Spectrograph design

The OtterVIS LGL spectrograph is a lens-grating-lens design.

  • The lenses are two manual 50mm standard camera lenses. Most modern (post-1970) standard lenses are excellent performers, and because they were “standard” in their time, they are plentiful and cheap today.
  • The grating is a very cheap diffraction grating slide with a grating constant of 1000 lines/mm.
  • The slit is comprised of to razor blades mounted on a ring magnet.
otter-lgl

Diagram for the optical path of the OtterVIS LGL spectrophotometer.

Principles of operation:

The first lens collimates the light from the slit. The second lens focuses the diffracted light onto the CCD.

The general diffraction equation is:

dif-eq

The grating constant is 1000 lp/mm and the lower wavelength is chosen to be 380 nm as the lenses start absorbing here. From 760 nm second order diffraction starts to overlap so 760 nm is chosen as the upper limit for the spectrum.

The CCD (TCD1304) is 29.1 mm long and the focal length of the imaging lens is 50 mm, so the desired angular dispersion for 380 nm and 760 nm is plus-minus:

tan-ang-disp

Inserting this into the diffraction equation gives:

Which solved for the two angles gives:

where θm is the center of the diffracted light. (it’s not the exact solution, it leaves a few pixels on the CCD unused).

The center angle of deviation, ie. the difference between the incident and the center of the diffracted light, is the angle between the optical axes of the two lenses (53⁰).

Theoretical resolution:

Assuming that the diffraction grating is perfect (ahem), and focus and alignment is perfect (AHEM), and that there are no chromatic, comatic and/or spherical abberations, the width of the slit becomes the resolution limiting factor (I think).

Since both the collimating lens and the imaging lens are of identical focal lenght, there’s no enlargement of the slit, and the slit width projected onto the CCD is equal to the actual slit width.

It’s doable, albeit difficult, to achieve a slit width of ~100µm. This equals to 12-13 pixels on the CCD (the pixel width of the TC1304 is 8µm). With a dispersion of roughly 0.15 nm/pixel that gives a resolution of 2 nm.