Differential Ghost Imaging

We present a new technique, differential ghost imaging (DGI), which dramatically enhances the signal-to-noise ratio (SNR) of imaging methods based on spatially correlated beams. DGI can measure the transmission function of an object in absolute units, with a SNR that can be orders of magnitude higher than the one achievable with the conventional ghost imaging (GI) analysis. This feature allows for the first time, to our knowledge, the imaging of weakly absorbing objects, which represents a breakthrough for GI applications. Theoretical analysis and experimental and numerical data assessing the performances of the technique are presented.

Figure 1

Schematic diagram of the experimental setup.

Figure 2

Conventional GI (a) and DGI (b) of two totally absorbing particles 820 and $400\mu \mathrm{m}$ in diameter, retrieved after $m={10}^4$ averages. The number of speckles in the beam was $N_{\mathrm{speckle}}\sim 4590$.

Figure 3

Comparison between normalized SNR’s of GI and DGI techniques for an obstacle object as a function of relative size $ϵ=A_{\mathrm{obst}}/A_{\mathrm{beam}}$ and $\overline{T}$(top horizontal axis). Theoretical behaviors [Eqs. (7, 16)] are indicated by the two lines. The experimental data (solid symbols) and numerical simulations (open symbols), match accurately the theory only for DGI. Crosses indicate SNR values for the object of Fig. 2.

Figure 4

Panel (a): DGI of an object made of two absorption filters partially staggered together, so to create four regions of transmission $T(\mathbf{x})=0.16$ (4th quadrant), 0.40 (1st and 3rd quadrants), 1.0 (2nd quadrant). Panel (b): averaged horizontal sections of the 2nd and 1st (solid line) and 3rd and 4th (dashed line) quadrants. Absolute accuracies were 0.04, number of averages $m=4\times {10}^4$.

Figure 5

Original slide (a),DGI (b) and GI (c) images of a detail of the famous painting “Nascita di Venere” by S. Botticelli (Firenze, Italy, A.D. $\sim 1484$) retrieved after $m={10}^5$ averages. The original image was convolved with a PSF of width equal to the speckle size ${\delta }_0\sim 85\mu \mathrm{m}$.