I have a divergent beam coming from a sample in the NIR region. I need to converge the light into a fiber and take the spectrum. A rough sketch of the set up is attached here. Could some please suggest on how to select the specifications of the lenses and the optical fiber so that the emitted radiation is effectively coupled into fiber.
When you couple light into a fiber you have to match the beam diameter at the fiber to the fiber core and the divergence of your beam to the numerical aperure of your fiber.
So you should estimate or measure the beam diameter before the fiber and calculate a suitable lens or telescope in order to match these conditions.
Edit: in your specific case, I would assume the telescope you should choose depends on the size of the area you want to investigate on the metal surface.
The main question is what do you mean while saying "effectively couple". From your sketch it seems that the problem relates to non-imaging optics. It means that if you take any lenses and place them at any distances, some radiation of your heated metal will be launched into the fiber.
The choice for actually effective coupling should be made by two steps.
1) Paraxial estimates: Dmet x NA1 = Dfib x NA2 (NA2 < NAfib),
where NA1, NA2 are numerical apertures in object and image space. Dfib is the fiber core diameter and Dmet = spotsize on the metal you want to monitore. Surely, NA2 < numerical aperture of the fiber. Afrer making this short estimates you should made
2) Numerical simulations in any optical design software (Code V, Zemax....) and design you optical system made by OEM or standard components
In case when you want launch radiation from Dmet to Dfib with more than 90% efficience a system "Lens1+Lens2" should be diffraction-limited (or aberration-free). So it should be simulated as a whole so collimation is not necessary (finite source-finite image). I think it will actually require not 2, but 3-4 lenses.
The larger NA1/NA2 ratio the larger total F-number. So, in extreme situation If you want to study extended region of the metal the component "Lens1" can be eliminated and total F-numbet will be maximum.
essentially, you have to match the collection angle of the your collecting lens to the NA numerical aperture of the optical fiber as well as the image size should be matched to the core diameter of the optical fiber.
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