Clear aperture

The clear aperture of a lens, mirror, window or filter is the central region of its surface over which the manufacturer guarantees the other specifications: surface figure and wavefront error, coating reflectance or transmittance, and scratch-dig. It is usually given as a diameter, often 85–90% of the physical diameter, or as the diameter less a fixed edge margin; for a 25.4 mm optic, 90% is 22.9 mm. Outside it nothing is promised. The edge zone exists because polishing tends to roll off near the rim, chamfers remove material, and coating thickness and uniformity degrade near the fixtures that hold the part in the coating chamber.

In optical system design the same phrase also means the unobstructed diameter of an element as mounted, after the retaining ring or cell has covered part of it. The smallest of these, relative to the beam or ray bundle, is the aperture stop, which sets the f-number of the system; elements that cut off off-axis bundles cause vignetting. A datasheet's clear aperture and a mount's free opening should both be checked.

Sizing a Gaussian beam

A Gaussian beam has no sharp edge, so any finite aperture cuts off some power. For a centered beam of $1/e^2$ radius $w$ passing a circular aperture of radius $a$, the fraction lost is

$$\frac{P_\text{clipped}}{P} = \exp\!\left(-\frac{2a^2}{w^2}\right).$$

An aperture equal to the $1/e^2$ diameter ($a = w$) loses 13.5%, or 0.63 dB. The common rule of making the clear aperture at least 1.5 times the $1/e^2$ beam diameter corresponds to $a = 1.5w$ and loses 1.1%; a clear aperture of $\pi w$, a rule of thumb from laser design, loses 0.72%; twice the beam diameter loses 0.034%. Applied to the 22.9 mm clear aperture above, the 1.5× rule allows a beam up to 15.2 mm in $1/e^2$ diameter.

The lost power is often the smaller problem. A hard edge cutting into the beam's wings imposes diffraction: ripples across the transmitted profile in the near field, and rings around the focal spot in the far field. If the beam is truncated well inside $a = w$, the focus approaches the Airy pattern of a uniformly filled aperture, with a larger spot and more energy in the rings than the Gaussian prediction. For interferometry and high-power work, where the ripples become phase errors or hot spots downstream, the 2× rule or larger is safer. Shaping the edge smoothly, as in apodization, reduces the rings when a beam must be truncated.

Tilted optics

A fold mirror or beam splitter at 45° presents a projected clear aperture reduced by $\cos 45°$ in the plane of incidence: a 22.9 mm clear aperture becomes 16.2 mm across the beam, and with the 1.5× rule the beam should be no larger than about 10.8 mm at $1/e^2$. Elliptical mirrors are made for this reason. The same geometry applies to a window or filter tilted to keep back-reflections off axis.

Pitfalls

• Sizing the beam to the physical diameter instead of the clear aperture, which places part of the beam on an unspecified, possibly uncoated or rolled-off zone.
• Sizing to the $1/e^2$ diameter alone, which clips 13.5% of the power.
• Forgetting that a beam expander or telescope must pass the expanded beam through every element, including the last mirror at 45°.
• Ignoring beam pointing drift and misalignment, which move the beam toward one edge.

Common questions

What is the clear aperture of a lens?

The diameter of the central zone over which its surface figure, wavefront, surface quality and coating specifications are guaranteed. It is smaller than the physical diameter, often 85–90% of it; the optics specification guide lists it among the other datasheet lines.

How large should an optic be relative to the beam?

Its clear aperture should be at least about 1.5 times the $1/e^2$ beam diameter, which passes 98.9% of a centered Gaussian beam, and about 2 times for low diffraction ripple.

References: A. E. Siegman, Lasers (University Science Books, 1986); E. Hecht, Optics, 5th ed. (Pearson, 2017); W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw-Hill, 2008).