I probably should have clarified: Its looking for "stereotypically thin" areas. In practice, the thinnest point of any missile or conal object is just beneath the rim of its nosebone (which is very thick) or the length-ways bodyplate which incurs minimal stress during transit to target.
Determining shape using a laser is actually really really easy: Its identical to how we do it using radar: You have an expected return and a recieved return (which relies on the principle of expected and received return based on caustic diffusion: That 99% of the light does not return as you've stated is a required function for this to work) and by comparing the data you have, you can build values of depth which are both above and beneath which are compensated against some clever programming to build up an optical echo-location of what the target object looks like.
Our lag-times involved here are the capacitors feeding the laser, the intra-laser feed-system which forms the beam and any subtle correction of lenses and of course the biggest bottle-neck, computer control.
I think I need to add somewhere that this depends on a passive detection system, or that our goose knows someones shooting at it: It has a pretty narrow conal vision but can be adjusted like a turret and swept to focus on a specific target based on information fed for other systems.
And actually, you can sweep lasers in such a way. We do it today: The principle is the backbone of Google and DARPA's unmanned vehicle programs because laser-optical return times are much lower than those of radar which has a lower frequency: Meaning it piles up like a spring before bouncing off a target much slower, has a lower velocity and a lower detection/process return because you need to wait longer to recieve the entire thing which as I said is moving slower.
The only issue against this is many types of cathode used for these projects tend to overheat quickly which is an IRL concern. They also have wicked energy requirements: In SARP, I'm surprised we're not all using gamma-emission based radar due to its insane terrahertz frequency response-times over long distances an the higher aperture/imaging resolution.
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