"Conoscopic viewing" is simply imaging the back pupil plane of the objective lens rather than the sample. Typically, this is done with the use of a "Bertrand lens" in the optical path. Conoscopy a useful technique that images the Fourier Transform of the sample plane, which has a lot of meaning in crystallography in particular and light scattering in general.
As a warm-up to my next set of images, here I'm showing a simple sample that is easy to make at home- a piece of plastic overhead transparency sheet, placed between a slide and coverslip. Common transparency sheets are biaxial materials- there are 2 optical axes generated during the stretching/pulling process of fabrication. This can be easily visualized via conoscopy:
The bulls-eye patterns are centered on the optical axes, which are propagation directions that do not change the polarization state. This setup used crossed polarizers, an immersion condenser (NA 1.3) and an immersion lens (Leica HCX PL APO 100/1.47). Stacking two transparency sheets with relative orientations of 45 degrees given this:
And two sheets at 90 degrees relative orientation gives this:
Try this out- it's easy!
Transparency sheet
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