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Antireflective coatings are designed to reduce the amount of light lost to reflection at the surfaces of individual, transmissive elements. Historically, motivation for the development of antireflective coatings came from problems with loss of light and ghost images in compound, multi-element lens systems.

Uncoated glass will reflect some of the light incident upon its surface. For a lens element immersed in air, Fresnel's equation predicts surface reflection for normally incident light:

R = ( n-1/n+1 )2

Reflectivity, R, of uncoated glass is a function of its refractive index, N. The higher the index, the higher its reflectivity.

In a multi-element lens, there can be many glass-to-air interfaces because many of the elements are separated by air spaces. Lens designers use air spaces as degrees of freedom in the pursuit of a quality lens design. Unfortunately, uncoated crown glass will reflect about 4% of the light incident upon its surface, and uncoated flint glass can reflect as much as 8% because of its higher refractive index. Therefore, one crown glass lens element will transmit only 92% of incident light; 4% is reflected away at each of its two surfaces. One flint element will transmit only 85%. For a basic three-element, air-spaced, compound lens with two crown elements and one flint, transmission is limited to 72%. In other words, image brightness is reduced by 28% unless reflection at each glass surface can be reduced.

In this basic example of an air-spaced triplet, 28% of the total light that could have helped to brighten the image never reaches the image plane. In an uncoated, air-spaced, six-element lens with four crown glass elements and two flint glass elements, reflective loss is about 50%! Clearly, this significant loss of image brightness is a heavy penalty to pay for the improved resolution of a sophisticated compound lens.

Antireflective coatings can save most of the light that is lost on uncoated glass. For example, if a single-layer coating of magnesium fluoride (MgF2) were used, then reflection at each glass surface would be reduced to about 2%. A hypothetical six-element lens would then transmit 89% of the incoming light; only 11% would be lost! A more efficient, multi-layer antireflective coating would reduce losses to 0.5% at each surface. Then total transmission would be raised to 97%, and only 3% of the light would be lost to reflection!

Antireflective coatings circumvent the penalty of low image brightness incurred by an uncoated compound lens.

Another penalty associated with uncoated elements that can be minimized with these same antireflective coatings is ghost images, which can deteriorate the image and contrast of a multi-element lens. Their name, ghost images, comes from the observation that they are superimposed over the primary image but do not obstruct it. Instead, they appear as shadowy apparitions floating among the details of the image. Reflections from internal elements can cause ghost images. Most of the time they appear as halos, spots, and starlike patterns.

What is the nature of a reflection that creates a ghost image? There can be a large number of reflections in a compound lens. Reflections that originate from the incoming beams of light may be called primary reflections. They propagate out of the lens toward the object and carry away energy that could have contributed to the brightness of the image. Many other reflections travel through the lens toward the image plane. These are the secondary reflections of the original, primary reflections (Figure G-2).

Secondary reflections directed at the image plane encounter some lens elements before they reach the image. They experience refraction as if they emanated from the object; however, since they were created inside the lens itself, they produce strange patterns in the image plane.