
282 11. Transfer Functions; Hubble Space Telescope
Given a symmetric PSF and a circular aperture with a central obscuration, the
methods of Fourier transforms give the following relations between the PSF, EE,
and MTF:
7^2/1 _ e2)r)2 poo
T(v) = —^ 2"^— /(a)yo(27rva)a da, (11.1.8)
22
Jo
Q;2
nv,
PSF(a) = ^^—-^ J^ nv)/o(27rva)v dv, (11.1.9)
EE(a) = 2n(x\^ T(v)J^(2nvoc)dv, (11.1.10)
Jo
where v is the frequency in angular units, a is the angular radius of the image, and
JQ
and Ji are Bessel functions. Because v is given in angular units, the cutoff
frequency
v^
in these units is D/X. Equations (11.1.8)-(l
1.1.10)
can be written in
linear units b