Imaging through multi-mode fibres using model-based calibration

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In the last few years, several papers have looked at how it might be possible to use a multimode fibre as an ultra-narrow endoscope (see this post and this post for a bit of background). The most common approach is to use a spatial light modulator to shape the wavefront entering the fibre. If this is done in precisely the right way, interference between light coupled into the different modes of the fibre will result in a focused spot at the far end. By adjusting the input wavefront it’s then possible to scan the spot in two dimensions, allowing point-by-point imaging. Of course, we need to know what wavefronts to use, making it necessary to perform a calibration which requires access to the far end of the fibre. Unfortunately, this calibration is highly dependent on the configuration of the fibre – if the fibre is bent then the calibration changes. This means the technique is only applicable to rigid probes, greatly limiting the scope of potential applications. Now, in a paper published in Nature Photonics, Tomáš Čižmár and colleagues from the University of Dundee have suggested a possible solution to this problem.

Their approach1 is to generate a highly accurate model of the fibre, from which they can identify certain ‘eigenmodes’ or ‘propagation invariant modes’. Light coupled into one of these modes stays in that mode as it travels along the fibre. However, when the fibre is bent, there’s a change in the phase of the light emerging from each of these modes. This results in a change in the interference pattern and invalidates the calibration. However, if the shape of the bend is measured, and the effect of this degree of bending on each mode’s output phase can be modelled, then the calibration can be corrected on the fly.

In practice, there were many complications that had to be worked out. Small variations in the fibre structure, as well as mis-alignments in the optical setup, meant that a purely theoretical model doesn’t provide a good match to experimental reality. So the authors devised correction algorithms that adapt the model to obtain truly propagation invariant modes. They were then able to demonstrate imaging through a fibre with a 90 degree bend using the calibration obtained from a straight fibre. They were also able to show that, if multiple bends are presents, the order of the bends shouldn’t matter too much, greatly simplifying corrections.

There are certainly practical limitations to this approach. It relies on knowing the exact shape of the fibre, and it’s not clear how this information would be obtained in an endoscopic system. And we haven’t yet seen imaging results through fibres formed into more complex shapes. Nevertheless, this is an important advance over the state-of-the-art, and it challenges existing assumptions about the unpredictability of ‘chaotic’ media such as multimode fibres.

References

  1. Plöschner, Martin, Tomáš Tyc, and Tomáš Čižmár. “Seeing through chaos in multimode fibres.” Nature Photonics 9, no. 8 (2015): 529-535.

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