**Chromatic sensitivity cannot exceed limits set by noise in the cone photoreceptors. To determine how close neurophysiological and psychophysical chromatic sensitivity come to these limits, we developed a parameter-free model of stimulus encoding in the cone outer segments, and we compared the sensitivity of the model to the psychophysical sensitivity of monkeys performing a detection task and to the sensitivity of individual V1 neurons. Modeled cones had a temporal impulse response and a noise power spectrum that were derived from in vitro recordings of macaque cones, and V1 recordings were made during performance of the detection task. The sensitivity of the simulated cone mosaic, the V1 neurons, and the monkeys were tightly yoked for low-spatiotemporal-frequency isoluminant modulations, indicating high-fidelity signal transmission for this class of stimuli. Under the conditions of our experiments and the assumptions for our model, the signal-to-noise ratio for these stimuli dropped by a factor of ∼3 between the cones and perception. Populations of weakly correlated V1 neurons narrowly exceeded the monkeys' chromatic sensitivity but fell well short of the cones' chromatic sensitivity, suggesting that most of the behavior-limiting noise lies between the cone outer segments and the output of V1. The sensitivity gap between the cones and behavior for achromatic stimuli was larger than for chromatic stimuli, indicating greater postreceptoral noise. The cone mosaic model provides a means to compare visual sensitivity across disparate stimuli and to identify sources of noise that limit visual sensitivity.**

*Macaca mulatta*monkeys were used in the V1 recording and behavioral experiments. Behavioral data only were obtained from two others (one male, one female). We obtained isolated retinas of macaque monkeys (

*M. mulatta*

*,*

*M. nemestrina*, and

*M. fascicularis*) through the Tissue Distribution Program of the Washington National Primate Research Center. All procedures conformed to the guidelines provided by the US National Institutes of Health, the University of Washington's Animal Care and Use Committee, and the Association for Research in Vision and Ophthalmology.

**Figure 1**

**Figure 1**

*L*represents the difference in L-cone excitation between the maximum of the Gabor and the background, and

*L*

_{b}represents the L-cone excitation due to the background.

*l*,

_{i}*m*, and

_{i}*s*specify the cone weights to the

_{i}*i*th visual mechanism. The parameter

*ψ*determines the degree of interaction among the mechanisms. Fitting was performed by minimizing the squared log of the difference between the actual and predicted thresholds.

*n*= 6). The kinetics of the modeled cone responses were taken from a single cone whose temporal IRF was representative of those studied.

*A*

_{ret}is the area of a retinal region,

*θ*is the angle of elevation subtended by a single pixel of the Gabor stimulus, and

*F*

_{post}is the distance between the nodal point and the retina, which was set to 12.75 mm (Lapuerta & Schein, 1995; Qiao-Grider, Hung, Kee, Ramamirtham, & Smith, 2007). We assume that each pixel of the Gabor stimulus projects onto the same retinal area regardless of eccentricity. We ignore both blurring of the image as it passes through the eye's optics and eye movements that displace the stimulus on the retina during visual fixations (Banks, Geisler, & Bennett, 1987; Campbell & Gubisch, 1966; Hass & Horwitz, 2011; Martinez-Conde, Macknik, & Hubel, 2004). These assumptions are reasonable for the low-spatial-frequency stimuli we focus on here.

*x*is the eccentricity (in degrees of visual angle) at the center of each retinal region. After determining the number of cones in each retinal region, we determined their type (i.e., L-, M-, or S-cones). The number of S-cones per degree of visual angle was determined using published estimates of S-cone density in the macaque temporal retina (De Monasterio, McCrane, Newlander, & Schein, 1985), and the remaining cones were allocated equally to the L- and M-cone classes (Jacobs & Deegan, 1999). The two monkeys investigated most intensively (Monkeys S and K) had flicker thresholds consistent with a ∼1:1 ratio of L- to M-cones (Lindbloom-Brown et al., 2014). The number of cones computed this way was doubled to account for the fact that the monkeys viewed the stimulus through both eyes. Human subjects performing similar tasks use information from both eyes to detect the stimulus, but appear to combine inputs using a binocular contrast-energy calculation (Legge, 1984a, 1984b). The ideal observer, however, combines signals via linear summation. A detection model using a binocular energy calculation performed nearly as well as the linear ideal observer of the cones that we used (data not shown).

_{(}

_{λ}_{)}is the emission spectrum of a CRT phosphor measured at its maximum intensity. The number of steradians subtended by the pupil was calculated by dividing pupil area by the square of the eye's diameter. Pupil area (12.6 mm

^{2}) was measured using an optical eye tracker (iView X Hi-Speed Primate, SensoMotoric Instruments, Teltow, Germany). The eye's diameter was set to 19 mm following published values (Lapuerta & Schein, 1995; Qiao-Grider et al., 2007). Multiplying by 10

^{−12}converts watts per square meter into watts per square micrometer.

*m*

_{(}

_{λ}_{,}

_{x}_{)}was calculated by converting the Wyszecki and Stiles (1982) absorbance function into transmittance adjusted for the eccentricity dependence of macular-pigment density: where

*m*

_{(}

_{λ}_{)}is the macular-pigment absorbance spectrum, which was scaled to have a value of 0.35 at 460 nm at 0° of eccentricity (Snodderly, Auran, & Delori, 1984; Stockman, MacLeod, & Johnson, 1993; Wooten & Hammond, 2005). We calculated

*m*

_{(}

_{λ}_{,}

_{x}_{)}at a single eccentricity

*x*defined by the center of the Gabor stimulus. The lens transmittance function

*t*

_{(}

_{λ}_{)}was based on published estimates of lens optical density (Stockman et al., 1993), scaled to 10% transmittance at 400 nm (Lindbloom-Brown et al., 2014).

*A*

_{(}

_{λ}_{)}by a photopigment optical density of 0.3 (Stockman et al., 1993) and converting absorbance to absorptance via the Beer–Lambert equation:

^{2}; Baylor et al., 1984; Schneeweis & Schnapf, 1999).

*L*

_{(}

_{x}_{,}

_{y}_{,}

_{t}_{)}represents the linear response of a single cone in the retinal region defined by the stimulus pixel at location (

*x*,

*y*) at time

*t*, in picoamperes. The variable

*G*

_{(}

_{x}_{,}

_{y}_{,}

_{t}_{)}represents the Gabor stimulus in R* per second. We denote by

*γ*a scale factor that is unique to each cone type and scales the linear response to account for adaptation due to the background; it followed a Weber–Fechner relationship with a half-desensitization constant of 2250 R* and a dark sensitivity of 0.32 pA/R* (Angueyra & Rieke, 2013; note that the half-desensitization constant here corrects a calibration error and hence differs from that originally reported). The Gaussian noise component was shaped to match the measured power spectrum of cone noise (Figure 1C).

_{sig}of the pooled response by projecting the linear response of the cones onto a spatiotemporal weighting function

*wt*and summing across space and time:

_{noise}of the pooled response was computed as the dot product of the weighting function (Figure 1E) and a noise vector whose temporal statistics were given by the measured cone-noise power spectrum (Figure 1C). We are primarily interested in the sensitivity of the ideal observer across many repeated trials, so instead of computing PR

_{noise}on individual trials, we compute the variance of this quantity across trials. The variance of the dot product of the noise

*ε*onto the weight function

*wt*can be written as where Σ

*is the covariance matrix of the noise. This matrix multiplication is computationally intensive in the time domain but relatively simple in the Fourier domain, where it can be written as with*

_{ε}*N*denoting the number of frequencies,

*WT*the Fourier transform of the weighting function, * complex conjugation, and Σ

*the covariance matrix of the Fourier coefficients, which is a diagonal matrix whose diagonal elements E*

_{E}_{(}

_{f}_{)}correspond to the cone-noise power spectrum (Leon-Garcia, 1994). This expression can be rewritten as the sum of element-wise products: where E

_{(}

_{f}_{)}is the cone-noise power spectrum. Equation 15 defines the variance of a single cone's response after weighting the response by the spatiotemporal weighting function. Assuming independence across cones, we sum variances within and across retinal subregions to calculate the noise of the pooled response:

_{sig}and variance PR

_{noise}(Figure 1F).

*G*

_{(}

_{x}_{,}

_{y}_{,}

_{t}_{)}in Equation 11. The actual number of photon catches was assumed to follow a Poisson distribution with this time-varying rate. The photon-observer model differs from the photocurrent model in two key respects: First, it is equally sensitive across temporal frequencies, whereas the photocurrent model is relatively insensitive to high temporal frequencies. Second, variance in photon catches is assumed to be equal to the mean, whereas photocurrent noise is assumed to be additive and independent of the mean.

*G*

_{(}

_{x}_{,}

_{y}_{,}

_{t}_{)}in Equation 11—had a contrast of 0.

*cc*is the cone contrast of the stimulus,

*α*is the contrast at detection threshold, and

*β*defines the slope of the neurometric function. The Weibull function was chosen for consistency with our earlier comparison of V1 neuronal and psychophysical chromatic sensitivity (Hass & Horwitz, 2013).

**Figure 2**

**Figure 2**

*R*

^{2}= 0.98,

*n*= 6; Figure 2B). Fitting this relationship with nonlinear models improved the correlation between the model predictions and data by at most a few percent (see Methods).

*R*

^{2}= 0.93; Figure 2C). Cone responses to high-contrast (≥50%) stimuli showed clear deviations from linearity (data not shown); cone contrasts at behavioral threshold, however, were usually below 20%. Thus, for near-threshold chromatic stimuli, cone signals were close to linear and could be accurately estimated by convolving the stimulus with the IRF.

*M*±

*SD*correlation coefficient

*R*= −0.018 ± 0.13,

*n*= 4). This lack of correlation demonstrates that the noise can be modeled as additive under the conditions of our measurements (Figure 2D, inset). The power spectrum of the residual currents closely matched the power spectrum of the currents recorded during a baseline period, as expected from additive, stimulus-independent noise (Figure 2D).

**Figure 3**

**Figure 3**

**Figure 4**

**Figure 4**

**Figure 5**

**Figure 5**

*SD*= 0.5°), as expected at the eccentricities from which we recorded (Cavanaugh, Bair, & Movshon, 2002). When given access only to the cones inside these receptive fields, the photocurrent ideal observer was 12.5 times more sensitive than the V1 neurons (Figure 6A). With this restriction, the sensitivity relationship between the photocurrent ideal observer and V1 neurons was similar to that between the photocurrent ideal observer and the monkey's behavior (Figure 6B). A direct comparison between the monkeys' thresholds and those of V1 neurons confirmed a close match (Figure 6C). On average, V1 thresholds were a factor of ∼1.6 higher than the monkeys' in all four color directions.

**Figure 6**

**Figure 6**

*pooled*output of the cone mosaic, but the ideal observer of V1 considers only

*individual*neurons. Pooling the responses of V1 neurons would increase their collective sensitivity, but the joint distribution of spiking responses among V1 neurons is unknown, and the number of V1 neurons that could meaningfully contribute to a perceptual decision is poorly constrained by available data. Nevertheless, a simple model provides insight into the signal-to-noise ratio of such a pool.

*M*neurons, each of which responds with a mean

*μ*and a standard deviation

*σ*to the stimulus. The

*d*′ of the pooled response can be calculated as

*r*of 0.2, the

*d*′ of a pool of 10 neurons is 1.9 times higher than an individual neuron's

*d*′ and 1.2 times higher than the monkey's

*d*′ (under the conditions of our experiment, the monkey was 1.6 times more sensitive than an individual V1 neuron; see Figure 6C). The photocurrent ideal observer was ∼11 times more sensitive than the monkey under the conditions of our V1 experiments (Figure 6B) and was therefore ∼9 times more sensitive than this V1 pooling model. As the V1 pool is made larger, the

*d*′ of the pool increases to an asymptote that is 1.4 times higher than the monkey's

*d*′ but still 3.9 times lower than the photocurrent ideal observer's

*d*′. The

*d*′ of the V1 pool is therefore closer to the

*d*′ of the monkey than it is to that of the photocurrent ideal observer, implying a substantial noise source between the cone outer segments and the recorded V1 neurons. This interpretation is consistent with the observation that detection thresholds of monkeys and an ideal observer of V1 population responses differ by a factor of ≤2 (Chen, Geisler, & Seidemann, 2006).

*, 22, 420–426.*

*Ophthalmic and Physiological Optics**, 442 , 47–64.*

*Journal of Physiology**, 16 , 1692–1700.*

*Nature Neuroscience**, 27, 1915–1924.*

*Vision Research**, 8, 1775–1787.*

*Journal of the Optical Society of America A**Macaca fascicularis*.

*, 357, 575–607.*

*Journal of Physiology**Macaca fascicularis*.

*, 390, 145–160.*

*Journal of Physiology**, 12, 4745–4765.*

*Journal of Neuroscience**, 211 , 321–339.*

*Proceedings of the Royal Society B Biological Sciences**, 186, 558–578.*

*Journal of Physiology**, 111, 2752–2757.*

*Proceedings of the National Academy of Sciences, USA**, 88, 2530–2546.*

*Journal of Neurophysiology**, 361, 348–350.*

*Nature**, 9, 1412–1420.*

*Nature Neuroscience**, 10, 38–51.*

*Journal of the Optical Society of America A**, 392, 193–211.*

*Journal of Physiology**, 31, 139–151.*

*Visual Neuroscience**, 70, 121–123.*

*Journal of the Optical Society of America**, 29, 349–360.*

*Vision Research**, 96 , 267–314.*

*Psychological Review**Callithrix jacchus*.

*, 366, 55–75.*

*Journal of Comparative Neurology**. New York: Wiley.*

*Signal detection theory and psychophysics**, 109, 2483–2494.*

*Journal of Neurophysiology**, 15, 913–919.*

*Nature Neuroscience**, 266, 2023–2028.*

*Proceedings of the Royal Society of London, Series B: Biological Sciences**, 4, 409–416.*

*Nature Neuroscience**, 64, 983–990.*

*Journal of the Optical Society of America**, 29, 657–670.*

*Journal of the Optical Society of America A**, 35, 2245–2254.*

*Vision Research**, 414, 223–243.*

*Journal of Physiology**, 10, 1403–1412.*

*Journal of the Optical Society of America A**, 24, 373–383.*

*Vision Research**, 24, 385–394.*

*Vision Research**Probability and random processes for electrical engineering*(2 ed.).

*Reading, MA: Addison-Wesley Reading*.

*, 112, 3164–3172.*

*Journal of Neurophysiology**, 33, 2321–2336.*

*Vision Research**, 11, 3113–3122.*

*Journal of the Optical Society of America A**, 5, 229–240.*

*Nature Reviews Neuroscience**, 9, 776–783.*

*Journal of Neuroscience**, 359 , 381–400.*

*Journal of Physiology**, 19, 109–118.*

*Visual Neuroscience**, 34, 951–959.*

*Perception**Macaca nemestrina*).

*, 288, 165–183.*

*Journal of Comparative Neurology**Macaca mulatta*).

*, 47, 1424–1444.*

*Vision Research**, 39, 2387–2398.*

*Vision Research**Macaca fascicularis*.

*, 427, 681–713.*

*Journal of Physiology**, 19, 1203–1216.*

*The Journal of Neuroscience**, 10, 2118–2133.*

*Journal of the Optical Society of America A**, 10, 2491–2521.*

*Journal of the Optical Society of America A**, 25, 219–237.*

*Vision Research**, 586, 5947–5967.*

*Journal of Physiology**, 219, 191–193.*

*Science**, 33, 113–120.*

*Perception & Psychophysics**, 90, 9770–9777.*

*Proceedings of the National Academy of Sciences, USA**, 82, 378–386.*

*Optometry & Vision Science**. New York: Wiley.*

*Color science**, 370, 140–143.*

*Nature*