... why don't we just have big pixels (and thus large sensor surfaces, because we keep the number of pixels fixed)?

There are camera models with lower resolution sensors, but the reason they are made is for increased light sensitivity, not DOF.

• If you want deeper depth of field, consider small sensors, wide-angle lenses, and small apertures. This combination is fairly common in compact cameras and cell phones.

• What people usually seek is increased background blur, not DOF. People often incorrectly state this as shallow DOF (as I have in the past). However, it is possible to have same DOF, but differing amounts of background blur. See Does amount of background blur change with focal length given equal framing?

... the DoF (all other parameters fixed) increases with the pixel surface... What is the drawback ?

The problem is the relationship between DOF and parameters, like pixel or sensor size, is indirect. This is illustrated by contrary opinions. For instance, some claim large sensors produce shallow DOF, while others claim the opposite. Both claims can be correct, depending on the specific scenario and which parameters you adjust to compensate.

Consider a single-pixel sensor of any size. It pretty much does have infinite depth of field (all images are equally sharp or blurry), but it's not possible to have "all other parameters fixed". When they can be kept constant, DOF stays the same. Similarly for sensor size. When parameters are kept constant, DOF is the same.

• The usual formula for Depth of Field (DOF) is:

  DOF = 2 u2 N C / f2

  N = aperture F-number
  C = circle of confusion
  u = distance to subject
  f = focal length

  The size of the Circle of Confusion (CoC) is chosen, arbitrarily, based on perceived sharpness. The Wikipedia CoC page states:

  The common criterion for “acceptable sharpness” in the final image (e.g., print, projection screen, or electronic display) is that the blur spot be indistinguishable from a point.

  The DOF formula comes from the film era. In the digital age, CoC can (but doesn't have to) be substituted with the pixel, which is the "spot" that is "indistinguishable from a point".

• When pixel peeping, pixel size affects DOF by altering the size of the circle of confusion that is being considered. You can achieve the same effect by viewing the image at reduced magnification or downsizing the image, as juhist describes.

  For the pedantic, let:

  CoC = sensor-diagonal / [magnification * (x2 + y2)1/2]

  where (x, y) is the sensor dimension in sensels ("pixels").

  Those who insist that pixel size is unrelated to DOF appear to intentionally ignore the pixel-peeping scenario. If you stick with film or do not pixel peep at all, pixel size is irrelevant to you. Pixels are relevant to those who do pixel peep, even if only occasionally. Nearly all modern lens reviews involve some pixel peeping.

  See Why are my pictures blurry even though a DOF calculator shows everything should be in focus?

• Sensor size affects DOF indirectly by affecting focal length, distance, and circle of confusion. When capturing the same field of view, DOF is usually increased with smaller sensors. However, it is possible to choose parameters where DOF is kept constant. See Would a 50mm lens on a Canon APS-C crop produce the exact same image as an 80mm lens on a full frame camera?

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DOF Calculator for Pixel Peeping

1. Use the Cambridge in Colour: Depth of Field Calculator

2. Click Advanced.

3. Type in a max print dimension = pixel-width/96 inches. For a 24mp camera that produces 6000x4000 images, 6000/96 = 62.5 inches.

4. Leave viewing distance at 25cm, unless you're a super peeper, in which case, change it to 10cm.

5. Select 20/20 vision.

6. Select sensor size and other parameters as desired.

7. Although this calculator does not report the size of the circle of confusion, based on the large viewing size, it should pick something close to that of the pixel size. Note that DOF increases when sensor size (therefore pixel size) is increased.

8. With a 50/4 lens at about 5ft, DOF is usually reported at around 15-20cm, depending on sensor size. However, when pixel peeping, it's only about 1cm.