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==Imaging model==
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[[File:Oversampled binary sensor imaging model.jpg|thumb|right|250px|Fig.1 The imaging model. The simplified architecture of a diffraction-limited imaging system. Incident light field <math>\lambda_0(x)</math> passes through an optical lens, which acts like a linear system with a diffraction-limited point spread function (PSF). The result is a smoothed light field <math>\lambda(x)</math>, which is subsequently captured by the image sensor.]]
Consider a simplified camera model shown in Fig.1. The <math>\lambda_0(x)</math> is the incoming light intensity field. By assuming that light intensities remain constant within a short exposure period, the field can be modeled as only a function of the spatial variable <math>x</math>. After passing through the optical system, the original light field <math>\lambda_0(x)</math> gets filtered by the lens, which acts like a linear system with a given impulse response. Due to imperfections (e.g., aberrations) in the lens, the impulse response, a.k.a. the [[point spread function]] (PSF) of the optical system, cannot be a Dirac delta, thus, imposing a limit on the resolution of the observable light field. However, a more fundamental physical limit is due to light [[diffraction]].<ref name="Optics">M. Born and E. Wolf, ''[[Principles of Optics]]'', 7th ed. Cambridge: Cambridge University Press, 1999</ref> As a result, even if the lens is ideal, the PSF is still unavoidably a small blurry spot. In optics, such diffraction-limited spot is often called the [[Airy disk]],<ref name="Optics"/> whose radius <math>R_a</math> can be computed as
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where <math>w</math> is the [[wavelength]] of the light and <math>f</math> is the [[F-number]] of the optical system. Due to the [[lowpass]] (smoothing) nature of the PSF, the resulting <math>\lambda(x)</math> has a finite spatial-resolution, i.e., it has a finite number of [[Degrees of freedom (physics and chemistry)|degrees of freedom]] per unit space.
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[[File:binary sensor model.svg|thumb|right|480px|Fig.2 The model of the binary image sensor. The pixels (shown as "buckets") collect photons, the numbers of which are compared against a quantization threshold ''q''. In the figure, we illustrate the case when ''q'' = 2. The pixel outputs are binary: <math>b_m = 1</math> (i.e., white pixels) if there are at least two photons received by the pixel; otherwise, <math>b_m = 0</math> (i.e., gray pixels).]]
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