Spatial Filter Pinhole Sizing
Focal spot, recommended pinhole diameter, throughput of any pinhole and the output beam profile of a lens–pinhole spatial filter.
Focal spot 1/e² diameter 2w_f
67.74 µm
w_f = M²λf/(πw_in)
Recommended pinhole 3w_f
101.6 µm
1.5 × the spot diameter: passes 98.89 %
Smallest pinhole for 99 %
102.8 µm
Your pinhole passes
98.72 %
1.48 × the spot diameter
Finest input structure passed
1064 µm period
Noise of shorter period, λf/a, is blocked
Output beam 1/e² diameter
2.000 mm
After the collimating lens, uncut beam
Airy diameter 2.44λf/D (flat-top input)
129.8 µm
For comparison: a uniformly filled aperture
wf = M²λf/(πwin), T = 1 − exp(−2a²/wf²) for a pinhole of radius a
Output field: E(ρ) ∝ ∫₀ᵃ exp(−r²/wf²) J₀(2πrρ/(λf₂)) r dr, the Hankel transform of the cut Gaussian.
Pinhole throughput
- Throughput
- Recommended (3w_f)
- Your pinhole
Beam profile at the collimating lens
- Without pinhole
- Through your pinhole
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 Gaussian beam focused by an ideal lens onto a centred pinhole. For M² > 1 the spot and throughput use the embedded Gaussian, an estimate. The output profile is the Fraunhofer pattern of the cut Gaussian.
- Uehara K., Kikuchi H. (1986). Transmission of a Gaussian beam through a circular aperture. Appl. Opt. 25, 4514. doi:10.1364/ao.25.004514
- Kogelnik H., Li T. (1966). Laser beams and resonators. Appl. Opt. 5, 1550–1567. doi:10.1364/ao.5.001550