How does the 3D Cell Explorer produce cell images with better than 200 nm lateral resolution?
Classical Microscopy (e.g. fluorescence imaging)
The cell is directly imaged; so what you see on your camera is the image of the cell. Therefore, one absolutely needs to apply Nyquist sampling on the camera. But, this is NOT true for the 3D Cell Explorer. The paradigm shift to make is that there is no direct imaging of the cell on the camera.
Non-invasive optical nanoscopy can achieve such a lateral resolution by using a quasi-2π-holographic detection scheme and complex deconvolution. The spatial frequencies of the imaged cell do not make any sense to the human eye. But these SCATTERED frequencies are converted into a hologram and synthesize a bandpass which has a resolution DOUBLE the one normally available. Holograms are recorded from different illumination directions on the sample plane and observe sub-wavelength tomographic variations of the specimen. Nanoscale apertures serve to calibrate the tomographic reconstruction and to characterize the imaging system by means of the coherent transfer function. This gives rise to realistic inverse filtering and guarantees true complex field reconstruction.
All the math and proofs are explained in great detail in our peer reviewed Nature Photonics publication here: https://www.nature.com/articles/nphoton.2012.329.
Explaining the Resolution Jump
Rayleigh resolution for incoherent light (e.g. fluo) is 400nm=0.61*520nm/(0.8), for coherent light (e.g. holography) 533nm=0.82*520nm/(0.8) with the diffraction limit (e.g. any imaging by niquist) of 325nm=0.5*520nm/(0.8). In our case for the 3D Cell Explorer configuration, the maximal expected resolution is around 160nm=0.5*520nm/(2*0.8) and we estimate the real resolution (according to Rayleigh) to be about ~190nm. Therefore, taking into account the illuminating wavelength the experimental resolution is 190nm=/lambda/(3.5 NA), indicating a sub-diffraction resolution (d=325 nm at given wavelength and NA) imaging in far-field (non-fluorescent) transmission microscopy.
In conclusion, the 2 terminologies of (i) optical resolution (the real one) and (ii) sampling resolution (the one on the screen) are separated for 3D holotomographic microscopy. For the sake of computational cost-reduction, Nanolive chose to have the sampling optimal at the optical resolution, hence about 180 nm. Again, we can do this, thanks to our technology WITHOUT loosing any real resolution, but of course a user could over-sample the images and have double/triple/etc sampling on the screen with the same optical resolution (e.g. simple zero-padding in fft space to have a smoother image).
We have chosen Mitochondria as a great candidate to demonstrate resolution. Below is an image calculating the separation between Mitochondria using standard signal profiling. In the example we resolve mitochondria tubules as thin as 186 nm (using full width at half maximum standard measurement of object thickness).