My PhD work dealt with the topic of sensing and imaging using light that had been transmitted through a random medium. This topic is often applied to practical problems such as imaging through a turbulent atmosphere or detecting objects, like a tumor, buried beneath an opaque substance, like skin and muscle tissue. Though I don't necessarily work in this field anymore, I still follow its developments occasionally.
A few articles appeared within the last week in journals like Nature Photonics]] about the problem of imaging through walls. This problem has been studied since the late 1980's in a number of papers, including the notable Feng, Kane, Lee, and Stone paper and Freund's discussion of using cross-correlating two speckle patterns, one of which is a reference wave, to do a sort of holographic imaging. The recent work continues from these original ideas and applies them to microscopy.
One article appeared on the arXiv and is from the Mosk and Lagendijk camp. In this article, they exploit the optical memory effect, whereby a speckle pattern generated by the multiple scattering of a plane wave by a random slab is simply translated as the angle of incidence of the plane wave is varied. If a thin fluorescent target is placed directly on the opposite face of the scattering slab, it will be excited by the speckle pattern and emit a fluorescence signal that can be captured by an objective. Changing the angle of incidence of the plane wave then allows for multiple points to scan the sample in parallel. Ultimately, a number of images are taken with the sample illuminated by several transversally shifted speckle patterns and the resulting 4D data cube (corresponding to the sample's x-y dimensions and the two tilt angles of the incident plane wave) is used to render an image with improved resolution.
As stated in the article's title, the resolution improvement is relative to that of a widefield microscope. They obtain an effective point spread function of about 140 nm and a field of view of 10 microns by 10 microns.
So how does the technique work? My first thought was that the memory effect is simply another way of saying that the speckle pattern acts as a number of confocal-like point sources, which essentially means this is something of a parallelized confocal microscope. However, I'm not sure this is correct for two reasons: 1) there is no detection pin hole, and 2) the angle of incidence of the plane wave is scanned over a small angular range so that the speckle pattern is simply translated. If the angle of incidence is so great that the linear change in phase of the plane wave is greater than roughly the size of the scattering slab, the speckle pattern is no longer simply translated but changes completely.
In reality, the ultimate resolution of this technique is the average speckle grain size, which can't be less than about half the wavelength. This suggests that the angular spectrum of the speckle pattern is what determines the resolution improvement.
The speckle pattern in a region bounded by the maximum extent of the memory effect has a fixed angular spectrum and translating the speckle pattern only changes the phase of the spectrum. So, scanning a target with a speckle pattern produces beat patterns containing high spatial frequency information that can propgate on the low spatial frequency waves that reach the objective. Translating the speckle pattern then performs a sort of phase-shifting interferometry that allows for both intensity and phase retrieval of the object.
Importantly, if the speckle pattern is scanned outside the range of the memory effect, the speckle's angular spectrum within the region changes completely so that the original reference wave is lost. The fact that the object is fluorescent and not simply scattering the light shouldn't matter if the fluorescence intensity is linear with the excitation light intensity. However, if the fluorescence has saturated at the average intensity of the speckle pattern, then I'm not exactly sure that this technique will work (though maybe some sort of nonlinear structured illumination microscopy could be achieved).
Overall it's a neat demonstration and worth the exercise to understand it, though I'm doubtful that at this point it would be useful for applications in the life sciences. This is because the resolution isn't that much better than a spinning disk confocal microscope, which has a larger field of view and would arguably be easier to use by biologists.