I understand why starshades have the shape they do, but i don't seem to understand why they have to be put so far away from the telescope. Why can't we keep the same apodization function, but just make it smaller and thus bring it closer?

An answer i give to myself but i would like to have a confirmation is that the dimension of the actual stashade affects the diffraction given a wavelength $\lambda $ as in the single split experiment the diffraction is affected by the width of the slit $\alpha $.

In case i am right does this mean that a given starshade will be usefull only for certain kind of stars? Does this mean for example that a given starshade might block perfectly the light from a white dwarf but not so well from a red giant?



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