Perspective Distortion (photography) - Optics

Optics

Consider an idealised Gaussian optical system. For most purposes, we can assume the image space and the object space are in the same medium. Thus, for an object in focus, the distance between the lens and image plane, the distance between lens and the object, and the focal length are related by:

The transverse magnification is related by

The axial magnification of an object at is the rate of change of the lens-image distance as the lens-object distance changes. For an object of finite depth, one can conceive of the average axial magnification as the ratio of the depth of the image and the depth of the object:

One can see that if magnification remains constant, a longer focal length results in a smaller axial magnification, and a smaller focal length a larger axial magnification. That is, when using a longer focal length while moving the camera/lens away from the object to maintain the same magnification M, objects seem shallower, and the axial distances between objects seem shorter. The opposite-- increased axial magnification -- happens with shorter focal lengths while moving the camera/lens towards the object.