  In psychophysics (without access to physiological measurements at retina and
the behaviourally relevant stages within the visual system), early and late
noise in within the visual system seem hard to tell apart because
discrimination depends on the inner noise or effective noise which is a
non-trivial combination of early and late noises. In this work we analyze this
combination in detail in nonlinear vision models and propose a purely
psychophysical methodology to quantify the early noise and the late noise. Our
analysis generalizes classical results from linear systems (Burgess and
Colborne, 1988) by combining the theory of noise propagation through a
nonlinear network (Ahumada, 1987) with the expressions to obtain the perceptual
metric along the nonlinear network (Malo and Simoncelli, 2006; Laparra,
Mu\~noz, and Malo, 2010). The proposed method shows that the scale of the late
noise can only be determined if the experiments include substantial noise in
the input. This means that knowing the magnitude of early noise is necessary as
it is needed as a scaling factor for the late noise. Moreover, it suggests that
the use of external noise in the experiments may be helpful as an extra
reference. Therefore, we propose to use accurate measurements of pattern
discrimination in external noise, where the spectrum of this external noise was
well controlled (Henning, Bird, and Wichmann, 2002). Our psychophysical
estimate of early noise (assuming a conventional cascade of linear+nonlinear
stages) is discussed in light of the noise in cone photocurrents computed via
accurate models of retinal physiology (Brainard and Wandell, 2020). Finally, in
line with Maximum Differentiation (Wang and Simoncelli, 2008), we discuss how
to the proposed method may be used to design stimuli to decide between
alternative vision models.
