Improved Spatial Resolution Achieved by Chromatic Intensity Interferometry

Interferometers are widely used in imaging technologies to achieve enhanced spatial resolution, but require that the incoming photons be indistinguishable. In previous work, we built and analyzed color erasure detectors, which expand the scope of intensity interferometry to accommodate sources of different colors. Here we demonstrate experimentally how color erasure detectors can achieve improved spatial resolution in an imaging task, well beyond the diffraction limit. Utilizing two 10.9-mm-aperture telescopes and a 0.8 m baseline, we measure the distance between a 1063.6 and a 1064.4 nm source separated by 4.2 mm at a distance of 1.43 km, which surpasses the diffraction limit of a single telescope by about 40 times. Moreover, chromatic intensity interferometry allows us to recover the phase of the Fourier transform of the imaged objects—a quantity that is, in the presence of modest noise, inaccessible to conventional intensity interferometry.

Figure 1

Geometry of the intensity interferometer. Consider a coordinate system with the interferometer baseline and its perpendicular bisector as the axes. Then the telescopes $T_A$ and $T_B$ are positioned at ${\mathbf{r}}_A=(-x/2,0)$ and ${\mathbf{r}}_B=(x/2,0)$, respectively, and the sources $S_1$ and $S_2$ are positioned at $(L\alpha -d/2,L)$ and $(L\alpha +d/2,L)$ in the small angle approximation, respectively.

Figure 2

Scheme of the chromatic intensity interferometer. In the “Target” panel, two sources are coupled to free space by collimators. The 1063.6 nm light passes through the BS and the 1064.4 nm light is reflected, forming two point sources separated by 4.2 mm. The interferometer is 1.43 km away from the target. Two telescopes $T_A$ and $T_B$ move with a translation stage to change the baseline of the interferometer. Photons of different wavelengths collected by $T_A$ ($T_B$) are divided by BS1 (BS2), and coupled into PPLN1 and PPLN2 (PPLN3 and PPLN4). PPLN1 (PPLN4) is pumped by a 1548.6 nm laser, and PPLN2 (PPLN3) is pumped by a 1550.3 nm laser. The polarization of the pump is controlled by a PC. After the SFG, the up-converted 630.8 nm photons in PPLN1 and PPLN2 (PPLN3 and PPLN4) are combined by the BS and guided to SPAD1 (SPAD2). The arrival time of the detected photons is recorded by TDC. By calculating the second-order correlation of the signal recorded by TDC with different baselines, we spatially resolve the two sources separated by 4.2 mm at the target. Some abbreviations used in the figure are as follows: periodically poled lithium niobate waveguide (PPLN), beam splitter (BS), polarization controller (PC), and wavelength division multiplexing (WDM).

Figure 3

Experimental data for the chromatic intensity interferometer. (a) A plot of the $g^{(2)}(\tau )$ measurement at $x=0.16\mathrm{m}$ with optimized parameters. The orange curve is a least squares fit to the measured data (blue dots). (b) A graph of ${\lambda }_h{\varphi }_c/(2\pi )$ as a function of $x$ on the entire baseline. The orange line is a least squares fit to the measured data (blue dots). The slope of the fitted line provides a measurement of $\theta$. This set of data corresponds to the fifth point in (c). (c) Shown are 10 measurements of $\theta$ and their distribution. The vertical position of the orange solid line is the actual value of $\theta$, and the vertical position of the orange dashed line is the average of these measurements (blue dots).