Structured Illumination Microscopy
SIM cut-off frequency, lateral resolution and raw image count for linear and saturated structured illumination microscopy.
Results
The pattern frequency lies beyond the detection cut-off: the stripes are not visible in the raw images, so the pattern phase and frequency are estimated from the overlap of the shifted passbands.
k₀ = p · 2NA/λex: two beams at the pupil edge give the finest pattern (p = 1). Linear SIM: k_c = 2NA/λem + k₀ (Gustafsson 2000).
Saturated SIM adds harmonics m·k₀ (Gustafsson 2005). Separating orders −m … m needs 2m + 1 phases per angle.
The resolution 1/k_c is the Abbe-type period, like λ/(2NA) for widefield. Reconstruction (Wiener filtering) and noise set how much of the support is usable.
Frequency support along one pattern direction
Each copy is drawn at unit height; in the raw data the first orders carry half the modulation depth, and harmonics less.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Frequency-support model: the cut-off is the detection cut-off 2NA/λem plus m times the pattern frequency. It gives the Abbe-type resolution 1/k_c and the number of raw images, not the noise or the reconstruction quality.
- Gustafsson M. G. L. (2000). Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy. J. Microsc. 198, 82–87. Shifted passbands, k_c = 2NA/λem + k₀, three phases per angle. doi:10.1046/j.1365-2818.2000.00710.x
- Gustafsson M. G. L. (2005). Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution. PNAS 102, 13081–13086. Harmonics m·k₀ of saturated SIM. doi:10.1073/pnas.0406877102