The format type of a digital camera sensor is one of the most confusing in the vision industry. The format type is a remanent from how video camera tubes were constructed prior to the advent of CCDs or CMOS sensors.
These 'video tubes' had opaque regions outside the active area of the cathode tube, which reduced the light sensitive region. These resulted from the mechanics holding either the larger tube or cathodes.
For example:
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A 1 image sensor with 4:3 aspect ratio is 12.8mm Horizonal * 9.6mm Vertical * 16mm Diagonal
A 1/3 image sensor with 4:3 aspect ratio is 4.8mm Horizontal * 3.6mm Vertical * 6mm Diagonal
Well that doesnt seem to make any sense, does it? 1" is 25.4mm and 1/3 of 1" is 8.5mm! Even 1/3 of the 1" Format Diagonal should be 5mm!
Let's take the 1" format type as an example. Part of the cathode ray tube's diameter was the tube wall and was not used for imaging purposes.
So, the area was reduced from 25.4mm to 16mm.
So, a lens suitable for a 1" type cathode ray tube did not need an image circle that extended to the entire 25.4mm tube diameter.
Some historical references state that the sensor size is 3/2 * Format Type then rounded, however, there are still exist many discontinuities.
With modern day imaging, there exist a nearly infinite number of image sensor diagonal dimensions for which there was no original video tube size corresponding to.
So, we've done our best to derive a "modern-day" equation that defines image sensor format type more precisely. We used commonly agreed upon datapoints of 1" = 16.0mm, 1/2" = 8.0mm, 1/3" = 6.0mm, 1/4" = 4.5mm and backed out a fitting equation, then cross-referenced as many other articles as possible.
Unfortunately, the formula for the digital image sensor type has a discontinuity occurring between the 1/2" image sensor and 1/2.3" image sensor format size.
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