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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:

(1) $\begin{equation*} MTF_{sys} = MTF_{lens} (\cdot MTF_{AA}) \cdot MTF_{pixel} \end{equation*}$

all in two dimensions Continue reading Taking the Sharpness Model for a Spin →

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 related to the lens: 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 point source 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:

Figure 1. Back Focus, In Focus, Front Focus. — Figure 1. Top to bottom: Back Focus, In Focus, Front Focus. To the right is how the relative PSF would look like on the sensing plane. Image under license courtesy of Brion.

Continue reading A Simple Model for Sharpness in Digital Cameras – Defocus →

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