Disclosed are several technical approaches of using low coherence interferometry techniques to create an autofocus apparatus for optical microscopy. These approaches allow automatic focusing on thin structures that are positioned closely to reflective surfaces and behind refractive material like a cover slip, and automated adjustment of focus position into the sample region without disturbance from reflection off adjacent surfaces. The measurement offset induced by refraction of material that covers the sample is compensated for. Proposed are techniques of an instrument that allows the automatic interchange of imaging objectives in a low coherence interferometry autofocus system, which is of major interest in combination with TDI (time delay integration) imaging, confocal and two-photon fluorescence microscopy.