In a spectral image formed by two orthogonal axes, one of which is an axis of the amount of energy loss and the other of which is an axis of positional information, by the use of an electron spectrometer and a transmission electron microscope, distortion in the spectral image of a sample to be analyzed is corrected with high efficiency and high accuracy by comparing electron beam positions calculated from a two-dimensional electron beam position image formed by the two orthogonal axes (the axis of the amount of energy loss and the axis of positional information) with reference electron beam positions, and calculating amounts of the distortion based on the differences of the electron beam positions. Method and apparatus are offered which correct distortion in a spectral image with high efficiency and high accuracy, the image being formed by the two orthogonal axes (the axis of the amount of energy loss and the axis of positional information).