Interactions between receptor-isolating rod and long (L)- or middle (M)-wavelength-sensitive cone modulations at 2 Hz and 10 Hz were analyzed in terms of underlying inferred magnocellular (MC) and parvocellular (PC) postreceptoral pathways. Stimuli originated from a colorimeter with 4 primaries in both the center and surround fields. The first experiment employed a phase paradigm in which the thresholds for mixed rod and cone modulations were measured as a function of relative phase. The amplitudes of the rod and cone modulations, equated in threshold units, were varied in tandem. In the second experiment, thresholds for mixed rod and cone modulations were measured as a function of the ratio of the rod and cone modulation amplitudes for 2 fixed phase offsets. Both experiments yielded similar interpretations of rod and L- (or M-) cone interactions. At 1 and 10 troland (td), rod and L- (or M-) cone interactions varied depending on the postreceptoral pathways underlying the detection. When cone thresholds were mediated by the inferred MC pathway, rod and cone thresholds showed almost linear summation. When cone thresholds were mediated by the inferred PC pathway, rod and cone thresholds showed probability summation. Assuming that signals within the same pathway follow linear summation, and signals traveling in different pathways follow probability summation, we concluded that the rod thresholds were mediated by the inferred MC pathway for both the 2-Hz and 10-Hz conditions.

*V*’(λ), and the L, M and S cone spectral sensitivities by the Smith-Pokorny transformation (Smith & Pokorny, 1975) applied to the 1964 10° color-matching functions (Shapiro, Pokorny, & Smith, 1996a). In a previous study of temporal modulation sensitivity (Sun, Pokorny, & Smith, 2001b), we established that the rod- and cone-isolating stimuli appeared uniform in the 6° center and gave temporal contrast sensitivity functions characteristic of the rod, S cone, or L (or M) cone.

*f*is the temporal modulation frequency, θ

_{rod}is the phase of the rod modulation, and

*C*is threshold contrast of the rod modulation. The response to the rod stimulus

_{rod-threshold}*A*at the locus in the visual system where the rod and cone signals combine can be written as where Φ

_{rod}_{rod}is the physiological phase of the rod response.

_{cone}is the phase of the cone modulation, and

*C*is threshold contrast of the cone modulation. The response to the cone stimulus

_{cone-threshold}*A*at the locus in the visual system where the rod and cone signals combine can be written as where Φ

_{cone}_{cone}is the physiological phase of the cone response.

_{cone}can be replaced by the physical phase offset between rod and cone stimuli θ

_{rod-cone}.

*A*to the mixed rod and cone modulations can be written as and the threshold ratio of mixed rod and cone modulation to rod modulation alone is determined by the ratio of the response amplitudes where θ

_{rod+cone}_{rod-cone}is the independent variable in the template. Φ

_{rod}-Φ

_{cone}represents the physiological phase delay between rod and cone responses, and it is a free parameter that allows the template to shift horizontally. Both the shape and the vertical position of the template are fixed.

*P*is given by where

_{rod+cone}*P*and

_{rod}*P*are the probability of detecting rod modulation and cone modulation.

_{cone}*P*and

_{rod}*P*represent two points on the psychometric functions of rod and cone modulation, respectively. If rod and cone thresholds show probability summation, the ratio of mixed rod and cone modulation threshold to rod threshold alone

_{cone}*C*/

_{rod+cone}*C*must be smaller than 1. The exact value of the threshold ratio depends upon the slopes of the psychometric functions. If rod and cone signals follow probability summation, the rod and cone phases should have no effect on the threshold.

_{rod}Threshold Contrast (%) | |||||||
---|---|---|---|---|---|---|---|

Subject | Frequency (Hz) | Retinal Illuminance (td) | L cone | M cone | Luminance | Chromatic | Rod |

2 | 1 | 3.19 | 3.37 | 9.77 | 2.59* | 7.61 | |

2 | 10 | 1.69 | 2.05 | 2.75 | 1.09* | 7.65 | |

10 | 1 | 15.23 | 16.05 | 12.12* | 6.05 | ||

10 | 10 | 2.20 | 5.69 | 2.09* | 10.17 | 3.83 | |

2 | 1 | 7.18 | 7.68 | 11.37 | 5.69* | 10.20 | |

2 | 10 | 2.16 | 2.85 | 3.67 | 2.47* | 6.64 | |

10 | 1 | 17.12* | 10.85 | ||||

10 | 10 | 5.92 | 4.92 | 3.80* | 7.80 | 5.57 |

_{F}< .01, except for the 10-td, L-cone condition for S.G. where P

_{F}< .05. We, therefore, show the probability summation fits for the 2-Hz data and linear summation fits for the 10-Hz data.

*P*

_{F}< .01) and for S.G. at 10 Hz (

*P*

_{F}< .05). The linear summation fits are shown for luminance and rod modulation at both 2 Hz and 10 Hz. For the luminance data at 2 Hz for S.G., probability summation could not be rejected (

*P*

_{F}< .10), but the trends of the data were similar to those seen for H.S.

*x*and

*y*represent the responses to a rod modulation and a cone modulation, respectively, and

*A*represents the response to the mixed rod and cone modulations.

*a*and

*k*are the free parameters in the models, and they indicate the strength of summation between rod and cone modulations.

*a*for the best vector-summation model fits and exponential

*k*for the best Quick pooling model fits for all experimental conditions.

Rod + | Retinal Illuminance (td) | Frequency (Hz) | Phase (°) | Vector-summation a(°) | Vector-summation a(°) | Quick pooling k | ||
---|---|---|---|---|---|---|---|---|

HS | SS | HS | SS | |||||

L Cone | 10 | 2 | 30°/60° | 102 | 84 | 2.43 | 1.69 | |

210°/240° | 102 | 105 | 3.24 | 3.27 | ||||

10 | 30°/60° | 0 | 0 | 0.91 | 0.94 | |||

210°/240° | 127 | 149 | ||||||

M cone | 10 | 2 | 30°/60° | 79 | 95 | 1.54 | 2.02 | |

210°/240° | 98 | 90 | 2.43 | 2.02 | ||||

10 | 30° | 72 | 1.41 | |||||

210° | 122 |

*k*in the Quick formula varied from 1.54 to 3.27 among conditions and observers without any systematic trends. The corresponding values of angle

*a*in the vector summation formula varied from 79° to 105°.

*k*in the Quick formula are from 0.91 to 1.41 for observer H.S. and 0.94 for observer S.S. The corresponding values of angle

*a*in the vector-summation model varied from 0° to 72°. The Quick model could not fit the cancellation data. The values of

*a*in the vector-summation model ranged from 122° to 149°.