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Generally, the technical image quality of a digital image (before we get to the post-processing stage) is the product of the characteristics of the lens and the recording medium, with an important dash of good technique from the photographer.

Lenses are covered under What image-quality characteristics make a lens good or bad?, but what about the other important component, the sensor? DxOMark famously publishes some measurements, but what's really important? Obviously megapixels are part of it, but what else matters? Are there non-lens camera features other than the sensor which can have a positive or negative effect on image quality?

Most importantly, what do these things look like in actual real-world images, and how can I recognize them by looking it photographs rather than just review charts and graphs?

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    \$\begingroup\$ +1 great question! Amazing that it was not asked until now. \$\endgroup\$
    – Regmi
    Commented Apr 7, 2013 at 16:46
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    \$\begingroup\$ MOAR MEGAPIXELS! ;) \$\endgroup\$ Commented Apr 11, 2013 at 22:49
  • \$\begingroup\$ Good question! I cannot help thinking that the D800, for example, could offer much better dynamic range and ISO performance if Nikon would pack in less pixels. Say, 24M instead of 35M. Am I thinking wrong here? \$\endgroup\$ Commented Jul 2, 2013 at 10:01

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I'll try to avoid getting too technical - there are others that can fill in more detail. I think, apart from resolution, the most important aspects to me would be dynamic range and low light performance. DxO rates sensors on the following:

Resolution

With sharp lenses and good technique, more pixels can never hurt, especially if you are printing large or cropping wildlife images for example. Apart from those two scenarios, higher resolution is something you usually don't see unless you are pixel peeping, and comparing two similar spec cameras may be hard to distinguish the difference.

Colour Depth

Sensors with more colour depth can resolve more tonal values. I would think that the colour spaces most people use would limit the ability to see real life differences. DxO rates colour depth under the "Portrait" score.

Dynamic Range

I have shot a few frames with a D800, and it's incredible what detail you can pull from both the shadows and highlights compared to older cameras. This is easily seen in real life high-contrast images such as landscapes. In a few years we can ditch HDR, bracketing and throw out our grad ND filters :) DxO rates dynamic range under their "Landscape" score, as extended range is useful to avoid blown out skies.

Low Light (High ISO) performance

This is another measurement that's easy to see in real life examples, as some sensors are certainly better at limiting noise in low light. DxO rates low light performance under their "Sports" score, given its usefulness in poorly lit gyms, stadiums and hocky rinks.

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    \$\begingroup\$ You left out a critical metric: cost. Except for the D4 and 1Dx, every other camera cares about the cost of the sensor. No matter if it can out-resolve the Hubble, you have to be able to afford it. \$\endgroup\$ Commented Mar 17, 2013 at 3:01
  • \$\begingroup\$ For the purposes of this question, I think it's most appropriate to consider cost as an inherent factor in making any real-world device rather than a "metric". Like power consumption or size, it's something that real designs inevitably balance against rather than an aspect of quality in itself. \$\endgroup\$
    – mattdm
    Commented Apr 1, 2013 at 17:58
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The existing answer has most of the properties that make a sensor good, but I would add one more property:

Autofocus

Today, with mirrorless cameras, the camera may require autofocus features from the imaging sensor. Without special autofocus support, only slow contrast detect autofocus (CDAF) is possible. With special autofocus support, one can use phase detect autofocus (PDAF). For example, the autofocus support could be Canon's dual pixel autofocus which is a form of PDAF.

The autofocus features may be important too with DSLRs when shooting using the live view mode. Then, the only autofocus features available are CDAF, flip mirror + do PDAF (sometimes said to be quick mode as it's quicker to flip the mirror than to do CDAF), and only if the imaging sensor has it, on-sensor PDAF. Generally, on-sensor PDAF is so much better than CDAF that it may not be possible to even select CDAF if on-sensor PDAF is supported. Furthermore, when shooting video (out of the scope of this site but necessary to mention), the autofocus features are needed.

You really don't want to use CDAF due to its slow speed.

On-imaging-sensor autofocus is today better than using a dedicated focus sensor. For example, you get more autofocus points with the on-imaging-sensor autofocus than you do with a dedicated focus sensor. Furthermore, you get autofocus even using f/11 lenses (dedicated sensors do only f/5.6 or f/8), and you also get autofocus down to -5 or -6 EV if using f/1.2 lens (for example, 5D Mark IV does autofocus only down to -3 EV).

Most importantly, what do these things look like in actual real-world images, and how can I recognize them by looking it photographs rather than just review charts and graphs?

If you have a photograph that is out of focus, you will immediately recognize it. Nothing is sharp on the subject. Actually, focus problems are something you won't see in review charts and graphs. Only using the equipment in real-life conditions will tell you how well autofocusing works. With on-imaging-sensor AF, it works just fine.

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