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This is the delayed-choice quantum-eraser experiment of Kim diagram described on Wikipedia https://en.wikipedia.org/wiki/Delayed-choice_quantum_eraser

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Why do I need a lens in front of the D0? Why we should focus photons? The classic Double-slit experiment does not require a lens.

What pattern will we see on D0 if we remove the lens from the experimental setup? Why don't we see interference fringes?

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From the paper Taming the Delayed Choice Quantum Eraser by Johannes Fankhauser:

The lens in front of detector D0 is inserted to achieve the far-field limit at the detector and at the same time keep the distance small between slits and detector.

So the reason is that using the lens allows them to keep D0 closer to the slits.

Different patterns by different focus:

And even closer peaks from Kim et al's paper's results:

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