Spinning Disk Confocal Calculator
Pinhole size, optical sectioning with pinhole crosstalk and its background floor, and frame rate for spinning disk confocal microscopy.
Results
In a thick, uniformly labelled sample the floor is collected from every depth: about 39 µm of labelled sample out of focus, in total on both sides (disk section FWHM / floor), gives as much light as the in-focus section.
Pinhole (AU) = (d / M) / (1.22 λ/NA)
Frame rate = RPM/60 × scans per revolution (12 on Yokogawa CSU disks)
Open area = π d²/(4 s²) for a square lattice of pitch s; each point is lit for this fraction of the exposure
Lateral and section FWHM: scalar paraxial confocal model, one pinhole; the disk section adds the neighbouring pinholes (square lattice, incoherent beams)
Optical Section & Throughput vs Pinhole Size
Response to a Thin Fluorescent Plane vs Defocus
Light from a defocused plane spreads over many pinholes and returns through the neighbours of the one that lit it (pinhole crosstalk). Summed over the lattice (Poisson summation of the single-pinhole section), the response levels off at the floor instead of falling to zero. Scalar paraxial pupil, no Stokes shift, square lattice, each beam focused to a point in its pinhole (microlens disk), mutually incoherent beams: laser-lit microlens beams interfere, which is not modelled, and a lamp-lit disk (extended sources) has a higher floor.
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. The disk section adds crosstalk through the neighbouring pinholes: Each beam is focused to a point in its pinhole (microlens disk). Poisson summation over a square lattice of mutually incoherent beams turns the crosstalk into a finite sum of squared defocused OTFs, which levels off at a floor far out of focus (4.4 % for 50 µm holes at 250 µm pitch, 60×, NA 0.8, 488 nm, n 1.33). Interference between laser-lit microlens beams is not modelled; a lamp-lit disk has a higher floor. Frame rate is RPM/60 × scans per revolution.
- Egner A., Andresen V., Hell S. W. (2002). Comparison of the axial resolution of practical Nipkow-disk confocal fluorescence microscopy with that of multifocal multiphoton microscopy: theory and experiment. J. Microsc. 206, 24–32. Axial response of Nipkow disks with pinhole crosstalk. doi:10.1046/j.1365-2818.2002.01001.x
- Tanaami T., Otsuki S., Tomosada N. et al. (2002). High-speed 1-frame/ms scanning confocal microscope with a microlens and Nipkow disks. Appl. Opt. 41, 4704–4708. Yokogawa CSU disk, 12 scans per revolution. doi:10.1364/AO.41.004704
- 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.