How Do Radiance Units and F-Number Relate in Optics?

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SUMMARY

The discussion focuses on the relationship between radiance units and f-number in optics, specifically addressing a scenario where a projector has a radiance of 20 mW/cm² expanding onto an f/18 cone. The f-number, which is 18 in this case, correlates to a numerical aperture of 0.028, resulting in a cone half-angle of 0.028 radians or 0.0024 steradians. This relationship illustrates how radiance is not solely defined by power per area but also involves geometric considerations dictated by the f-number.

PREREQUISITES
  • Understanding of radiance units in optics
  • Familiarity with f-number and numerical aperture concepts
  • Basic knowledge of solid angles in three-dimensional geometry
  • Ability to perform unit conversions in physics
NEXT STEPS
  • Explore the relationship between numerical aperture and f-number in detail
  • Learn about solid angle calculations in optics
  • Investigate the implications of radiance in optical system design
  • Study the effects of different f-numbers on light distribution
USEFUL FOR

Optics students, optical engineers, and professionals involved in projector design or light distribution analysis will benefit from this discussion.

springBreeze
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While reading a paper on optics, I came across "the radiance of the projector is 20 mW/cm2, expanding out onto an f/18 cone."

What does the "expand out onto an f/18 cone" part mean? I thought that radiance is just in units of power/area/steradians. What does f-number have to do with anything?
 
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You just need to convert the f/# into solid angle:

http://calctool.org/CALC/phys/optics/NA_to_f

an f/18 is a numerical aperture of 0.028, which gives a cone half-angle of 0.028 radians, or 0.0024 steradians, if I've converted everything correctly.
 

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