Multi-Coating

[stuart_pratt]

You know when you ask a question with some trepidation that you won’t look like a complete idiot?....

 

I’ve been reading up on the multi-coating of lenses, just out of curiosity really, as I’ve often wondered about the physics of it, but never got round to educating myself. There are various web sites that describe, in layman’s terms, what the basic principle is. You have light, entering a lens and at glass/air or glass/glass interfaces, some of it (a few percent) gets reflected. If you coat the lens with something a quarter the light wavelength in thickness, there are then two reflections, one at the glass surface beneath the coating, and one at the coating surface. As the reflection at the glass surface travels half a wavelength further than the one at the coating surface (a quarter wavelength more in and a quarter more out), there is destructive interference as the light exits, and they cancel out. Hence ‘no reflection’. Well, something like that anyway.

 

I understand why the reflection is not desirable for elements within the lens, as you don’t want stray light pinging around in all directions fogging your image. But if the light is cancelled after it is reflected, what use is it on the outside front element of a lens? That few percent of light wasn’t going to make it through an un-coated lens, and it doesn’t make it past when it’s coated either, it gets cancelled after being reflected? At least that’s how I understand it. How is that increasing the amount of light entering the lens? . That got me thinking maybe it isn’t on the front elements, but then plenty of single lens spectacles have multi-coating on the front surface. Is that just to make me look pretty?

 

No doubt there is some fundamental of Physics or the technical details of multi-coating I’m missing here, and maybe someone can educate me further?

Thanks

[conrad_hoffman]

An uncoated piece of glass reflects about 4% of the light hitting it, so you get an improvement in transmission. The light, AFAIK, isn't "cancelled"; you get an actual increase in transmission. You also reduce internal reflections because less light is reflected back into the lens from other elements and such. At least that's how I understand it.

[Alan Marcus]

John William Strutt, 3rd Baron Rayleigh, Astronomer Royal, Chancellor University Cambridge, Nobel Prize Physics 1904, observed that old lenses on the shelf pass more light than new one of the same designs. New ones reflect away about 4%, whereas old ones only 2%.

 

Additionally, Harold Taylor, in 1892 also observed this phenomenon. Seems old lenses on the shelf were blemished with a coat of soot, bad air due to coal burning. Air pollution had deposited a thin transparent coat that somehow reduced surface reflections, thus allowing more light to transverse the lens.

 

Taylor experimented and found a way to artificially bloom (age) lenses. This truly was an important discovery, because new lenses suffer a 4% loss in light due to reflections off their polished surfaces. Consider that a multi element lens array like a telescope or camera often suffers a light loss of 40 – 50%.

 

Additionally, there are inner reflections as each element has two polished surfaces. This will induce a loss at each junction. Internal reflections induce stray light in the optical system. This is devastating as it greatly reduces image contrast and spawns glare spots and ghost images.

 

Many coating methods are used. One method is to place the lens to be coated in a vacuum chamber. The air is evacuated, and the mineral that will be deposited is heated causing it to vaporize. This vapor condenses on the glass lens and coats and etches. It is the thickness of the coat plus the material that does the trick. It works best when it is ¼ wavelength high. The incoming light ray passes easily through the coat/air junction. It then hits the polished glass and 4% is reflected away. These reflected rays hit the coating air junction and about half of them are re-reflected backwards into the lens, boosting the number of photons that will traverse the lens.

 

Because coat thickness is key, a coat is naturally optimized for a specific color. A modern lens has multiple coats applied. Each coat is different in thickness. A high-quality lens can have as many as 7 thru 11 coats.

 

As time passes, coating technology advances. Likely each discovery will give small improvements.

 

A tip of the hat to William Strutt and Harold Taylor.

[JDMvW]

Very nice, alan.!

[stuart_pratt]

The incoming light ray passes easily through the coat/air junction. It then hits the polished glass and 4% is reflected away. These reflected rays hit the coating air junction and about half of them are re-reflected backwards into the lens, boosting the number of photons that will traverse the lens.

 

 

Thanks Alan for that comprehensive reply. It was that bit I’ve re-posted that was missing from my understanding, and now it all makes sense!

[glen_h]

When I bought my first lens (AI 35/2.0), I bought a single coat skylight filter. For one, I would be less bothered if I got fingerprints on it.

 

One detail you didn't get in your description is that the 1/4 wavelength coating should have index of refraction the geometric mean of the two sides. That would be sqrt(1.5) for most lenses. But there is no convenient material with that index of refraction.

 

MgF2 is about 1.38, and is commonly used. With multiple layers and appropriate indices of refraction, one can get very close.

 

Note also that it can only be 1/4 wavelength for one wavelength. It will work less well at different wavelengths.

 

With appropriate number of coatings and indices of refraction, one can make it (close enough to) zero and two or three wavelengths.

 

Some years ago, my optometrist convinced me to get the best antireflection coating for my glasses. It was very good, with a very small reflection, but the actual (small) reflection was bright pink. So next time I got the more ordinary one, which is dark green.

 

And one more thing. While the coatings with different indices of refraction, and canceling reflections, is the usual way, there is another way.

That is to (more or less) continuously go from one index of refraction to the other, over maybe a wavelength or two. Something like this is commonly used for acoustic antireflection surfaces. The above described soot coatings work that way. If there is random dust on the surface, made from dust particles much smaller than the wavelength, the effect is similar to the continuous index change.