Matrix technology of measurements. Path to nanometers

The new technology for measuring linear and angular coordinates uses an optical pattern with a very large number of elements (tens/hundreds of thousands). A simultaneous measurement of the position of all elements of the pattern image using a digital camera increases the accuracy of measuring the position of the pattern by hundreds of times or more. For the new meters, the predicted resolution is fractions of a nanometer on the linear scale and thousandths of an arc second on the angular scale. The resolution of a real meter is limited by a random measurement error caused by a limited bit depth and thermal noise of a digital camera. The study of this component of the error is the purpose of this work. The authors carried out long-term measurements of the coordinates, the angle of rotation and the period of the stationary pattern in conditions of slowly changing temperature. The analysis of the data obtained made it possible to determine a random component of the measurement error, separating it from the changes caused by thermal deformations. With the dimensions of the pattern and the matrix of the digital camera of less than 10 mm, the standard deviation of angular measurements was 0.005 angular seconds, of linear measurements - about 0.1 nm, and the random error in measuring the period value of the pattern elements was less than 0.01 nm. The obtained estimates of the standard deviation of the measurement results are in good agreement with the analytical estimates given in the article. The high resolution of the matrix technology of linear and angular measurements has been experimentally proven.