How Anti-Reflection Coating Is Selected for a Lens

An anti-reflection (AR) coating for a lens is not picked from a catalog name. It is selected by working backward from the optical system: what wavelengths the lens has to serve, how much reflected light the system can tolerate, what angles of incidence actually occur across each curved surface, what the lens material allows, and what power and environment the coating must survive.

The Selection Sequence at a Glance

Each step narrows the options for the next one. Skipping a step usually shows up later as a coating that measures well on a flat witness sample but underperforms in the finished lens.

Step 1: Define the Band the Lens Actually Has to Serve

The working band is the overlap of the light source spectrum and the detector’s useful response—not the full sensitivity range of the sensor. A monochrome camera that responds from 400 nm to 1000 nm but images only under an 850 nm LED needs low reflection around the LED emission band plus allowance for LED wavelength tolerance and temperature drift. An RGB camera needs the whole visible band. A laser system may need one line, or a process line plus a visible aiming beam.

This step matters because bandwidth is not free. For a given substrate and number of layers, a wider AR band generally leaves a higher residual reflectance than a coating optimized for one wavelength. Asking for a broadband AR “to be safe” can therefore make performance worse at the wavelength that matters. The trade-off between narrowband and broadband designs is covered in more detail in V-Coat vs Broadband AR Coating: Specs and Trade-Offs.

Step 2: Set a Reflection Budget for the System

At normal incidence, the reflectance of an uncoated interface between media of index n₁ and n₂ is given by the Fresnel equation:

The starting point depends strongly on the lens material. Using representative refractive indices:

Values are calculated from the Fresnel equation using nominal indices; actual index depends on the exact glass type, wavelength and temperature.

How much of that reflection must be removed depends on what limits the system. Three cases lead to different coating requirements:

Throughput-limited systems

Losses multiply through a multi-element lens. A lens with six uncoated air-spaced crown-glass elements has twelve air–glass surfaces; at about 4.2% per surface, the transmitted fraction is roughly 0.958¹² ≈ 60%, before absorption is counted. At 0.5% per surface, the same calculation gives about 94%. For throughput, the average reflectance across the working band is usually the right metric.

Contrast-limited systems

A ghost image is formed by light that reflects twice—once from one surface and again from another—before reaching the sensor. Its intensity scales roughly with the product of the two reflectances: about 0.042 × 0.042 ≈ 0.18% for two uncoated crown surfaces, versus 0.005 × 0.005 = 0.0025% at 0.5% each, roughly seventy times weaker. Whether a ghost is visible also depends on where it focuses, but in imaging, metrology and low-light systems the maximum reflectance in the band, not only the average, often decides the specification.

Feedback-limited systems

In laser and fiber systems, light reflected back along the beam path can return into the laser cavity or fiber. Here the reflectance at the exact laser line, under the actual polarization, matters more than any band average. That usually favors a coating optimized at the line rather than a general-purpose broadband design.

Step 3: Find the Real Angle of Incidence on Each Lens Surface

This is where coating a lens differs most from coating a flat window. On a curved surface, the angle of incidence (AOI) is measured from the local surface normal, which tilts with radial position. For a collimated beam striking a spherical surface of radius r, the normal at height h is tilted by arcsin(h / r).

Consider a fast plano-convex condenser for an 850 nm illuminator with a 25 mm radius on the curved side and a 20 mm clear aperture. At the edge of the clear aperture (h = 10 mm), a collimated ray meets the surface at arcsin(10/25) ≈ 23.6°, even though the beam is parallel to the optical axis. A slow lens with a large radius may see only a few degrees.

Two effects then move the AR performance toward shorter wavelengths at the edge of the lens:

• Oblique incidence. The phase thickness of each layer scales with the cosine of the ray angle inside that layer. At 23.6° in air, this shortens the effective design wavelength by roughly 2–4%, depending on layer indices—a shift of a few tens of nanometres at 850 nm. Reflectance for s- and p-polarized light also separates as the angle increases.
• Thinner layers on sloped areas. In many deposition geometries, film deposited on a steep part of a curved surface is thinner than at the center. Thinner layers shift the reflectance curve further toward shorter wavelengths, adding to the AOI effect.

The practical consequence: the reflectance minimum can sit correctly at the lens center while the long-wavelength end of the band rises near the edge. Common responses are to extend the design band toward longer wavelengths, specify reflectance over the actual AOI range rather than at 0°, or choose a design whose performance changes less across the aperture. For steep lenses, the AOI range and the lens radius should be part of the coating discussion from the start.

Step 4: Check What the Substrate Allows

The substrate index determines what a given layer stack can achieve. The classic example is a single quarter-wave layer of MgF₂ (n ≈ 1.38). Zero reflectance at the design wavelength requires a layer index equal to the square root of the substrate index (for a lens in air). For N-BK7 that ideal is about 1.23, so a single MgF₂ layer leaves roughly 1.3% residual reflectance at its design wavelength. On a glass with index near 1.9, the same single layer approaches zero at the design wavelength. That is why single-layer MgF₂ remains a reasonable choice on some high-index glasses, while crown glass and fused silica need multilayer designs when sub-percent reflectance is required.

Other substrate considerations that change the selection:

• Infrared materials. Germanium, silicon and ZnSe have high indices and therefore large uncoated reflection—an uncoated germanium element transmits less than half the incident light even where the material absorbs little. Their AR designs must use layer materials that are transparent across the infrared band, which narrows the choice considerably compared with visible coatings.
• Cemented surfaces. Interfaces inside a cemented doublet are glass–cement–glass, not glass–air. Their reflection is much lower because the index step is small, and they are normally not given an air-type AR coating.
• Material absorption. An AR coating reduces reflection; it does not fix bulk absorption. If the lens material absorbs in the working band, changing the coating will not recover that loss. The difference between these mechanisms is explained in Transmission, Reflection, and Absorption Explained.

Step 5: Add Laser Power and Environmental Constraints

For laser lenses, low reflection is necessary but not sufficient. Absorption in the layers and contamination at the substrate interface can limit laser damage resistance. A laser-damage requirement should name the wavelength, pulse duration, repetition rate, beam diameter and test method; ISO 21254 is the commonly referenced test standard family. A coating that performs well spectrally may still need a different layer design or deposition process to meet a demanding damage requirement.

For environmental exposure, separate the outer, exposed lens surface from internal surfaces inside a sealed housing. The exposed surface may face cleaning, humidity, abrasion or salt fog, while internal surfaces usually do not. Durability tests such as abrasion, adhesion and water resistance are described in ISO 9211-4; the drawing should state which tests and severities apply. Deposition process also plays a role: less dense films can take up moisture and shift spectrally between vacuum and humid air, while denser processes such as ion-assisted or sputtered coatings are generally more stable. See IBS vs IAD Optical Coating for the process trade-offs.

Step 6: Choose the AR Coating Family for the Lens

With the band, reflection budget, AOI range, substrate and constraints defined, the coating family usually becomes clear. The table summarizes typical matches; the final design still depends on the specific substrate and requirements.

Once the family is chosen, the requirement still has to be written in measurable terms—per surface or per element, average or maximum, at which AOI and polarization. Those drawing and RFQ details are covered in AR Coating for Optical Lenses: What Engineers Need to Specify.

Worked Example: AR Coating for a 1064 nm Focusing Lens with a Red Aiming Beam

Illustrative example. The target values below were chosen for this scenario only; they are not a standard GIAI specification or a measured result.

Compare this with the fast 850 nm condenser in Step 3. There, the 23.6° edge AOI and coating thickness falloff push the spectral response toward shorter wavelengths near the edge, so a single-line V-coat centered exactly at 850 nm would leave little margin. A narrow-band AR with its design band extended toward longer wavelengths, specified over the real AOI range, is usually the safer choice.

Common Mistakes When Selecting a Lens AR Coating

• Choosing broadband by default. A wider band generally raises residual reflectance at the wavelength that matters most.
• Specifying only at 0° AOI for a steep lens. Edge-of-aperture performance can differ significantly from center performance.
• Applying one coating to every surface. Surfaces facing air, cement or a sealed cavity, or seeing different ray angles, may need different treatment.
• Using a band average when ghosts or feedback are the problem. Average reflectance can hide a peak at the critical wavelength.
• Treating a flat witness curve as the finished-lens result. A witness sample represents the lens center well, but not necessarily the sloped edge zone.
• Leaving out laser and environmental conditions. These can change the layer design and process, not just the test plan.

How the Selected Coating Is Verified

Reflectance is commonly measured with a spectrophotometer on witness samples coated in the same run, at a near-normal angle stated in the report. Because a witness represents conditions near the lens center, steep lenses may need additional checks: a point-measuring reflectometer at defined radial zones on the actual lens, or witnesses mounted at a tilt that represents the edge zone. The measurement AOI, polarization and wavelength range should match what the specification states. Durability and laser-damage testing, when required, should be defined before production rather than after the first lot. GIAI’s general approach to spec-based inspection is described on the Quality Assurance page.

Lens Coating Projects at GIAI Photonics

GIAI supports lens coating as part of custom optics projects, alongside the fabrication of optical lenses and infrared optics. Each project is reviewed against the drawing or sample, lens material, radii and clear aperture, spectral targets, AOI conditions and inspection criteria before the coating and inspection route is defined. Achievable reflectance, damage resistance and durability are confirmed per project rather than assumed from a generic coating name.

References for general optical principles: Laser Focus World — design principles of antireflection coatings; Fraunhofer IOF — broadband antireflection coatings for optical lenses; Schneider-Kreuznach — non-destructive measurement of AR coatings; ISO 9211-4:2022 — optical coatings test methods. More coating topics: Filters & Coatings resources.