  In optical imaging, achieving high resolution often comes at the expense of a
shallow depth of field. This means that when using a standard microscope, any
minor movement of the object along the optical axis can cause the image to
become blurry. To address this issue, we exploit inverse design techniques to
optimise a phase mask which, when inserted into a standard microscope, extends
the depth of field by a factor of approximately four without compromising the
microscope's resolution. Differentiable Fourier optics simulations allow us to
rapidly iterate towards an optimised design in a hybrid fashion, starting with
gradient-free Bayesian optimisation and proceeding to a local gradient-based
optimisation. To fabricate the device, a commercial two-photon 3D laser
nanoprinter is used, in combination with a two-step pre-compensation routine,
providing high fabrication speed and much better than subwavelength accuracy.
We find excellent agreement between our numerical predictions and the
measurements upon integrating the phase mask into a microscope and optically
characterising selected samples. The phase mask enables us to conduct
simultaneous multiplane imaging of objects separated by distances that cannot
be achieved with the original microscope.
