  In wide-field nonlinear microscopy, wavefront modulation by means of
phase-only spatial light modulators (SLMs) allows achieving simultaneous
two-photon excitation and fluorescence emission from specific
region-of-interests (ROIs) of biological specimens. This is basically
accomplished at the illumination path of the microscope by the reconstruction
of computer generated holograms (CGHs) onto the sample plane. However, as
two-photon absorption (TPA) is inherently an intensity-square dependent process
and iterative Fourier transform algorithms (IFTAs) can only approximate the
illumination of selected ROIs with the reconstructed CGHs, both signal
acquisition and/or image formation can be largely affected by the spatial
irregularities of the illumination patterns. In addition, the speckle
associated with the superposition of coherent light at the selected ROIs
prevents illumination strategies based on CGHs to be successfully used for
large-area (more than 50x50 $\mu$m2) excitation tasks. To overcome these
limitations, we propose an alternative complex illumination method (CIM) able
to generate simultaneous nonlinear excitation of large-area ROIs with full
control over the amplitude and phase of the optical wavefront. We
experimentally demonstrate spatially uniform illumination, as well as
structured illumination with user-defined intensity levels onto micrometric but
large-area ROIs. Furthermore, a proof-of-concept experiment on wide-field
second harmonic generation (SHG) is provided. We believe that the proposed CIM
could find applications in wide-field nonlinear microscopy, particularly for
speed up signal acquisition time or improve two-photon image formation.
