Fig. 1: Linear and nonlinear dim light detection models exhibit fundamentally different performance characteristics for detection and discrimination tasks.
From: Primate retina trades single-photon detection for high-fidelity contrast encoding
a The classical dim light detection model assumes linear retinal processing and that behavioral sensitivity is only limited by noise and potentially a downstream thresholding mechanism beyond the retina. The post-retinal nonlinearity is adjustable allowing a tradeoff between sensitivity and false-positive rate. With the most lenient criterion (=highest false-positive rate), this nonlinearity disappears and perception has access to each absorbed photon4. b The new model, in turn, postulates that behavioral sensitivity is fundamentally limited by a thresholding mechanism along the retinal ON pathway and that the linear OFF pathway does not contribute to this detection task, but serves other visual functions (denoted by question mark). c, d The presence of thresholding nonlinearities can be observed by evaluating the dimmest light increment needed for detection (blue) and discrimination (red) of dim lights in a two-alternative forced choice (2AFC) setting. Linear processing (c) allows an ideal observer to access all isomerization events (R*; Poisson distributed signals): S1 (mean = 4 R*), S2 (mean = 8 R*) and S3 (mean = 12 R*) and noise N (mean = 2 R*), whereas a threshold (6 R*) (d) restricts access to the events that surpass the threshold. e, f Ideal 2AFC performance for detection (blue) of a dim flash against a background noise (N), and for discriminating (red) a probe flash from a reference flash (S1). For linear processing (e), detection is easier than discrimination (quantified by the just noticeable difference; \(\varDelta {I}_{{{{{{\rm{JND}}}}}}}\)), whereas the situation is reversed for nonlinear processing (f; the blue curve is now on the right side of the red one). g, h The ΔIJND as a function of the reference flash intensity: the detection task (blue dot) corresponds to blank reference flash. The dotted black line shows the theoretical performance limit set by quantum fluctuations in the number of stimulus photons. The dip in h occurs approximately at a reference intensity of 4 R*, as 4 additional R*s are needed to surpass a threshold of 6 R* when the noise level is 2 R*. Source data are provided as a Source Data file.
