Two-color ghost imaging

Nondegenerate-wavelength (or two-color) ghost imaging using either thermal or quantum light sources is studied theoretically. We demonstrate that a high-quality ghost image can be obtained even when the wavelengths of light used in the object and reference arms are very different. The spatial resolution of the ghost image is found in general to depend on each of these wavelengths, although in many practical situations it depends primarily on the wavelength used to illuminate the object. The resolution of nondegenerate-wavelength thermal ghost imaging can be higher than that of its quantum counterpart despite the fact that the photons have the same degree of spatial correlation in the two cases.

Figure 1

(Color online) (a) Setup for nondegenerate-wavelength thermal ghost imaging. Identical random intensity patterns are impressed onto two laser beams of wavelengths ${\lambda }_o$ and ${\lambda }_r$ by passing them through the same spatial light modulating system (SLMS). One of the beams is then used to illuminate the object and the transmitted power is measured by a bucket detector. The transverse intensity distribution of the other beam, known as the reference beam, is measured by an imaging detector such as a charge coupled device (CCD) camera. The correlation signal between the outputs of the two detectors produces the “ghost” image of the object. (b) The corresponding setup for nondegenerate-wavelength quantum ghost imaging. Here, correlations between the two beams are created by the process of PDC. DM: dichroic mirror; PBS: polarizing beam splitter.

Figure 2

(Color online) Unfolded ray diagrams used to describe ghost imaging. Both thermal and quantum ghost imaging entail imaging an effective object plane onto the image plane. The position of the effective object plane depends on both ${\lambda }_o$ and ${\lambda }_r$. For definiteness the figure is drawn for the situation ${\lambda }_o<{\lambda }_r$.

Figure 3

(Color online) (a) Width of the point-spread function ${\Delta }_{\text{PSF}}$ as a function of ${\lambda }_r$ for (from bottom to top) ${\lambda }_o=0.1$, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, and $5.0\mu \text{m}$. Parameters used are ${\sigma }_x=5\mu \text{m}$, $w=10\text{mm}$, $D=20\text{mm}$, $l_{r1}=100\text{mm}$, and $l_o=150\text{mm}$. The dots denote the cases with ${\lambda }_r=\left(l_o/l_{r1}\right){\lambda }_o=1.5{\lambda }_o$, in which case ${\Delta }_{\text{PSF}}$ attains the smallest value for a given ${\lambda }_o$. (b) The corresponding plot of ${\Delta }_{\text{PSF}}$ for nondegenerate-wavelength quantum ghost imaging.