Comparison of the signal-to-noise characteristics of quantum versus thermal ghost imaging

We present a theoretical comparison of the signal-to-noise characteristics of quantum versus thermal ghost imaging. We first calculate the signal-to-noise ratio of each process in terms of its controllable experimental conditions. We show that a key distinction is that a thermal ghost image always resides on top of a large background; the fluctuations in this background constitutes an intrinsic noise source for thermal ghost imaging. In contrast, there is a negligible intrinsic background to a quantum ghost image. However, for practical reasons involving achievable illumination levels, acquisition times for thermal ghost images are often much shorter than those for quantum ghost images. We provide quantitative predictions for the conditions under which each process provides superior performance. Our conclusion is that each process can provide useful functionality, although under complementary conditions.

Figure 1

Typical thermal ghost imaging experimental setup.

Figure 2

Typical experimental setup for performing quantum ghost imaging. SPDC, spontaneous parametric down-converter.

Figure 3

Signal-to-noise (SNR) ratio achievable by either quantum or thermal ghost imaging plotted against the total number of photons used in the illuminating field. The dotted portion of the quantum imaging curve cannot be realistically attained using current biphoton sources but is shown for completeness. The three curves for thermal ghost imaging correspond to different numbers $K$ of realizations (speckle patterns) that are averaged together to form the ghost image. We take the object to be a binary object with total transmitting area of ${10}^4$ pixels and the characteristic area of a speckle to be $\pi {\sigma }^2=100$ pixels. We assume that the illumination beam has a cross-sectional area of ${10}^5$ pixels.