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Geometric optics: When you place a half-circle screen in front of a lens, do you cut off the image?
Given the ff. arrangement: Light source -------- LENS ------- half-circle screen -------- rectangular screen or board
When the half-circle screen is placed directly in front of the lens, does the formed image on the rectangular screen get cut off by half, too?
I'm not sure what the ff. arrangement is nor where your object is located (I didn't really follow your ASCII diagram). But I'll guess anyway.
Venturing a guess, I would say that your object and image are located a distance of 2f away from your lens (opposite sides, of course). If this is the case, putting an aperture like that will NOT cause half the image to disappear. It will likely reduce the intensity in half and perhaps cause a little blurring (but unless you are studying aberration theory, this is not that important). The explanation: each point on the object will travel through EVERY point on the lens, which refocuses the light to the image plane. Thus, blocking half the light on the lens will only block half the light coming from each point on the object, reducing the intensity of the image by half everywhere.