A common problem in astronomy is the determination of the time
shift between two otherwise identical time series of measured flux
from a variable source, in short the determination of a time delay. One
example of where this problem occurs is in the determination of the
Hubble constant from multiple images of gravitationally lensed variable
quasars. I will demonstrate that this problem is very similar to the
problem of reverberation mapping of active galactic nuclei (AGN),
and therefore the determination of time delays can also be seen as a
restricted inverse problem.
I will describe a method developed to solve this inverse problem and it
is applied to the time series measured for the double quasar QSO 0957+561.
The resulting time delay is $425 \pm 17\ {\rm d}$. This leads to a best
value for the Hubble constant of
$H_0\ =\ 66 \pm 10\ {\rm km\ s^{-1}\ Mpc^{-1}}$.
An additional advantage of this method is that it determines the magnification ratio(s) of the images as well as the delay, and can detect contamination from foreground or background sources as well as microlensing.