Super resolving binary-source hypothesis testing with a double-clad fiber coupler

Abstract

We present a technique for binary spatial mode demultiplexing, using a double-clad fiber coupler as an optical mode sorter, for hypothesis testing for one or two point sources in an incident optical field. By directly coupling an optical field through a double-clad fiber coupler, we demultiplex the field into the fundamental mode and a superposition of higher-order modes. We use the ratio of multi-mode to single-mode power to distinguish between single and double point sources. In a tabletop demonstration of the technique, we demonstrate the capability to accurately identify the presence of two sources separated below the Rayleigh limit for relative brightnesses from 0 dB to -20 dB. For sources with less than 5 dB difference in their relative powers, our imaging protocol can correctly determine the presence of a second optical source even when the two sources have separations 50x smaller than the Rayleigh limit. These results highlight the potential of this technique as a simple tool for super-resolving classification of a pair of point emitters, especially in the context of astronomical imaging for binary systems.

Figures (3)

• Figure 1: Experimental Setup for source preparation and Binary SPADE-based source classification. EDFA, Erbium-doped fiber amplifier; AOM, acousto-optic modulator; FC, fiber-collimator; TS, Translation stage; BS, beam splitter; DCF-C, Double-clad fiber coupler; PD, photodetector.
• Figure 2: Left: Contour plot of the ratio of the coupled power in the multi-mode port to the single-mode port as a function of the relative power of the two sources (y-axis) and separation between them (x-axis). As expected, larger separation results in a larger multi-mode to single-mode coupling ratio for a given power ratio. The black dashed line shows the threshold we calibrated to classify a source as a binary. Right: Hypothesis test of whether the imaged source was created by one or two point sources. The color indicates how likely our system is to classify the source correctly. The black dashed curve is fit to the transition from correct to incorrect classification. The red dashed curve is the simulated performance limit of ideal direct imaging.
• Figure 3: Multi-mode to single-mode response ratio of the DCF when a single source is translated a small amount from the center of the imaging system. Note that vertical error bars are too small to show on the plot. The red dashed line is a linear fit to the data below 0.04 wr. The green dashed line is the expected coupling ratio given crosstalk.