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I want to be able to see a frame and 'calculate' (either mathematically or intuitively) the DoF of the picture to be taken.

The most basic variable would be the aperture; my question is do other variables also have effect on DoF? Especially the distance from sensor to object.

Suppose I want to photograph an object with dimensions X and my camera with aperture set on f/1.4 only focuses on half of the object. Can I change something other than the aperture to ensure the whole object is in focus?

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There are three main factor that determine the DOF:

  • Distance to the subject
  • Focal length
  • Aperture

There are useful online calculators to calculate the required distance to have the subject(s) within the DoF.

Regarding equations to calculate the Hyperfocal distance, near distance of acceptable sharpness, you can use the following formulas:

Hyperfocal

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Near distance of acceptable sharpness

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Far distance of acceptable sharpness

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where:

  • H is the hyperfocal distance, mm

  • f is the lens focal length, mm

  • s is the focus distance
  • Dn is the near distance for acceptable sharpness
  • Df is the far distance for acceptable sharpness
  • N is the f-number
  • c is the circle of confusion, mm

Source

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Mathematically i don't know these equations but the other way you can change you DoF is by changing your focal Length, using a prime lens and increasing and decreasing of the subject from the film plane.

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