Point Spread Function Calculator
Visualize the 2D and 1D point spread function (PSF) for a diffraction-limited system.
Airy radius (first zero)
239.6 nm
Lateral FWHM
202.1 nm
Axial FWHM
523 nm
First axial zero
±591 nm
Formulas
I(r) = [2J₁(v)/v]², v = 2π NA r/λ
Airy radius r = 0.610 λ/NA; lateral FWHM = 0.514 λ/NA
I(z) = sinc²(π z (n − √(n² − NA²))/λ)
Axial FWHM = 0.886 λ/(n − √(n² − NA²)) → 1.77 nλ/NA² at low NA
Scalar theory, uniformly filled pupil, no aberrations, λ in vacuum. Above NA ≈ 0.9 the vector focus differs: with linear polarization it is ≈ 30 % wider along the polarization and slightly narrower across it at NA 1.4 (Richards & Wolf 1959); the 10–20 % average widening holds for unpolarized or circular light. A coverslip or index mismatch stretches the axial PSF further.
2D PSF (Lateral)
Lateral PSF Profile
Axial PSF Profile
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 PSF of an aberration-free, uniformly filled pupil: the Airy pattern laterally, the on-axis Debye sinc² axially (FWHM 0.886 λ/(n − √(n² − NA²)), the paraxial sinc²(u/4) at low NA). No polarization, coverslip or index-mismatch effects.
- Born M., Wolf E. (2019). Principles of Optics, 7th ed., §8.5.2 and §8.8. Cambridge University Press. Airy pattern and the paraxial intensity near focus. doi:10.1017/9781108769914
- Wilhelm R., Gröbler B., Gluch M., Heinz H. (2003). Confocal Laser Scanning Microscopy: Principles. Carl Zeiss. Axial FWHM 0.88 λ/(n − √(n² − NA²)).
- Richards B., Wolf E. (1959). Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system. Proc. R. Soc. Lond. A 253, 358–379. Vector focus behind the polarization note. doi:10.1098/rspa.1959.0200