Concave Mirror Throughput
Solid angle, f-number and slit étendue of a spherical-mirror spectrometer, with its slit-limited resolving power and the Jacquinot advantage of an FTIR of the same aperture.
Focal Length f = R/2
25.00 mm
f/1.00
Rim Half-Angle α
28.10°
NA = sin α = 0.4710; includes the mirror sag
Solid Angle Ω = 2π(1 − cos α)
0.7405 sr
paraxial π(D/2f)² = 0.7854 sr (6.06 % off)
Slit Étendue w·h·π sin²α
0.03484 mm²·sr
Lambertian slit, mirror filled
Slit-Limited Resolving Power
577.4
R = 2f tan θ/w (Littrow)
Jacquinot Advantage
136.0×
FTS of the same mirror area and R: π f/(h tan θ); 2πf/h = 157.1
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Geometric optics: exact cone to the mirror rim including the sag, Lambertian slit filling the mirror, Littrow grating limited by the slit width, not by diffraction or aberrations.
- Jacquinot P. (1954). The luminosity of spectrometers with prisms, gratings, or Fabry-Perot etalons. J. Opt. Soc. Am. 44, 761–765. doi:10.1364/JOSA.44.000761
- Smith W. J. (2008). Modern Optical Engineering, 4th ed., ch. 12 (radiometry and photometry). McGraw-Hill.
- Palmer C., Loewen E. (2005). Diffraction Grating Handbook, 6th ed., ch. 2. Newport Corporation.