Home → Products → Dagra → Examples → Energy

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 Constant Speed of light Boltzmann's constant
Plank's Law 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.

Detector area Area of the detector
Numerical aperture Numerical aperture of the lens in front of the detector
Minimum wavelength Minimum wavelength the detector is sensitive to
Maximum wavelength Maximum wavelength the detector is sensitive to
Source temperature 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.

Lens transmittance imported from Dagra
Transmittance equation
Plot of lens transmittance

Lens Transmittance

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.

Calculate Power

Power falling on the detector This is the power falling on the detector.