The x10 is the daylight magnification of the M581 gunner’s telescopic primary sight, not the magnifications of its Castor thermal camera.
The optical characteristics of tank sights are actually like binoculars, and its magnification can be defined by the ratio of the focal length of objective lens to the focal length of eyepiece lens, or the ratio of the effective objective lens diameter to the exit pupil diameter.
M=f_objective/f_eyepiece =D/d
But most parameters such as the focal length or lens diameter of military AFV sights are confidential. Therefore, we can use the original definition of magnification, that is, how large or small a object can be reproduced on the image plane (the degree to which the object being viewed is enlarged) to calculate an approximate value.
The dimension of the object that a sight can observe generally depends on how wide the field of view is. The field of view is inversely proportional to magnification, that is, lower magnification expands it and higher magnification narrows it.
For example, at a specific observation distance, the image dimension observed at a high magnification M_h is M_l/M_h times the image size at a low magnification M_l.
In order to calculate a specific magnification, it can be simplified to the following formula
M_(low for WFoV)=D_(image dimension for NFoV)/D_(image dimension for WFoV) ×M_(high for NFoV)
The Castor thermal camera used by the AMX-40 is a dual field-of-view thermal imager. The following diagram is a typical step-zoom dual-field optical system, which uses different lens arrangements to change the focal length to provide different magnifications (rather than continuous zoom).
Thomson-TRT has designed three lens configurations for Castor for different applications, and the Castor/DIVT-16 system used by AMX-40/AMX-30B2 Brenus is variant 1.
Spoiler
The Castor thermal camera provides x2 electronic zoom. Other sources indicate that the DIVT-16 has a maximum magnification of x20, so the optical high magnification of the Castor is x10.
Spoiler
The approximate value of low magnification can be solved as follows:
Now if assume the object distance = 100 meters, then the given horizontal field in narrow FoV is 71 mils (NATO) and the given horizontal field in wide FoV is 160 mils (NATO).
We may choose base of isosceles triangle formula
(2∙h)/tan((180-β)∙0.5∙π/180)
Thus the horizontal image dimension in NFoV and in WFoV, respectively, which are
D_(horizontal for NFoV)=(2∙100)/tan((180-(71∙360/6400))∙0.5∙π/180)
and
D_(horizontal for WFoV)=(2∙100)/tan((180-(160∙360/6400))∙0.5∙π/180)
Then we use the given NFoV magnification x10 and the magnification rate formula derived above to get
M_(horizontal for WFoV)=10∙D_(horizontal for NFoV)/D_(horizontal for WFoV) =4.4301658696
So here we solve the magnification rate in WFoV, obtaining
M_(low for WFoV)=4.4
Note that this magnification value is an approximation. To verify the accuracy of this formula, we substitute the parameters of other sights to check the error.
AN/VSG-2 TTS, given x8 magnification and NFOV, solve for the lower magnification under WFOV
AN/VSG-X TIS, given x9.8 magnification and NFOV, solve for the lower magnification under WFOV
PERI-ZL, given x10 magnification and NFOV, solve for the lower magnification under WFOV
OIP Mk-2 FCS, given x12 magnification and NFOV, solve for the lower magnification under WFOV
The error is between ±0.5, and the error will increase if the given magnification or field of view is approximate. If one magnification is known, the formula can still calculate the approximate value of the other magnification.
