because of strain by the film. Lasers are reflected off the wafer in a grid pattern and distortions in the grid are used to calculate the curvature. Strain in thin films can also be measured by x-ray diffraction or by milling a section of the film via focused ion beam and the relaxation observed via scanning electron microscopy. Strain engineering Stress and relaxation of stresses in films can influence the materials properties of the film, such as mass transport in microelectronics applications. Therefore precautions are taken to either mitigate or produce such stresses; for example a buffer layer may be deposited between the substrate and film. Strain engineering is also used to produce various phase and domain structures in thin films such as in the domain structure of the ferroelectric Lead Zirconate Titanate (PZT). Applications Decorative coatings The usage of thin films for decorative coatings probably represents their oldest application. This encompasses ca. 100 nm thin gold leaves that were already used in ancient India more than 5000 years ago. It may also be understood as any form of painting, although this kind of work is generally considered as an arts craft rather than an engineering or scientific discipline. Today, thin-film materials of variable thickness and high refractive index like titanium dioxide are often applied for decorative coatings on glass for instance, causing a rainbow-color appearance like oil on water. In addition, intransparent gold-colored surfaces may either be prepared by sputtering of gold or titanium nitride. Optical coatings These layers serve in both reflective and refractive systems. Large-area (reflective) mirrors became available during the 19th century and were produced by sputtering of metallic silver or aluminum on glass. Refractive lenses for optical instruments like cameras and microscopes typically exhibit aberrations, i.e. non-ideal refractive behavior. While large sets of lenses had to be lined up along the optical path previously, nowadays, the coating of optical lenses with transparent multilayers of titanium dioxide, silicon nitride or silicon oxide etc. may correct these aberrations. A well-known example for the progress in optical systems by thin-film technology is represented by the only a few mm wide lens in smart phone cameras. Other examples are given by anti-reflection coatings on eyeglasses or solar panels. Protective coatings Thin films are often deposited to protect an underlying work piece from external influences. The protection may operate by minimizing the contact with the exterior medium in order to