Coatings

Lens coatings

By Bob Newman, first published April 2013

How lens coating works

The modern multi-element lens, which might have 20 or more elements, but still produce a sharp, contrasty image, is made possible due to lens coating technology. Without coating, something like four percent of all light passing and air-glass surface of a lens gets reflected straight back again. Take a lens with 8 air-glass surfaces (such as the classic double-Gauss or Planar design) as shown in Figure 1 and the total proportion of light that makes it to the image is just 72% of the light incident.

Figure 1. A double-Gauss lens design, such as this Zeiss Planar, has eight air to glass surfaces. Without anti-reflection coating 28% of the light passing through is reflected back again, causing flare and contrast loss.

The 28% of the light that doesn’t get refracted through the lens doesn’t disappear. Rather, it is reflected off other surfaces of the lens. Some of it might appear at the image in the form of flare, either bright spots or blobs in the image, or as an overall haze, known as ‘veiling flare’, which reduces the contrast of the image produced by a lens. This reflection is best avoided if image quality is to be maximized.

As early as 1886 it was noticed by the physicist John Strutt, 3rd Baron Rayleigh, that some old lenses acquired a patina or ‘bloom’ that seemed to improve their transmission properties. This was caused by the leaching out of some of the heavy elements in the glass by atmospheric moisture. What remained of the glass was a very thin layer of relatively pure silicon dioxide, which has a lower refractive index than the bulk of the glass –the heavy elements increase the refractive index. The reason this limits reflections (or at least, the commonly given explanation) is illustrated in figure 2.

Figure 2. A single anti-reflection coating consists of a quarter wavelength film with a refractive index between that of the air and glass, causing reflections at both sides of the film. Since the reflected waves are in ant-phase, they cancel out killing the reflection.

Reflection happens at any abrupt change in refractive index. On the bloomed surface there are two such reflections, one at the interface from the air to the surface layer, and the second at the surface layer to the bulk glass. If the thickness of the layer is one quarter of the wavelength of light, then the reflected light is out of phase with the incoming light, which means that it effectively cancels out the reflection. That is, anyway, the standard explanation. It cannot be correct, because if the reflection is cancelled out it never happened, and if it never happened it cannot be cancelled out. We are in a situation where intuitive understandings of Physics fail to match reality. It would be more correct to say that the wave function of the light should be understood as a probability distribution, and the quarter-wave reflection reduces the probability of the light reflecting.

Abstruse physical arguments aside, the end result of blooming the surface of the lens is to reduce the surface reflection from about 4% to about 2% per surface. For our 8 surface lens above, this results in an increase of the proportion of light transmitted to about 85% and the reflected light is reduced to about 15% - in the end halving the flare-producing light.

Artificial blooming began to be applied to lenses from the early 1930’s, using various processes. Some involved boiling the lens elements in strong alkalis to leach out the heavy elements. Others involved dripping carefully controlled amounts of salts in solution which when evaporated left the required thin film on the surface. Neither of these solutions was entirely satisfactory, the wet coating process in particular producing a very fragile or ‘soft’ coating.

‘Hard’ coating required the vacuum deposition of a substance with a suitable refractive index (usually magnesium fluoride) onto the surface of the glass. This process involves heating a crucible of the coating material to sufficient temperature that is vaporises. This is done in a vacuum, so that no air molecules impede the flight of the vapour molecules. They fly until they hit the lens to be coated, when they adhere one at a time, allowing a very thin and hard film to be deposited in a very controllable manner. The process was perfected by Olexander Smakula of Carl Zeiss and was applied to production lenses in 1934. This method was closely guarded as a military secret until after the second World War, when the allies voided all German patents, making the technique generally available worldwide, leading to wholesale adoption of lens coating in the 1950’s. The same process continues to be used to this day, although refined by the use of advanced methods for heating the coating substance, including electron beam deposition, where a high energy electron beam is used to dislodge atoms of the coating substance, and laser beam deposition using a laser beam. These techniques offer two main advantages. Firstly, very high local temperatures can be achieved, allowing the use of coating materials more sophisticated than Magnesium Fluoride. Secondly, they allow very precise control of the coating process.

Multi-coating

The ability to make very precise films of differing materials has produced a further enhancement of coating technology – multi-layer coating in which multiple coats are applied to the lens, making possible two optical improvements. Firstly, a reduction of the reflected proportion of the light to less than 0.5%. The use of such coatings on all 8 surfaces of the double-gauss lens would increase the overall transmitted proportion of the light to 96%, and the reflected proportion to 4%. It would require 32 lens surfaces to reach the same 15% reflected light of the single-coated lens, making feasible the zoom lens for very high quality work.

Secondly, multicoating techniques can work over a more extended range of colours than can a single coating. A single coating is maximally effective only for one colour while several layers can provide anti-reflection properties over the whole spectrum. The layers may use different materials, with a variety of refractive indices (the amount that light is bent) and dispersions (the change in refractive index with colour). Two different design principles are available. The first is to make a set of quarter wave films combined together to provide the required anti-reflection properties. For instance, the simplest enhancement to the single layer of magnesium fluoride is to include another quarter wave layer of a higher refractive index material under the magnesium fluoride (alumina, refractive index of 1.76, commonly being used). Figure 3 shows the improvement that this type of coating can offer.

Figure 3. This graph shows the percentage of light transmitted through a single air-glass surface. The green line shows the effect of an uncoated surface, the purple a single coating and the yellow that of a simple three layer coating consisting of ¼ wavelength of magnesium fluoride, a half wavelength of zirconia and a further ¼ wavelength of alumina.

Ideally the refractive index of the coating should be the square root of the substrate ensuring that the reflected wave at both surfaces is of the same strength, so that they precisely cancel out. The square root of 1.76 is 1.33, very close to the refractive index of magnesium fluoride (1.38). This approach can be extended with alternate layers of the two materials being laid down to produce a precisely engineered coating. The design of such coatings is far from simple and can involve as much computation as the design of the lens itself.

The second approach to multi-layer coating is to lay down successive layers of materials with a graded refractive index, so that rather than an abrupt change of index, there is a more gradual and less reflection prone change. Some multi-layer coatings will make use of both strategies.

Nano-coating

The gradual change of refractive index strategy is the one used by the newest and highest technology variety of lens coating, the nano-technology coating. Imagine that a pattern of cone shaped peaks is laid down on the surface of the glass, at a scale smaller than the wavelength of light (about 1/500th of a millimetre). Since the peaks are so small, they will not be ‘visible’ to the light. On the other hand, the effective refractive index of the material that the peaks are made of will vary smoothly from 1 (the index of air) near the summits, where the coat is mostly air to the full refractive index of the material at the base, where the coat is solid. Thus, a nano-technology coat achieves the aim of an almost ideal graded refractive index. The major advantage of this approach is that it shows anti-reflective properties for almost any angle of incidence, while the quarter wavelength approach works well only for relatively perpendicular light waves (the reason that coated lenses often look highly reflective when viewed from oblique angles). Nano-technology coatings are usually applied on highly curved surfaces, such as for instance the inner front element of the Nikon 14-24/2.8 lens.

The advent of digital photography has increased the importance of anti-reflection coatings. A digital sensor is much more reflective than film, so during an exposure there can be an amount of light reflected back through the lens in the reverse direction. If the lens were to reflect this back to the sensor, further image degradation would result. Therefore, lenses designed for use with digital cameras have coatings designed to handle light passing in the reverse direction as well as the normal forward direction.