Table 1. Summary of experiments measuring absolute visual threshold
SpeciesReferenceRetinal eccentricityStimulus durationStimulus wavelengthRetinal image areaaRods subtended by targetbAverage number of photons at the corneac
degreesmsnmμm2
HumanHecht et al., 194220 (T)15101,80024090 ± 15 (4)
Hallett, 196220 (T)2.65202503590 (1)
Hallett, 196220 (T)2.652065,0008,775100 (1)
Sakitt, 19727 (N)164955405055, 66 (3)
Teich et al., 198217.5 (T)1514928110 ± 10 (4)
Sharpe et al., 199312 (N)105071,80023543 ± 5 (3)
Koenig and Hofer, 201111 (T)344905106650 ± 16 (6)
Tinsley et al., 2016d23 (T)<1e504Not specified73 ± 9 (3)
MousefNaarendorp et al., 2010Inferior<1e5002,20096031 ± 7 (5)
Naarendorp et al., 2010Inferior<1e50019,0008,35067 ± 6 (6)

The second column identifies the study. In the third column, N and T represent nasal and temporal, respectively. This table does not report the number of experiments per subject, nor measurements per experiment; it consequently does not fully capture the precision of the values. For example, in the experiments of Hecht et al., for two of the subjects, thresholds were measured in seven different experiments, whereas in only three and four experiments for two other subjects. In the mouse experiments, for one animal, 1,369 trials from ∼30 experimental sessions comprised the frequency of seeing data (this included 35% blank trials, for which the false positive rate was 1%). In addition, the psychophysical methodology (yes/no; 2AFC; rating scale) varied among the studies. Results and analyses in papers from Sakitt (1972) onward concur that statistically reliable information about the target was occasionally available to the subject at stimulus energies threefold or more lower than classical threshold values (midpoint of the frequency of seeing curves) generated by subjects using a high criterion.

  • a For the human experiments, target areas in deg2 were converted to mm2 using the standard adult schematic eye, with a scaling factor of 0.291 mm/deg (Wyszecki and Stiles, 1982).

  • b To calculate the number of rods subtending the target, the retinal area was multiplied by the rod density at the appropriate retinal eccentricity as given in Curcio et al. (1990). For the smaller targets, the areas and number of rods subtended are nominal, and likely considerably larger because of optical aberrations.

  • c The last column of the table gives the average threshold at the cornea of the study. Error terms are the SEMs over subjects, and the values in parentheses are the number of subjects. For the mouse experiments, flashes were generated by time-gated LED pulses, which ranged in duration from 10 µs to 1 ms to control the total flash energy. The photon energy density at the cornea was multiplied by an effective dark-adapted pupil area of 2 mm2; the mouse retinal rod density of ∼340,000 mm−2 was taken from Jeon et al. (1998); this is more than twofold larger than the maximal human rod density, ∼140,000 mm−2, which occurs at ∼18° eccentricity on the temporal retina (Curcio et al., 1990).

  • d Tinsley et al. (2016) used a quantum optical technique, spontaneous parametric down conversion, in which a nonlinear crystal is used to down convert a higher energy (shorter wavelength) photon into two lower energy (longer wavelength) photons, one of which was delivered to the eye and the second (the “idler”) used to determine when a down conversion took place. Although this technology cannot create single-photon trials at will, at the low source strength used, it produced mainly blank trials (92%), one-photon trials (8%), and extremely rare multiphoton trials. In a total of 2,420 postselected one-photon trials (out of a total of 30,767 trials), the average probability of a correct response was 0.516 ± 0.010 (mean ± SEM), a value just greater than chance success (0.5) at the P = 0.05 statistical significance level. Similar results were obtained with a Poisson light source delivering a mean of one photon at the cornea, increasing the overall significance level of one-photon detection to 0.01. The authors also obtained intriguing results suggesting that the capture of a single photon can elevate the probability of detecting another photon over an interval of several seconds. The conventional threshold of the subjects was measured with a temporal 2AFC procedure and stimuli ranging from 20 to 140 photons at the cornea. The thresholds (defined at the 75th percentile of the detection functions; see Fig. S3 [A–C] in Tinsley et al., 2016) were close to those obtained in the other experiments cited in this table.

  • e Stimuli of <1 ms are effectively instantaneous for mammalian rods, whose SPRs peak at ∼100 ms in vivo (Peinado Allina et al., 2017)

  • f Mice maintained a false positive rate of 1–2%, likely because each trial involved running a random number in the hundreds of cycles on a wheel to achieve a water reward, and so both false positive (type I) and false negative (type II) errors were energetically costly.