When describing the visual spectrum range, most researchers (including myself) will describe it as spanning 400-700 nm, using round numbers as a convenience. Some will use the narrower region 420-680 nm, allowing only for the region where the eye’s sensitivity is reasonably high, while some use the expanded region 380-720 nm, allowing for regions where vision sensitivity is quite low, and some even extending the visual red range out to 750 nm. Beyond this is the light spectrum which is generally not visible to our eyes, and so this red cutoff determines the starting point of the infrared spectrum. For a long time, I believed that beyond this cutoff the sensitivity of the human eye was essentially zero, but then I experienced having my retina measured with an 850 nm OCT system. This system focuses a narrowband LED directly onto the retina, and I could easily see the red measurement spot. Clearly, the human eye can see wavelengths well beyond 750 nm, though at poor sensitivity. And a paper that I ran across just recently shows that human infrared sensitivity extends as far as 1350 nm.

There is some interesting background material to show how it can be possible to sense wavelengths this long. So, I will review a bit of the biochemical basis of light sensing in the retina, before reviewing the argument given by Palczewska2014 about how the human retina appears to sense light in the 900-1200 nm range.

Note on scotopic vs. photopic vision

Many discussions of vision sensitivity differentiate between dark-adapted (scotopic) vision and light-adapted (photopic) vision, with the transition occurring at twilight light levels. However, they generally do not give a quantitative measure of this, which is important because twilight actually contains a very broad range of brightness levels. For example, people who study this stuff often separate twilight into three categories: “civil twilight” for solar elevation angles of −6° < θ < 0° (where skylight is dominated by red-shifted direct light and blue-shifted Rayleigh-scattered light), “nautical twilight” for solar elevation angles of −12° < θ < −6° (where skylight is dim but intensely blue due to the ozone layer), and “astronomical twilight” for elevation angles of −18° < θ < −12° (where ambient light is predominantly from airglow, integrated starlight, and zodiacal light). [Hulbert1953]

In order to make this quantitative, we can extract data from Waldman1988, who listed the spectral irradiance (evaluated at 459.3 nm) at the Earth’s surface from natural skylight as a function of the Sun’s zenith angle. For this table, I will include the zenith = 0° case (the Sun is directly overhead) for reference. Note that this irradiance value does not include the direct irradiance from the Sun; it only includes indirect skylight.

As we can see from the table, the irradiance at “twilight” ranges from 3.85×10-2 to 2.34×10-7, i.e. by five orders of magnitude, even when we exclude astronomical twilight. My best guess for the actual point where scotopic and photopic vision are equally active is that it is somewhere near the top of this range, i.e. 3.0×10-2 W m-2 nm-1 (evaluated at wavelengths near 459.3 nm).

Photo-chemical sensing by retinal rods and cones

When a photon enters a rod or cone in the retina, it has a probability of being absorbed one of the photopigments there — variants of the protein photopsin (for photopic vision) and rhodopsin (for scotopic vision). The absorbed photon has a probability of transforming the photopsin molecule — a process called photoisomerization. The isomerized form of the molecule is no longer sensitive to incident light (it has been “bleached”), but gains the ability to initiate a sequence of chemo-electrical signals, the “phototransduction cascade”. This cascade sends a signal to the visual processing center of the brain, and initiates the regeneration of the photopsin molecule back into its original photosensitive state. In general, the visual processing centers pool together the signals from multiple photoreceptors: each pathway pools together roughly 6 cones or roughly 100 rods.

For long wavelengths of light, going beyond 600nm or so, the photopsin photopigment becomes less and less likely to isomerize due to a photon absorption. For a bright light source, however, there is a small probability that two photons are absorbed at the same time and together act to excite the pigment — a nonlinear two-photon process. In addition to this, thermal energy fluctuations can also play a role in aiding or suppressing isomerization by increasing or decreasing the energy needed to induce the transformation of the protein. Thus, if the photopsin protein has a higher sensitivity to thermal fluctuations, it would allow detection of light at longer wavelengths. However, this increased sensitivity would also add to noise created by spontaneous thermally-induced transformation of the protein. This tradeoff possibly explains why all animals have so little light sensitivity above ~700nm: a mutation that modifies the photopigment to allow longer-wavelength detection would also increase noise. [Ben-Yosef1978,Luo2011]

Photosensing for infrared wavelengths

At shorter wavelengths, an incident photon will by itself have enough energy to isomerize the photopigment. At longer wavelengths, however, photons need thermal fluctuations to aid isomerization. Lewis1955 presents a mathematical model to approximate the variation in sensitivity with wavelength by assuming that the dependence follows an $f = A \exp [- (E – E_0) / kT]$ for fractional sensitivity $f$, photon energy $E_0$ at the sensitivity peak, Boltzmann constant $k$, and temperature $T$ in Kelvin. The parameter $A$ in front is used to scale the sensitivity peak value. This holds for one single mode of vibration in the absorbing molecule. For a complex molecule with $m$ vibration modes, the superposition generates the expression$$f = A e^{-\tilde{E} / kT} \Big[ \frac{(\tilde{E} / kT)^m}{m!} + \frac{(\tilde{E} / kT)^{m-1}}{(m-1)!} + \dots + 1 \Big]$$for $\tilde{E} = E – E_0$. Fitting this to the sensitivity curve of the eye, then, involves estimating the fitting coefficients $m$, $E_0 = hc / \lambda_0$, and $A$. This provides a nice fit to the data for the scotopic sensitivity curve between 500 and 1000 nm. To make this more quantitative, we can say that, at human body temperature, with 1050 nm incident light, the cone sensitivity to single-photon stimulation is less than 10-12 of its maximum value at 505 nm.

While Lewis1955 does not show a fit, presumably one can change the parameters to fit the photopic curve as well.

After investigating the literature for the background on Palczewska2014, I ran across Dmitriev1979 which anticipates many of the results that Palczewska et al. present on second-harmonic detection in the eye. In this light, I can see that the primary novelty of Palczewska2014 is actually their theoretical modelling of the second-harmonic detection curve. Figure 3 below show Dmitriev1979’s results, in which intense infrared light is perceived by viewers as a color of visible-light that roughly corresponds to half the infrared wavelength — a clear indication of a two-photon absorption effect. Figure 4 shows the variation in sensitivity with infrared wavelength, indicating that there is a minimum in sensitivity around 1um, and then a broad increase to a peak around 1.1 um, followed by a steady decrease out to 1.3 um. No data is given for wavelengths longer than 1.3um, so it is left unknown whether some sensitivity remains for $\lambda > \text{1.4um}$.

Palczewska2014 expands on these results with a lot more detail on the underlying biochemistry and physics, and providing an estimate of the sensitivity curve derived from a theoretical model, showing a reasonable correspondence to Dmitriev1979’s curve.

So, we can see that the sensitivity curve of the eye doesn’t really have any hard cutoff beyond which it cannot see. The sensitivity falls off steadily with increasing wavelength, but somewhere between 900 nm and 1000nm the sensitivity briefly increases due to two-photon absorption effects, but then returns to falling off at longer wavelengths. Above about 850 nm, however, the sensitivity is so low that only extremely bright light sources, such as lasers or superluminescent diodes focused directly onto the retina, are visible to the eye.

• [Ben-Yosef1977] N. Ben-Yosef and A. Rose, “Spectral response of the human eye,” JOSA 68:935-937 (1977).
• [Dmitriev1979] V. G. Dmitriev, V. N. Emel’yanov, M. A. Kashintsev, V. V. Kulikov, A. A. Solov’ev, M. F. Stel’makh, and Ο. Β. Cherednichenko, “Nonlinear perception of infrared radiation in the 800–1355nm range with human eye,” Sov. J. Quantum Electron. 9:475-479 (1979).
• [Griffin1947] D. R. Griffin, R. Hubbard, and G. Wald, “The sensitivity of the human eye to infra-red radiation,” JOSA 37:546-554 (1947).
• [Hulbert1953] E. O. Hulburt, “Explanation of the brightness and color of the sky, particularly the twilight sky,” JOSA 43:113-118 (1953).]
• [Lewis1955] P. R. Lewis, “A theoretical interpretation of spectral sensitivity curves at long wavelengths,” J. Physiol. 130:45-52 (1955).
• [Luo2011] D.-G. Luo, W. W. S. Yue, P. Ala-Laurila, and K.-W. Yau, “Activation of visual pigments by light and heat,” Science 332:1307–1312 (2011).
• [Palczewska2014] G. Palczewska, F. Vinberg, P. Stremplewski, M. P. Bircher, D. Salom, K. Komar, J. Zhang, M. Cascella, M. Wojtkowski, V. J. Kefalov, and K. Palczewski, “Human infrared vision is triggered by two-photon chromophore isomerization,” PNAS 111:5445-5454 (2014).
• [Sliney1976] D. H. Sliney, R. T. Wangemann, J. K. Franks, and M. L. Wolbarsht, “Visual sensitivity of the eye to infrared laser radiation,” JOSA 66:339-341 (1976).
• [Waldman1988] C. H. Waldman, “Daylight and twilight sky radiance and terrestrial irradiance,” Naval Ocean Systems Center Technical Report NOSC-TD-1226 (1988).