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Zoom vs sensor size -- break even point?

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Perry L

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I think I understand the physics of cameras well enough to say that putting a large sensor in a small camera effectively limits the optical zoom that can effectively use the area on the sensor. At least this is practically true with the cameras on the market: the compact cameras with larger sensors have smaller optical zooms.

I also think I understand that digitally zooming is not really different than cropping an image. The subject in the frame appears larger, but only because less of the sensor is being used to create the image.

My question is about the break even point between an optical zoom with a small sensor and a digital zoom with a large one. As a math question, at what digital zoom is the effective area of a large sensor equal in size to a small sensor? Or as a practical question, at what point does an optical zoom on say a Panasonic Lumix DMC-ZS40 or a Canon PowerShot SX700 HS produce a better image than a digital zoom on a Canon PowerShot S120 or a Sony Cyber-shot DSC-RX100 III?
 
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The difference is minimal between the 1/2.3" and 1/1.7" sensor cameras in the best of circumstances, given a similar feature set, like having RAW available. Performance is so close that I don't think you can really say what the break even point is.

For the RX100, given the high resolution and quality of the pixels, I'd say that the break even point is about 1.5 to 2x zoom. A crop equivalent to a 2x zoom from the RX100 is only 5 MP. Another 2x and you're down to 1.25 MP, which is getting pretty light for anything but some web use.

This is about the breakeven point for APS-C sensors as well. At some point, you start running out of pixels.
First of all, there is very little difference in the sensor size for these cameras - only about 50% which is nothing compared with the difference between these sensor and a DSLR which is 1000%+.

With the cameras that you are comparing and other things being equal, e.g. pixel density, you can crop the larger sensor by about 25% before the resolution drops below that of the smaller sensor. In terms of zoom that is nothing, the difference between 100mm focal length and 125mm focal length.

Looking at it another way, if the smaller sensor camera has a maximum equivalent focal length of 200mm and the larger sensor camera has a maximum equivalent focal length of 100mm, you have to crop the image from the larger sensor by 50% in each direction to get the same angle of view. That would reduce the resolution by 75%, e.g. a 16MP image would become 4MP.

So optical zoom is always better than digital zoom unless you don't mind reducing the resolution of the image drastically.

Your question on image quality is difficult to answer because the primary reasons why larger sensor cameras have better image quality than smaller sensor cameras are less noise and better dynamic range rather than higher resolution.

So, if you need a high zoom, i.e. a larger maximum focal length, and you don't want a huge camera, go for the smaller sensor camera or buy an interchangeable lens camera.

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Chris R
 
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The difference is minimal between the 1/2.3" and 1/1.7" sensor cameras in the best of circumstances, given a similar feature set, like having RAW available. Performance is so close that I don't think you can really say what the break even point is.

For the RX100, given the high resolution and quality of the pixels, I'd say that the break even point is about 1.5 to 2x zoom. A crop equivalent to a 2x zoom from the RX100 is only 5 MP. Another 2x and you're down to 1.25 MP, which is getting pretty light for anything but some web use.

This is about the breakeven point for APS-C sensors as well. At some point, you start running out of pixels.
 
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