Collimation issue with an DIY echelle spectrograph

Question

I am trying to make an educational echelle spectrograph using easily available materials, basically in a cardboard box. An echelle grating (36 lines/mm) needs another prism to do a cross dispersion and generate a two dimensional spectrum like the following (taken from a astro website).

The design I have is a very "crude" version of the following taken from Astro website. The key difference is that I want to use a slit and a fluorescent lamp as a light source instead of a fiber and the camera is an ordinary digital camera rather than a fancy DSLR. http://www.astrosurf.com/buil/echelle/first.htm

One can readily generate this type of spectrum using any white LED without any collimation. Simply illuminate the echelle and view it via prism. The problem starts with any other light source such as a fluorescent lamp. The requirement to generate a successful echellogram is to have collimated light.

Questions:

1. What is special about LED that it does not need collimation? Even a cell phone light produces a beautiful echellogram, exactly as pictured above.

2. As stated above, problem is with other light sources such as a fluorescent lamp or street light. Does anyone know of a good trick for decent collimation of light from slits made in a cardboard box? Light spreads out a lot from the slit as a wide cone of light.

If we make a simple slit with the help of blades on a cardboard (approximately 0.5 mm wide, 0.8 cm long) and if we place a fluorescent lamp very close to the slit and a lens with its focus at the slit, collimation is poor. The lens is a 25mm Dia. x 100mm Focal length, Achromatic Doublet Lens. By poor collimation, I mean that the echellogram shows repeating images which is a sign that the light is not well collimated.

Answer 1

There are two issues here I think warrant comment.

First, the collimation of an extended source by a mirror or lens is limited by the lateral extent of the source and the focal length of the collimating lens or mirror. If you consider the path of a ray from the edge of the slit through the center of the lens, the angle with respect to the optical axis is given by ArcTan[w/(2 f)], where w is the full width of the slit. For a 0.5mm slit and a 100mm focal length lens this is 0.14 degrees. So the collimated beam will have a half-angle angular extent of 0.14 degrees. For a 500mm focal length, that is reduced to 0.029 degrees. I don't know if that is a sufficient improvement. To really quantify this would best be done with a simulation in an optical design tool such as Zemax OpticStudio.

The second comment concerns where unwanted light goes. Spectrometers are etendue limited devices and in your case is appears you are designing for F/4 . ( 100m / 25mm). This is typical in that slower systems capture less light and faster systems have more aberrations. Good designs generally manage stray light by internal baffles but also by limiting the light cone into the system to that which progresses through the system as intended. By placing the fluorescent lamp directly against the slit you are allowing a much wider cone of light than the spectrometer will accept. You are relying on the mount around the collimating lens to block the excess light. Another way to do this would be to focus the light from this first slit onto a second slit with a lens and housing that permits only F/4 light to reach the second slit.

Kind regards, David