Ghost imaging at an XUV free-electron laser

Here we present the results of a classical ghost imaging experiment accomplished at an XUV free-electron laser (FEL). To perform such experiment at an FEL source each x-ray pulse was transmitted through a moving diffuser, which created a noncorrelated speckled beam. This beam was then split in two identical branches by introducing a beam splitter in the form of a transmission grating. In one of these branches the sample was positioned. We demonstrate the possibility of image formation, a double bar in our case, in the beam that has never interacted with the sample. With this experiment we extend the quantum optics methodology to the FEL community.

Figure 1

Conceptual layout of (a) a ghost imaging experiment and (b) schematic setup used at FLASH, which allowed successful ghost imaging using an FEL beam.

Figure 2

Single pulse speckle pattern obtained at a selected position of the diffuser. White boxes define different probed positions, the color bar defines the number of detected photons and the length of the white bar is equal to one millimeter.

Figure 3

Results of ghost imaging reconstruction G($x,y$) [see Eq. (1)] (a) without and (b) with intensity normalization of the reference signal. (c) An averaged image at the bucket detector position. The white scale bar in [(a)–(c)] is $200\mu \mathrm{m}$. (d) Comparison of intensities projected along the vertical direction in (a), dashed blue line; (b), dotted red line; and (c), black empty dots.

Figure 4

(a) Time-averaged intensity over 2115 realizations. (b) Intensity at a selected position of the diffuser, shown to highlight the speckle pattern. White boxes define different probed positions. In (a), (b) the color bar defines the number of detected photons whereas the length of the white bar equals $500\mu \mathrm{m}$. (c) Results of the time-averaged zero mean normalized cross-correlation function, ranging from $+1$ (perfect correlation) to 0 (no correlation). Each of the boxes corresponding to $-1$ order in (a) is correlated with every detector position and the line through each box center is drawn. The structure of the diffracted beam is especially evident from position I, demonstrating strong correlation for $\pm 1$, $\pm 2$, and zero order as well as half-orders, corresponding to diffraction from the second harmonic in the FEL beam.

Figure 5

Results of an averaged intensity and ghost imaging reconstruction at (a), (b), (c) positions I and (d), (e), (f) II defined in Fig. 4 after 20000 realizations. An averaged intensity in the bucket (a), (d) and reference area (b), (e). (c), (f) Results of the ghost imaging reconstruction G($x,y$) [see Eq. (1)]. The scale bar is $200\mu \mathrm{m}$.

Figure 6

Intensity normalization procedure in the reference area corresponding to position III in Fig. 4. (a) A single realization as measured; (b) the background $\alpha (x,y)$ of (a), extracted by polynomial fitting of (a); (c) the light modulation $\beta (x,y)$; (d) the final result of the procedure, the function $I^{corr}(x,y)$. The time-averaged intensity (20000 realizations) after the normalization procedure (e), compared to the unnormalized averaged-intensity (f). The cyan scale bar is $200\mu \mathrm{m}$.

Figure 7

Simulation procedure. (a) An initial beam consisting of a random speckle patterns; (b) same beam propagated to the reference detector; (c) simulated sample (fully opaque, with the same geometry as the one employed in our experiment); (d) beam defined in (a) propagated though the sample; (e) result of the ghost imaging reconstruction G($x,y$) [see Eq. (1)] using a speckle size of $100\mu \mathrm{m}$ FWHM.

Figure 8

Ghost imaging simulations G($x,y$) [see Eq. (1)] with the FWHM of speckles of (a) $30\mu \mathrm{m}$, (b) $100\mu \mathrm{m}$, and (c) $200\mu \mathrm{m}$.

Figure 9

Ghost image reconstruction G($x,y$) [see Eq. (1)] with 20000 realizations and $100\mu \mathrm{m}$ speckle size when the number of photons per pulse in both the reference and bucket arm is (a) $5000\mathrm{ph}/\mathrm{pulse}$, (b) $500\mathrm{ph}/\mathrm{pulse}$, and (c) $50\mathrm{ph}/\mathrm{pulse}$. The scale bar corresponds to $200\mu \mathrm{m}$.