to arrive at the interface. 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. Textured coatings Reflection can be reduced by texturing the surface with 3D pyramids or 2D grooves (gratings). These kind of textured coating can be created using for example the Langmuir-Blodgett method. If wavelength is greater than the texture size, the texture behaves like a gradient-index film with reduced reflection. To calculate reflection in this case, effective medium approximations can be used. To minimize reflection, various profiles of pyramids have been proposed, such as cubic, quintic or integral exponential profiles. If wavelength is smaller than the textured size, the reflection reduction can be explained with the help of the geometric optics approximation: rays should be reflected many times before they are sent back toward the source. In this case the reflection can be calculated using ray tracing. Using texture reduces reflection for wavelengths comparable with the feature size as well. In this case no approximation is valid, and reflection can be calculated by solving Maxwell equations numerically. Antireflective properties of textured surfaces are well discussed in literature for a wide range of size-to-wavelength ratios (including long- and short-wave limits) to find the optimal texture size. History As mentioned above, natural index-matching "coatings" were discovered by Lord Rayleigh in 1886. Harold Dennis Taylor of Cooke company developed a chemical method for producing such coatings in 1904. Interference-based coatings were invented and developed in 1935 by Olexander Smakula, who was working for the Carl Zeiss optics company. These coatings remained a German military secret for several years, until the Allies discovered the secret during World War II. Katharine Burr Blodgett and Irving Langmuir developed organic anti-reflection coatings known as Langmuir–Blodgett films in the late 1930s. See also Anti-scratch coating Dichroic filter Lens flare, which AR coating helps to reduce. References Sources External links Browser-based thin film design and optimization software Browser-based numerical calculator of single-layer thin film reflectivity Thin-film optics