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:
This article 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. The filter typically sits right on top of the sensing plane and its objective is to block as much of the aliasing and moiré creating energy above the Nyquist spatial frequency while letting through as much as possible of the real image forming energy below that, hence the low-pass designation.
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:
The next few posts will describe a linear spatial resolution model that can help a photographer better understand the main variables involved in evaluating the ‘sharpness’ of photographic equipment and related captures. I will show numerically that the combined spectral frequency response (MTF) of a perfect AAless monochrome digital camera and lens in two dimensions can be described as the normalized multiplication of the Fourier Transform (FT) of the lens Point Spread Function by the FT of the (square) pixel footprint, convolved with the FT of a rectangular grid of Dirac delta functions centered at each pixel, as better described in the article
With a few simplifying assumptions we will see that the effect of the lens and sensor on the spatial resolution of the continuous image on the sensing plane can be broken down into these simple components. The overall ‘sharpness’ of the captured digital image can then be estimated by combining the ‘sharpness’ of each of them. Continue reading A Simple Model for Sharpness in Digital Cameras – I→