Slightly Technical Discussion of Focus and Depth of Field

This page summarizes some technical details about camera focus.

A key idea is depth of field (DOF).

Depth of Field is defined as the distance between the nearest and farthest objects that are in acceptably sharp focus in an image captured by a camera.

Increasing DOF means more of the subject can be in focus.
Decreasing DOF means that less of the subject can be in focus.

Summary

Before you wade through the math, the key takeaways are

• Only objects at one distance from the lens can be in focus at the same time.


• Increasing the distance from the lens increases DOF.
  • But this makes the object look smaller (fewer pixels are on the subject).
  • To get more pixels on the subject, we can increase the zoom.
    This ends up shrinking the DOF.


• Reducing the aperture increases DOF.
  • But apertures smaller than around F9 or F11 introduce diffraction which degrades the image.
  • Changing aperture can help, but is limited.


• Flat objects (like tsuba) facing the camera can be in focus.
  • This is the standard approach.
  • But not all features can be seen from this perspective.


• To get good focus in photos of thicker objects or from additional perspectives, another approach is needed.

Technical Discussion

Definition:
Depth of field (DOF) is defined as the distance between the nearest and farthest objects that are in acceptably sharp focus in an image captured by a camera.

Approximate Depth of Field Formula

depth_of_field ≈ 2 * F_number * c * (distance_to_subject / focal_length_of_lens)²

• The F_number (also known as f-ratio, f-stop and f-ratio) describes the aperture of the camera.
  For a fixed lens focal length, a larger F number corresponds to a smaller aperture (less light entering the camera).
  
  Definition: F_number = lens_focal_length / effective_aperture_diameter.



• The parameter "c" is the acceptable circle of confusion which describes acceptably sharp focus.
  It is the diameter of the circle of light resulting from a defocused point.
  For context, I have seen recommendations of 0.03-0.05 mm to produce a good 8x12 inch print from a full frame camera sensor.



• Example:
  c = 0.05 mm
  F_number = 9
  focal_length_of_lens = 100 mm
  distance_to_subject = 200mm
  depth_of_field = 2 * 9 * 0.05mm * (200 mm/100 mm)^2 = 3.6 mm

Implications of the Formula

If I assume c is fixed (based on the desired image quality), then to increase the amount of an object that is in focus, I can either

• increase the F_number
• increase the distance_to_subject
• decrease the focal_length_of_lens.

Increasing the F_number works up to about F8 or F11.
At higher F_numbers, the images are softened by diffraction
So this works, but is limited.

If I increase the distance to the subject, then more of the subject is in focus.
But the object appears smaller in the image.
Since fewer pixels are on the object, I would lose resolution.

Can I use a zoom lens to make the subject look larger?
Unfortunately, optical zoom increases the lens focal length, which reduces the depth of field.

Implication:
No matter what lens and camera I use, there will be a limited range that will be in focus.