  We report the discovery of optical emission from the non-radiative shocked
ejecta of three young Type Ia supernova remnants (SNRs): SNR 0519-69.0, SNR
0509-67.5, and N103B. Deep integral field spectroscopic observations reveal
broad and spatially resolved [Fe XIV] 5303{\AA} emission. The width of the
broad line reveals, for the first time, the reverse shock speeds. For two of
the remnants we can constrain the underlying supernova explosions with
evolutionary models. SNR 0519-69.0 is well explained by a standard
near-Chandrasekhar mass explosion, whereas for SNR 0509-67.5 our analysis
suggests an energetic sub-Chandrasekhar mass explosion. With [S XII], [Fe IX],
and [Fe XV] also detected, we can uniquely visualize different layers of the
explosion. We refer to this new analysis technique as "supernova remnant
tomography".
