This article and the following one will discuss the effect on resolution of digitizing a continuous optical image.
The sampling process carried out by the sensor results in digital values corresponding to an intensity at each pixel’s location. These so-called Data Numbers are stored ideally as-is in the raw file and are proportional to infinitesimal point samples of a new continuous image: the optical image smoothed by the characteristics of the pixels’ effective active area, known as the pixel aperture function.
Figure 1. Simulated Pixel Aperture Function of a 4um pitch Back Side Illuminated pixel in isolation. Note diffusion beyond the -2/+2um theoretical pixel boundaries suggested by pitch.
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 it all detail is lost and no additional spatial information can be captured from the scene.
Increasingly small detail smeared by the imaging process, highly magnified.
The units of resolution are spatial frequency, 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.
The key variable as far as the tolerances required to position the lens for accurate focus are concerned (at least in a simplified ideal situation) is an appropriate approximate distance between the desired in-focus plane and the actual in-focus plane (which we are assuming is slightly out of focus). It is a distance in the direction perpendicular to the x-y plane normally used to describe position of the image on it, hence the designation delta z, or dz in this post. The lens’ allowable focus tolerance is therefore +/- dz, which we will show in this post to vary as the square of the format’s diagonal. Continue reading Focus Tolerance and Format Size→
