The use of two-dimensional scales for measuring angle and linear displacement

Recently the authors proposed a new angle measurement technology based on the use of the two-dimensional scales. The rotation angle measurement is based on measuring the rotation of the pattern image on the sensor of a digital camera. The report presents the results of generalization of the developed earlier technology of angular measurements using a two-dimensional scale to measurements of linear displacements. It is shown that using a simple optical-digital system with a physical resolution, for example, of the order of several micrometers, it is possible to measure angles with an error of one thousandth of an arc second and linear displacements with an error of a fraction of a nanometer.