Spectral Resolution Calculator
Compare spectral resolution across grating, prism, and Fabry-Pérot spectrometers.
Spectral Resolution δλ
41.0 pm
slit-limited
Resolving Power λ/δλ
1.219e+4
Resolution (wavenumber)
1.64 cm⁻¹
Slit-Limited Bandpass
41.0 pm
w·cos α/cos β × reciprocal linear dispersion (anamorphic r)
Diffraction Limit
8.33 pm
λ/(mN), N = 60,000 grooves
Reciprocal Linear Dispersion
1.51 nm/mm
β = 25.2°
Bandpass vs Slit Width
Model
Grating: mλ = d(sin α + sin β), δλ_slit = w·d·cos α / (m·f), δλ_diff = λ / (mN)
Prism: δλ_slit = w / (f · dθ/dλ), δλ_diff = λ / (D · dθ/dλ) = λ / (b·|dn/dλ|)
Fabry-Pérot: δλ = FSR / ℱ, T = 1 / [1 + (2ℱ/π)² sin²(π Δλ / FSR)]
Collimator and camera have the same focal length f. A grating images the slit r = cos α/cos β times its width (anamorphic magnification; r = 1 for a prism at minimum deviation), and the slit image times the reciprocal linear dispersion d·cos β/(m·f) is the slit-limited bandpass. Diffraction by the illuminated aperture sets a floor (Rayleigh criterion: resolving power mN for a grating, b·|dn/dλ| for a prism of base b). The resolution shown is the larger of the two, an approximation: the real line shape is the slit image convolved with the diffraction pattern, broadened further by aberrations and detector pixels, which are not modelled. Widening the slit past the point where the two lines cross costs resolution for throughput.
References: C. Palmer, E. Loewen, Diffraction Grating Handbook, 6th ed. (Newport, 2005), ch. 2; E. Hecht, Optics, 5th ed., §9.6.1 (Fabry-Pérot).
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
The slit and diffraction limits are computed separately and the resolution is taken as the larger; the real line shape is their convolution. Aberrations and detector pixels are not modelled.
- Palmer C., Loewen E. (2005). Diffraction Grating Handbook, 6th ed., ch. 2. Newport.
- Hecht E. (2016). Optics, 5th ed., §9.6.1. Fabry-Pérot resolution δλ = FSR/ℱ.