# Single Photon Counting Performance and Noise Analysis of CMOS SPAD-Based Image Sensors
## 6 Spatio-Temporal Oversampling of Photon Counting Pixels
### Single Photon Binary Quanta Imaging  
Using SPAD-based single photon image sensors with binary response, a variety of oversampling techniques have been evaluated in our recent work [16; 17; 18; 19] and in the work of others [14; 39]. \"Field\" images are individual reads from the image sensor and the oversampled frame is a summation of fields. The simplest technique in order to oversample a set of binary single photon field images, is to temporally or spatially sum a set of input binary pixel (or \"jot\") values, to create an output \"macro\" pixel with grey levels. This is the equivalent operation of a first-order low-pass infinite impulse response (IIR) filter with a periodic filter reset operation as shown in Figure 7a. Considerin temporal oversampling only (as demonstrated in [17]), to achieve a certain output frame rate in FPS, with oversampled ratio OSR and input binary field rate f, the output rate is: FPS =_f_/OSR and inversely the IIR reset period = OSR/_f_, thus attaining an output bit depth of B = Log2(OSR), increasing the image bit depth by a factor of OSR or 2B. It is clear that to attain frame rates \(>\)30 FPS, at bit depths B \(>\) 5 bit, a high field rate_f_\(>\) 1 k fields/s is required from the sensor. In [17], we demonstrated 7b bit depth at 40 FPS, and 8b at 20 FPS with 5.12 k global shutter fields per second. SPADs with picosecond temporal precision enable Indirect Time of Flight (ITOF) imaging to be performed. Previous examples are pulsed ITOF using analogue pixels [33] and continuous wave ITOF  
Figure 7: Per-pixel spatio-temporal oversampling techniques. (**a**) Intensity image using IIR with periodic reset [17]; (**b**) Time-resolved image: four IIR per pixel [18]; (**c**) High frame rate intensity image using first-order FIR per pixel [19]. using digital pixels [40]. However, both approaches had very large pixel pitch and low fill factor. A similar oversampling technique was applied in [18] with compact binary SPAD pixels, to investigate time-gated binary image oversampling to produce a high resolution QVGA Indirect Time of Flight (ITOF) output image as shown in Figure 7b. Two primary gated field images (A & B) are sequentially captured in interleaved fashion synchronous to a pulsed laser. Two secondary gated images (A' & B') are set with the same time-gate without the laser for background removal. With four field images, the output time-resolved frame rate is therefore a quarter of the previous intensity-only technique (assuming a pipelined division operation). A third technique in [19], addresses the low frame rate, and evaluates a continuous-time moving average operation by applying a first-order low-pass finite impulse response (FIR) filter. As shown in Figure 7c, the FIR is implemented as a shift-register of length equal to the over-sampling ratio (i.e., a FIR with number of taps = OSR) and a tracking counter. The benefit of this technique is the output frame rate has no relationship with the OSR and is equal to the input field rate of the sensor. The frame rate increase over the IIR technique is at the cost of the shift register per pixel. Longer integration time increases temporal blur, therefore, higher OSR increases image lag of fast moving scene elements. On the other hand, an increased bit depth (from greater OSR) decreases quantisation noise in areas of slow movement in an imaged scene. We compare our recent work in this area, to two others demonstrating high binary field rates with column parallel single bit flash ADCs for single bit QIS in Table 3. In a 3T CIS implementation [41], amplification and CDS is employed and suitable for pixels with low signal swing (i.e., CVF \(\leq\) input-referred offset and read noise). In our work [16] and another SPAD-based example [42], no CDS or column amplifier circuits are required as the pixel sensitivity is >1 V/SPAD event which is much greater than offsets and RN. The RN and non-linear exposure characteristics of such oversampled binary imagers are theoretically described in [9] and experimentally confirmed in our work in [16; 18].