Fig. 1. The QIS conceptual illustration. An 8 × 8 × 4 spatial-temporal data cube of jots in the QIS (left) is reconstructed to a 2 × 2 data plane of pixels in the output image (right). Each data of pixels is equal to the sum of a 4 × 4 × 4 data sub-cube of jots.

Fig. 2. The signal chain model of quanta image sensors.

Fig. 3. (Color online) The PDF P[U_RO] as a function of U_RO on the condition that μ_e = 2 e- and u_n = 0.2 e- r.m.s.. N₀, N₁, N₂, and N₃ are four quantization levels corresponding to 0, 1, 2, and 3 ADU for a 2-bit QIS. The dashed lines are three quantization boundaries corresponding to 0.5, 1.5, and 2.5 e- for a 2-bit QIS.

Fig. 4. (Color online) The ideal D-logH response curves for 1-bit to 5-bit QISs in solid lines. And the ideal linear response curves for 1-bit to 5-bit CISs in dashed lines.

Fig. 5. (Color online) The realistic response curves for the 3-bit QIS. The different conditions of curve 1 to 5 are listed in Table 2.

Fig. 6. (Color online) The photon counting signal error rate SER_ph as a function of the mean value of incident photons μ_ph for ideal 1-bit to 5-bit QISs.

Fig. 7. (Color online) The photon counting signal error rate SER_ph as a function of the mean value of incident photons μ_ph for the 3-bit QIS. The five conditions of curve 1 to 5 are listed in Table 2.

Fig. 8. (Color online) The photoelectron counting signal error rate SER_phe as a function of the mean value of incident photons μ_ph for the 3-bit QIS. The five conditions of curve 1 to 5 are listed in Table 2.

Fig. 9. The conceptual illustration of the Airy disk and jot array. The Airy disk diameter D_A = 3.8 μm, the jot area A_jot = 1 μm² (left) and A_jot = 0.25 μm² (right).

Fig. 10. (Color online) The photon counting signal error rate SER_ph as a function of the mean value of incident photons μ_ph for 1-bit to 5-bit QISs based on the parameters listed in Table 3.

Fig. 11. (Color online) The photoelectron counting signal error rate SER_phe as a function of the mean value of incident photons μ_ph for 1-bit to 5-bit QISs based on the parameters listed in Table 3.

Fig. 12. (Color online) The relationship between jot area A_jot, the mean value of incident photons μ_ph, and integration time τ under different illuminance level I_lux for the 3-bit QIS in Fig. 11. (a) I_lux = 0.1 lux. (b) I_lux = 1 lux. (c) I_lux = 10 lux. (d) I_lux = 100 lux. (e) I_lux = 1000 lux. (f) I_lux = 10 000 lux.

Table 1. The parameters of the signal chain model in Fig. 2.

Table 2. Different conditions for realistic QISs in Figs. 5, 7, and 8.

Table 3. The correlation parameters of the QIS chip in Ref. [16].