A Unique Advantage for Giant Eyes in Giant Squid - Duke Biology ...

More documents

Recommendations

Info

ut with T/r replacing d/f, and assuming a square rather than Gaussian profile of the angularsensitivity (replacing 1.13 with π/4):#N space= π &% ($ 4 '2A 222# T &# T &% ( qΔt ⋅ I$ r 'space= 0.617A 2% ( qΔt ⋅ I$ r 'space. Eq. 10€The amount of detected light entering the line of sight between the target and the eye, N black , canbe worked out by replacing I space of Eq. 10 with I space1− e ( κ −α)r( ) as in Eq. 4:" T %N black= 0.617A 2$ '# r &2( ) Eq. 11qΔt ⋅ I space1− e ( κ −α)r€€€€Bioluminescence triggered by the target is likely to be composed of randomly distributed pointsources. With the mean distance x between nearest neighbours, the number of point sources perunit area of the target is 1/(4x 2 ) [S4]. The product of this density and the area viewed by the targetchannel, ( π 4)T 2 , yields the total number of point sources seen by the target channel:π ⋅ T 2 16x 2 . We can now multiply the expression of Eq. 3 with the number of viewed pointsources to obtain N bio for the extended source case:€N bio= π ⋅ T 2 EA 2256x 2 r 2 e−α⋅r qΔt Eq. 12This expression also holds for small targets seen at long distances, because the modulationtransfer function of deep oceanic water is practically flat from zero spatial frequency up to 10cycles per degree [21]. We can thus safely ignore effects caused by spatial degradation of theimage.We now substitute Eqs. 9-12 for X ch , N space , N black and N bio in Eq. 8 and solve for A to obtain:A =R4π ⋅T 2 EqΔt256x 2 r e −α⋅r + 0.617 T 26' * . '52 ) , I space)( r + / 0 (764π ⋅T 2 EqΔt256x 2 r e −α⋅r − 0.617 T 26' * .52 ) ,( r + / 0762 − e( κ −α )rI space')(8*,1 6+ 239: 6 + 2 TM2' *) , XΔt( 2rd +8*,1 6+ 239: 6(e κ −α )r, Eq. 13€which is the desired relation between A and r for detection of extended sources. The visibility ofnon-luminous extended black targets (dark silhouettes) can also be analysed by Eq. 13, simply byallowing E = 0.
Definition of variables (units in brackets)N TN BN bioN spaceN blackX chMean number of real and false photons detected per integration time in a visual channel aimed at thetarget (photons)Mean number of real and false photons detected per integration time in a visual channel viewing thebackground space-light (photons)Mean photon count (per integration time) originating from bioluminescent sources (photons)Mean photon count (per integration time) from background space-light (photons)Mean photon count (per integration time) originating from light scattered into the line of sightbetween target and observer (photons)Number of false photons (dark noise) per integration time in a visual channel (photons)X Dark noise rate per photoreceptor (photons s –1 )ArPupil diameter (m)Range: maximum visibility distance to target (m)E Number of photons emitted by bioluminescent point source in all directions per second (photons s –1 )I spaceTxRadiance of space-light background in the direction of view at the position (depth) of the eye (photonsm –2 s –1 sr –1 )Width of extended target (m)Average distance between point sources across an extended object (m)α Beam attenuation coefficient of sea water (m –1 )κ Attenuation coefficient of background radiance (backscattering coefficient) (m –1 )λWavelength of light, taken as 480 nm for bioluminescence and transmitted daylightn Refractive index in object and image space, taken as the value for water, 1.33d∆tqfMRPhotoreceptor diameter (m)Integration time (s)Detection efficiency: ratio of detected to incident photons, which depends on losses in the ocularmedia, the fraction absorbed by photopigment and the transduction efficiencyFocal length (m)Matthiessen’s ratio, 2f/AReliability coefficient
Page 1 and 2: Please cite this article in press a
Page 3: Please cite this article in press a
Page 6 and 7: Please cite this article in press a
Page 12 and 13: €Values assumed for modelling We
Page 14: Supplemental ReferencesS1. Snyder,
Page 17: Current Biology Vol 22 No 8R270Figu

A Unique Advantage for Giant Eyes in Giant Squid - Duke Biology ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?