Consecutive double slits exepriment

Question

do you know whether there are some modification of Davisson–Germer double slit experiment when we replace one screen with double slit with two consecutive screens with double slits separated by some distance $d$. At the first screen we could apply some sort of detector to one or another slit, at the second we have no detectors. What will be the behaviour of output interference pattern? Intuition could suggest 2 answers:

1. If $d < L\propto \lambda$ where $\lambda$ is the De Brooglie wavelength, we will see no interference pattern, if $d > L$ we will see interference pattern as no first screen presented.
2. No matter whatever $d$ is we will see no interference pattern, because wavefunction is collapsed.

But what are real behaviour of particles in these experiments?

Answer 1

If you detect the particle you destroy or collapse it, so it really can't travel on. For electrons you can alter the path but its not a detection, for photons you can use polarizers which is a form of detection but everything gets entangled. If you put many successive slits, diffraction will occur each time although many particles will never make it through.