1. Simulating super-resolution structured illumination microscopy
Nathan Staffa
Department of Electrical Engineering, Stanford University
Motivation
Methodology
Separate and shift to corresponding position in spectrum
The Diffraction Limit
Though microscopy techniques continue to improve, the diffraction limit presents a fundamental barrier to resolution. Fortunately, numerous methodologies have emerged to bypass this limitation, including super-resolution structured illumination.
Structured illumination presents a simple, yet effective, method to achieve a doubling of spatial resolution versus conventional optical microscopy.
Illuminate with high frequency cosines varied in phase and direction
Weight and combine via Wiener filtering
Full spectrum
Overlaid spectral copies; one set for each direction
Diffraction-limited spectrum
Next steps
Results
While still working within the pass-band of the optical transfer function (the OTF support), we are able to extend the spectral coverage in the reconstructed image by a factor of two in each direction. This increase creates a corresponding two-times increase in the resolution capability of the imaging system.
This resolution increase presents as another limitation and a function of the original diffraction limit, due to the maximum observable frequency of the illumination also being constrained by the extent of the OTF support.
Compared to confocal microscopy, which also enables surpassing of the diffraction limit, SR-SIM utilizes the full strength of emission light, resulting in a higher SNR.
The methods employed here constitute well-characterized systems allowing for straightforward inversion. Applying compressive imaging concepts to the problem would facilitate an exploration into possible optimizations for the method. Potential methods include random point illuminations and reduction in number of excitations necessary.
PSNR =
Conventionally observed spectrum
References
Gustafsson, Mats GL. "Surpassing the lateral resolution limit by a factor of two using
structured illumination microscopy." Journal of microscopy 198.2 (2000):
Lukeš, Tomas, et al. "Comparison of image reconstruction methods for structured
illumination microscopy." SPIE Photonics Europe. International Society for Optics
and Photonics, 2014.
Vindin, Howard. Depth Coded Phalloidin Stained Actin Filaments Cancer Cell. Digital
image. Wikimedia Commons. 20 May Web. 9 Mar  CC BY-SA 4.0
PSNR =
Reconstructed spectrum relative to diffraction limit