HW1 - BME 6500 What is the cut-off frequency-3 dB for this...

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University of Connecticut BME 4500/6500 HP Set #1 Biomedical Engineering Program ` Due Thursday, 17 September 2009 Name: ___________________________________ 1.1) An infrared imaging system uses an IR laser diode as a point source test object; it can be modeled as f(x,y)=Io δ (x,y) . For simplicity, we analyze the system in 1D, so f(x)=Io δ (x) . The imaging system is assumed to be linear and shift-invariant, so the image can be computed by the Fourier Transform relation: G(u)=H(u)F(u) , where u is the spatial frequency in radians/mm. The system’s modulation transfer function is known to be: ( ) ( ) 1 0 (0) co co co u H u MFT u for u u and for u u H u = = - < > A) Find an expression for the Fourier Transform of the image, G(u), plot and dimension G(u) vs. u. B) Find an expression for and plot & dimension the image intensity, g(x).
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Unformatted text preview: BME 6500: What is the cut-off frequency (-3 dB ) for this imaging system (Note that the system works as a low pass filter)? 1.2) A one-dimensional spatial sampling array (line sensor) has a element spacing of 40 x m μ Δ = . Find the spatial Nyquist frequency associated with the array. What is the maximum spatial frequency that we can capture with this imaging system? 1.3) Describe what is the packing fraction of a fiber optics bundle? What is its relationship with quality in imaging capture? 1.4) Find the CFT of the 1-D object ( ) ( ) sin / ( ) / DC A x F x I I x π λ = + , f(x) >0 a) Sketch & dimension f(x) vs x. b) Sketch & dimension F(u) vs u. c) What is the recommended sampling frequency of an imaging system to recover all the features of this object?...
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