Defocus-Insensitive Microscopy via Spatial Phase Modulation Using End-to-End Learning

In optical microscopy, high spatial resolution comes at the cost of a short depth of field. This trade-off prevents the formation of sharp images of three-dimensional objects or objects moving in and out of focus. Moreover, it is often difficult to know the extent to which the object is out of focus, which makes it challenging to determine the point spread function that describes the blurring. This hinders the ability to restore the blurred image using digital postprocessing. To resolve these issues, we design a phase mask that, when inserted into the microscope, extends the depth of field, making the point spread function insensitive to the location of the object. We leverage end-to-end machine learning tools to design this phase mask together with a Richardson-Lucy-type deconvolution algorithm to remove image blurring. The phase mask is then manufactured with a commercial 3D nanoprinter and used in a microscope to demonstrate defocus-insensitive imaging of microfabricated objects. The experiments successfully verify the operation of both the phase mask and the image restoration algorithm.