  Exploring high sensitivity on the measurement of angular rotations is an
outstanding challenge in optics and metrology. In this work, we employ the
mn-order Hermite-Gaussian beam in the weak measurement scheme with an angular
rotation interaction, where the rotation information is taken by another HG
mode state completely after the post-selection. By taking a projective
measurement on the final light beam, the precision of angular rotation is
improved by a factor of 2mn+m+n. For verification, we perform an optical
experiment where the minimum detectable angular rotation improves
$\sqrt{15}$-fold with HG55 mode over that of HG11 mode, and achieves a
sub-microradian scale of the measurement precision. Our theoretical framework
and experimental results not only provide a more practical and convenient
scheme for ultrasensitive measurement of angular rotations, but also contribute
to a wide range of applications in quantum metrology.
