Convert irradiance to radiance under a geometry assumption.

The relationship between irradiance E and radiance L depends on the angular distribution of the light field. The caller must supply the geometry; the function refuses to silently apply the wrong identity.

Usage

irradiance2radiance(
  E,
  geometry = c("lambertian", "scalar", "collimated", "custom"),
  solid_angle = NULL
)

Arguments

E

Irradiance value(s) in W/m^2 (or any energy unit). Vectorised.

geometry

One of:

"lambertian": Planar (vector) irradiance from a Lambertian surface, or equivalently from an isotropic hemisphere of radiance — the cosine-weighted integral \(\int L \cos\theta\, d\Omega = \pi L\). This is what a cosine collector (e.g. a downwelling-irradiance sensor) measures: \(L = E / \pi\). Default.
"scalar": Scalar irradiance (fluence rate) over a \(2\pi\) sr hemisphere — the un-weighted integral \(\int L\, d\Omega = 2\pi L\), as measured by a spherical collector. Scalar and vector irradiance are different physical quantities, not two flavours of the same measurement (Johnsen 2012, ch. 2): \(L = E / (2\pi)\).
"collimated": Normal-incidence collimated beam: \(L = E\) (solid angle \(\to 0\)).
"custom": User-specified solid angle \(\Omega\): \(L = E / \Omega\). Requires solid_angle.

solid_angle

Finite solid angle in (0, 4 pi] steradians. Required when geometry = "custom" and rejected for other geometries.

Value

Radiance in W/m^2/sr (same numeric unit as E).

References

Johnsen S (2012) The Optics of Life: A Biologist's Guide to Light in Nature. Princeton University Press. (Ch. 2: vector vs scalar irradiance.)

Examples