# Understanding image depth of field

Depth of field is a distance range at which the optical resolution of an image is as high as possible for that lens. (ie an image appears to be in focus) When starting an lens design program, having a good understanding of the physics of this parameter will help you and your consultant achieve the best possible design.

In the video and test below we explain depth of field in more detail.

## ‘Circle of confusion’ and depth of field

•Real system can’t form ideal image of Object Point. Because of physical and manufacturing limitations Object point images into spot with diameter named as “Circle of confusion”.

•Larger the circle of confusion means larger depth of field

## Key formula

Depth of Field: DF=(2f^2 S^2 Nd_c)/(f^4-N^2 (d_c )^2 S^2 )

Where dc – diameter of circle of confusion

f-focal length

N=D/s – effective aperture

S= Object distance

## Simplified formula

For distant object where S is much larger than f then S’=f and formula of Depth of Field :

DF=(2S^2 Fd_c)/f^2

## Alternative formula

F=D/f – relative aperture

The distances to near and far zone of DF

S1=(Sf^2)/(f^′2+Fd_c S)

S2=(Sf^2)/(f^′2-Fd_c S)

## Sources of ‘Circle of confusion’

## 1.) Diffraction

•Because of finite aperture of optical system optical systems have a limit of Airy diffraction pattern.

•Diameter of circle of confusion correspond to width of central maximum of Airy diffraction pattern.

•Therefore d_c=d_Airy

## 2.) Aberrations

•Residual aberrations result in blurring of image of point.

•Residual spherical aberrations result in different point of intersection of rays going through different aperture height. Intersection rays which each other forms Caustic surface that has waist. Diameter of waist corresponds to Circle of confusion

d_c=d_Waist

## 3.) Pixel size

•All image detectors have particular Pixel size.

•Diameter of Circle of confusion corresponds to pixel size Pixel size.

d_c=d_Pix

Finite size of pixel results in Depth of focus (Df) in image space.

## Summary

•Depth of Field is inherent property of real optical system because of physical and technological limitations.

- DF depends on 1st with F-number

- DF depends on 2nd order of object distance S

•But real systems have different correction of residual aberrations and aperture value. herefore circle of confusion depends on most influence factor either diffraction , residual aberrations or pixel size. For example microscope lens has very small residual aberrations and DF depends on mostly of diffraction.