The half lens thread is interesting. Try the experiment with a simple
lens. You do NOT have to split the lens to observe that a full image
is obtained with half or more of the lens covered. The image intensity
is just reduced.
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If you place the obstruction some distance in front of the lens THEN
part of the image can be blanked.
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A detailed study of the effect on the image as a function of the
distance of the obstruction in front of the lens might be interesting.