Expansion Microscopy Calculator

Expansion microscopy effective resolution with pre- or post-expansion labelling, field of view and expanded gel size.

Model: Illustrative

Expansion factor E (×)Microscope resolution d (nm)Probe size (nm)Label-linker length (nm)

Labelling

Gel thickness before expansion (µm)

Results (pre-expansion units)

Optical term d/E62.5 nm

Label displacement √(probe² + linker²)18.0 nm

Label term (not reduced)18.0 nm

Effective resolution65.0 nm

With post-expansion labelling62.7 nm

Field of view (linear)25.0 %

Field of view (area)6.25 %

Expanded gel thickness200 µm

Volume to image (× unexpanded)64×

d_eff = √((d/E)² + L²) for labels applied before expansion; √((d/E)² + (L/E)²) for labels applied after it.

Assumes isotropic expansion; distortion of a few per cent and incomplete labelling add to the error.

Effective resolution vs expansion factor

Model and references

Illustrative. A simplified model that shows trends and orders of magnitude. Don't use its numbers for design. About the tiers

The microscope's resolution divided by the expansion factor, combined in quadrature with the label displacement, which only post-expansion labelling divides by E. Assumes isotropic expansion; distortion and labelling density are not included.

Chen F., Tillberg P. W., Boyden E. S. (2015). Expansion microscopy. Science 347, 543–548. Physical expansion of the specimen, effective resolution d/E and the measured distortion. doi:10.1126/science.1260088
Wassie A. T., Zhao Y., Boyden E. S. (2019). Expansion microscopy: principles and uses in biological research. Nat. Methods 16, 33–41. Linkage error of pre- and post-expansion labelling. doi:10.1038/s41592-018-0219-4

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