Table 1.
Definition of variables (units in brackets). For some variables, we use a typical value (TV) for modelling, if nothing else is indicated.
| variable | definition |
|---|---|
| NT | mean number of real and false photons detected per integration time in a visual channel aimed at the target (photons) |
| NB | mean number of real and false photons detected per integration time in a visual channel viewing the background space-light (photons) |
| Nbio | mean photon count originating from bioluminescent sources (photons) |
| Nspace | mean photon count from background space-light (photons) |
| Nblack | mean photon count originating from light scattered into the line of sight between target and observer (photons) |
| Xch | number of false photons (dark noise) per integration time in a visual channel (photons) |
| X | dark-noise rate per photoreceptor (photons s–1), TV = 2.8 × 10–5 s−1, see [15] |
| A | pupil diameter (m) |
| r | range: maximum visibility distance to target (m) |
| E | number of photons emitted by bioluminescent point source in all directions per second (photons s–1) |
| Ispace | radiance of space-light background in the direction of view at the position (depth) of the eye (photons m–2 s–1 sr–1) |
| T | width of extended target (m) |
| x | average distance between point sources across an extended object (m) |
| α | beam attenuation coefficient of seawater (m–1), see [5] and the electronic supplementary material |
| κ | attenuation coefficient of background radiance (m–1), see [5] and the electronic supplementary material |
| λ | wavelength of light, taken as 480 nm for bioluminescence and transmitted daylight |
| n | refractive index in object and image space, taken as the value of water, 1.33 |
| d | photoreceptor diameter (m), TV = 3 µm, see [7] |
| Δt | integration time (s), TV = 1.16 s [8,16,17] |
| q | detection efficiency: ratio of detected and incident photons, depending on loss in the ocular optics, fraction absorbed in photopigment and transduction efficiency, TV = 0.36 [8] |
| f | focal length (m) |
| M | the ratio of focal length and pupil radius, 2f/A, here set to Matthiessen's ratio (2.55) |
| R | reliability coefficient, here set to 1.96 for 95% confidence [14] |