DoF and Subject Magnification

The magnification of the subject is the parameter that influences the most the Depth of Field, much more than the aperture. This articles explains what is the magnification of the subject  and in which way it impacts the DoF.

Definition of the Subject Magnification

The magnification of the subject is the ratio between the size of its image on the sensor and its real size. It depends on the focal length and the subject distance. In the picture below the magnification correspond to the ratio Hi/Hs.

lens_magnification_drawing_compression0

The magnification of the subject can be simply expressed as a function of the focal length and distance do subject, assuming that the focal length is much smaller than the distance to the subject.

dof_magnification_formulaWhere :
 - Hs is the size of the subject in the focus plane
 - Hi is the size of the image in the sensor plane
 - M is the subject magnification
 - f is the focal length
 - s is the subject distance

To keep the focal lens and the subject distance in the same ratio maintains the same magnification. The series below shows this principle, the 3 pictures are taken at a different focal length and distance, but the magnification of the subject remains the same. For example a focal lens of 10mm at a distance of 0.25m provides the same magnification of the subject than a focal lens of 100mm at a distance of 2.5m. In the example below the magnification of the subject is 0.04 or 1/25, meaning that 25cm of the subject is projected as 1cm on the sensor. It is also interesting to observe that contrary to the subject, the background does not keep the same magnification in the series of pictures.

dof_magnification_serie1

Example of pictures with the same magnification

Influence of lens magnification on the DoF

When the distance to the subject is much greater that the focal length and much smaller that the hyperfocal distance, to keep the same magnification and aperture provides the same DoF. So when you get 2 times closer and zoom out 2 times, the magnification remains the same, and the DoF as well. The following pictures have all the same magnification and DoF.

dof_magnification_serie2

To maintain the magnification maintains the DoF

You may observe that those pictures do not have the same blur in the background, yet they have the same DoF. The blur in the background or foreground does not say anything about the DoF which is the sharpness around the plane of focus. This is a common misconception, many people say that they want a short DoF when what they really want is to blur the background. “How to blur the background” is a different topic than “how to achieve a short DoF”, it will be discussed in a separate article.

When the distance to the subject is much greater that the focal length and much smaller that the hyperfocal distance, the DoF varies with the square of the magnification. In other words, increasing by x2 the magnification decreases by x4 the DoF, this can be done by either getting x2 closer to the subject, or zooming x2 the focal length. It is crucial to understand this effect since it is a powerful way to change the DoF by orders of magnitude. In the same situation the DoF varies only proportionally to the aperture.

dof_magnification_serie3

Here is another way to look at it, the graph below plots the DoF corresponding to the picture above. Since the focal length is fixed at 200mm,  to change the distance to the subject changes the magnification.

dof_magnification_graph1

Conclusion

  • The subject magnification is a function of the focal length and the distance to subject
  • The subject magnification has more impact on the DoF than the aperture. The DoF varies with the square of the magnification, and proportionally with the aperture.
  • To keep the same aperture and the same subject magnification keeps the same DoF. There is no need to know the focal length and the distance to subject to know the DoF, it is enough to look at the magnification while composing the photograph. I will explain in another article how to use this principle to quickly estimate the DoF while composing the photograph.
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