All telescopes produce some linear polarization. This is usually measured by observing nearby stars known to be unpolarized. For the WHT such observations indicate an instrumental polarization of less than 0.1 %, which is excellent; Fig. 12 shows such an observation. After re-aluminization of the telescope mirrors, the telescope polarization may have changed.
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Figure 12: Tests on `unpolarized' star during commissioning (courtesy Dave Axon, Jim Hough). Lower panel is with calibration Polaroid in the beam; drop-off of degree of polarization at low pixel numbers is due to Polaroid failure.
Metallic slits can produce polarization. Because the halfwave plate precedes the slit, slit polarization will be cancelled as long as the stellar image is recentred for each exposure. The low value of instrumental polarization indicates that effective slit polarization cannot be very strong. A way to search for it would be to open the slit wide, under good conditions, and observe a zero-polarization star. Move the star from centre to slit edge when rotating the halfwave through 45 degrees; this introduces any slit polarization that may be present while you are inverting the object polarization. Compare this with a normal observation of the object. For normal use, one should be almost totally immune from slit polarization when operating ISIS like a photometer, with a 5-arcsec slit and Dekker in 1-arcsec seeing (accepting some uncertainty of the wavelength scale).
An out-of-focus image can lead to polarization effects if one samples it asymmetrically with the spectrograph slit. To some extent, one samples a certain part of the primary mirror and will see the polarization due to oblique incidence on that part of the mirror. With accurate focusing, all parts of the primary contribute equally and the average is zero.