A method for homogenizing glass includes the method: providing a cylindrical blank composed of the glass having a cylindrical outer surface that extends along a longitudinal axis of the blank between a first end face and a second end face, forming a shear zone in the blank by softening a longitudinal section of the blank and subjecting it to a thermal-mechanical intermixing treatment, and displacing the shear zone along the longitudinal axis of the blank. The displacement of the shear zone along the longitudinal axis of the blank is superimposed by a simultaneous oscillating motion of the shear zone along the longitudinal axis of the blank. The first end of the blank is rotated at a first rotational speed and the second end of the blank is rotated at a second rotational speed. An oscillating motion of the shear zone is generated by periodically varying the first and/or second rotational speed.

A blank made of titanium-doped silica glass for a mirror substrate for use in EUV lithography is provided. The blank includes a surface portion to be provided with a reflective film and having an optically used area (CA) over which a coefficient of thermal expansion (CTE) has a two-dimensional inhomogeneity (dCTE) distribution profile averaged over a thickness of the blank. A maximum inhomogeneity (dCTE.sub.max) of less than 5 ppb/K is defined as a difference between a CTE maximum value and a CTE minimum value. The dCTE.sub.max is at least 0.5 ppb/K. The CA forms a non-circular area having a centroid. The dCTE distribution profile is not rotation-symmetrical and is defined over the CA, such that straight profile sections normalized to a unit length and extending through the centroid of the area yield a dCTE family of curves forming a curve band with a bandwidth of less than 0.5dCTE.sub.max.