Many coatings consist of transparent thin film structures with alternating layers of contrasting refractive index. Layer thicknesses are chosen to produce destructive interference in the beams reflected from the interfaces, and constructive interference in the corresponding transmitted beams. This makes the structure's performance change with wavelength and incident angle, so that color effects often appear at oblique angles. A wavelength range must be specified when designing or ordering such coatings, but good performance can often be achieved for a relatively wide range of frequencies: usually a choice of IR, visible, or UV is offered.
Single lens coatings were invented in November 1935 by Alexander Smakula, who was working for the Carl Zeiss optics company. Anti-reflection coatings were a German military secret until the early stages of World War II. They were independently invented by Katharine Burr Blodgett in the late 1930s.
Antireflective ophthalmic lenses should not be confused with polarized lenses, which decrease (by absorption) the visible glare of sun reflected off of surfaces such as sand, water, and roads. The term "anti-reflective" relates to the reflection from the surface of the lens itself, not the origin of the light that reaches the lens.
Many anti-reflection lenses include an additional coating that repels water and grease, making them easier to keep clean. Anti-reflection coatings are particularly suited to high-index lenses, as these reflect more light without the coating than a lower-index lens (a consequence of the Fresnel equations). It is also generally easier and cheaper to coat high index glasses.
The most common type of optical glass is crown glass, which has an index of refraction of about 1.52. An optimum single layer coating would have to be made of a material with an index equal to about 1.23. Unfortunately, there is no material with such an index that has good physical properties for an optical coating. The closest 'good' materials available are magnesium fluoride, MgF2 (with an index of 1.38), and fluoropolymers (which can have indices as low as 1.30, but are more difficult to apply). On a crown glass surface, MgF2 gives a reflectance of about 1%, four times less than the 4% reflection from bare glass. MgF2 coatings perform much better on higher-index glasses, especially those with index of refraction close to 1.9. MgF2 coatings are commonly used because they are cheap, and when they are designed for a wavelength in the middle of the visible band they give reasonably good antireflection over the entire band.
When the light meets the interface at normal incidence (perpendicularly to the surface), the intensity of light reflected is given by the reflection coefficient or reflectance, R:
For the simplified scenario of visible light travelling from air (n0≈1.0) into common glass (nS≈1.5), value of R is 0.04, or 4% on a single reflection. So at most 96% of the light (T=1–R=0.96) actually enters the glass, and the rest is reflected from the surface. The amount of light reflected is known as the reflection loss.
In the more complicated scenario of multiple reflections, say with light travelling through a window, light is reflected both when going from air to glass and at the other side of the window when going from glass back to air. The size of the loss is the same in both cases. Light also may bounce from one surface to another multiple times, being partially reflected and partially transmitted each time it does so. In all, the combined reflection coefficient is given by 2R/(1+R). For glass in air, this is about 7.7%.)
From the equation above, and the known refractive indices, reflectivities for both interfaces can be calculated, and denoted R01 and R1S, respectively. The transmission at each interface is therefore T01 = 1-R01 and T1S = 1-R1S. The total transmitance into the glass is thus T1ST01. Calculating this value for various values of n1, it can be found that at one particular value of optimum refractive index of the layer, the transmittance of both interfaces is equal, and this corresponds to the maximum total transmittance into the glass.
This optimum value is given by the geometric mean of the two surrounding indices:
For the example of glass (nS≈1.5) in air (n0≈1.0), this optimum refractive index is n1≈1.225, the optimum refractive indices for a multi-layer coating can be computed by the procedure given in . The optimum refractive indices for a multi-layer coating at angles of incidence other than 0° is given by Moreno et al. (2005).
The reflection loss of each interface is approximately 1.0% (with a combined loss of 2.0%), and an overall transmission T1ST01 of approximately 98%. Therefore an intermediate coating between the air and glass can halve the reflection loss.
Practical antireflection coatings, however, rely on an intermediate layer not only for its direct reduction of reflection coefficient, but also use the interference effect of a thin layer. Assume the layer thickness is controlled precisely, such that it is exactly one quarter of the light's wavelength thick (λ/4). The layer is then called a quarter-wave coating. For this type of coating the incident beam I, when reflected from the second interface, will travel exactly half its own wavelength further than the beam reflected from the first surface. If the intensities of the two beams R1 and R2 are exactly equal, they will destructively interfere and cancel each other since they are exactly out of phase. Therefore, there is no reflection from the surface, and all the energy of the beam must be in the transmitted ray, T. In the calculation of the reflection from a stack of layers, the transfer-matrix method can be used.
Real coatings do not reach perfect performance, though they are capable of reducing a surface's reflection coefficient to less than 0.1%. Practical details include correct calculation of the layer thickness; since the wavelength of the light is reduced inside a medium, this thickness will be λ0 / 4n1, where λ0 is the vacuum wavelength. Also, the layer will be the ideal thickness for only one distinct wavelength of light. Other difficulties include finding suitable materials for use on ordinary glass, since few useful substances have the required refractive index (n≈1.23) which will make both reflected rays exactly equal in intensity. Magnesium fluoride (MgF2) is often used, since this is hard-wearing and can be easily applied to substrates using physical vapour deposition, even though its index is higher than desirable (n=1.38).
Further reduction is possible by using multiple coating layers, designed such that reflections from the surfaces undergo maximum destructive interference. One way to do this is to add a second quarter-wave thick higher-index layer between the low-index layer and the substrate. The reflection from all three interfaces produces destructive interference and antireflection. Other techniques use varying thicknesses of the coatings. By using two or more layers, each of a material chosen to give the best possible match of the desired refractive index and dispersion, broadband antireflection coatings which cover the visible range (400-700 nm) with maximum reflectivities of less than 0.5% are commonly achievable.
The exact nature of the coating determines the appearance of the coated optic; common AR coatings on eyeglasses and photographic lenses often look somewhat bluish (since they reflect slightly more blue light than other visible wavelengths), though green and pink-tinged coatings are also used.
If the coated optic is used at non-normal incidence (that is, with light rays not perpendicular to the surface), the antireflection capabilities are degraded somewhat. This occurs because the phase accumulated in the layer relative to the phase of the light immediately reflected decreases as the angle increases from normal. This is counterintuitive, since the ray experiences a greater total phase shift in the layer than for normal incidence. This paradox is resolved by noting that the ray will exit the layer spatially offset from where it entered, and will interfere with reflections from incoming rays that had to travel further (thus accumulating more phase of their own) to arrive at the inteface. The net effect is that the relative phase is actually reduced, shifting the coating, such that the anti-reflection band of the coating tends to move to shorter wavelengths as the optic is tilted. Non-normal incidence angles also usually cause the reflection to be polarization dependent.