In photography Resolution refers to the ability of an imaging system to capture fine detail from the scene, making it a key determinant of Image Quality. For instance, with high resolution equipment we might be able to count the number of tiny leaves on a distant tree, while we might not with a lower-res one. Or the leaves might look sharp with the former and unacceptably mushy with the latter.
We quantify resolution by measuring detail contrast after it has been inevitably smeared by the imaging process. As detail becomes smaller and closer together in the image, the blurred darker and lighter parts start mixing together until the relative contrast decreases to the point that it disappears, a limit referred to as diffraction extinction, beyond which all detail is lost and no additional spatial information can be captured from the scene.
The units of resolution are spatial frequencies, the inverse of the size and distance of the detail in question. Of course at diffraction extinction no visual information is captured, therefore in most cases the criteria for usability are set by larger detail than that – or equivalently at lower frequencies. Thresholds tend to be application specific and arbitrary.
The type of resolution being measured must also be specified since the term can be applied to different physical quantities: sensor, spatial, temporal, spectral, type of light, medium etc. In photography we are normally interested in Spatial Resolution from incoherent light traveling in air so that will be the focus here.
= 3.65 microns. That’s about the size of the estimated effective square pixel aperture of the Nikon Z7 camera that we are using in these tests.
twice in sequence.
space to a Fast Fourier Transform routine and, presto, it produces MxN numbers representing the amplitude of the PSF on the 
sensing plane. Figure 1a shows a simple case where pupil function 
arrives at the front of the lens. It goes through the lens being partly blocked and distorted by it as it arrives at its virtual back end, the Exit Pupil, we’ll call this blocking/distorting function 
. Other than in very simple cases, the Exit Pupil does not necessarily coincide with a specific physical element or Principal surface.
as shown below (not to scale, the product of the two arrays is element-by-element):
), that is the individual MTFs of the perfect lens PSF, the perfect square pixel and the delta grid; 
represents two dimensional convolution.
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. ![\[ MTF_{2D} = \left|\widehat{ PSF_{lens} }\cdot \widehat{PIX_{ap} }\right|_{pu}\ast\ast\: \delta\widehat{\delta_{pitch}} \]](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")
) that reflects the performance of the hardware only; and an output-referred one (
) that also takes into consideration how the image will be displayed. Both are valid and differences are typically minor, though the weights of the latter are scene, camera/lens, illuminant dependent – while the former are not. Therefore my recommendation in this context is to stick with input-referred weights when comparing cameras and lenses.