Heuristic scalar contrast remaining after a sighting path through water.

Attenuates an inherent contrast over a horizontal (or vertical) viewing path as a teaching/scenario heuristic: \(C(r) = C_0 \, e^{-c_{\mathrm{eff}} r}\) (Johnsen 2012, ch. 5). The beam attenuation \(c\) is approximated as Kd * kd_to_c; looking up uses \(c - K_d\) and looking down \(c + K_d\).

Usage

contrast_at_distance(
  C0,
  distance,
  Kd,
  kd_to_c = 1.5,
  direction = c("horizontal", "up", "down"),
  beam_c = NULL
)

Arguments

C0: Inherent (zero-distance) contrast (achromatic Weber contrast or chromatic \(\Delta S\)). Scalar or vector.
distance: Finite, non-negative viewing distance(s) in metres. Scalar or vector.
Kd: Diffuse attenuation coefficient at the sighting wavelength (1/m).
kd_to_c: Ratio \(c / K_d\). Default 1.5. See visual_range. Ignored when beam_c is supplied.
direction: Viewing direction: "horizontal" (default), "up", or "down".
beam_c: Optional measured beam attenuation \(c\) (1/m), e.g. from beam_attenuation(), used instead of Kd * kd_to_c. Kd is still used for the "up"/"down" corrections.

Value

Heuristic contrast remaining at each distance.

Details

This scalar calculation does not propagate spectra or recompute receptor catches. In particular, applying it to a chromatic JND is not a validated chromatic-vision model; use detection_range(model = "spectral_path") for wavelength-resolved propagation.

References

Johnsen S (2012) The Optics of Life. Princeton University Press, ch. 5.

Examples

contrast_at_distance(C0 = 1, distance = c(0, 5, 10), Kd = 0.06)
#> [1] 1.0000000 0.6376282 0.4065697