F g

giving for small values of g/f' a distance g from the focus about twice that of the doublet with correspondingly larger diameter. This is an advantage for higher order aberrations, but we must remember that the Gascoigne plate does not correct S/// - indeed it is vastly increased.

Equation (4.59) effectively expresses the scaling law first enunciated in a major paper on RC telescopes and correctors by Wynne [4.14]. Since g ^ f', the spherical aberration of the corrector will increase roughly linearly with g/f'. But if the corrector is scaled in the same proportion, this metric change has no effect on its angular contributions to coma and astigmatism. (This can easily be formally confirmed from Eqs. (4.47), (4.48) and (4.51)). This property is precisely what is required for different eccentricities of different RC telescope primaries of constant focal length and relative aperture, for which the coma and astigmatism contributions are constant. Only minor changes will need to be made for real lens thicknesses. Wynne shows that the same principle applies to a more complex corrector such as one consisting of three lenses.

Consider now the case of a thin, afocal doublet combined with an aspheric plate separated from the doublet. The E-values are now different, Eqs. (4.47) giving

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