We present a method to obtain diffraction limited spectrograms of exte
nded sources from a series of ground-based slit-spectrograms. The meth
od is a combination of speckle deconvolution (Keller and von der Luhe
1992) and a rapid spectrograph scanning scheme (Johannesson et al. 199
2). The slit of a spectrograph is scanned over the solar surface while
simultaneous slit-jaw images and spectrograms are recorded. The expos
ure time is short with respect to seeing-induced variations. A Knox-Th
ompson speckle reconstruction scheme is applied to the slit jaw images
. From the individual slit-jaw images and their speckle reconstruction
the instantaneous point spread function can be determined for any loc
ation. The spectrograms are reconstructed by inverting a matrix that d
escribes the action of the point-spread function on the spectrograms.
The final product is a three-dimensional cube formed by the two spatia
l coordinates and the wavelength. In the spatial domain the data is ne
arly diffraction limited while the spectral resolution is not affected
by the reconstruction. The method is applied to observations of the q
uiet solar granulation.