Energy, Quanta, and Vision

{{Summary
 * title=Energy, Quanta, and Vision
 * authors=Selig Hecht, Simon Shlaer, Maurice Henri Pirenne
 * url=http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2142545/pdf/819.pdf
 * tags=vision quanta light eye
 * summary=The authors note that there have been many studies of the visual threshold of the human eye, many improving on those before.  This paper includes a survey and history of experiments in the area, notes some inadequacies in past work and opportunity for improvement, and lays out and implements a new technique for measuring visual sensitivity.  Their practical noise-reduction is somewhat better than previous experiments, and they add a widely useful statistical technique that allows for a much stronger signal to be extracted from the intrinsically noisy data of observation.

The result is both a new and lower upper bound on the visual threshold, and a useful exercise in statistical data analysis.

Goals and Methods
The question of the fundamental sensitivity of the human eye is a long-standing one, and had been tested sporadically for decades. This experiment reduced noise in a few ways, and analyzed the results assuming detection and observation of light would follow a Poisson distribution.


 * Noise reduction and measurement:
 * Subjects were adapted to the dark for 40 minutes,
 * Light was focused on an area in the retina's peripheral vision (where light response is optimal)
 * Light was flashed at 510nm, a wavelength we are particularly sensitive to
 * Flashes of 1 ms and a spot size smaller than 10 arcminutes were chosen. A set of diaphragms and filters were used to vary the spot size and brightness without moving the rest of the setup.  The flashes were generated using a circular shutter with a tiny hole cut in it, rotating so quickly that at any give moment it lets light through for 0.001 s of a revolution
 * All light was carefully passed through an equal thickness of glass for uniform illumination, with entrance and exist slits both 1.2mm wide, corresponding to the desired bandwidth of the beam.
 * A red light was provided to help fixate the eye so it did not jitter.

Measurements were taken with this apparatus over the course of two years and seven subjects. Each of a series of intensities was presented many times, with the frequency of seeing a flash determined for each intensity, and calculating the associated number of quanta sent to the eye.

This and the rest of the experiment assume that observer response is intrinsically probabilistic. The participants in the study were trained to say they had seen a light only if they were sure, to minimize false positives. A threshold was defined as the intensity which could be seen with a 60% frequency.

One of the more careful aspects of this paper is its analysis of reflection and absorption of light by the eye, and the estimated portion of light that reaches the retina.
 * Light intensity and absorption

The details of the filter and the light source were calibrated (more han once, to ensure constancy) so as to estimate the energy density sent to the pupil. This was varied over the course of the experiment, and used as a gauge of how many quanta of light had potentially been absorbed by the eye.

Based on the absorption analysis, the number of quanta absorbed by the eye can be estimated from the total light intensity.

This suggested a value lower than any found in previous experiments. So an additional statistical model is used to cross-check the result, based on the Poisson distribution of light emitted in any one flash.

The probability of a given flash being observed is then assumed to be the probability that more than a hidden threshhold of quanta are detected by the eye. In this version of the model it is primarily the signal that varies -- whenever the signal passes some threshold, it is assumed to be seen. However it is noted that human variability combines with the signal variability in this case and is not a significant factor in the analysis.

The threshold estimated by this was compared to that estimated by calculating the % of total photons absorbed by the eye.

Results and Analysis
Contemporary studies were used to estimate that 50% of light is transmitted through the cornea, and an upper limit of 20% of impinging light absorbed by retinal pigments (visual purple). The latter is estimated anew in this paper based on data from frog retinas and pigment density. Earlier work by Hecht provided data on scoptopic luminosity at the retina and the optimal frequency for detection. This would mean a total absorption of 10% of incoming photons.

The total energy density at the cornea is 54-148 quanta of light, which maps to 5-14 quanta absorbed by rods. This is over a field of ~500 rods, suggesting that no rod absorbs more than one.

For the statistical comparison, it is noted that the absolute threshold for vision seems to be small - 5 to 8 quanta. And that this statistical estimate is easier to see when the total number of detections is small. Variation in the biological capacity of the participants doesn't effect this analysis much. So the agreement between this estimate and the energy-absorption estimate is significant.

This suggests that, while in the past it has been assumed that light stimulus is constant and the observer variable, the primary factor in light detection is the variability of the signal.

Future experiment is needed to determine whether there are differential threshold at some level of intensity, separate from the absolute threshold, for which a small number of events determines the differentiation. Moreover, this is simply an upper bound, and the bound used to identify the number of photons absorbed by the retina is noted to seem high by a factor of 2. The paper did not dwell on the training of the observers (most of whom were also co-authors). However later studies would make a point of training people differently to note uncertainty differently than they note definite non-observation of light - a variation that lowers the threshold further. }}
 * relevance=This paper has become a canonical reference for any discussion about how sensitive the human eye is to individual quanta of light. While it was not the first to ask the question and carry out experiments to measure how small a signal was needed to stimulate the eye, it used a simple and universal technique, was careful in its error analysis, and compared its work cleanly with those of past attempts to measure the visual threshold.  Previous estimates of the visual threshhold were on the order of 20 quanta of light; this work used statistical analysis to reduce that to 5-7.
 * journal=The Journal of General Physiology
 * pub_date=1942
 * doi=10.1085/jgp.25.6.819
 * subject=Neuroscience