control logic  52  to input the electrical pulses to respective counters  58  in different, respective gating intervals, at different respective delays relative to the optical pulses from illumination assembly  24 . Counters  58  are interconnected by an overflow line  64 , which stops all of the counters when one of them reaches saturation. 
     Based on the histogram generated by counters  58 , system controller  44  computes the times of flight of the optical pulses that are emitted from illumination assembly and reflected back to each super-pixel  50 . The system controller combines the TOF readings from the various super-pixels in array  34  in order to generate a 3D map of the target scene. In one embodiment, the system controller identifies an object of interest in the 3D map, for example object  22  ( FIG. 1 ), and then sets the gating interval for counters  58  so that processing circuits  42  acquire a 2D image of the object of interest. In this 2D imaging mode, the gating interval and multiplexers  54  are set, based on the depth of the object of interest in the 3D map, so that each counter  42  will count only the electrical pulses output by the corresponding detector  40  during the interval in which optical pulses reflected from object  22  are expected to reach the detectors. Sensing array  34  will thus output a high-resolution 2D image of object  22 , with low levels of background interference and noise. 
     In the embodiment shown in  FIG. 4 , another one of the AND gates, identified as gate  56 ′ (labeled “stray”), is triggered to input electrical pulses from detectors  40  to a counter  58 ′. The gating interval applied to gate  56 ′ is selected so that counter  58 ′ receives and counts electrical pulses that are indicative of a background component of the optical radiation that is incident on detectors  40 . In computing the time of flight, system controller  44  uses the value of counter  58 ′ in compensating for the background component, and thus improving the accuracy of the histogram analysis. 
     For example, the gating interval applied to gate  56 ′ can be synchronized with the optical pulses emitted by illumination assembly  24  so that counter  58 ′ counts stray photons in the optical pulses that are incident on super-pixel  50  without having reflected from the target scene (in some cases due to photons with very short times of flight as a result of internal reflections within apparatus  20 ). Alternatively or additionally, the gating interval applied to gate  56 ′ may be chosen to occur at a time during which optical pulses from illumination assembly are not expected to reach sensing array  34 , for example at a long delay after emission of the pulses. In this case, the electrical pulses counted by counter  58 ′ are indicative of the intensity of ambient optical radiation that is incident on super-pixel  50 . Although only one background counter  58 ′ is shown in  FIG. 4 , two or more such counters may alternatively be allocated in order to count both stray and ambient optical intensities. 
     TOF Measurement Using Modulated Gating Delays 
       FIG. 5  is a timing diagram that schematically illustrates a method for measuring TOF to a target scene, in accordance with an embodiment of the invention. This method, as well as the methods illustrated in the figures that follow, will be described, for the sake of concreteness and clarity, with reference to the elements of apparatus  20 , as described above and shown in the preceding figures. The principles of this embodiment, however, may similarly be applied using other sorts of sensing arrays with suitable gating and counting capabilities. 
     Specifically,  FIG. 5  shows a series  70  of optical pulses  72  that are directed toward a target scene, such as object  22 . The optical pulses are reflected from the target scene, giving rise to a corresponding series of reflected pulses, referred to as “echoes”  74 , which are imaged onto super-pixels  50  in sensing array  34 . When echoes  74  are incident on a given super-pixel  50 , detectors  40  output corresponding electrical pulses with a delay, relative to the corresponding optical pulses  72 , that is equal to the TOF of the optical pulses to and from the target scene. 
     Counters  58  are gated to count the electrical pulses output by the single photon detectors in multiple different gating intervals, which are synchronized with each of the optical pulses at different, respective delays relative to the optical pulses. The gating intervals are represented in  FIG. 5  by corresponding bins  76  and  78 , which hold the counts of the aggregated electrical pulses that are accumulated by the corresponding counters  58 . Two additional bins  80  and  82  hold the counts of photons due to ambient and stray radiation, respectively, as explained above. Bin  82  receives echoes  84  occurring in close time proximity to each of optical pulses  72 , substantially less than the expected TOF to the target scene. 
     The delays of bins  76  and  78  relative to optical pulses  72  are not fixed, but rather are swept over a sequence of different delay times during series  70  of the optical pulses. (In  FIGS. 5-7 , for clarity of illustration, the emission times of pulses  72  are shown as varying, while bins  76  and  78  are stationary, but the modulation of the delay times could equivalently be shown in terms of varying bin times relative to a stationary pulse time.) Bins  76  and  78  are synchronized at different, respective delays relative to optical pulses  72 . The difference between the respective delays of bins  76  and  78  remains fixed, while both delays are swept over the sequence of different delay times during the series of the optical pulses. 
     In the specific scheme that is shown in  FIG. 5 , the durations of the gating intervals of bins  76  and  78  are both set to correspond to the maximum range of the target scene that is to be mapped by apparatus  20 , with bin  78  beginning upon termination of bin  76 . In other words, the temporal width of each bin  76 ,  78  is equal to the TOF of the optical pulses at the maximum range. Taking this maximum TOF to be T, the number of optical pulses  72  in series  70  to be N, and the additional dead time between successive optical pulses  72  to be D (due, inter alia, to the time needed by detectors  40  to recover after having output an electrical pulse), the pulse repetition interval (PRI) of the optical pulses is set to be PRI=2T+D+T/N+S. (The parameter S≥0 is chosen to account for dead time variation, control the average power of the pulsed illumination, and prevent range folding. Furthermore, S may be varied among successive series of pulses in order to mitigate the effects of electromagnetic and optical interference on other devices in the vicinity of apparatus  20 .) 
     Thus, as shown in  FIG. 5 , series  70  spans the duration of bin  76  (which is equal to the duration of bin  78 , as noted above). As a result of these choices of the durations of series  70  and bins  76  and  78 , the photons in optical pulses  72  that are reflected from the target scene are incident on detectors  40  only during the gating intervals of bins  76  and  78   
     System controller  44  computes the TOF for super-pixel  50  by comparing the respective counts of the electrical pulses in bins  76  and  78  over series  70  of optical pulses  72 . Specifically, in the present case, the system controller subtracts the ambient count in bin  80  from the counts in both of bins  76  and  78 , and also subtracts the stray count in bin  82  from the count in bin  76 , thus canceling out the background effects of ambient light and stray reflections. After subtracting these background components, system controller  44  computes the ratio R of the remainder of the count in bin  78  to the remainder of the count in bin  76 . The TOF is proportional to the ratio, i.e., TOF=R*T. This approach enables system controller  44  to find depth coordinates with high resolution, even using only two bins for count accumulation. 
       FIG. 6  is a timing diagram that schematically illustrates a method for measuring TOF to a target scene, in accordance with another embodiment of the invention. The principles of this method are similar to those of  FIG. 5 , except that in this case, the gating intervals of counters  58  in super-pixel  50  are set so as to define a larger number of successive bins  90  in which the electrical pulses from detectors  40  are aggregated, in order to enhance the resolution of the TOF measurement. 
     In the embodiment of  FIG. 6 , echoes  74  may be distributed over M+1 bins, wherein in the present example M=4 (in addition to background bins  80  and  82 ). The duration of the gating interval of each bin  90  is T/M. The PRI of optical pulses  72  in this case is set to the value 
     
       
         
           
             PRI 
             = 
             
               
                 
                   
                     M 
                     + 
                     1 
                   
                   M 
                 
                  
                 T 
               
               + 
               
                 T 
                 
                   M 
                    
                   N 
                 
               
               + 
               D 
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                 S 
                 . 
               
             
           
         
       
     
     In the pictured example, the range of the target scene is such that echoes  74  are divided between bin  3  and bin  4 , and the ratio of the counts in these bins (after subtraction of the ambient background) gives the TOF relative to the start time of bin  3 . 
       FIG. 7  is a timing diagram that schematically illustrates a method for measuring TOF to a target scene, in accordance with yet another embodiment of the invention. This embodiment is similar to the embodiment of  FIG. 6 , except that in this case the counts of electrical pulses are aggregated in successive bins  92  with respective gating intervals that partially overlap one another. In other words, the initial part of each gating interval overlaps with the final part of the preceding gating interval. 
     The overlap in this embodiment reflects the fact that optical pulses  72  have a finite width. The overlap between the gating intervals of successive bins is typically on the order of the pulse width. In this case, the simple ratio formula presented above is not strictly accurate. The precise relation between the numbers of counts in the bins and the corresponding time of flight can be estimated, for example, using a maximum likelihood analysis or a suitably trained neural network. System controller  44  compares the counts in the various bins  92  using this relation, and thus computes the TOF for each super-pixel  50 . 
     It will be appreciated that the embodiments described above are cited by way of example, and that the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and subcombinations of the various features described hereinabove, as well as variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art.