Confocal Pinhole Size
Size the pinhole in Airy units (1.22 λ/NA × M) and see the trade-off between optical section, lateral resolution and signal.
1 Airy unit at the sample = 1.22 λ/NA = 425.3 nm
1 Airy unit at the pinhole = 25.52 µm
Pinhole diameter (1 AU) = 25.52 µm
Throughput of an in-focus point = 83.8 %
Lateral FWHM = 175.0 nm
Optical section FWHM = 457 nm
Wilhelm's geometric formula (valid ≥ 1 AU) = 796 nm
Model
1 AU = 1.22 λ/NA at the sample, × M at the pinhole
Throughput = 1 − J₀²(v) − J₁²(v), v = 3.832 × pinhole (AU)
Lateral FWHM: 0.37 λ/NA (pinhole → 0) to 0.51 λ/NA (open)
Section FWHM: 0.68 λ/(n − √(n² − NA²)) (pinhole → 0), 0.88 at 1 AU, growing with the pinhole
Scalar paraxial theory of a confocal fluorescence microscope with equal excitation and emission wavelengths; a Stokes shift widens both FWHMs slightly. The optical section is the response to a thin fluorescent plane. Wilhelm's geometric formula √[(0.88 λ/(n − √(n² − NA²)))² + (√2 n PH/NA)²] lies 74 % above it here. From 1 to 0.5 AU the lateral FWHM narrows from 0.50 to 0.40 λ/NA (20 %) while the throughput falls from 84 % to 59 %.
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
Scalar paraxial confocal theory with equal excitation and emission wavelengths and a uniformly filled pupil, computed numerically for pinholes of 0–5 AU; the axial scale n − √(n² − NA²) follows Wilhelm. Throughput is the Airy encircled energy of an in-focus point.
- Wilson T., Sheppard C. J. R. (1984). Theory and Practice of Scanning Optical Microscopy. Academic Press. Confocal PSF as the product of the illumination PSF and the pinhole-integrated detection PSF.
- 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. Airy units, the 0.37/0.51 λ/NA and 0.64 limits, and the geometric section formula.
- Born M., Wolf E. (2019). Principles of Optics, 7th ed., §8.5.2 and §8.8. Cambridge University Press. Airy pattern, encircled energy and the defocused PSF. doi:10.1017/9781108769914