This relation was given by Gascoigne [4.9]. Taking the value of (bsi)rc from Table 3.2 as -1.03629, (4.10) gives g = (0.017 822)/' , only about 1.8% of | /1. The single Gascoigne plate can correct the first two conditions of (4.5) by its two parameters of position and asphericity; but it cannot correct the third condition for astigmatism. In fact, it makes this far worse, but is still a most useful form of corrector as we shall now prove.
For a single plate, the astigmatism is from the third equation of (4.5), and from (4.7) and (4.8):
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