  We present an implementation of dispersion-scan based on self-diffraction (SD
d-scan) and apply it to the measurement of over octave-spanning sub-4-fs
pulses. The results are compared with second-harmonic generation (SHG) d-scan.
The efficiency of the SD process is derived theoretically and compared with the
spectral response retrieved by the d-scan algorithm. The new SD d-scan has a
robust inline setup and enables measuring pulses with over-octave spectra,
single-cycle durations and wavelength ranges beyond those of SHG crystals, such
as the ultraviolet and the deep-ultraviolet.
