Planck Functions Introduction Page

Monochromatic Planck Functions

The following table shows the equations used in the monochromatic Planck function in the Planck_Functions module.

Function Frequency input (cm^-1) Wavelength input (µm)

Radiance Planck radiance for frequency spectral ordinate Planck radiance for wavelngth spectral ordinate

Temperature Planck temperature for frequency spectral ordinate Planck temperature for wavelngth spectral ordinate

dB/dT Planck dB/dT for frequency spectral ordinate Planck dB/dT for wavelngth spectral ordinate

dT/dB Planck dT/dB for frequency spectral ordinate Planck dT/dB for wavelngth spectral ordinate

where the Planck coefficients c₁ and c₂ are given by,

First Planck coefficient

and,

Second Planck coefficient

Scalings are applied such that the radiances are in the units of mW/(m².sr.cm^-1) for frequency input or W/(m².sr.µm) for wavelength input.

Sensor Planck Functions

The sensor Planck routines call the monochromatic routines after appropriate corrections are made to take account of the polychromaticity of broadband sensor channels.

Function Correction

Radiance A polychromatic correction is applied to the input temperature, T,
Polychromatic correction of temperature
where b₀ and b₁ are sensor channel dependent constants. The corrected temperature, T_c, is then used in the monochromatic Planck radiance calculation.

Temperature The Planck temperature is calculated using the input polychromatic radiance assuming monochromaticity. This result yields a "polychromatic temperature", T_c, which is then corrected for polychromaticity to yield the returned temperature T,
Inverse of polychromatic correction of temperature
where b₀ and b₁ are sensor channel dependent constants.

dB/dT A polychromatic correction is applied to the input temperature, T,

where b₀ and b₁ are sensor channel dependent constants. The corrected temperature, T_c, is then used in the monochromatic Planck dB/dT calculation.

dT/dB The Planck dT/dB derivative is calculated using the input polychromatic radiance assuming monochromaticity. This result yields a "polychromatic derivative", dT_c/dB, which is then corrected for polychromaticity to yield the returned derivative, dT/dB,
Inverse of polychromatic correction of dT/dB
where b₁ is a sensor channel dependent constant.

Function	Correction
Radiance	A polychromatic correction is applied to the input temperature, T, where b₀ and b₁ are sensor channel dependent constants. The corrected temperature, T_c, is then used in the monochromatic Planck radiance calculation.
Temperature	The Planck temperature is calculated using the input polychromatic radiance assuming monochromaticity. This result yields a "polychromatic temperature", T_c, which is then corrected for polychromaticity to yield the returned temperature T, where b₀ and b₁ are sensor channel dependent constants.
dB/dT	A polychromatic correction is applied to the input temperature, T, where b₀ and b₁ are sensor channel dependent constants. The corrected temperature, T_c, is then used in the monochromatic Planck dB/dT calculation.
dT/dB	The Planck dT/dB derivative is calculated using the input polychromatic radiance assuming monochromaticity. This result yields a "polychromatic derivative", dT_c/dB, which is then corrected for polychromaticity to yield the returned derivative, dT/dB, where b₁ is a sensor channel dependent constant.

This page maintained by Paul van Delst

Last updated 2004/12/21 16:06:24