Modern industrial fabrication processes put high requirements on the quality of the surface form of precision-machined components, e.g. optical lenses or microelectromechanical systems (MEMS). Optical sensors provide high precision non-contact surface measurement to verify these quality requirements, even on fragile surfaces. The low-cost line-scanning interferometer that is presented in this contribution is based on a Michelson interferometer configuration in combination with a high-speed line-scan camera. The sensor can operate in scanning white-light or in optical path length modulation (OPLM) mode. The white-light mode is used to automatically align the sensor perpendicular in the working distance of 13 mm to the surface of the specimen. In OPLM-mode, an oscillating reference mirror and a band-pass filtered light source are used, to measure the form of a radial symmetric specimen with a diameter of up to 25.4 mm with interferometric accuracy. Several overlapping ring-shaped sub-apertures are measured iteratively in different radial positions until the whole surface is scanned. The sub-apertures are stitched together to reconstruct the complete 3D-topography, while overlapping areas can be used to correct movement errors of the scanning axes. This concept is highly adaptive and can be applied to many different specimen geometries e.g. planes, spheres or aspheric glass lenses.