Spectrograph Systems

Czerny-Turner ray tracing, Littrow autocollimation, Echelle cross-dispersed formats

Incident Angle (a)25.0deg

Grating Density600 l/mm

Wavelength550nm

Diffraction Orderm = 1

Beam Width50mm

Focal Length250mm

Diffracted Angle

-5.31deg

Angular Dispersion

602.59 urad/nm

Linear Dispersion

150.65 um/nm

Resolving Power

R = 30,000

Min Resolution

18.333 pm

Free Spectral Range

550.0 nm

Czerny-Turner Configuration

Two concave mirrors (M1 collimating, M2 focusing) with a plane diffraction grating. The grating equation d(sin a + sin b) = m*lambda determines where each wavelength is focused on the detector. Rays of different colors separate spatially, producing a resolved spectrum. Adjusting alpha rotates the grating to scan wavelength.

Grating Equations Reference

Grating equation:

d(sin a + sin b) = m * lambda

Angular dispersion:

db/dlambda = m / (d * cos b)

Resolving power:

R = lambda / dlambda = m * N

Free spectral range:

FSR = lambda / m

Blaze condition (Littrow):

lambda_b = 2d * sin(theta_b) / m

Linear dispersion:

dx/dlambda = f * db/dlambda