1. An electronic microscope apparatus for measuring an element image of a specimen, comprising: an electron beam application section which applies to the specimen an electron beam generated in an electron beam source; an elastically scattered electron detector which detects elastically scattered electrons transmitted through the specimen; an electron beam energy analyzer which analyzes the energy of an electron beam of nonelastically scattered electrons transmitted through the specimen; and a controller which controls the electron beam application section, the elastically scattered electron detector and the electron beam energy analyzer to obtain an image relating to the specimen; wherein the controller controls the electron beam application section so that the electron beam application section applies the electron beam to the same application position on the specimen for a predetermined time period, forms a plurality of time-divided elastically scattered electron images from the elastically scattered electrons detected by the elastically scattered electron detector, and forms, in a time division manner, on the basis of outputs from the electron beam energy analyzer, a plurality of first energy filter images including a core loss of the element to be observed, and at least two sorts of second and third energy filter images of lower-loss energy in comparison with the first energy filter images, and wherein the controller further computes an amount of specimen drift by using the plurality of elastically scattered electron images, corrects a specimen drift in the plurality of first to third energy filter images on the basis of the amount of specimen drift to add up the plurality of first to third energy filter images in each which the specimen drift has been corrected, and forms a first element image with respect to the element to be observed on the basis of the first to third energy filter images drift-corrected and added up.