Energy Falling on an IR Sensor
In this example, Dagra was used to trace the transmittance of a Fresnel lens to estimate the amount of energy from a black body source that would be focused onto an infrared sensor. The MathCad component was used in this analysis to load the data traced in Dagra into the worksheet.
The data-sheet for the lens included both the visible and infrared transmission properties of the material. Notice how a separate axis pair was used for each. The visible transmission is very smooth; two Bezier control points are sufficient to describe it.
Black Body Equation
Plank's law describes the spectral radiance, I(l, T), from a black-body at some temperature T and wavelength l. It requires Plank's constant (h), the speed of light in a vacuum (c) and Boltzmann's constant (k).
|Plank's law [J/sm2⋅sr⋅m]|
Lens and Detector Properties
The energy falling on the detector will depend on the area of the detector, the wavelengths it is sensitive to, the transmission of the lens, the numerical aperture of the lens and the temperature of the source.
|Area of the detector|
|Numerical aperture of the lens in front of the detector|
|Minimum wavelength the detector is sensitive to|
|Maximum wavelength the detector is sensitive to|
|The temperature of the black-body source|
The transmission of the lens material traced using Dagra, was imported making the data available to MathCad. The imported data is an array with two columns (x- and y-values) and enough rows to accurately match the Bezier curves. A MathCad function is defined so it is easy to use the data in the Worksheet.
Calculate Power on Detector
The power at the detector is given by the product of the source power and lens transmission summed over wavelengths the detector is sensitive to.
|This is the power falling on the detector.|