Monthly Archives: September 2016

Optics, Sharpness, Spatial Resolution

A Simple Model for Sharpness in Digital Cameras – Polychromatic Light

Leave a comment

We now know how to calculate the two dimensional Modulation Transfer Function of a perfect lens affected by diffraction, defocus and third order Spherical Aberration  – under monochromatic light at the given wavelength and f-number.  In digital photography however we almost never deal with light of a single wavelength.  So what effect does an illuminant with a wide spectral power distribution, going through the color filter of a typical digital camera CFA  before the sensor have on the spatial frequency responses discussed thus far?

Monochrome vs Polychromatic Light

Not much, it turns out. Continue reading A Simple Model for Sharpness in Digital Cameras – Polychromatic Light →

Optics, Sharpness, Spatial Resolution

A Simple Model for Sharpness in Digital Cameras – Spherical Aberrations

6 Comments

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 →

Optics, Sharpness, Spatial Resolution

A Simple Model for Sharpness in Digital Cameras – Defocus

10 Comments

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 →

Sharpness, Spatial Resolution

A Simple Model for Sharpness in Digital Cameras – AA

2 Comments

This article is part of a continuing series on the determinants of sharpness in an imaging system and will discuss a simple frequency domain model for an AntiAliasing (or Optical Low Pass) Filter, a hardware component sometimes found in a digital imaging system[1].  The filter typically sits just above the sensor and its objective is to block as much of the aliasing and moiré creating energy above the monochrome Nyquist spatial frequency while letting through as much as possible of the real image forming energy below that, hence the low-pass designation.

Downsizing Box 4X
Figure 1. The blue line indicates the pass through performance of an ideal anti-aliasing filter presented with an Airy PSF (Original): pass all spatial frequencies below Nyquist (0.5 c/p) and none above that. No filter has such ideal characteristics and if it did its hard edges would result in undesirable ringing in the image.

In consumer digital cameras it is often implemented  by introducing one or two birefringent plates in the sensor’s filter stack.  This is how Nikon shows it for one of its DSLRs:

d800-aa1
Figure 2. Typical Optical Low Pass Filter implementation  in a current Digital Camera, courtesy of Nikon USA (yellow displacement ‘d’ added).

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