Effect of increasing sensor size or focal length on resolution of target object

Question

Suppose I have a camera of sensor size 8mmx8mm, optical class (2/3)" with a compatible lens of also (2/3)". The focal length of my lens is fixed (say 8mm), and the distance to my target object is also fixed. My goal is to increase the resolution of my target object (I want my object to be represented by more pixels).

My questions are:

1. If I increase my focal length, am I also increasing the number of pixels on my object? or is the object just getting magnified? My guess is just magnifying.

2. If I increase my sensor size to 16mm, I think that means I'm increasing the number of pixels(resolution of the camera). So if 8mm means 2000 pixels for the width on my image, then 16mm means around 4000 pixels for the width of my image. In that case did I increase the number of pixels in my object? My guess is yes.

I was using this calculator on this webpage: https://www.scantips.com/lights/subjectdistance.html and when I put in the numbers, I realized both my guesses are wrong. It seems like because sensor size and pixel width of image are proportional to each other, increasing both doesn't actually increase the number of pixels represented on my object, but when I increase just the focal length and keep everything else constant then the number of pixels represented by my object also increases. I don't understand why though.

Answer 1

Your guesses are exactly the opposite of what actually happens.

In the first scenario, you are magnifying your subject more, so the subject covers more pixels on the same sensor because it takes up more of the total image area. Since the number of pixels has not changed, your subject now covers more of them because it is larger as projected onto the sensor.

In the second scenario, your subject covers the same number of pixels in the middle of the sensor, but now there is more area around your subject being shown.

If you double the width and height of your sensor, you quadruple the area and the number of pixels. 2000 pixels in an 8x8 mm area equals 8000 pixels in a 16x16 mm area. But the size of the subject being projected by the lens is the same, no matter what the size of the sensor is. It's just showing a wider angle of view.

There is a third scenario: Keep the same lens and sensor size, but increase the pixel density so that there are more pixels in the same sensor area. This will increase resolution of your subject if the resolution limit of the lens had not already been exceeded by the resolution of the original sensor.

Answer 2

As a general rule-of-thumb, the larger the sensor size, the more pixels (picture element) contained, plus larger sensors support larger pixels. Together, this is why larger sensors have the advantage. As to focal length, longer lenses magnify more. Thus your sensor can record more subject detail by simply working in closer or mounting a longer focal length. Will such moves improve subject acuity? It all depends on subject content. If your subject is a human face, taken at a distance, likely with this lash-up, individual hairs will not be resolved. Move in closer or mount a telephoto and likely individual hairs will become discernable. So what’s the advantage of a larger sensor? More pixels coupled with larger pixels noticeably impact image quality.