Rotating coherent scattering microscopy

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Rotating coherent scattering microscopy or ROCS microscopy is a label-free optical imaging technique based on coherent elastic backscattering of an obliquely incident, collimated laser beam that rotates azimuthally around the optical axis. The method can be used to image both biological cells and sub-wavelength particles. Under highly oblique illumination, the achievable spatial resolution approaches nearly twice that obtained with conventional normal illumination. During the rotation within the camera exposure time, intensity images corresponding to different illumination directions are integrated by the camera.

ROCS typically employs bluish laser wavelengths to enhance contrast and spatial resolution. The technique can be operated in dark-field and bright-field configurations, as well as in total internal reflection (TIR) and non-TIR illumination modes.

History

The imaging method was developed in 2013 by Alexander Rohrbach and his group at the University of Freiburg, Germany. It was initially introduced under a different name and implemented in both darkfield (DF) and total internal reflection (TIR) illumination modes. In later publications, the method became known as Rotating Coherent Scattering (ROCS) microscopy.

Principles

File:ROCS principle.jpg

ROCS principle: An incident laser beam (blue arrow) rotates typically at f = 100 Hz under oblique angles illuminating the object from all azimuthal directions. Right: Wavefronts of scattered light from variable illuminations propagate towards the camera, thereby forming a ROCS image.

File:4 ROCS modes.jpg

ROCS modes: An incident laser beam (blue arrow) obliquely illuminates particles. Back scattered light is shown by a dashed arrow.

Coherent intensity images $I_{\mathrm{c}\mathrm{a}\mathrm{m}}(\mathbf{𝐫},\varphi )={|E_{\mathrm{c}\mathrm{a}\mathrm{m}}(\mathbf{𝐫},\varphi )|}^2$ acquired from different azimuthal directions $\varphi$ are integrated during the camera exposure time. The back-scattered electro-magnetic fields propagate through the optical system and interfer at the camera plane, resulting in the detected field $E_{\mathrm{c}\mathrm{a}\mathrm{m}}(\mathbf{𝐫},\varphi )$. The ROCS image is given by

$I_{\mathrm{R}\mathrm{O}\mathrm{C}\mathrm{S}}(\mathbf{𝐫})==\underset{0}{\overset{2\pi }{\int }}{|E_{\mathrm{c}\mathrm{a}\mathrm{m}}(\mathbf{𝐫},\varphi )|}^{2}d\varphi$

At a laser wavelength of 445 nm, ROCS can achieve spatial resolutions of approximately 160 nm and temporal resolutions of 5 ms using illumination powers of only a few microwatts. ROCS requires no computational post-processing and can acquire thousands of images without loss of quality. These properties represent significant advantages compared with many fluorescence-based sub-diffraction imaging methods.

Theory of image formation

A ROCS image is obtained by $\varphi$ = 0...2π azimuthal rotation and integration of coherent intensity images acquired for each illumination direction. Neglecting polarizations effects, the angle-dependent interference between the reflected field $E_r(\mathbf{𝐫},\varphi )$​ and the backscattered field $E_s(\mathbf{𝐫},\varphi )$​ yields

$I_{\mathrm{R}\mathrm{O}\mathrm{C}\mathrm{S}}(\mathbf{𝐫})=\underset{0}{\overset{2\pi }{\int }}{|E_r(\mathbf{𝐫},\varphi )+E_{\mathrm{s}}(\mathbf{𝐫},\varphi )|}^{2}d\varphi$

The ROCS image intensity can be decomposed into three contributions: a background term, a dark-field scattering term, and an interferometric enhancement term. Explicitly,

$I_{\mathrm{R}\mathrm{O}\mathrm{C}\mathrm{S}}(\mathbf{𝐫})=\underset{0}{\overset{2\pi }{\int }}(I_r(\mathbf{𝐫},\varphi )+I_s(\mathbf{𝐫},\varphi )+I_{inf}(\mathbf{𝐫},\varphi ))d\varphi$

with background intensity $\int I_{r}d\varphi$ , with the darkfield image $I_{\mathrm{R}\mathrm{O}\mathrm{C}\mathrm{S}}^{\mathrm{D}\mathrm{F}}(\mathbf{𝐫})=\int I_s(\mathbf{𝐫},\varphi )d\varphi$

and with an interferometric enhancement term, controlled by the degree of coherence $\gamma$.

$I_{\mathrm{R}\mathrm{O}\mathrm{C}\mathrm{S}}^{\mathrm{i}\mathrm{n}\mathrm{f}}(\mathbf{𝐫})=2\gamma \int \sqrt{I_r(\mathbf{𝐫},\varphi )I_s(\mathbf{𝐫},\varphi )}\sin (\mathrm{\Delta }\phi (\mathbf{𝐫},\varphi ))d\varphi$

For a distribution of N scatterers, the object function is $f(\mathbf{𝐫})=\sum _{j=1}^N{f}_j(\mathbf{𝐫}-{\mathbf{𝐫}}_j)$ and the backscattered fields at the camera are $E_{cam}(\mathbf{𝐫},\varphi )=\sum _j{E}_{cam,j}(\mathbf{𝐫},\varphi )=\sum _j|E_{sj}(\mathbf{𝐫},\varphi )|e^{i{\phi }_j(\mathbf{𝐫},\varphi )}$.

Interferometric amplification in darkfield ROCS

File:ROCS Astrazeneca BGS20 glow2.webm

Adeno viruses in AstraZeneca vaccination fluid

Also dark-field ROCS images exhibit enhanced spatial resolution and contrast due to the mutual interference of the scattered fields originating from multiple particles. For N scattering particles the scattered fields $|E_{sj}|e^{i{\phi }_j}$ from individual particles interfere coherently at the camera plane (with index j < N).

The dark-field ROCS intensity is therefore given by

$I_{\mathrm{R}\mathrm{O}\mathrm{C}\mathrm{S}}^{\mathrm{D}\mathrm{F}}(\mathbf{𝐫})=\underset{0}{\overset{2\pi }{\int }}{|\sum _j|E_{sj}(\mathbf{𝐫},\varphi )|e^{i{\phi }_j(\mathbf{𝐫},\varphi )}|}^2$$=\underset{0}{\overset{2\pi }{\int }}\sum _j{I}_{\mathrm{c}\mathrm{a}\mathrm{m},j}(\mathbf{𝐫},\varphi )d\varphi +\gamma \underset{0}{\overset{2\pi }{\int }}\sum _{j\ne k}\sqrt{I_{\mathrm{c}\mathrm{a}\mathrm{m},j}{I}_{\mathrm{c}\mathrm{a}\mathrm{m},k}}\cos (\mathrm{\Delta }{\phi }_{jk}(\mathbf{𝐫},\varphi ))d\varphi$

The first term represents the angular integration of the N self-interference (intensity) contributions from individual particles. The second term contains N(N−1) cross-interference contributions, weighted by the degree of coherence γ between the scattered fields:

Increase in spatial resolution

The increase in spatial resolution results from the oblique illumination of the object by a plane wave, $e^{-i{\mathbf{𝐤}}_i(\varphi ,\theta )\cdot \mathbf{𝐫}}\cdot f(\mathbf{𝐫})$ with $\theta$ being the polar angle of illumination. In Fourier space, the object spectrum is shifted, $F(\mathbf{𝐤}-{\mathbf{𝐤}}_i(\varphi ,\theta ))$ enabling transfers of higher spatial frequencies of the fields backscattered from the object. The ROCS image intensity reads

$I_{\mathrm{R}\mathrm{O}\mathrm{C}\mathrm{S}}(\mathbf{𝐫},q)=\underset{0}{\overset{2\pi }{\int }}{|[(q+if(\mathbf{𝐫}))e^{-i{\mathbf{𝐤}}_r(\varphi ,\theta )\cdot \mathbf{𝐫}}]\star h_c(\mathbf{𝐫})|}^{2}d\varphi$

Here $h_c(\mathbf{𝐫})$ denotes the coherent point spread function (PSF) and the $\star$ - symbol a convolution, prior to modulus squaring. The parameter q distinguishes between darkfield $I_{\mathrm{R}\mathrm{O}\mathrm{C}\mathrm{S}}^{\mathrm{D}\mathrm{F}}=I_{\mathrm{R}\mathrm{O}\mathrm{C}\mathrm{S}}(q=0)$ and brightfield $I_{\mathrm{R}\mathrm{O}\mathrm{C}\mathrm{S}}^{\mathrm{B}\mathrm{F}}=I_{\mathrm{R}\mathrm{O}\mathrm{C}\mathrm{S}}(q=1)$.

ROCS microscopy is based on field modulation and can be considered the coherent counterpart of structured illumination microscopy (SIM), which relies on intensity modulation. In both techniques, oblique illumination is used to generate spatial modulation of the object illumination, resulting in shifts of the object spectrum in Fourier space.

Speckles

Angular rotation does not average out speckles. The speckle patterns observed under illumination from a single direction represent direction-dependent distortions of the object structure. As the illumination rotates and the object is probed from multiple azimuthal directions, these distorted patterns combine to reconstruct the correctly shaped object features in the integrated backscattered image.

Applications

ROCS can be used to image both cells and small particles. ROCS was applied to

• nano-scale colloids
• viruses (see movie of AstraZeneca (Covid-19) vaccination fluid)
• microtubules
• helical bacteria
• filopodia growth and retrograde flow
• reorganization of macrophage actin cortex structures
• degranulation and pore opening in mast cells
• tunneling nanotube dynamics of cardiac fibroblasts
• thermal noise driven binding behavior of virus-sized particles at cells
• bacterial lectin dynamics at lung cells cortices
• migration of platelets and endothelial cells
• sub-particle chemcial transformation
• deep-learning in ROCS image formation
• Terahertz Imaging

References

This article "Rotating coherent scattering microscopy" is from Wikipedia. The list of its authors can be seen in its historical and/or the page Edithistory:Rotating coherent scattering microscopy. Articles copied from Draft Namespace on Wikipedia could be seen on the Draft Namespace of Wikipedia and not main one.

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