Photoreceptor absorptance from a normalised absorbance template (self-screening).

Converts a normalised visual-pigment absorbance spectrum (e.g. from govardovskii_template) into the receptor's absorptance — the fraction of incident photons actually captured at each wavelength — given the axial optical density of the photoreceptor. At low optical density the absorptance is nearly proportional to the template; at high optical density the peak saturates toward 1 and the curve broadens ("self-screening"), so the realised spectral sensitivity is wider than the bare pigment absorbance. This is the sensitivity that should be fed to quantum_catch for long or dense photoreceptors (e.g. deep-sea rods).

Usage

receptor_absorptance(
  S,
  optical_density = NULL,
  alpha = NULL,
  path_length = NULL
)

Arguments

S: A data frame with columns lambda and S (a normalised absorbance template, e.g. from govardovskii_template), or a bare numeric vector of normalised absorbance values. Re-normalised to a peak of 1 internally, so the optical density refers to the peak.
optical_density: Peak axial optical density (base-10 absorbance), dimensionless. Typically ~0.3–0.5 for vertebrate cones, up to ~1 or more for long deep-sea rods. Supply this or (alpha and path_length), not both.
alpha: Peak absorption coefficient per unit length (e.g. per µm).
path_length: Outer-segment (path) length, in the same length unit as alpha.

Value

If S is a data frame, a data frame with columns lambda and S holding the absorptance (so it drops straight into quantum_catch); if S is numeric, a numeric vector of absorptance values in $[0, 1]$.

Details

For a peak-normalised absorbance $S(\lambda)$ and axial optical density $D$ (base-10 absorbance along the outer segment at the peak), the absorptance is $$A(\lambda) = 1 - 10^{-D\,S(\lambda)} = 1 - e^{-\kappa\,S(\lambda)},$$ with $\kappa = D\ln 10$. Equivalently, supply the peak absorption coefficient $a_{\max}$ (alpha, per unit length) and the outer-segment path_length $\ell$, giving $\kappa = a_{\max}\ell$ (Johnsen 2012, ch. 4, eq. 4.8).

References

Johnsen S (2012) The Optics of Life: A Biologist's Guide to Light in Nature. Princeton University Press. (Ch. 4: absorptance and self-screening.)

Examples

lam  <- seq(300, 750, by = 1)
tmpl <- govardovskii_template(lam, lambda_max = 500)

# Realised sensitivity of a moderately dense cone (axial OD 0.4):
A <- receptor_absorptance(tmpl, optical_density = 0.4)

# A long deep-sea rod via Johnsen's absorption coefficient (0.064 / um):
A75 <- receptor_absorptance(tmpl, alpha = 0.064, path_length = 75)