How to Read an Optics Spec Sheet: Lenses, Mirrors, Windows and Filters

Scope

This article goes through the specifications printed for catalog optics (lenses, mirrors, windows and filters) and explains what each one means for a system. Most optics are specified the same way: dimensions and their tolerances, the material, the optical function (focal length, reflectance, passband), surface figure, surface quality, and coatings. The useful question for each line is how much error it allows in the quantity the system depends on, usually the wavefront, the pointing, or the transmitted power.

A typical specification

Dimensions and material

Dimensional tolerances matter mainly for mounting and for the axial position of the focus. The material line sets the refractive index, the dispersion (the Abbe number), the transmission range and the thermal behavior; glass names refer to a manufacturer's catalog, which gives the index at standard wavelengths. The site's refractive index calculator evaluates common materials across wavelength.

Focal length

Catalog lenses state the effective focal length, measured from the principal plane, often with a tolerance of about ±1% to ±2% for stock parts. The back focal length, from the last surface to the focus, is what is measured on the bench and differs from the effective focal length by an amount that depends on the lens shape and thickness. A ±1% tolerance on a 100 mm lens moves the focus by up to 1 mm, usually taken up by adjusting the lens position. How to check a focal length is in How to Measure Focal Length.

Surface figure and wavefront

Surface flatness (for flat optics) or irregularity (for curved ones) is given as a fraction of a test wavelength, usually 632.8 nm, as peak-to-valley height. λ/4 at 632.8 nm is 158 nm; λ/10 is 63 nm.

What matters to the system is the wavefront error the surface introduces:

• In reflection, the wavefront error is twice the surface height error, because the light travels to the surface and back. A mirror flat to λ/10 can add up to λ/5 of reflected wavefront error.
• In transmission, a surface height error $h$ adds a wavefront error of $(n-1)h$, which for glass of index 1.5 is half the height. A window flat to λ/10 on each face adds well under λ/10.

Some manufacturers specify the transmitted wavefront error of the whole part instead, which is the more useful number for lenses and windows. A system's total wavefront error is roughly the root sum square of its parts' contributions when they are random; see the Strehl ratio for how wavefront error lowers the peak of the focused spot.

As a rough guide, λ/4 is adequate for most general laboratory work and imaging; λ/10 or better is used for interferometry, laser cavities, and systems with many surfaces in series.

Surface quality and roughness

Surface quality, written as a scratch-dig pair such as 60-40 or 20-10, is a cosmetic specification of visible defects, compared against reference standards (MIL-PRF-13830B, or ISO 10110-7 in a different notation). Lower numbers mean fewer and smaller defects. It affects scatter and, for high-power lasers, the risk of damage at defects; it says nothing about the surface's shape. Tighter values cost more and matter most for laser optics, optics near a focus or an image plane, and low-scatter applications.

Surface roughness, given as an RMS value in ångströms or nanometers, governs scatter from the polished surface itself and matters for low-loss mirrors and ultraviolet optics.

Wedge and centration

A window or plate with faces that are not parallel deviates the beam by approximately $(n-1)\theta$ for a small wedge angle $\theta$. A 3 arcminute wedge in N-BK7 ($n$ = 1.5168) deviates the beam by 1.55 arcminutes. A lens whose optical axis is not centered on its mechanical axis does the same, and the centration specification bounds this deviation. Deliberately wedged windows are used to keep the reflections from the two faces from interfering or returning to a laser.

Clear aperture

The clear aperture is the central region over which the other specifications are guaranteed, often 85% to 90% of the diameter. Beams should be kept within it; a Gaussian beam is commonly sized so that its 1/e² diameter is no more than about two-thirds of the clear aperture, to keep the clipped fraction and diffraction from the edge small.

Coatings

Coating specifications give reflectance or transmittance over a band, either as an average or as a maximum (an average below 0.5% may still have peaks above it), at a stated angle of incidence and sometimes polarization. Away from the design angle the band shifts toward shorter wavelengths; at 45° the s and p polarizations behave differently. Anti-reflection coatings can be checked with the AR coating calculator, and filters are often specified by optical density in the blocking band.

Damage threshold

The laser-induced damage threshold states the fluence (J/cm²) for pulsed lasers or the linear power density (W/cm) for continuous lasers at which the surface or coating is damaged, at a given wavelength, pulse length, repetition rate and beam size. It is only comparable between parts tested under similar conditions, and a margin is normally kept below it. Compare a beam's fluence or irradiance at the optic with the stated value, remembering that the peak of a Gaussian beam is twice its average over the 1/e² area.

Common errors

Comparing figures at different test wavelengths. λ/4 at 633 nm and λ/4 at 1064 nm are different heights; convert to nanometers.

Reading a surface specification as a wavefront specification. In reflection the error doubles; in transmission it scales by $(n-1)$.

Using the coating outside its angle or band. A 0° AR coating at 45°, or a dielectric mirror at the wrong polarization, can reflect several times more than specified.

Assuming the whole diameter is usable. Beyond the clear aperture, nothing is guaranteed.

References: D. Malacara (ed.), Optical Shop Testing (3rd ed., Wiley, 2007); International Organization for Standardization, ISO 10110 series, Optics and photonics: Preparation of drawings for optical elements and systems; U.S. Department of Defense, MIL-PRF-13830B, performance specification for optical components.