3-2 Digital camera Solution - At that spacing how many...

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Physics 214 Problem 2 Week 3 Digital Camera A modern digital camera looks basically something like this: a. Assuming “diffraction-limited optics”, calculate the spot size that a point source (for example, a far-away star) would make on the photosensor. Estimate the spot size as the distance between the zeroes on either side of the central diffraction lobe, and assume λ = 550 nm). In this problem, Δθ is just twice the angle from the center to the first zero α c = (1.22 λ /D). Thus Δ y = f Δθ = 2 f (1.22 λ /D) = (10 mm)2(1.22)(0.55 μ m/3mm) = 4.47 x 10 -6 m = 4.47 μ m b. Now assume that for two pixels to get fairly distinct signals they must be separated by half the distance you calculated in part (a). That corresponds to the standard value for the ‘resolution criterion’. (Using more closely spaced pixels just increases cost and degrades signal-to-noise.)
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Unformatted text preview: At that spacing, how many pixels would this camera use? A = Area of Photosensor = 5 x 7 mm 2 = 3.5 x 10-5 m 2 d 2 = Area of Pixel = 5.02 x 10-12 m 2 Number of pixels in photosensor = A/d 2 = 7.0 megapixels . FYI: The “f-number” (also called “f-stop”) of a lens is written as “f/#’, and is simply the focal length divided by the diameter of the effective aperture, so that as you open the aperture (letting more light in, so you can take pictures more quickly), the f-number decreases. At large apertures – f/4 and above – resolution is typically limited by lens aber-rations. At small apertures, starting around f/16 for the 35mm format, the resolution is limited by diffraction. Photosensor lens Focal length, f = 10 mm Aperture, D = 3 mm d Photosensor: 7 mm 5 mm Pixel Solution...
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