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This paper mentions two conditions crucial for the classical ghost imaging experiment which are:-

  1. the spatial incoherence of light, and
  2. a measurement time $\ll \tau_{coh}$.

Why is the spatial incoherence required?
It mentions the reason that

a high degree of mutual spatial correlation is present in both planes, as a consequence of the spatial incoherence of the light produced by our source.

Here by plane, they mean the object and the image plane and the source here is the laser followed by a rotating ground glass and a scattering medium followed by it.

What I don't understand here is that they use a 50:50 beam splitter to create identical copies which generates the correlations. How does a spatially incoherent light generate better spatial correlation in the plane than just a normal gaussian beam.

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1 Answer 1

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«Why is the spatial incoherence required?»

figure from https://www.tandfonline.com/doi/full/10.1080/09500340500147240

enter image description here

The spatial incoherence of the “thermal” beam (in the figure in front of the diaphragm D after the turbulent solution) is required here in order to obtain the size of the speckles in its cross section as small as possible (the same flickering spots that we all saw in the red light from a conventional optical computer mouse). With small speckles, there will be a large spatial correlation of intensities between the object and ghost beams (in the figure these are two beams after BS) and the ghost image will be clear (its intensity is calculated as a value proportional to this cross-correlation). For the same reason, the intensities of both beams need to be measured (CCD in the figure) very quickly (in a time shorter than the correlation time of speckles in the cross section of the primary beam). Then the “snapshot” of the correlation between the object and ghost intensities on the CCD will be “instantaneous” (otherwise it will blur due to speckle fluctuations during the measurement time).

«How does a spatially incoherent light generate better spatial correlation»

The greater the spatial coherence of the primary beam, the larger the speckles in its cross section. This primary beam is split into 2 identical beams (object and ghost), of which one is scattered by the object, and the other is used to measure the instantaneous spatial correlation of their intensities on the CCD (a ghost image is essentially a spatial picture of the simultaneous coincidences of photons in these beams). The larger the speckles in these beams, the flatter the graphs of this correlation become (i.e., the resolution of the ghost image decreases). Therefore, it is precisely the decrease in the spatial coherence of the primary beam (the size of the speckles in it) that leads to an increase in resolution (increase in the spatial correlation of the object and ghost beams).

The overall brightness is proportional to the ratio of the speckle area to the area of the object (it is proportional to the total number of spatial modes of incident light that can diffract on the object). Therefore, as the resolution increases (as the speckle size decreases), the brightness decreases. To compensate for this drop (for example, when imaging an object of a smaller area), it is necessary to increase the statistics - to average the correlations of tens and hundreds of thousands of repeated measurements.

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