  Fourier-based optical computing operations, such as spatial differentiation,
have recently been realized in compact form factors using flat optics.
Experimental demonstrations, however, have been limited to coherent light
requiring laser illumination and leading to speckle noise and unwanted
interference fringes. Here, we demonstrate the use of optimized multilayer
films, combined with dual color image subtraction, to realize differentiation
with unpolarized incoherent light. Global optimization is achieved by employing
neural networks combined with the reconciled level set method to optimize the
optical transfer functions of multilayer films at wavelengths of 532 nm and 633
nm. Spatial differentiation is then achieved by subtracting the normalized
incoherent images at these two wavelengths. The optimized multilayer films are
experimentally demonstrated to achieve incoherent differentiation with a
numerical aperture up to 0.8 and a resolution of 6.2 {\mu}m. The use of
multilayer films allows for lithography-free fabrication and is easily combined
with existing imaging systems opening the door to applications in microscopy,
machine vision and other image processing applications.
