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from what I see you are calculating a formula for the uncertainty disc from uncertainty princip saying tht the momentum/wavelength is known. This gives a formula for a 'blob' of light passing through an aperture..but does not account for any diffraction. The airy disc is a diffraction feature and the 1.22 comes from the zero in the Bessel function. You might want to calc the 'smudge' of the airy disc due to the uncertainty princip.
Now even if we interpret Uncertainty principle to be standard deviation in measurement, meaning value of deltap is just standard deviation, and relation to gaussian approximation to airy disk is R ~ 3 x sigma, meaning that radius of airy disk is 3 times sigma of gaussian profile that approximates it, we still get
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So I was just trying to see if applying uncertainty principle would let me calculate effects of diffraction (or some aspects of it). I've found couple of references to this exact thing, but authors seem to run into same numerical mismatch which then try to circumvent by using "more relaxed version": delta_x * delta_p >= h/2 (as opposed to hbar)
I was under the impression that two are related in that by restricting position of photon - letting it pass thru aperture, momentum is spread out - and that is what is "causing" diffraction (well not causing per se, but related in the same way as geometry of allowed trajectories influences path integral - by presenting an obstruction in path we are changing path integral. Similarly obstruction is changing "allowed" values of position from "allover" to "narrower context").
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Meaning that exact uncertainty depends on case but can never be less than hbar/2. It can't be used to estimate airy disk diameter, but it can tell us for a fact that airy disk diameter will not be smaller then .... calculated value.
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I was trying to derive airy disk size from Uncertainty principle, but I have numeric mismatch that I can't really explain.
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The MY-CAM002U USB Digital Camera Module is released by MYIR specially for working on MYIR's ARM development boards. It is connected with the boards through USB2.0 Host port and supports resolution up to 1280 by 800 pixels. It is using a CMOS image sensor which is a 1.0MegaPixel digital camera. The module is measuring only 60mm by 8mm with small form factor, low power consumption, high performance which can be used in various products.