1. Visual acuity depends on the brightness contrast between test object and background; and conversely, brightness discrimination depends on the target size. Both functions vary with the brightness of the background. Measurements with rectangular targets of length-width ratio 2 were made over a range of sizes, contrasts, and brightnesses sufficient to determine the relations among these three variables. The rectangles were from 2' to 50' wide; the contrast fraction, ΔI/I, ranged from 0.01 to 40; the background brightness varied from 0.0001 to 2500 millilamberts.
2. When ΔI/I or visual acuity is plotted as a function of brightness the data do, in general, follow Hecht's equation. The departure from a simple photochemical theory which the larger targets show is probably due to changes in the functional retinal mosaic with changing brightness.
3. In general also, the relation between visual acuity and brightness, at selected contrasts, fits Hecht's derivation. At low contrasts, as the brightness is reduced a point is reached at which the test object becomes invisible at any size.
4. No simple relation emerges from the data relating visual acuity to contrast, at set levels of illumination. Over only a very short range are visual acuity and contrast directly related. At high contrasts, visual acuity reaches a maximum, whereas at low visual acuity, ΔI/I reaches a minimum which cannot be passed regardless of size.
5. The shape of the curves relating ΔI/I to brightness is not significantly altered by changing the exposure time. There is some evidence to show that a 3 second exposure of the target is equivalent to two looks of 0.2 second each.
6. In all these studies the thresholds were determined by a frequency of seeing method, and the data have been considered in terms of a quantum theory of threshold seeing. It was found that a threshold response involves between four and eight independent critical events, which are largely independent of size, brightness, and criterion of seeing.