Optical Sectioning Thickness Calculator
Compare optical sectioning capability across widefield, confocal, and multiphoton microscopy techniques.
Widefield (focus to first axial zero, λ/(n − √(n² − NA²)))
0.59 µm
No true sectioning: out-of-focus light is blurred, not rejected
Confocal section, Wilhelm (1 AU)
0.90 µm
Point-pinhole limit 0.38 µm
Confocal section, wave-optical (1 AU)
0.52 µm
Scalar paraxial theory; Wilhelm is 74 % above it
Two-photon axial FWHM (point object, at 2λ)
0.74 µm
λ_exc = 1100 nm; a thin-plane section is ≈ 8 % larger (0.677 vs 0.638 in scalar theory)
Pinhole diameter (object side)
0.48 µm
× magnification at the pinhole plane
Formulas (FWHM, textbook approximations)
Confocal: √[(0.88λ / (n − √(n² − NA²)))² + (√2·n·PH / NA)²], PH = AU × 1.22λ/NA
Point pinhole: 0.64λ / (n − √(n² − NA²))
Wave-optical: FWHM of S(u) = ∫d²r |h(u, r)|² ∫pinhole |h(u, r − w)|² d²w, a thin fluorescent plane at defocus u
Two-photon: 2√(ln 2) · 0.532λ / (√2 (n − √(n² − NA²)))
Confocal formulas from Zeiss, "Confocal Laser Scanning Microscopy: Principles" (Wilhelm et al.); the pinhole formula is the geometric-optical one, valid from 1 AU up. The wave-optical section is the scalar paraxial theory of Wilson & Sheppard (equal excitation and emission wavelengths, uniformly filled pupil), with Wilhelm's high-NA axial scale; Wilhelm's geometric sum lies 23 % (low NA) to about 140 % above it, most as the NA approaches the immersion index. Two-photon from Zipfel, Williams & Webb, Nat. Biotechnol. 21, 1369 (2003), excitation at twice the entered wavelength. Widefield: distance from focus to the first axial zero of the sinc² axial PSF (Born & Wolf §8.8); out-of-focus light is blurred, not rejected.
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
Paraxial and fitted formulas: confocal sections for a finite (≥ 1 AU) and a point-like pinhole, two-photon from Zipfel's fit. Widefield has no optical sectioning; its depth of field is the first axial zero λ/(n − √(n² − NA²)). Two-photon is the point axial FWHM. The scalar wave-optical plane response (0.1–5 AU, no Stokes shift) is shown next to Wilhelm's geometric sum, which lies 23 % (low NA) to about 140 % (NA near n) above it.
- Wilson T. (2011). Resolution and optical sectioning in the confocal microscope. J. Microsc. 244, 113–121. Lateral, axial and plane responses against pinhole size. doi:10.1111/j.1365-2818.2011.03549.x
- Wilhelm R., Gröbler B., Gluch M., Heinz H. (2003). Confocal Laser Scanning Microscopy: Principles. Carl Zeiss. Optical-section FWHM for a finite and a point-like pinhole.
- Zipfel W. R., Williams R. M., Webb W. W. (2003). Nonlinear magic: multiphoton microscopy in the biosciences. Nat. Biotechnol. 21, 1369–1377. Axial radius of the two-photon excitation (fit for NA > 0.7). doi:10.1038/nbt899
- Born M., Wolf E. (1999). Principles of Optics, 7th ed., §8.8. Cambridge University Press. Widefield depth of field 2nλ/NA².