Start with what the Engines Reference says, because it is short. Sharp filter sits in the Basic Operations Module under FiltersLoading.... It enhances image details by generating a better contrast, it can improve slightly out-of-focus images, and its one setting is Kernel radius (px), default 7. In the reference example an 8-bit, 3-channel brightfield image of colon goes in and a color image of the same type comes out, with the details enhanced and a better contrast.
The reference prints no formula. So what follows is the textbook register: how sharpening is usually built, offered so you can picture what a window-based sharpener does, not as a description of the engine's code.
The usual construction splits an image into a smooth part and a detail part. Blur the image with something like the Gauss filterLoading... or the Average filterLoading..., and call the blur B(I). The detail is what the blur removed, H = I − B(I). A sharpened image adds some of that detail back, O = I + α·H, which is the classic unsharp mask, with α setting the strength.
Another common form subtracts a scaled LaplacianLoading..., O = I − k·∇²I, which adds back curvature directly. In both forms the size of the blur, or of the kernel, determines which scale counts as detail. That is the role a Kernel radius setting would naturally play, though the reference doesn't confirm it for this filter.
Sharpeners of this kind overshoot at a step edge. Near the step the blur straddles both sides, so on the bright side it sits below the image and the output brightens, and on the dark side it sits above and the output darkens. The result is a bright ridge beside a dark moat. A little reads as crispness; a lot shifts the intensities you might later measure.
The names are easy to confuse. StrataQuest's Unsharp filterLoading... computes only the detail part, I − B(I), and doesn't add the image back: it subtracts a blurred background model to remove high background. So within StrataQuest, Sharp is the filter for detail and contrast, and Unsharp is a background tool, alongside Background RemovalLoading....
Source: StrataQuest 8.1 Engines Reference, ch. 6.3 (Sharp filter pp. 141–143; Unsharp filter pp. 152–154; Average filter p. 117 and Gauss filter p. 130 for kernel sizes) and ch. 5 (p. 15).