A device for detecting a travel distance of a sheet is provided. The device includes a light source for irradiating the sheet surface; an imaging sensor for capturing an image of a pattern of the sheet surface by light reflected from the sheet; a discrete Fourier transformation portion for performing discrete Fourier transformation on two patterns obtained by image capturing at a time interval by the imaging sensor; a high wave number component removal portion for using a threshold determined based on a cycle of concave-convex of the sheet surface to remove a high wave number component from the two patterns having been subjected to the discrete Fourier transformation; and a travel distance calculation portion for determining a travel distance of the sheet based on a phase relationship between the two patterns from which the high wave number component removal portion has removed the high wave number component.