Spectral Range Calculator
Spectral coverage, resolution, and dispersion for a grating-based spectrometer.
λ at Short Edge
394.0 nm
λ at Long Edge
605.3 nm
Spectral Range
211.3 nm
0.1032 nm/pixel on average
Reciprocal Dispersion (centre)
8.321 nm/mm
d·cos β₀ / (m·f)
Grating Angles
α 33.09°, β₀ 3.09°
anamorphic r = 0.839
Resolution δλ (centre)
0.208 nm
pixel-limited (2 px)
Resolving Power λ/δλ
2.40e+3
Limits: slit / 2 px / diffraction
0.175 / 0.208 / 0.0167 nm
R = mN = 3.00e+4
Wavelength Across the Detector
Spectral Range vs Groove Density
Model
mλ_c = 2d·cos(D_v/2)·sin ψ, α = ψ + D_v/2, β₀ = ψ − D_v/2, β(x) = β₀ + atan(x/f)
δλ_slit = w·d·cos α/(m·f), δλ_pixel = 2p·d·cos β₀/(m·f), δλ_diff = λ/(mN)
A spectrograph with a fixed angle D_v = α − β between the collimator and camera arms (Czerny–Turner; D_v = 0 is Littrow) turns its grating to put λ_c on the centre of a flat detector normal to the central ray. Each detector edge sees the wavelength the grating equation gives for β₀ ± atan(W/2f). Collimator and camera have the same focal length, so the slit image is r = cos α/cos β₀ times the slit width. The resolution is the largest of the slit, two-pixel and diffraction limits; aberrations, the focal-plane tilt and the real line shape (their convolution) are not modelled. Order m + 1 overlaps order m above λ_min(m + 1)/m.
Reference: C. Palmer, E. Loewen, Diffraction Grating Handbook, 6th ed. (Newport, 2005), ch. 2.
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
Exact grating geometry for a flat detector normal to the central ray at a fixed deviation angle (α < 90° needs mλ_c < d(1 + cos D_v)); the resolution is the largest of the slit, two-pixel and diffraction limits, without aberrations or focal-plane tilt.
- Palmer C., Loewen E. (2005). Diffraction Grating Handbook, 6th ed., ch. 2. Newport.