Angular response of idealized entrance optics used in light measurements.
Usage
angular_response(
elevation.angle = 90,
geometry = "cosine",
zenith.angle = 90 - elevation.angle,
diameter = NULL
)Arguments
- elevation.angle, zenith.angle
numeric The elevation angle of a point light source such as the sun or its zenith angle [degrees].
- geometry
character The type of entrance optics, one of
"flat disk","cosine","dome","hemisphere","ball", or"sphere".- diameter
numeric The diameter of the entrance optics. If
NULL, the default, a relative value is returned.
Value
A numeric vector of the same length as the numeric arguments following
the recycling rules of R expressions. With diameter = NULL, the
returned values are positive fractions or one, and otherwise the projected
area expressed in the area units matching the length unit in which the
argument passed to diameter is expressed.
Details
The maximum projected area (\(A_\mathrm{max}\)) is always computed for a circle of diameter \(d\) as \(A_\mathrm{max} = \pi \times d^2 / 4\) when computing actual projected areas, or set to \(A_\mathrm{max} = 1\) for computation of relative values.
The cosine response for a flat disk is computed as $$A_\mathrm{p} = A_\mathrm{max} \times \cos(z)$$
The hemispherical response for a dome is computed as $$A_\mathrm{p} = A_\mathrm{max} \times 0.5 \times (1 + \cos(z))$$
The spherical response for a "ball" is computed as $$A_\mathrm{p} = A_\mathrm{max} \times 1$$
See also
all_diffusers and diffusers.lst for
data for real sensors and entrance optics.
Examples
angular_response(45)
#> [1] 0.7071068
angular_response(45, "cosine")
#> [1] 0.7071068
angular_response(45, "dome")
#> [1] 0.8535534
angular_response(45, "sphere")
#> [1] 1
angular_response(c(0, 30, 60, 90))
#> [1] 0.0000000 0.5000000 0.8660254 1.0000000
angular_response(-c(0, 30, 60, 90))
#> [1] 0 0 0 0
angular_response(c(0, 30, 60, 90), "dome")
#> [1] 0.5000000 0.7500000 0.9330127 1.0000000
angular_response(c(0, 30, 60, 90), "sphere")
#> [1] 1 1 1 1