In interferometric microscopy, the image of a micro-object is synthesized numerically as a coherent combination of partial images with registered amplitude and phase. For registration of partial images, a conventional holographic set-up is used with a reference wave, as is usual in optical holography. Capturing multiple exposures allows the numerical emulation of a large numerical aperture objective from images obtained with an objective lens with smaller-value numerical aperture. Similar techniques allows scanning and precise detection of small particles. As the combined image keeps both amplitude and phase information, the interferometric microscopy can be especially efficient for the phase objects, allowing detection of light variations of index of refraction, which cause the phase shift or the light passing through for a small fraction of a radian.