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Upper Limit of Resolution Determined by Slit Width in a Spectrometer

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Calculates the upper limit of resolution based on slit width for astronomical spectrographs.
Focal length F of a telescope
mm
Telescope aperture diameter D
mm
Order of diffraction m
Diffraction grating groove density ρ
Book/mm
Slot width w
μm
Focal length f of a collimator lens
mm
Incident angle α to the diffraction grating
°
Observed wavelength λ
nm
Resolution (diffraction grating) 
Resolution (slit width) 
R = m f ρ D / ( F cosα )
R = m f ρ λ / ( w cosα )

The upper limit of resolution is the smaller of these two values.
Note that this is an approximation valid only when the slit width is sufficiently smaller than the focal length of the collimator lens.
Furthermore, this calculation provides the upper limit of resolution. The actual resolution will be lower than the calculated value due to factors such as the pixel size of the camera sensor and the signal-to-noise ratio.

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