The series of articles starting here outlines a model of how the various physical components of a digital camera and lens can affect the ‘sharpness’ – that is the spatial resolution – of the images captured in the raw data. In this one we will pit the model against MTF curves obtained through the slanted edge method^{[1] }from real world raw captures both with and without an anti-aliasing filter.

With a few simplifying assumptions, which include ignoring aliasing and phase, the spatial frequency response (SFR or MTF) of a photographic digital imaging system near the center can be expressed as the product of the Modulation Transfer Function of each component in it. For a current digital camera these would typically be the main ones:

This series of articles has dealt with modeling an ideal imaging system’s ‘sharpness’ in the frequency domain. We looked at the effects of the hardware on spatial resolution: diffraction, sampling interval, sampling aperture (e.g. a squarish pixel), anti-aliasing OLPAF filters. The next two posts will deal with modeling typical simple imperfections in the system: defocus and spherical aberrations.

Defocus = OOF

Defocus means that the sensing plane is not exactly where it needs to be for image formation in our ideal imaging system: the image is therefore out of focus (OOF). Said another way, light from a distant star would go through the lens but converge either behind or in front of the sensing plane, as shown in the following diagram, for a lens with a circular aperture:

The key variable as far as the tolerances required to position the lens for accurate focus are concerned (at least in a simplified ideal situation) is an appropriate approximate distance between the desired in-focus plane and the actual in-focus plane (which we are assuming is slightly out of focus). It is a distance in the direction perpendicular to the x-y plane normally used to describe position of the image on it, hence the designation delta z, or dz in this post. The lens’ allowable focus tolerance is therefore +/- dz, which we will show in this post to vary as the square of the format’s diagonal. Continue reading Focus Tolerance and Format Size→