Measurement of Photon Statistics with Live Photoreceptor Cells
Author: Leonid Krivitsky
Affiliation: Data Storage Institute, Agency for Science Technology and Research (A*STAR), Singapore
Conventional light sources, such as lamps, stars, laser pointers etc. are known to exhibit intrinsic photon fluctuations. This means that the number of photons emitted by the source is not strictly defined but is given by a specific statistical distribution. For example, the photon number distribution of a laser obeys a Poisson distribution, whilst the photon number distribution of a thermal source (lamp, star) obeys an exponential distribution.
The question which we address in this work is how fluctuations of various light sources are perceived by visual systems of living organisms . A simple analogy which illustrates this is our human perception of the stars in the night sky. It is known that faint stars blink because of the atmospheric turbulence, which disturbs the star light on its way to the eye. At the same time, we may notice that bright stars, e.g. Polaris, observed under the same conditions, seem almost stable. This observation suggests that the ability of the eye to perceive blinking (fluctuating) lights is related to the brightness of the source. This scenario can be carefully reproduced in the lab by interfacing photosensitive eye cells, known as photoreceptors, with flashes of light from sources with different photon statistics.
Photoreceptor cells within the eye, known as retinal rods, are responsible for vision under low light conditions . They are capable of detecting light down to the single photon level. When stimulated by light, the cells respond in ways that can be measured. In particular, the electrical activity of the cell, which is driven by the absorption of individual photons by the cells, can be measured by using fine glass microelectrodes. Moreover, since the cell is constrained within the recording microelectrode, moving the microelectrode allows us to position the cell close to the tip of an optical fiber, which is used to perform targeted light delivery into the cell (see Fig. 1) .
Fig.1 Microscope image of the retinal rod cell constrained in a glass suction pipette (on the right) and a tapered optical fiber (on the left) used for light delivery to the cell.
In our experiment, we send flashes of light into the cell by feeding flashes of light from the laser and pseudo-thermal light source into an optical fiber. We then measure the average and standard deviation of the cell response to repetitive light flashes at different flash intensities. The relation between the average <A> and the standard deviation ΔA of the amplitude of the cell response is characterized by a signal-to-noise ratio SNR= <A>/√ΔA.
It turns out that the fluctuation of the cell’s response depends crucially on the saturation of the cell response. Firstly, the dependence of the average cell response on the number of impinging photons behaves differently for light sources with different photon statistics (see Fig.2). As we can see, for the case of the pseudo-thermal light source (open symbols) the saturation is considerably smoother than for the laser light (solid symbols). This is explained by the fact that for bright (on average) pseudo-thermal light source there is always a considerable chance of observing flashes with low photon numbers, which prevents sharp saturation of the average response.
Fig.2 Dependence of the average normalized amplitude of the cell response on the normalized number of impinging photons for laser (solid symbols, solid lines) and pseudo-thermal (open symbols, dashed lines) light sources. Lines are results of theoretical modelling. Typical values of saturation amplitudes are in the range of 18-25 pA, and of photon numbers are in the range of 700-2500 photons per pulse. Saturation of the response is different for the two sources due to the difference in their photon statistics.
Secondly, the saturation of the cell at relatively bright flashes leads to a sharp increase of the SNR (see Fig.3). Indeed, if the cell is saturated by bright lights, its response does not fluctuate and this automatically results in a high value of SNR since ΔA becomes vanishingly small. This may be the reason why we are able to see fluctuating dim stars, but the bright stars in the night sky appear almost stable.
Fig.3 Dependence of the Signal to Noise Ratio (SNR) on the normalized number of impinging photons for laser (solid symbols, solid lines) and pseudo-thermal (open symbols, dashed lines) light sources. Lines are results of theoretical modelling. Sharp increase of SNR is a signature of the bleaching of the cell.
In conclusion, this work contributes to a better understanding of the sensitivity of retinal rod cells to photo-stimulation. It shows that under certain conditions, the cell can, like other man-made photodetectors, be used to measure the photon statistics of various light sources. It is of further interest to us to investigate how the cell interacts with sources of non-classical light and this study is currently in progress. More practical applications of the above work could include building a detector with retinal rods that can mimic the natural detection of light by our eyes.
 "Measurement of Photon Statistics with Live Photoreceptor Cells", Nigel Sim, Mei Fun Cheng, Dmitri Bessarab, C. Michael Jones, Leonid A. Krivitsky, Physical Review Letters, 109, 113601 (2012). Abstract.
 "Single-photon detection by rod cells of the retina", F. Rieke and D. A. Baylor, Review of Modern Physics, 70, 1027 (1998). Abstract.
 "Method of targeted delivery of laser beam to isolated retinal rods by fiber optics", Nigel Sim, Dmitri Bessarab, C. Michael Jones, Leonid Krivitsky, Biomedical Optics Express, 2, 2926 (2011). Abstract.