Conndomat
United States of Europe
Hi,
Quote: Holger Merlitz,
The confusion arises from the contradictory claims of the manufacturers. While the objective visual angle can be converted exactly into the visual field, a calculation of the subjective visual angle, requires knowledge of the distortion. Unfortunately, the manufacturers do not indicate the distortion of their optics. Alternatively, they could at least publish the actual subjective visual angle, but only a few do (Swarovski, and Zeiss only in his SF series, but not in the other models!). In all other cases, they use standard conversion formulas that either overestimate or underestimate the subjective visual angle.
Nikon consistently uses the ISO 14132-1: 2002 conversion formula
a = 2 atan [m tan (A / 2)] (1)
where 'a' is the subjective visual angle and 'A' is the objective angle of vision, and 'm' is the magnification. This formula is valid only in the absence of distortion (strictly speaking, in the absence of the radial distortion V), and this condition is almost never fulfilled in practice. In the presence of a radial distortion, the above formula must be extended to
a = 2 atan [m (V + 1) tan (A / 2)]
where 'V' indicates the relative radial distortion at the field of view. If this equals zero, then you immediately get the ISO formula again. Almost always V is a positive number, one speaks then of a pillow-shaped distortion. Stupid only that no manufacturer indicates the value of V. A special case is of interest, namely the so-called angle condition in which
tan (mA / 2)
V = ------------ - 1 (angle condition)
m tan (A / 2)
applies. This leads to the well-known simple conversion formula
a = m A (2) (angle condition)
It can be shown that this special case, if satisfied for each pixel, leaves the angular distances of all pixels unchanged when panning across the entire field of view. In astronomy, this means, for example, that an open star cluster is represented in the center of the image as well as at the edge of the field of view (when the eye follows the position of the cluster in the direction of the edge of the field of view). In the English-speaking world one speaks then of the absence of an angular magnification distortion (AMD) - for which there does not seem to be any expression in German (one could speak somewhat casually of 'angular distortion').
Historically, the manufacturers initially aimed for a distortion-free image (V = 0), since about 1950 then increasingly on the angular condition set (in which V> 0 and a significant pincushion distortion exists) to avoid the globe effect when pivoting the binoculars. In almost all binoculars currently on the market, the value of the distortion lies somewhere between V = 0 and the angle condition, so that neither (1) nor (2) reflects the correct ratios. We then have no choice but to measure the apparent visual angle ourselves."
https://www.juelich-bonn.com/jForum/read.php?9,443747,443808#msg-443808
Andreas
Quote: Holger Merlitz,
The confusion arises from the contradictory claims of the manufacturers. While the objective visual angle can be converted exactly into the visual field, a calculation of the subjective visual angle, requires knowledge of the distortion. Unfortunately, the manufacturers do not indicate the distortion of their optics. Alternatively, they could at least publish the actual subjective visual angle, but only a few do (Swarovski, and Zeiss only in his SF series, but not in the other models!). In all other cases, they use standard conversion formulas that either overestimate or underestimate the subjective visual angle.
Nikon consistently uses the ISO 14132-1: 2002 conversion formula
a = 2 atan [m tan (A / 2)] (1)
where 'a' is the subjective visual angle and 'A' is the objective angle of vision, and 'm' is the magnification. This formula is valid only in the absence of distortion (strictly speaking, in the absence of the radial distortion V), and this condition is almost never fulfilled in practice. In the presence of a radial distortion, the above formula must be extended to
a = 2 atan [m (V + 1) tan (A / 2)]
where 'V' indicates the relative radial distortion at the field of view. If this equals zero, then you immediately get the ISO formula again. Almost always V is a positive number, one speaks then of a pillow-shaped distortion. Stupid only that no manufacturer indicates the value of V. A special case is of interest, namely the so-called angle condition in which
tan (mA / 2)
V = ------------ - 1 (angle condition)
m tan (A / 2)
applies. This leads to the well-known simple conversion formula
a = m A (2) (angle condition)
It can be shown that this special case, if satisfied for each pixel, leaves the angular distances of all pixels unchanged when panning across the entire field of view. In astronomy, this means, for example, that an open star cluster is represented in the center of the image as well as at the edge of the field of view (when the eye follows the position of the cluster in the direction of the edge of the field of view). In the English-speaking world one speaks then of the absence of an angular magnification distortion (AMD) - for which there does not seem to be any expression in German (one could speak somewhat casually of 'angular distortion').
Historically, the manufacturers initially aimed for a distortion-free image (V = 0), since about 1950 then increasingly on the angular condition set (in which V> 0 and a significant pincushion distortion exists) to avoid the globe effect when pivoting the binoculars. In almost all binoculars currently on the market, the value of the distortion lies somewhere between V = 0 and the angle condition, so that neither (1) nor (2) reflects the correct ratios. We then have no choice but to measure the apparent visual angle ourselves."
https://www.juelich-bonn.com/jForum/read.php?9,443747,443808#msg-443808
Andreas
