Non-Invasive Microscopy in Complex Environments Using Overlapping Speckle Correlation Algorithm

By Aryaman PattnayakReviewed by Susha Cheriyedath, M.Sc.Nov 30 2023

A study published in the journal Nature Communications introduces an innovative computational imaging technique named "speckle kinetography." Developed by a research team from Nanjing University of Aeronautics and Astronautics in China, this method leverages the relative motion between microscopic objects and scattering media. It enables non-invasive microscopy-level resolution imaging within complex turbid environments, surpassing previous limitations by imaging through layers multiple times thicker.

The strategy involves processing sequences of randomized speckle interference patterns generated as objects shift behind biological tissues or other disordered media. The computational approach retrieves hidden sample information from embedded cues related to the speckle translations.

The method extracts and correlates data about the overlap between the object's sequential positions without knowledge of the scattering properties. This enables the reconstruction of a sample's autocorrelation, allowing for retrieving the sample's image at up to 1 μm resolution. The significance of this advancement lies in its ability to provide high-resolution imaging in challenging environments without relying on prior knowledge of scattering properties.

New Speckle Kinetography Technique

The Nanjing University team devised an innovative computational imaging strategy centered around an "overlapping speckle correlation algorithm" that pursued this challenging but rewarding goal through an entirely different process, circumventing the fundamental limitations of previous approaches. Their technique completely bypasses the need to characterize, optimize, or interact with the complex intervening media.

Instead, speckle cinematography reconstructs hidden sample information from inherent data imprinted within sequences of speckle interference patterns as microscopic objects shift relative to the static scattering layers. Even if the media are entirely unknown, the method can digitally expose cues related to the overlapping relationships between the object's sequential positions by analyzing how the speckles translate over time.

Correlating this motion-induced speckle data yields the relative displacement between states. Summation after speckle multiplication returns the autocorrelation value at that determined point. Repeating this entire computational workflow for all movements systematically maps out the complete autocorrelation, a blurry image registering the pattern similarity across the object, which can then be inverted through an iterative algorithm to recreate a pixel-sharp estimated original object view.

Technical Details and Demonstrations

On the hardware side, speckle cinematography requires an essential fluorescent, white light, or low-coherence light-emitting diode (LED) microscope imaging setup with an attached camera to sequentially capture magnified speckle images as objects traverse microscopic motion trajectories behind the static scattering layers. Custom code digitally filters and processes this stack of interference patterns into critical constituent components, localized speckles, and slowly varying envelopes, containing essential hidden positional and structural cues. Cross-correlation of envelopes centered around the summation of element-wise speckle multiplication products elegantly extracts relative displacement and overlap relations needed to construct the all-important autocorrelation blueprint from which the object is resurrected after a slight iteration.

Remarkably, this technique neatly sidesteps any considerations of memory effects or wave optics treatments altogether. Instead, information retrieval happens entirely computationally from processing inherent scrambling effects exhibited in arbitrary speckle movements. Notably, the breakthrough approach accommodates spontaneously shifting objects under white light, relaxing lockstep laser illumination constraints typical of wavefront methods. Besides insensitivity to sample motion randomness and spectral properties, the lack of reliance on the imaging system also permits microscopy resolutions using ordinary setups.

However, most critically, by circumventing cumbersome characterization of opaque media a priori necessary for transmission matrix approaches, speckle kinetography significantly advances the capability to image unknown samples like biological tissues quantitatively. The technique capitalizes on more profound penetration limits offered by low-coherence incoherent light to push imaging depths to new extremes.

In demonstrations, the team achieved 1 μm resolution non-invasive imaging through parafilm layers up to ~6 transport mean accessible paths (lt) deep, doubling the usual ~2-3 lt range. Parafilm scatterers realistically mimic tissue. Recovering recognizable microscopic structures even after 16.9 ls traversal highlights breakthrough potential. In separate fluorescence experiments, ten μm fluorescent beads were imaged through a 700 μm chicken breast slice (~3.6 ls), on par with single cell dimensions. This confirms applicability in biomedical and other contexts where high resolution is mandatory.

Using compact microscope components under $750, these results showcase versatile high-accuracy imaging unlocked in complex samples through an easily implemented yet robust computational algorithm―a pivotal early step towards deployable new optical capabilities ranging from augmented microscopy to smart endoscopy and new microscopic biopsies able to overcome the restrictive opacity barriers of tissues using only simple speckle movements and code.

Principle Behind Speckle Kinetography

Conceptually, speckle kinetography rests on visual information preservation principles tied to the innate physics of speckle formation in scattering media. Under incoherent illumination supplying ample photons, discrete microscale regions within diffuse object samples emit quasi-point light sources, producing impulse response patches on the opposite side whose interference yields localized speckle grains. Object translations before the static scattering layers induce speckle movements, retaining data about internal structural relationships through the degree of positional overlap, extractable by cross-correlating the relative translations of the intensity patterns.

Mathematically, this is expressed by the discovery that summing element-wise speckle multiplications yields the autocorrelation value associated with that relative shift. Repeating this masked speckle correlation at all successive object positions incrementally constructs the complete autocorrelation. Enabling lossless retrieval from intensity-only recordings, the autocorrelation describes light property similarity between pattern translations, indirectly encoding object structure priors leveraged by phase retrieval algorithms to reconstruct images digitally.

In effect, dispersed photons passing through complex opaque media undergo entirely randomized trajectories, scrambling any direct imaging. Speckle kinetography, however, shows that helpful positional cues survive propagation through the turbid layers. Computational reconstruction of hidden object information relies solely on capturing and clever processing of these scattered speckle movements instead of ever needing to understand or physically counteract the warping introduced by disordered intervening layers.

Conclusion

This groundbreaking computational imaging technique expertly transforms fundamental speckle formation physics into versatile algorithms and simple microscopes, unlocking newfound powers to non-invasively unveil microscopic structuring details even through the densest opacity boundaries.

Based on software insights and microscope motion cues, speckle kinetography expands imaging capabilities in currently inaccessible living and natural samples, overcoming decade-old depth limits plaguing prevailing approaches. By circumventing complex medium control using only basic instrumentation and portable code exploiting inherent speckle movements, the technique offers accessible, immediate solutions while reshaping future directions across scattering-limited microscopy fields at the heart of scientific discovery.