Tag Archives: spatial domain

A Simple Model for Sharpness in Digital Cameras – Aliasing

Having shown that our simple two dimensional MTF model is able to predict the performance of the combination of a perfect lens and square monochrome pixel we now turn to the effect of the sampling interval on spatial resolution according to the guiding formula:

(1)   \begin{equation*} MTF_{Sys2D} = \left|(\widehat{ PSF_{lens} }\cdot \widehat{PIX_{ap} })\ast\ast\: \delta\widehat{\delta_{pitch}}\right|_{pu} \end{equation*}

The hats in this case mean the Fourier Transform of the relative component normalized to 1 at the origin (_{pu}), that is the individual MTFs of the perfect lens PSF, the perfect square pixel and the delta grid.

Sampling in the Spatial and Frequency Domains

Sampling is expressed mathematically as a Dirac delta function at the center of each pixel (the red dots below).

Footprint-PSF3
Figure 1. Left, 1a: A highly zoomed (3200%) image of the lens PSF, an Airy pattern, projected onto the imaging plane where the sensor sits. Pixels shown outlined in yellow. A red dot marks the sampling coordinates. Right, 1b: The sampled image zoomed at 16000%, 5x as much, because each pixel’s width is 5 linear units on the side.

Continue reading A Simple Model for Sharpness in Digital Cameras – Aliasing

The Slanted Edge Method

My preferred method for measuring the spatial resolution performance of photographic equipment these days is the slanted edge method.  It requires a minimum amount of additional effort compared to capturing and simply eye-balling a pinch, Siemens or other chart but it gives immensely more, useful, accurate, quantitative information in the language and units that have been used to characterize optical systems for over a century: it produces a good approximation to  the Modulation Transfer Function of the two dimensional Point Spread Function of the camera/lens system in the direction perpendicular to the edge.

Much of what there is to know about a system’s spatial resolution performance can be deduced by analyzing such a curve, starting from the perceptually relevant MTF50 metric, discussed a while back.  And all of this simply from capturing the image of a black and white slanted edge, which one can easily produce and print at home.

Continue reading The Slanted Edge Method