Light is reflected at both interfaces of an AR coating. The two reflected wave trains of a certain wavelength can cancel each other out totally by interference if both the phase and amplitude requirements are met.
The crest and trough of the two reflected wave trains must coincide, i. e. they must have a path difference of one half a wavelength relative to each other to ensure that cancellation by interference can take place for this wavelength.
By the appropriate choice of layer thicknesses and layer types, the phase requirement can be met for the reference wavelength (wavelength for which the AR coating is optimised). Interference then leads to a minimisation of residual reflection. To achieve this, the layer thickness (t) must total one quarter of the reference wavelength.
The amplitudes of the two reflected wave trains must be identical to ensure that total cancellation can take place for the reference wavelength.
By appropriately selecting the refractive indices of the AR coating layers, interference leads to a minimisation of residual reflections. A suitable combination of lens and AR coating materials is decisive if the AR coating is to have an optimum effect.
In single layer coatings a minimum of greater or less magnitude is obtained at the reference wavelength, depending on the AR coating material used. The reduction of reflections is only optimised for a small wavelength range.
However, if a reduction in reflections is required over a large range of the spectrum, several AR coatings must be applied. With a multiple layer coating, light transmission of up to just under 99% can be obtained.
Structure of a single layer coating
In a single layer coating on glass lenses the refractive index of the coating is always lower than that of the lens. The coating material used is magnesium fluoride. In plastic lenses a single AR coating always consists of a high-index and a low-index layer. Here, one of the materials used is silicon dioxide (SiO2).
Structure of Super ET by ZEISS
In multiple layer coatings on both plastic and glass lenses, alternate layers consisting of high-index and low-index materials of different thickness are deposited. The coating layers are approx. 100 to 250 nm thick. Comparison: One hundred multiple layer coatings have approximately the same thickness as a human hair.
From spectacle crown glass (n = 1.5) to high-index lenses with n = 1.9, the proportion of annoying reflections rises from approx. 8% to just under 20%. This means that reflections are twice as irritating in lenses with a high refractive index. An AR coating is therefore an absolute must for medium-index and high-index lenses.
In a non-coated lens with n = 1.9, only about 80% of incident light actually reaches the wearer’s eye, compared to as much as 92% in lenses with n = 1.5.
The graph showing reflectance as a function of the refractive index n clearly illustrates that the greater the refractive index of the selected material, the more important an AR coating becomes.
AR-coated lenses for better vision
In the past, only solid-tinted materials were used to produce lightly tinted glass filter lenses. Nowadays, the absorptive layer can be deposited on the lens surface together with the AR coating in vacuum conditions.
The advantage of vacuum filter coatings over solid tint lenses is that the tint is distributed evenly over the entire lens surface, irrespective of the dioptric power. This is why the use of solid tint filter lenses is now constantly decreasing.
The enhancement of colour contrast associated with solid tint lenses is also achieved by lenses with a filter AR coating.
The residual reflection is the distinguishing feature of the various AR coatings available. Every ZEISS AR coating displays a characteristic residual reflection colour, regardless of the lens material.
A ZEISS Super ET coating, for example, always displays a bluish green residual reflection, irrespective of whether the lens concerned is glass or plastic, or whether the material has a high or low refractive index. To achieve this high standard of quality, up to 50 different production techniques are used at ZEISS.