Crop Factor between the Pulsar Thermion XP50 and XM50 sensors

Ernest49

Member
Good evening to all the American night hunter friends. Today we have fun calculating the mysterious "Crop Factor". This factor is important for the calculation of the equivalent focal length between 2 thermal objectives having the same optics, but a different microbolometric sensor. Let's consider, as an example, the 2 top-of-the-range thermal riflescope of the Pulsar: Thermion XP50 vs. Thermion XM50 which have the same Germanium optics with an effective focal length of 50 mm. The XP50 sensor is 640x480 pixels with 17 micron / pixel. Instead the sensor of the Thermion XM50 is 320x240 pixels with 12 micron / pixel. Given that the ratio between the sides of the sensors 640/480 = 320/240 = 1.333 is the same, it means that the 2 sensors have the shape of 2 similar rectangles. So the Crop Factor can be calculated in 2 ways which give the same result: 1) Calculating the ratio between the diagonals of the sensors; 2) Calculating the square root of the ratio of the areas of the 2 sensors. We will use this second way because the calculation is simpler. CF = square root (640x17x480x17 / 320x12x240x12) = 2.8333.
So to find the "equivalent" focal length of the Pulsar Thermion XM50 lens, just multiply 50x2.833 = 142 mm. The same operation allows us to calculate the minimum magnification of the Pulsar Thermion XM50: 1.9x (minimum magnification of the XP50) multiplied by the crop factor (2.83333 ...) = 5.4x. From this calculation (approximated by default because the gaps between the pixels are neglected) we can understand why the Pulsar Thermion XM50 has a minimum declared magnification of 5.5 x and a significantly higher image definition, but with a much lower field of view. In fact it frames a considerably smaller area than the one framed by the XP50 which has the same objective but with the 640x480 pixel sensor.
 
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