Cylindricalcoordinates

The HFOV describes the horizontal dimensions of the measurement field in the measurement object plane. It can be defined based on the horizontal dimensions of the detector, the distance to the measurement object, and the horizontal visual angle of the lens.

The Helmholtz differential equation is separable in cylindrical coordinates and has Stäckel determinant (for , , ) or (for Morse and Feshbach's , , and ).

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The VFOV describes the vertical dimensions of the measurement field in the object plane. It can be calculated in the same way as the HFOV based on the vertical visual angle and the vertical dimensions of the detector.

Cylinder

Field of View (FOV) refers to the visual angle of a lens. For Optris IR cameras, depending on the lens, this ranges from 4° (telephoto lens) to 90° (wide angle lens). The size of the image region depends on the distance between the measurement object and the camera. Accordingly, the image section that an individual pixel captures increases or decreases.

Weisstein, Eric W. "Cylindrical Coordinates." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CylindricalCoordinates.html

The MFOV indicates the recommended minimum object size. This corresponds to the measurement field section of 3×3 or 2×2 pixels on the measurement object. The calculation is done in the same way as for the IFOV for a pixel field of 3×3.

The DFOV indicates the diagonal dimensions of the measurement field in the object plane and can be calculated based on the HFOV and VFOV.

IFOV describes the size of an individual pixel on the measurement surface. It can be calculated based on the pixel size, the distance to the measurement object, and the vertical and horizontal visual angle of the lens.

Cylindrical coordinates are a generalization of two-dimensional polar coordinates to three dimensions by superposing a height () axis. Unfortunately, there are a number of different notations used for the other two coordinates. Either or is used to refer to the radial coordinate and either or to the azimuthal coordinates. Arfken (1985), for instance, uses , while Beyer (1987) uses . In this work, the notation is used.