Jacquinot Advantage
Field of view, field-stop size and étendue of an FTIR interferometer, and its throughput ratio to a grating spectrometer of the same resolving power.
Interferometer
Resolution Δν̃ = 1/L
1.000 cm⁻¹
resolving power R = ν̃L = 1000
Max Solid Angle Ω = 2πΔν̃/ν̃
0.006283 sr
half-angle 44.73 mrad (2.56°)
Field (J-) Stop Diameter
8.951 mm
2f tan α at the collimator focus
FTS Étendue A·Ω
0.03084 cm²·sr
beam area 4.909 cm²
Grating Spectrometer at the Same R and Beam Area
Jacquinot Advantage Ω_FTS/Ω_slit
136.0×
π f/(h tan θ); Jacquinot's 2πf/h = 157.1 assumes 2 tan θ = 1
Slit Width Needed for R
288.7 µm
w = 2f tan θ/R (slit-limited; diffraction limit mNρ must exceed R)
The highest wavenumber in the band sets the field stop: a ray at angle θ sees the path difference x cos θ, so its lines appear at ν̃ cos θ; the field is limited to the cone where that shift stays below the resolution.
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: unapodized resolution 1/L, circular field stop, grating spectrometer in Littrow limited by its slit width; both instruments share the beam area.
- 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
- Griffiths P. R., de Haseth J. A. (2007). Fourier Transform Infrared Spectrometry, 2nd ed., ch. 7. Wiley.