Class-specific diffractive cameras with all-optical erasure of undesired objects

It blew my mind when I did in school, yet... there was the proof that it worked!

I don't quite understand the mathematics of how it was trained, but they were able to discretize the geometry of those layers somehow into little 0.4mm pixels of "trainable diffractive neurons" and they simulated light transmission through the layers to compute a loss function.

I'm really surprised that this was computationally feasible. Simulation of light through the gratings must have been cheap enough as a function evaluation to train the network.

There are a few gotchas in that statement though - for one, I didn't dive too far into the math, and I would assume that the convolutional algorithms as well as the underlying matrix functions may be different. But at the end of the day, you're approximating a complex function using an array of simple functions with different weights and scale factors. The other gotcha is that diffractive structures use monochromatic light, so it's probably not too useful in most normal situations with normal light sources.

>Importantly, this diffractive camera is not based on a standard point-spread function-based pixel-to-pixel mapping between the input and output FOVs, and therefore, it does not automatically result in signals within the output FOV for the transmitting input pixels that statistically overlap with the objects from the target data class. For example, the handwritten digits ‘3’ and ‘8’ in Fig. 2c were completely erased at the output FOV, regardless of the considerable amount of common (transmitting) pixels that they statistically share with the handwritten digit ‘2’. Instead of developing a spatially-invariant point-spread function, our designed diffractive camera statistically learned the characteristic optical modes possessed by different training examples, to converge as an optical mode filter, where the main modes that represent the target class of objects can pass through with minimum distortion of their relative phase and amplitude profiles, whereas the spatial information carried by the characteristic optical modes of the other data classes were scattered out.

It seems like that may not be so possible.

Later on in the article:

>It is important to emphasize that the presented diffractive camera system does not possess a traditional, spatially-invariant point-spread function. A trained diffractive camera system performs a learned, complex-valued linear transformation between the input and output fields that statistically represents the coherent imaging of the input objects from the target data class.

Note here that the learned transformations are linear, and the Fourier Transform is linear, but you cannot invert from output to input because the sensor measures real-valued intensities of complex-valued fields. All the phase information is lost.