Identifying doppelgange Black Holes through Shadow Images

Recently, an interesting \textit{doppelg\"ange} black hole solution is obtained in the string-inspired Euler-Heisenberg theory, where the black holes have the same radii but share different charges. We found, however, they possess different ISCOs and photon spheres, and hence affect their shadow images. In this work, we investigate the optical appearances, illuminated by an optically and geometrically thin disk, are investigated, of such black hole. One finds that doppelg\"ange black holes have different optical appearances. Even the horizon radii are the same, the size of shadows are not equal. Furthermore, we found that the large magnetic charge $Q_m$ black holes give rise to novel shadow images that the usual bright rings inside shadow are not clear, The optical appearances illuminated by spherically accretions are also examined, and it can also identify two doppelg\"ange black holes.