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The precision measurement of the cable positioning in superconducting coils is of great interest both at room and liquid nitrogen temperatures because mechanical and thermal deformations affect the quality of the magnetic field. The paper describes a new two-coordinate measuring device, which is able to obtain scanned images of flat composite samples at liquid nitrogen temperature. The sample is cooled at 77 K into a flat quartz tray to permit the optical access to the sample from the bottom. The comparison of the images taken at room and liquid nitrogen temperatures by a high-resolution flatbed scanner gives the thermal contraction of the components.