It probably started as something like the following kinda-simple idea, although I'm sure there are refinements and details.
We have an absorptive filter with a concentric ring pattern, sitting a certain distance in front of an image sensor.
I'm guessing that the ring pattern is:
$$T(x,y) = (1+\sin \phi)/2 \qquad , \qquad \phi = a(x^2 + y^2)$$
where $T$ is transmissivity of the filter at the point $(x,y)$, and $a$ is some constant with units of inverse length squared, whose value does not matter at this level of analysis.
(This is the same as a (parabolic) fresnel zone plate with focal length $f=\pi/(\lambda a)$, but that's just a coincidence! Indeed, I'll assume geometric optics!! Specifically: I'll assume that a light source, after passing through the filter, simply creates a shadow. Of course there is diffraction, but I think it causes distortion, rather than being the intended principle of operation. In practice, this probably requires putting the image sensor much closer to the filter than $f$.)
Now that we're assuming geometric optics, a point light source creates a shadow of the ring pattern on the image sensor. If the light source is at infinity, the shadow is shifted around based on the location of the light source. If the light source is closer than infinity, the shadow is both shifted and enlarged compared to the original ring-pattern filter.
Let's do the infinitely-far-away light source case. Then our image sensor will measure a sinusoidal ring pattern with intensity
$$I(x,y) = (1+\sin \phi')/2 \qquad , \qquad \phi' = a((x+\Delta x)^2 + (y + \Delta y)^2)$$
where $\Delta x$ and $\Delta y$ are the direction cosines of the source, times the distance from the filter to the image sensor.
We know $T$ digitally, and we just measured $I$, so therefore we can digitally superimpose them. We'll get Moiré fringes with phase
$$\phi'-\phi = (2a)(x,y)\cdot(\Delta x,\Delta y) + C$$
i.e. the Moiré fringes form a nice sinusoid whose 2D wavevector is proportional to the direction cosine of the incoming light.
($C$ is some constant.)
So take the image, multiply it (point-by-point) by $T$, and Fourier transform it, and you'll get an image focused at infinity. Or if you use a magnified version of $T$, you'll get an image focused at the object plane in which a light source would enlarge the shadow pattern by the same amount.
Or something like that, plus surely lots of refinements and details.