How AR coatings work

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A while back I did quite a bit of reading on the subject of AG/AR coatings and how they might be used to improve the picture quality of a large screen RPTV. Since this topic comes up from time to time, I copied and pasted some of it together and thought some might find it interesting reading. My apologies for not knowing the name of the author in order that her or his work might be properly acknowledged.

Why do coated lenses look purple (or blue or green or whatever)?
First, let’s get the most obvious misconception out of the way:
Lens coating has NO COLOR. It is a water-clear material throughout the visible spectrum. It has only 2 meaningful characteristics that make it appear colored: (1) Refractive Index, and (2) Thickness.

Light (for the purpose of this discussion at any rate) behaves as a wave: when a light wave strikes the glass surface, some of it bounces off as a reflection – the reflected ray still has the same wave characteristics as the incident ray, just moving in the opposite direction. Light reflects from the surface of the glass because the refractive index of the glass is different from that of the air. This reflection has no apparent color; it reflects all wavelengths equally and has a grayish or silver appearance.

Because the reflection is a wave, it has an important characteristic: it can be cancelled out by another wave, if that other wave can be made to be of equal frequency, direction and magnitude and opposite phase. A second wave spaced 1/2 wavelength out of phase would have its highest point aligned with our wave’s lowest point; if this can be made to happen, the 2 waves will cancel each other out.

It turns out that we CAN make this happen. What we need to do is to create a second reflection, in a slightly different location from the glass surface that created the first. In order to space the 2 reflections exactly 1/2 wavelength apart, the 2 reflective surfaces need to be spaced 1/4 wavelength apart: 1/4 wavelength for the incident wave going in plus 1/4 wavelength for its reflection coming back out = 1/2 wavelength. For this reason, antireflective coatings are sometimes referred to as “Quarter Wave” coatings.

Remember, though, that the reflection occurs where there is a difference in refractive index from one material to the next. So not just any coating material will work; the refractive index of the coating needs to be about halfway between that of glass (1.6) and air (1) so that the difference at each interface will be equal. The perfect single coating material would therefore have a refractive index of about 1.3. The material most commonly used for this purpose, Magnesium Fluoride, has a refractive index of about 1.37 – not a bad compromise, considering that it offers durability and other desirable properties

But why the color?
For any given wavelength it should be possible to obtain nearly 100% cancellation of reflections by means of applying a 1/4 wavelength-thick layer of Magnesium Fluoride to the surface of the glass. But the trick is, 1/4 of WHAT wavelength? Light isn’t all one wavelength, there’s a different wavelength for every color from 400nm (violet) to 700nm (red). No thickness of coating can be 1/4 wavelength of ALL of them…. so the designer has to choose. Typically, they choose a wavelength that’s close to the center of the visible spectrum, so that the beneficial effects of the coating will be as uniformly distributed over the visible range as possible. The visible range being 400-700nm, the wavelength generally chosen as the target was in the neighborhood of 550nm, or right in the center.

As you can see in Figure 1 below, the mathematical center of the visible spectrum, 550nm, corresponds to a color in the yellow-green range. A coating of 137.5nm thickness (550 divided by 4) would virtually eliminate any reflections of this color from the surface of the lens. It would reduce reflections of other wavelengths also, but the efficiency of its effect would become progressively lower as the wavelength deviates from 550. The net result is that the overall goal of suppressing reflections is achieved, but it is not achieved equally for all colors. We see this when we look at the reflections from the coated glass surface: there is no green light reflected at all, but there are reflections of the other colors. The overall effect is that of a reflection in the complement of the targeted color. These complements are shown in the lower chart in Figure 1 – 550nm corresponds to a blue-violet color; exactly what we see in a coated lens.


So, what’s the difference between “single” and “multi” coating?
Multi-coating is significantly more efficient, and slower and more expensive to achieve, than single coating, but the principles and the basic process are the same. The basic difference comes down to refractive index. A single coating must have a refractive index about halfway between those of glass and air, and it took a number of years to find a suitable material in Magnesium Fluoride. To apply multiple coatings with similar effect, they must be of materials with an even progression of refractive indices, calculated to correspond to the number of layers desired. For example, if you want to apply 5 layers, you would need 5 different materials with indices of roughly 1.1, 1.2, 1.3, 1.4 and 1.5 to span the range between air (1.0) and glass (1.6). From here on, the process is the same as with the single coating, except that each layer is made a slightly different thickness from the others, with the thicknesses selected to correspond to several different wavelengths within the visible spectrum so that the suppressive effect applies not only at the 550nm center but across the whole range. A multi-coated lens does not appear as strongly colored as a single coated lens – its general tendency is to appear black by comparison to the blue-violet single coated lens.