What are 'mist filters' and what do they do to your photographs?

Mist filters come in all shapes and sizes. Kolari Vision’s clip-in filters sit between your lens and sensor in compatible mirrorless camera systems. Pro Mist filters. Black Mist filters. Cinebloom filters. While the name varies from one company to the next, all of these filters are more or less the same thing: diffusion filters designed to soften an image by a pre-defined strength, usually defined by a fraction (1/8, 1/4) or a percentage (20%, 40%). But how do these filters diffuse...