IPhO-37_Th3-solve

# IPhO-37_Th3-solve - SOLUTIONS to Theory Question 3 Digital...

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Digital Camera Two factors limit the resolution of the camera as a pho- tographic tool: the diﬀraction by the aperture and the pixel size. For diﬀrac- tion, the inherent angular resolution θ R is the ratio of the wavelength λ of the light and the aperture D of the camera, θ R = 1 . 22 λ D , where the standard factor of 1 . 22 reﬂects the circular shape of the aperture. When taking a picture, the object is generally suﬃciently far away from the photographer for the image to form in the focal plane of the camera where the CCD chip should thus be placed. The Rayleigh diﬀraction criterion then states that two image points can be resolved if they are separated by more than 3.1 Δ x = R = 1 . 22 λ F], which gives Δ x = 1 . 22 μ m if we choose the largest possible aperture (or smallest value F] = 2) and assume λ = 500 nm for the typical wavelength of daylight The digital resolution is given by the distance ` between the center of two neighboring pixels. For our 5 Mpix camera this distance is roughly ` = L q N p = 15 . 65 μ m . Ideally we should match the optical and the digital resolution so that neither aspect is overspeciﬁed. Taking the given optical resolution in the expression for the digital resolution, we obtain 3.2 N = ± L Δ x ² 2 823 Mpix . Now looking for the unknown optimal aperture, we note that we should

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IPhO-37_Th3-solve - SOLUTIONS to Theory Question 3 Digital...

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