How does the full setup of a Lieberkühn reflector differ from a darkfield setup?
Short answer, you can think of a Lieberkühn reflector as being "a ringlight before they had ringlights".
The long answer depends on exactly what you mean by "darkfield setup".
"Darkfield" often refers to a setup where light striking the subject comes primarily from below/behind but to the side, angled such that undeflected light does not reach the sensor. In this case, light eventually reaching the sensor gets there primarily by refraction or diffusion from the body of the subject.
In microscopy, "darkfield epi-illumination" describes light striking the subject primarily from above/in-front, around the imaging lens but not through it, rather like a ringlight. In this case, light eventually reaching the sensor gets there primarily by reflection from the surface of the subject.
You might want to think of these two cases as being endpoints on some continuum. At one extreme, light comes from behind and undeflected light just barely misses the sensor, while at the other extreme, light comes from the front, starting just barely outside the lens. In many practical setups, particularly those involving some form of light tents, light comes from both in front and behind the specimen, and gets redirected toward the sensor through some combination of refraction, diffusion, and reflection by the subject.
The Olympus Lieberkühn reflectors are designed to take light coming from below that missed the subject, and reflect it back toward the subject from the front, in a broad area around the imaging lens. If simultaneously a "darkfield stop" is used to prevent undeflected light from reaching the lens, then the illumination pattern is similar to what you would get with a ringlight or a circular diffuser wrapped around the lens and illuminated from the lens side, with a dark background behind the subject.
Does this help?
--Rik
