Quantified Advantage of Ghost Imaging over Regular Imaging

Ghost imaging is a remarkable technique where light that never interacts with an object is detected with a camera and still the image of the object is recorded. The method relies on the use of correlated light and an additional bucket detector. Ghost imaging has been used in archaeology, bio-medicine, for seeing through turbid media, and promises X-ray imaging improvements, amongst many other applications. However, the advantage of ghost imaging over regular imaging can be difficult to quantify. For classical ghost imaging of a single pixel aperture (the object), we find a closed analytic expression for the signal-to-noise ratio using basic statistics. We find that this signal-to-noise ratio can exceed that of regular imaging with the same exposure of the aperture when the detectors are sufficiently noisy, illustrating a simple and quantifiable advantage. Numerical simulation confirms the theoretical analysis.