Source
r/Optics•
eyetracker

Conversion of (spectral) radiance

I have measurements of the same spectral sources using two different devices and I'd like to equate them, but one has Y data output as W/sr/m^2 and the other mW/m^2/sr/nm; it can possibly go either direction but ideally I'd like to convert to W/sr/m^2. These are indeed per wavelength and not total radiance under the curve, I'm not sure if that means if per nm is implied in the first one? The X data is also largely overlapping but different ranges and sampling rates, so I can interpolate and truncate or even extrapolate if needed.

I'm trying to work out the math for conversions and I'm stuck. I can scale either empirically by multiplying/dividing by a constant but the constant is different for each recording. And it's not as simple as applying a factor of 1000 for mW.

One solution is to normalize by dividing by the sum of radiance at all measured wavelengths, then they look reasonably the same. The problem is that I've lost all the information about the actual power at that point, I'd like to preserve that as possible because future data won't necessarily have both recordings.

Posted Feb 17, 2022, 7:59 PM UTC

14
anneoneamouse•

See Jim Palmer's Radiometry FAQ.

https://wp.optics.arizona.edu/jpalmer/radiometry/radiometry-and-photometry-faq/

The file you want is here: https://wp.optics.arizona.edu/jpalmer/wp-content/uploads/sites/65/2017/03/rpfaq.pdf

The data for your first device W/Sr/m^2 isn't spectrally resolved. This means they're (probably) giving you the integrated total.

The data for your second device (mW/Sr/m^2/nm) is (probably) spectrally resolved.

4
eyetrackerOP•

Thanks for the links. To be clear, I don't care about a single number to characterize the entire spectrum but the number at each wavelength, so I guess I don't actually need absolute radiance in w/sr/m^2. But these sources often use radiance and spectral irradiance confusingly in the same situation.

To give an idea of some values, the same source has a peak "intensity value" of 0.0071 "units", while the other has 2.7062 for the same. I need to dig into the manuals more I think. So maybe the aperture or something like that might be a factor, along with W vs mW?

1
julesdottxt•

gotta integrate over wavelength to get the non-spectral quantity (to go from spectral radiance to radiance), you can do it numerically. Depending on what your data looks like, and your tolerance for error, various textbook numerical integration algorithms can be used. Mind the wavelength units.

a factor of 1000 then separates W from mW

What is this for?

Also if you want answers in "math", stack exchange is probably a better spot for you. I don't think reddit can handle LaTeX.

1
eyetrackerOP•

Thanks, see in the other thread but I don't think I need to integrate because I don't want one value, but that makes sense. Also can I sum instead for the same purpose (if not the same result) as they're discrete measurements?

The original measurements feed into multiple other equations, but I don't want to assume that first device will always be used, so I'd like to scale the second higher measurements down at the outset instead of adjusting everything else.

I looked into SE but I can't find the right tag to use there besides maybe #physics. Nothing for optics or radiometry.

1