Observations of Time Delays in Gravitational Lenses from Intensity Fluctuations: The Coherence Function

Measurements of the spectrum of the fluctuations of the output current of the quadratic detector of a telescope can be used to find unresolved astronomical gravitational lenses and determine time delays between their image components. These time delays can be used for astronomical studies. The spatial correlation coefficient of a source is an important parameter that quantifies the loss of contrast, caused by the extendedness of the source, in the spectral modulation of the intensity fluctuations. This work shows that the correlation coefficient must not be evaluated at the frequency of observation, but must instead be evaluated at the much lower beat frequencies of the spectrum of the fluctuations. This opens up a powerful novel technique to find unresolved gravitational lenses and to study the lensing event and the source.