Experimentally exploiting the violation of the Lagrange invariant for resolution improvement

It is experimentally demonstrated that even though the numerical aperture in the object space is fixed, the resolution of an imaging system still can be improved by adjusting the parameters in the image space. This strategy cannot be realized until the discovery of the violation of the Lagrange invariant in a kind of self-interference holography. With the violation, parameters in the image space can escape the constraint of the object space for resolution improvement. Experiments that directly confirm this new ability are implemented and results agree well with the theoretical prediction. Additionally, better performance on frequency recording and finer details beyond the diffraction limit have been recorded with this method.