A hands-on walkthrough of structured-illumination reconstruction, the forward problem (how the raw data is made) and the inverse problem (how we get the detail back). Every picture on this page was computed live from the shape2fate code on real and synthetic data, none are copied from the paper.
Here's what we want to image: structure finer than the microscope can normally resolve, thin spokes and small rings (clathrin-coated pits).
SIM doesn't illuminate evenly. It projects a fine striped pattern, at 3 angles, each shifted through 3 phases: 9 patterns in all.
Where fine detail overlaps the stripes, coarse moiré fringes appear. Those fringes are large enough to pass through the lens, so the hidden detail rides in, disguised.
The objective is a low-pass filter, its OTF. Everything finer than its cutoff is erased… except what moiré smuggled into the passband.
Pixel binning and photon (Poisson) noise give the 9 raw frames you actually save to disk.
Average the 9 and the stripes cancel out, you're left with an ordinary, blurry widefield image. Every bit of the smuggled-in detail is still there, hidden across the individual frames. The inverse problem is getting it back.
Drag the slider (or scroll) to add frames one at a time.
In the frequency domain the widefield is a single disc, the passband. A structured frame secretly carries extra copies of the spectrum, shifted by the stripe's carrier frequency, folded on top of the disc.
First SHAPE recovers, from the raw pixels alone: the carrier frequency & angle (cross-correlation peak, Cao et al., BOE 2018), the phase (Perez, Chang & Stelzer, Sci. Rep. 2016), and the modulation depth (Müller et al. (fairSIM), Nat. Commun. 2016).
A consistency check follows: the three carriers must have equal length, sit ~60° apart, and show enough modulation.
For each angle, a 3×3 un-mixing matrix (built from the 3 phases) splits the frames into three overlapping Fourier orders: the centre band and two side-bands.
Each side-band is moved back to where it truly belongs. The passband grows from one disc into a seven-disc "flower", reaching about twice as far. That extra reach IS the resolution gain.
A Wiener filter weights the overlapping orders by signal-to-noise; an apodization taper smooths the edge to suppress ringing.
(SHAPE also runs a short Richardson–Lucy pre-deconvolution to sharpen first, 10 iterations by default.)
Inverse-FFT the combined spectrum and you have the super-resolved image. The spokes near the centre, a blur in widefield, are resolved.
Drag the divider to wipe between widefield and SHAPE.
Exactly the same steps on one region of a real clathrin (eGFP-CLCa) movie: 9 noisy frames → widefield → SHAPE. Real pits sharpen and separate.
The sharp image is only the setup. A CNN then detects the pits, and a linker stitches them into tracks over time, that's the biology. The full detection-and-tracking benchmark lives on page 1.