  We propose an analytical formulation for the Scanning Gate Microscopy (SGM)
response to local tips with arbitrary strength in two terminal nano-structures.
The real space resolved conductance is expressed in terms of the unperturbed
quantities underlying the scattering problem. Providing a non-dynamical
approach for obtaining the SGM maps, the proposed expression enables for a
significant reduction in the computational cost of SGM response calculations.
This feature is particularly advantageous for deep learning-based approaches
which have been recently proposed for accessing local properties and disorder
landscapes from conductance measurements. This opens up new possibilities for
the SGM technique and holds exciting prospects for quantum transport. Further,
the formula's versatility extends beyond this specific application, offering a
straightforward and computationally efficient method for obtaining the SGM
response in a more general context.
