1. A method of qualitatively ascertaining information on chatter marks in a finely-machined surface of a workpiece extending in a circumferential direction, the method comprising the acts of: generating an ideal-form data record from an idealized macroform of the workpiece surface in a data-processable form, said ideal-form data record being generated for surface data of a type and density corresponding to a type and density of surface data generated for an actual workpiece; generating an actual-form data record via a contactless measurement that senses a microtopography of the workpiece surface two-dimensionally in the form of a close grid of surface points, said microtopography being resolved at least to a depth of actual surface deviations, positions of the surface points being described by respective spatial coordinates; generating a flat-form raw-data record representing a flattened form of the microtopography of the workpiece surface by subtracting Z coordinate values directed orthogonally with respect to the workpiece surface of the ideal-form data record from mutually corresponding surface points of the actual-form data record; digitally in-phase bandpass filtering the flat-form raw-data record for instances of waviness of the data sequence of the Z coordinates directed in the circumferential direction of the workpiece surface, instances of waviness having a period length lying within an expected period length of chatter marks being allowed to pass, said filtering step generating a flat-form filter-data record representing a flattened form of the microtopography of the workpiece surface corrected to eliminate random instances of roughness; and performing a stationary multiple cross correlation of the flat-form filter-data record by multiply correlating with one another the Z coordinates of the surface points lying in the same position in the circumferential direction of the workpiece surface, so as to generate a chatter-mark data record in two-dimensional form, said chatter-mark data record representing the information about the chatter marks.