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Problem 685. Image Processing 2.1.1 Planck Integral

Created by Richard Zapor

Integrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.

Planck Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1

c1'=1.88365e23; % sec^-1 cm^-2 micron^3

c2=1.43879e4; % micron K

Me = integral ( Me(Lambda,T) ) at T over a range of Lambda

Radiance : L = Me/pi in units of ph sec^-1 m^-2

Input: (3.0 5.0 250) : From 3um to 5um at 250K

Output: 4.9612 E+018 : units ph/sec/m^2/ster

Performance Rqmts:

Accuracy: <0.001% error

Time: <100 msec (using cputime function)

Corollary problem will include spectral transmission and emissivity.

IR Calibration Reference:

Problem Group

Solution Statistics

4 correct solutions 4 incorrect solutions
Last solution submitted on May 14, 2015