Matrix technology for linear and angular measurements
In conventional linear-angular instruments, the measure of the measured value is, as a rule, the intervals between scale divisions. The divisions are usually made in the form of strokes, and the measured value corresponds to the difference in coordinates between the start and end strokes. Since the time of Descartes, measurements have been carried out “from point to point”, “from knot to knot”, “from line to line”.
The measurement accuracy is determined by the accuracy of determining the coordinates of a single scale element (strokes). Matrix technology uses a measuring pattern as a scale - a two-dimensional periodic structure of elements, e.g. small dots. The total number of elements can be tens or hundreds of thousands.
The system measures the coordinates of the images of these elements, and then calculates the parameters of the mathematical matrix with the same elements using least square method. In accordance with the laws of statistics, the weighted average linear and angular coordinates of a mathematical matrix determined in this way will have a coordinate error of square root of N less than the measurement result for one element, where N is the number of elements in the measuring mark.
Main components of the matrix meter:
1. measuring pattern with an area of several square centimeters
2. a digital camera with a sensor of the same size
3. reproduction lens with a focal length of 30–40 mm.
Sequence of operations:
1. Getting an image of an optical pattern on the sensor of a digital camera
2. Using pixels of camera sensor as a 2-D scale
3. Measuring the coordinates of each element of the image, for example, by calculating the center of the brightness distribution
4. Digital correction of the coordinates of the pattern image element using data for correcting optical image distortions (tilt, aberrations) and manufacturing
errors of the pattern
5. Calculation of the parameters of the matrix based on the coordinates of all elements of the image using the least squares method. The coordinates of the
matrix are the coordinates of the object’s movement. The typical size of a measuring pattern element is 30 microns, the pitch between elements is 50 microns. The error in measuring the coordinate of a single element of the stamp image is 0.5 µm. When using a measuring pattern that with 10,000 elements, an error in the coordinates of the elements is approximately 5 nm.
(A matrix angle meter with a scale diameter of 5 mm allows to obtain an angle
measurement error of the order of ±0.05";. For a device with a radial scale, a diameter of at least 100 mm is required.)
2D platforms for positioning with
1 nm accuracy
Guiding systems with an angular precision of 0.001"
1. A.N. Korolev, A.Ya. Lukin, G. S. Polishchuk, “New concept of angular measurement. Model and experimental studies”, J. Opt. Technol. 79(6), 352–356 (2012) Download
2. A.N. Korolev, and A.Ya. Lukin, E.D. Bokhman, V.Yu. Venediktov, “Digital goniometer with a two-dimensional scale,” J. Opt. Technol. 85(5), 269–274 (2018) Download
3. A.N. Korolev, A.Ya. Lukin, Y.V. Filatov, and V.Y. Venediktov “Reconstruction of the image metric of periodic structures in an opto-digital angle measurement system,” Sensors 21, 4411 (2021) Download
4. A.N. Korolev, A.Ya. Lukin, Y.V. Filatov, and V.Y. Venediktov “The use of two-dimensional scales for measuring angle and linear Displacement”, Proc. of SPIE Vol. 12274 p. 1-8 (2022) Download
5. A.N. Korolev, A.Ya. Lukin, Y.V. Filatov, and V.Y. Venediktov “Matrix technology of linear–angular measurements”, J. Opt. Technol. 85(5), 269–274 (2022) Download
6. Alexander Korolev, Pavel Ivanov, Yuri Filatov, Alexander Lukin, Eugeni Bokhman. Investigation of the Accuracy Characteristics of Matrix Methods of Linear-Angular Measurements. 31st SAINT PETERSBURG INTERNATIONAL CONFERENCE ON INTEGRATED NAVIGATION SYSTEMS, 2024, р. 323-326 Download
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Korolev Aleksandr NikolaevichDoctor of Technical Sciences, 100+ publications
Education ITMO, optician-physicist.
20 years of work at the State Optical Institute (GOI), Head of Laboratory
10 years of work at the All-Russian Research Institute of Metrology, Head of the Laboratory.
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Lukin Alexander YakovlevichPhD in Physics and Mathematics, 100+ publications
Education SpbPU (Peter the Great St. Petersburg Polytechnic University), physicist
50 years of work at SpbPU,
Department of Physics, Professor.