Imaging Through Scattering Media Using the Speckle Memory Effect

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A research team from the University of Twente has found a way to obtain high resolution images of a fluorescent object through a strongly scattering medium. This has been a goal of bioimaging scientists for some time, as it would allow us to use visible light to image much deeper into tissue. Various methods have been suggested, but they generally need some kind of ‘guide-star’ behind the scattering layer. The new approach uses the ‘memory effect’ of speckle to avoid the need for any calibration or guide-star, potentially making it much more applicable to real situations.

When light passes through an opaque medium, repeated scattering distorts the wavefront so that all the original spatial information is lost. If the light is coherent then interference effects result in a speckle pattern at far side of the medium. This seemingly random pattern of light and dark spots bears no apparent relationship to the input wavefront, making it impossible to image directly through the scattering material. If a fluorescent object is placed behind the scattering layer, and the returning fluorescent emission is measured, then we can find out the total amount of light emitted, but learn nothing about its spatial distribution.

However, while the speckle pattern may seem random, it does have some interesting properties. One of these is called the ‘memory effect’. If the incident laser beam is tilted by a small angle then, rather than completely decorrelating, the speckle pattern will be shifted a small distance. This means that by scanning the angle of the beam on two axes it’s possible to translate the speckle pattern in two dimensions across the fluorescent object.

If the fluorescent emission from each position of the speckle pattern is measured, then an image of the convolution between the speckle pattern and the object can be built up. In itself this isn’t terrible interesting, and it certainly bears no obvious relation to the real structure of the object. However, the Twente team noticed something interesting. If we take the autocorrelation of the convolutions (roughly speaking this means convolving it with itself) then this is mathematically equivalent to the autocorrelation of the object convolved with the autocorrelation of the speckle pattern. As the speckle pattern is random, its autocorrelation has a sharp peak. So, to a good approximation, the autocorrelation of the measured signal is equal to the autocorrelation of the object itself.

Again, while this might be interesting from a theoretical point of view, knowing the autocorrelation of the object doesn’t have a great deal of practical use. Autocorrelation is a ‘lossy’ procedure: there is no simple way to perform an ‘inverse autocorrelation’ and recover the original object. If we think about things in terms of spatial frequencies, then we can say that the taking an autocorrelation destroys the ‘phase’ information in the image while preserving only the amplitudes.

However, it turns out that the original object can be estimated using an iterative algorithm for phase recovery. The algorithm uses the constraint that all pixel values in the object must be non-negative. In their paper in Nature1, the team reported being able to obtain an estimate of the image in a few seconds using a standard PC. They demonstrated images of a ‘Pi’ symbol and an autofluroescent sample from a C. majalis plant through a ground diffuser plate. While the images certainly aren’t perfect, they faithfully reproduce the brightest features correctly over a field of view of a millimeter.

It’s probably too early to say whether this will become more than a curiosity and find real applications in bio-imaging. So far, the authors have only demonstrated that the techniques can be used to image through a diffuser plate – it will be interesting to see what would happen if they tried it on biological tissue. But it certainly seems that the idea of practical imaging though strongly scattering media has taken a step closer to reality.

References

  1. Bertolotti, Jacopo, et al. “Non-invasive imaging through opaque scattering layers.” Nature 491.7423 (2012): 232-234.

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