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I have a Nikon d5000 and just purchased a Tokina 11-16 lens. I was taking picture of a dog 1-2 meters away during winter at mid day today. Using the aperture priority setting, I set the camera to ISO 200, 15mm, f/2.8, 1/4000. Aperture priority photo

The exposure seems to turn out well, but when I zoom in, the dog and the background are both grainy but in focus. I then set the camera to auto; for the same photo it used ISO 200, 16mm, f/10, 1/400, and the exposure was still good, and the photo was much clearer and sharp when zoomed in.

Auto setting photo

Does the wide aperture cause the grainy photo?

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Looking at your samples, the answer seems clear to me: that's not grainy, that is, actually, out of focus.

Here's a 1:1 crop of your wide-open image:

blurred dog

It seems pretty apparent that the wooden sign is sharp but the dog isn't, and the appearance of the blur looks completely in line with what one would expect from out-of-focus blur, not noise or grain.

Outside of this crop, in the wide-open version, the trees are blurrier as well. I think that's a combination of decreased depth of field (as expected), and also increased chromatic aberration — an undesirable effect which is often strongest wide open. This is not particularly nice-looking blur, and might be what you are perceiving as grain.

Overall, in very small thumbnail size, neither defect is particularly apparent, but if you view or print larger.. not so nice. Since there is plenty of light, stopping down for more depth of field seems like a fine approach. Even the f/10 exposure gives you a plenty-fast shutter speed of ¹⁄₄₀₀th; there's nothing in the scene that benefits from 10× shorter. And, since the apparent depth of field is relatively large at such wide angle, with your subject in midfield,and when viewed at small sizes, wouldn't get strong subject isolation from background blur even if the focus were correct, so it's really not giving you much.

Also (and especially if you do keep the aperture wide, to see what it would be like with the blur more in the background), be more careful that the autofocus grabs the subject you are really interested in. (Note that AF areas are often actually much larger than the indicator dots in the viewfinder, so it's easy for AF to do something other than you expect.)

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    autofocus is not magic, and most cameras are going to do a priority on getting the center part of the image in focus if you use the default settings. The dog is a fuzzy subject and the edge of the sign is a hard line, and so the AF system found using that hard line easier to focus on... – chuqui Feb 23 '15 at 16:08
  • On a related note, when viewing an in-focus subject with a lot of detail, the viewer's eye/brain will focus on the subject; if the subject is out of focus but there is no graininess, the eye/brain may conclude that the eye is looking at the subject but having trouble focusing, and thus not be well focused on anything. If the subject is out of focus but the picture is grainy, however, the viewer's eye/brain will focus on the graininess. – supercat Feb 23 '15 at 20:50
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    The camera's AF will focus on the highest amount of contrast it can find within the active focus area. As @mattdm mentioned at the end of his answer, the active focus area is usually much larger than the little squares or dots in your viewfinder. Learning your camera's focus map will help you to insure the camera focuses on what you want it to. Although the camera is not a D5000 (not even a Nikon), the concept is the same as discussed in this answer which you should find helpful : photo.stackexchange.com/a/41179/15871 – Michael C Feb 23 '15 at 23:30

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