My previous blog discussed some historical papers related to the intensity interferometer and its connection to quantum optics. Here, I explain the basic physics of an intensity interferometer.
In the context of spatial coherence, the coherence theory expresses the degree of spatial coherence as,
$$ \gamma_{12} = \frac{\left\langle U_1(t) U_2^\ast(t) \right\rangle}{\sqrt{\left\langle |U_1|^2 \right\rangle \left\langle |U_2|^2 \right\rangle}} $$
with \( U_i(t) \) representing the fields of sources \( i = 1 \) and \( 2 \).
An intensity interferometer measures the intensity correlation function between such sources. If \( I_1(t) \) is the intensity of source 1 and \( I_2(t) \) is the intensity of source 2, then the intensity correlation function is given by:
$$ \left\langle I_1(t) \cdot I_2(t) \right\rangle $$
where the enclosing brackets denote a time average.
This correlation, measured in the intensity interferometer, is related to the degree of spatial coherence in the following way:
$$ \left\langle I_1 I_2 \right\rangle = \left\langle I_1 \right\rangle \left\langle I_2 \right\rangle \left(1 + \left| \gamma_{12} \right|^2 \right) $$
If one ignores the background (the first term in the sum of the above equation) and considers only the fluctuations in the signal (the second term), then the term of relevance will be:
$$ \left\langle \Delta I_1 \Delta I_2 \right\rangle = \left\langle I_1 \right\rangle \left\langle I_2 \right\rangle \left| \gamma_{12} \right|^2 $$
The signal in the intensity interferometer is thus proportional to \( \left| \gamma_{12} \right|^2 \).
A conventional interferometer measures a signal that is proportional to \( \left| \gamma_{12} \right| \), which includes the amplitude and phase, whereas an intensity interferometer measures a signal proportional to \( \left| \gamma_{12} \right|^2 \), which is not sensitive to the phase.
Intensity interferometers have certain advantages compared to conventional interferometers (such as the Michelson interferometer). Below is a partial list:
- Intensity measurements (unlike amplitude or phase) can be done directly using optoelectronic instruments.
- They do not require precise, sub-wavelength optical alignment, unlike amplitude- or wavefront-dividing interferometers.
- They can be used with two detectors that are placed far apart, thereby improving the spatial resolution of the measurement (relevant in astronomy).
A constraint of an intensity interferometer is that the intensity of the participating source should be bright.
Reference:
Dravins, Dainis. ‘Intensity Interferometry: Optical Imaging with Kilometer Baselines’. arXiv.Org, 12 July 2016. https://arxiv.org/abs/1607.03490