Assume you have a 4K or 10K camera without zoom (1x).

Case 1. Object width 2 cm and height 2 cm. It is 50 meter from the lens. The angle becomes << 1 so making the object invisible in the picture.

I am thinking how to choose the correct distance for a small object. I am making a plan where I position myself in filming one event.

You can assume the object is a piece of coal in coal mine i.e. object vs background properties are challenging. So quite low contrast and struggling with detection sensitivity vs reliability i.e. wanted 95% detectability and 5% false alarms.

Camera characteristics but can be improved if necessary

  • Camera 4K-10K
  • Focal length is 0.5 m
  • The resolving power is 50.6 MP
  • 150,000 pixel RGB+IR metering sensor
  • Sensor Size: 36x24mm, Full-Frame CMOS.
  • 10.1-micron pixel pitch

How do you choose the filming distance to the object?

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    Without knowing the focal length and resolving power of the lens and the size of the sensor and its pixel pitch it is not possible to answer your question. – Michael C Jan 25 '16 at 22:51
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    Not to mention your standard for "detection". – mattdm Jan 25 '16 at 23:43
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    Is the object a piece of coal in coal mine? Or is it a high-wattage lightbulb? – mattdm Jan 25 '16 at 23:44
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    I think that when it comes to object detection, Edmund optics' tutorials on machine vision might be of interest. I came across the tutorials while on their site buying something else, and I'm sure they're not the only people with a decent writeup, but it might help you get started. – Chris H Jan 26 '16 at 7:18
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    @Masi with no knowledge of your application I suggest you have a browse around the "Imaging" category. They've re-arranged everything and added some material since I last looked. Do you really mean f=0.5mm; that doesn't make sense. 0.5m would be more like it. – Chris H Jan 26 '16 at 9:32

An abject viewed from a distance of 3000 diameters, appears as an non-desirable point to a person with 20/20 vision. Thus a 1 meter circle or square viewed from 3,000 meters appears as a point.

For the photograph we are forced to use a lower standard because of unresolved aberrations in the camera’s optical system and because of the limitations of photo media as to contrast etc. This works out to an object with a diameter of 1/1000 of the viewing distance = 3.4 minutes of arc. This would be equivalent to 1/100 of an inch viewed from 10 inches (.25mm viewed from 250mm) or 1/50 of an inch viewed from 20 inches (.5mm viewed from 500mm).

Using this criteria of being viewed from 500mm, the permissible image size on film on chip is a square 0.5mm by 0.5mm.

To make an image size 0.5mm by 0.5mm from a 20mm by 20mm target using a 50mm lens: The distance lens to image is 50mm. The ratio of image height to focal length is 50 ÷ 0.5 = 100. To image using this ratio, the objet to lens distance must be 20 x 100 = 2000mm

In other words, a 20mm by 20mm object imaged with a 50mm lens from a distance of 2000mm yields an image those measures 0.5mm by 0.5mm. This is true is if the image remains native as to size.

If you wish to make an enlargement, say an 8x10, then the magnification used to make this enlargement must be taken into consideration. To make an 8x10 from a full frame, the minimum magnification is 8X. Using this criteria, the image size at the focal plane must be 0.5 ÷ 8 = 0.0625mm.

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    the assumption about aberrations is interesting but it makes us ignore the nominal camera resolution? the question refers to "4K" so the assumption was probably that our optics is good enough to make it count? anyway, answering this question is pointless without knowing the contrast and detection criteria... we can easily detect stars in the night sky even though our eyes resolution is too small (for resolving such tiny objects). – szulat Jan 26 '16 at 11:11
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    oh, i haven't noticed the "coal in the coal mine" clarification - so i guess it means quite low contrast and we will struggle with detection sensitivity vs reliability. any detection might be in fact noise. do we prefer 99,99% detectability and 0,1% false alarms or 99,9% detectability and 0,01% false alarms? these numbers would change with distance. and all this depends on the specific object vs background properties. – szulat Jan 26 '16 at 11:25

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