Why Do I Get W/nm Instead of W When Calculating Spectral Output?

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SUMMARY

The discussion centers on the calculation of spectral output from a monochromator, specifically addressing the confusion surrounding the units of spectral radiance, which are expressed as W/(cm² * sr * nm). Users are attempting to derive the total output in watts (W) by incorporating factors such as slit width, slit height, solid angle, and transmission optics. The key issue arises when the resulting units yield W/nm instead of W, leading to questions about the implications of this unit and the role of wavelength in the calculation. The conclusion emphasizes that multiplying by the wavelength (e.g., 400 nm) effectively cancels out the nm units, reinforcing the dependence of spectral radiance on the wavelength region.

PREREQUISITES
  • Understanding of spectral radiance and its units (W/(cm² * sr * nm))
  • Familiarity with monochromator operation and its parameters
  • Knowledge of solid angle calculations and f-number equations
  • Basic grasp of unit cancellation in physics and engineering calculations
NEXT STEPS
  • Research the concept of spectral radiance and its applications in optical measurements
  • Learn about monochromator design and performance characteristics
  • Study solid angle calculations and their relevance in optical systems
  • Investigate unit conversion techniques in photometry and radiometry
USEFUL FOR

Optical engineers, physicists, and researchers involved in photometric measurements and monochromator applications will benefit from this discussion, particularly those seeking to understand the implications of spectral radiance units in their calculations.

Umabel
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I'm told the spectral radiance of a source is in the following units

W
----------------
cm^2 * sr * nm

And I try to use this to figure the spectral output of monochromator (in W), but I can't seem to cancel out the units. I multiply the spectral radiance by four other terms

slit width (cm)
slit height (cm)
solid angle, using a quick "f-number" equation (sr)
and then the transmission optics factor, which I assume could be unitless but I could be wrong.

Anyways, anybody know why I get W/nm instead of W? Or is it really just W?
 
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What would be the wavelength of the transmitted light from the monochromator?
 
I assume the source is monochromatic here, so the wavelength coming out of monochromator is also monochromatic...let's just say that the radiation is at 400nm or something...
 
So...what happens when you multiply your original equation by the transmitted wavelength??
 
If I multiply the rest of the equation by let's say, 400nm, then the nm units cancel out...

edit: though I have to admit that I am not totally convinced that this is what the unit implies. Is it some invisible reminder that the spectral radiance depends on what wavelength region this source is emitting from?
 
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