What is the minimum optical power detectable by human eye?

If one is in complete darkness, what is the minimum optical power that the eye can "see" (let's say in 500-600 nm range).

I found that for 510 nm, 90 photons can be detected (http://en.wikipedia.org/wiki/Absolute_threshold).

Calculating the energy for these photons and considering 150 fs pulses with 80 Mhz repetition rate, results in an average power of ~ 3 nW.

• dfisica.ubi.pt/~hgil/FotoMetria/HandBook/ch02.html There you go. – Cheeku Mar 11 '13 at 15:15
• There is actualy rather a lot of ambiguity in this question right now. The sensing cells in your eye can respond to single photons (though their QE is not high). However, there is a preprocessing layer (which as a particle experimenter I would describe as a hardware trigger) which discards isolated hits so they never register in the conscience mind. I assume you mean to ask about the dimmest light which can be used to make decisions. – dmckee Mar 11 '13 at 22:01
• @dmckee Ya, he probably means the minimum number of photons required to judge whether light is coming or not. Citing the same example,90 photons be detected for 510 nm implies that if you detect about 50 photons at 510 nm, your eyes wouldn't know that you have light from 510 nm range. – Cheeku Mar 11 '13 at 23:26
• Sorry for being ambiguous, by detection I meant what excites the brain and takes to the sensation of vision. I was curious if there were other similar experiments like the one provided on Wikipedia link above. – Silviu Mar 12 '13 at 19:47

Albert Rose studied this question in the 1940's and developed the Rose Criterion which states that the signal-to-noise ratio ($SNR$):

$$SNR=\dfrac{\mu}{\sigma}$$

For $100$% identification of an object by the human eye is $SNR \approx 5$. He based this off of quantum arguments where he looked at the average number of photons per unit area in an photo image and stated gave the equation $\Delta N = kN^{\frac{1}{2}}$ where $\Delta N$ is the smallest perceptible change and $N$ is the average number of quanta absorbed in a pixel and $k$ is the $SNR$ (see eq 1, 1a and figure 1).

If one uses this ratio, then in two independent pixels one can distinguish one from the other if there are an average of $100$ quanta absorbed in the pixels, then one would be able to distinguish between the two, if one had $50$ quanta more than the other. This relationship has an obvious limit when the average number of quanta are $> 7$ and all the photon ($> 14$ total for two pixels) are found in one pixel and not the other, as shown in the table below.

From a recent paper,

Direct detection of a single photon by humans. JN Tinsley et al. Nature Comms 7, 12172 (2016) (open access).

Abstract:

[...] Here we report that humans can detect a single-photon incident on the cornea with a probability significantly above chance. This was achieved by implementing a combination of a psychophysics procedure with a quantum light source that can generate single-photon states of light. We further discover that the probability of reporting a single photon is modulated by the presence of an earlier photon, suggesting a priming process that temporarily enhances the effective gain of the visual system on the timescale of seconds

it appears humans can just about detect single photons in the visible range.

• Great find. Now all you need is the wavelength and the number of photons per second to get a "power" answer. Because if you consider "one photon, one femtosecond" as the energy/time scale, the power is rather large. The "priming" aspect that suggests (I didn't read the paper) "two photons within time x on the same cell" probably sets the lower power limit. – Floris Jul 21 '16 at 13:32
• @Floris To be honest I don't think minimum power is a particularly good measure. Cellular detection works on photons at the lower end, so the real measure is how many hits you need to get a measurable biological response, but this has relatively little to do with the power your eyes are absorbing, which will nominally increase for a shorter wavelength without any real change in the physics. – Emilio Pisanty Jul 21 '16 at 13:43
• I was just pointing out that that was what the question was asking... Maybe I am being pedantic. – Floris Jul 21 '16 at 16:07

Many years ago I have read about experiments of Vavilov and collaborators who claimed to have registered single photons by the human eye. I cannot, however, recall the source.