1. A biometric authentication device comprising: a biometric sensor that obtains an image of a biometric authentication portion of a user without contacting; a distance sensor that obtains a distance between the biometric sensor and the biometric authentication portion; a memory; and a processor configured to generate a guidance image for guiding the biometric authentication portion to a distance that is appropriate for the biometric sensor to obtain the biometric authentication portion by changing a reference image based on the distance obtained by the distance sensor by performing a blurring process on the reference image with use of a convolution theorem and to show the guidance image on a display, the guidance image changing continuously or in stages according to the distance obtained by the distance sensor.