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High-precision measurements of mechanical parts' surface topography represent an essential task in many industry sectors. Examples of such tasks are, e.g., precise alignments of opto-mechanical systems, large object deformation measurements, evaluation of object shape, and many others. Today, the standard method used for such measurements is based on use of coordinate measuring machines (CMMs). Unfortunately, CMMs have severe shortcomings: low measurement point density, long measurement time, risk of surface damage, etc. Indeed, the measurement time rapidly increases with the object complexity and with the density of measurement points. In this paper, we have developed a method for surface topography measurements called "frequency sweeping digital holography" (FSDH). Our developed FSDH method is based on the principles of wavelength scanning interferometry. It allows surface topography measurements of objects with a diameter of several hundred of mms and a high axial accuracy reaching 10 μm. The greatest advantage of the presented FSDH is the fact that the surface topology data are captured in a motionless manner by means of a relatively simple setup. This makes the FSDH method a suitable technique for topography measurements of objects with complex geometries made of common materials (such as metals, plastics, etc.), as well as for the characterization of complex composite structures such as acoustic metamaterials, active acoustic metasurfaces, etc. Measurement method principles, setup details, lateral resolution, and axial accuracy are discussed.