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Spherical Aberration (SA) is one key component missing from our MTF toolkit for modeling an ideal imaging system’s ‘sharpness’ in the center of the field of view in the frequency domain. In this article formulas will be presented to compute the two dimensional Point Spread and Modulation Transfer Functions of the combination of diffraction, defocus and third order Spherical Aberration for an otherwise perfect lens with a circular aperture.

Spherical Aberrations result because most photographic lenses are designed with quasi spherical surfaces that do not necessarily behave ideally in all situations. For instance, they may focus light on systematically different planes depending on whether the respective ray goes through the exit pupil closer or farther from the optical axis, as shown below:

371px-spherical_aberration_2 — Figure 1. Top: an ideal spherical lens focuses all rays on the same focal point. Bottom: a practical lens with Spherical Aberration focuses rays that go through the exit pupil based on their radial distance from the optical axis. Image courtesy Andrei Stroe.

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

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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