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 magnitude of the normalized product of the Fourier Transform (FT) of the lens Point Spread Function (PSF) by the FT of the pixel footprint (aperture), convolved with the FT of a square grid of Dirac delta functions centered at each pixel:
![\[ MTF_{2D} = \left|\widehat{ PSF_{lens} }\cdot \widehat{PIX_{ap} }\right|_{pu}\ast\ast\: \delta\widehat{\delta_{pitch}} \]](https://i0.wp.com/www.strollswithmydog.com/wordpress/wp-content/ql-cache/quicklatex.com-3409f065a49bb47fd4618ed595be72fc_l3.png?resize=320%2C37&ssl=1 "Rendered by QuickLaTeX.com")
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.
The stage will be set in this first installment with a little background and perfect components. Following articles will deal with the effect on captured sharpness of
We will learn how to measure MTF curves for our equipment, look at numerical methods to model PSFs and MTFs from the wavefront at the pupil of the lens and the theory behind them. Continue reading A Simple Model for Sharpness in Digital Cameras – I →
here indicating normalization to one at the origin). I used Matlab to generate the examples below but you can easily do the same with a spreadsheet. Continue reading A Simple Model for Sharpness in Digital Cameras – Diffraction and Pixel Aperture