The formula for X looks a lot like the formula for expected value of a continuous random variable. Is the measured signal X essentially the expected value of the spectral power s(lambda)?
Staffjamesfong1
@BrianSantoso Not quite, although I can see what you are referring to. A power spectrum is not a probability density function, and so there is no concept of an expected value here.
Here we want to calculate the total response of our detector for a given power spectrum. You can think of each wavelength as producing some scalar amount of response, expressed as r(λ). The integral here just sums up all of the contributions from each of the individual wavelengths weighted by their respective powers.
kkkhanl
I think it's interesting that the sensitivity of the detector various with the wavelength of light. Is this sensitivity something that is known for each detector, or is it something that needs to be measured?
The formula for X looks a lot like the formula for expected value of a continuous random variable. Is the measured signal X essentially the expected value of the spectral power s(lambda)?
@BrianSantoso Not quite, although I can see what you are referring to. A power spectrum is not a probability density function, and so there is no concept of an expected value here.
Here we want to calculate the total response of our detector for a given power spectrum. You can think of each wavelength as producing some scalar amount of response, expressed as r(λ). The integral here just sums up all of the contributions from each of the individual wavelengths weighted by their respective powers.
I think it's interesting that the sensitivity of the detector various with the wavelength of light. Is this sensitivity something that is known for each detector, or is it something that needs to be measured?