  We extend image scanning microscopy to second harmonic generation (SHG) by
extracting the complex field amplitude of the second-harmonic beam. While the
theory behind coherent image scanning microscopy (ISM) is known, an
experimental demonstration wasn't yet established. The main reason is that the
naive intensity-reassignment procedure cannot be used for coherent scattering
as the point spread function is now defined for the field amplitude rather than
for the intensity. We use an inline interferometer to demonstrate
super-resolved phase-sensitive SHG microscopy by applying the ISM reassignment
machinery on the resolved field. This scheme can be easily extended to third
harmonic generation and stimulated Raman microscopy schemes.
