Operator product expansion

Several laws describe a human's ability to visually detect targets on a uniform background. One such law is Riccò's law. This law explains the visual relationship between a target area and target contrast required for detection when that target is unresolved. It is given by

$Contrast=\frac{K}{Area}.$

Riccò's law is applicable for regions where the target being detected is unresolved. The resolution of the human eye (the receptive field size) is approximately one arc-minute in the center (the fovea) and increases in peripheral vision. Riccò's law is applicable for targets of angular area less than the size of the receptive field. This region is variable based on the amount of background luminance. Riccò's law is based on the fact that within a receptive field, the light energy (the number of photons) required to lead to the target being detected is summed over the area and is thus proportional to the area. Therefore, the contrast threshold required for detection is proportional to the signal-to-noise ratio multiplied by the noise divided by the area. This leads to the above equation.

See also

• Spatial Summation
• Weber's law

References

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