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By doing a quick search in Google, I find a series of pages dedicated to physics exercises claiming that the human eye threshold for light intensity is $10^{-10}$ W/m${}^2$. However I cannot find any reference for such a value. Is it even the right unit to use here? Considering the existence of the luminosity function and the difference between W, lumen and cd.

I am interested in the minimum light intensity (in W/m${}^2$ if possible) an average human eye can detect in the lowest part of the visible spectrum (red).

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    $\begingroup$ I would have thought the answer would contain a time component as well. (Although if it really is "the eye can detect as little as 1 photon" perhaps not). $\endgroup$ Dec 20, 2022 at 16:55
  • $\begingroup$ @SoronelHaetir The watts should account for the time component, since power is energy over time. $\endgroup$
    – JMac
    Dec 20, 2022 at 17:23
  • $\begingroup$ @SoronelHaetir some papers, listed below, claim to detect a single photon. $\endgroup$
    – Mauricio
    Dec 20, 2022 at 17:37
  • $\begingroup$ @SoronelHaetir Actually, for 1 photon the time component is very important: specifically, detecting just 1 photon requires that there be effectively zero photons from the outside ahead of time to detect it as a 'flash'/'something happened'. Nervous systems and brains in general are difference detectors. $\endgroup$
    – Bryan Krause
    Dec 22, 2022 at 15:18

2 Answers 2

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From Hecht, S., Shlaer, S., & Pirenne, M. H. (1942). Energy, quanta, and vision. The Journal of general physiology, 25(6), 819-840.:

Direct measurements of the minimum energy required for threshold vision under optimal physiological conditions yield values between 2.1 and 5.7 X 10-10 ergs at the cornea, which correspond to between 54 and 148 quanta of blue-green light

and

in order to produce a visual effect, one quantum must be absorbed by each of 5 to 14 rods in the retina

They're talking about blue-green light, which rods are most sensitive to. I agree with you that light intensity in units of power density doesn't seem quite right, I'd think about it in terms of counting photons instead. Basically they estimated you need somewhere around 10 photons absorbed, with about 1/10 photons being detected. A more recent paper suggests humans can detect as little as a single photon:

Tinsley, J. N., Molodtsov, M. I., Prevedel, R., Wartmann, D., Espigulé-Pons, J., Lauwers, M., & Vaziri, A. (2016). Direct detection of a single photon by humans. Nature communications, 7(1), 1-9.

As far as "red", it'll depend how "red" you go. Rods aren't particularly sensitive to deep red light (I see quite a range of estimates depending on experimental conditions, but e.g. Lamb, T. D. (1995). Photoreceptor spectral sensitivities: common shape in the long-wavelength region. Vision research, 35(22), 3083-3091. shows about 4 to 510 less sensitivity of human rods at 700 nm compared to peak), and cones are far less sensitive to light because they require multiple photon hits on a single cone to detect; they're also sparse in the periphery. See for example:

Donner, K. (1992). Noise and the absolute thresholds of cone and rod vision. Vision research, 32(5), 853-866.

As such, when people are interested in the thresholds of human vision, they're not usually looking in the red spectrum.

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    $\begingroup$ Thanks for the sources, I will check them out. I was interested in red because of the definition of the Draper point. I was wondering if it could be predicted more exactly by knowing the human eye threshold in the longwavelenght red. $\endgroup$
    – Mauricio
    Dec 19, 2022 at 21:23
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    $\begingroup$ @Mauricio Got it; I really wouldn't recommend using human perception for approximating physical quantities. For one, human perception is extremely influenced by conditions. These sensitivity values are effectively in perfectly dark conditions (though the Hecht paper I reference had participants focus on a dim red light and then presented the flash stimulus on the periphery; the dim red light was needed to keep the subjects eyes still). $\endgroup$
    – Bryan Krause
    Dec 19, 2022 at 21:36
  • $\begingroup$ If you're looking at Draper you're not only looking at just the edge of the light emitted which is mostly in infrared, but you're also looking at a measure that's basically a dude in a room looking at a rock - 1800s science-worthy, perhaps, but not really modern-day. $\endgroup$
    – Bryan Krause
    Dec 19, 2022 at 21:37
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    $\begingroup$ A single photon...?? That's really "out there" yet it's what the publication is claiming. Remarkable, despite requiring a bunch of special conditions. Would be nice to see an SE-like summary of that paper, I didn't dig into it. $\endgroup$ Dec 20, 2022 at 5:54
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    $\begingroup$ @OverLordGoldDragon It's probably better to characterize their result as a "single photo-isomerization", which is caused by a single photon. And this is not something noticed every time, mind you, it's that an observer can detect it (barely) above chance (about 52%). en.wikipedia.org/wiki/… likely applies. It's really not appreciably different from the Hecht result besides their technique. $\endgroup$
    – Bryan Krause
    Dec 20, 2022 at 16:55
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Apparently that value is coming from a study by Clarke & Denton in 1962 where it is extensively cited in book1 about sound scattering in ocean.

The threshold intensity which the human eye can detect a small source of light is indicated as about 10-10 µW/cm2 (Clarke & Denton, 1962)

Beside the threshold has also been measured in terms of flux2.

The threshold for a steady, effectively point, source of light presented against a zero intensity background, which represents the smallest energy flux detectable by the human eye, has apparently not been recently determined. Walsh (1953) gives a value of 750 quanta/sec entering the eye.

References

  1. International Symposium on Biological Sound Scattering in the Ocean, Airlie House, G. Brooke Farquhar, U.S. Government Printing Office, 1970
  2. THE MINIMUM FLUX OF ENERGY DETECTABLE BY THE HUMAN EYE, F. H. C. MARRIOTT,VALERIE B. MORRIS AND M. H. PIRENNE, J. Physiol. (1959) 145, 369-373 (PDF)
  3. https://www.olympus-lifescience.com/en/microscope-resource/primer/lightandcolor/humanvisionintro/
  4. https://sites.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/Sample-Chapter.pdf
  5. https://people.cs.umass.edu/~elm/Teaching/ppt/691a/CV%20UNIT%20Light/691A_UNIT_Light_1.ppt.pdf
  6. Light Detection and Sensitivity by Vasudevan Lakshminarayanan, Handbook of Visual Display Technology, 2012, ISBN : 978-3-540-79566-7 (link)
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    $\begingroup$ It should be noted that $10^{-10}~\mathrm{\mu W/cm^2}$ is 100 times less than the value given by the OP, since $10^{-10}~\mathrm{\mu W/cm^2}$ = $10^{-12}~\mathrm{W/m^2}$. $\endgroup$ Dec 20, 2022 at 16:55

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