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When shooting in Shutter and Aperture priority, the camera just needs to meter the scene and come up with the corresponding f-stop or shutter speed, a very algothrimitic and simple process. However, what if you shoot in full auto? The camera does not know how much depth of field you want — you may want to show the background or leave it blurred.

Shooting in automatic has two variables — shutter and aperture. How does the camera find out the best combination?

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possible duplicate of How do DSLRs figure out what aperture to select in P mode? –  dpollitt Nov 18 '13 at 1:12
    
While the concept is the same, what the camera decides and what it allows the user to decide are significantly different between Auto and P modes. –  Michael Clark Nov 18 '13 at 1:16
    
@MichaelClark I was speaking about those cheap point-and-shoot cameras who don't let the user set anything, not the semi-auto P mode. –  d.free Nov 18 '13 at 1:30
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Both shutter and aperture priority are significantly more complicated than you're making out - it's not just a matter of picking an aperture or shutter speed, it's a matter of picking an (aperture, ISO) or (shutter speed, ISO) pair, assuming you're shooting with auto ISO. Similarly, full auto / P is a matter of picking the (shutter speed, aperture, ISO) triple. None of this fundamentally varies between "cheap P&S" and "pro DSLR", although the pro DSLR may be better at it. –  Philip Kendall Nov 18 '13 at 8:37
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How do automatic cameras know the right depth of field?

The short answer is, "They don't." They, or more specifically the designers who wrote the camera's firmware, guessed at it.

Different cameras use different solutions to arrive at the shutter speed and aperture when shooting in full auto, along with deciding other variables such as white balance, contrast, color saturation, sharpening, etc. Ultimately it is determined by the writers or the camera's firmware. Some systems are more sophisticated than others and may use context awareness to compare the scene with a database stored in the camera's memory. A predetermined list of settings attached to a profile in the database are then selected when the current conditions match one of those stored profiles.

Having said that, there are some common traits you see shared by many cameras. Most automatic profiles will try to avoid shutter speeds slower than one of several variations of the 1/focal length rule. They typically try to stay in the middle of the road in terms of aperture unless the target shutter speed pushes it further open. They generally try to use the lowest ISO possible and still meet the target shutter speed.

Auto Mode is usually written to cover as wide a set of possible scenarios and conditions as is possible. Cameras with several specialized auto profiles known as Scene Modes will use different priorities and goals for shutter speed, aperture, contrast, etc. depending on which scenario the user has selected. Again, different camera models have various different Scene Modes. For example, Sports Mode will place the emphasis on a fast shutter speed. Portrait Mode, on the other hand, will place the emphasis on a wide aperture and color balance that makes skin tones look their best. Each Scene Mode will apply a set of rules written by the camera's designers based on best practices for that particular type of scene.

Most inexpensive compact cameras that are often referred to as point-and-shoot cameras have such small sensor chips that the focal lengths used to get angles of view in the wide angle to normal to short telephoto range are so short that the depth of field is rather wide at almost any aperture the camera is capable of using, and the selection of aperture is based on what works with the target shutter speed and ISO values.

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