6720 Lecture 5_imaging systems

6720 Lecture 5_imaging systems - Lecture V 1 2 3 4 5...

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1 PHYS 6720 - Lecture V 1 Lecture V Imaging System Analysis 1. Linear imaging systems 2. Fourier transform and discrete sampling 3. Image contrast and MTF 4. Effect of scattering 5. Other imaging quality parameters PHYS 6720 - Lecture V 2 V-1 Linear imaging systems Imaging system requirement Æ An imaging system maps an input signal I( r ) (object) to an output signal I’( r ’) (image) in real space Æ A signal I can often be acquired at a location r of a plane image sensor and (I, r ) make up a pixel ( pic ture se l ement) Æ A “clear” image for replica imaging requires a one-to-one relation existing between a pixel in the object I( r ) to the conjugate pixel I’( r ’) in the image PHYS 6720 - Lecture V 3 V-1 Linear imaging systems Imaging system requirement Imaging System Object space ( r ) image space ( r’ ) PHYS 6720 - Lecture V 4 V-1 Linear imaging systems Imaging system requirement The object and images spaces, r and r ’, can share the same dimensions, such as a pin-hole camera Object space ( r ) image space ( r’ ) PHYS 6720 - Lecture V 5 V-1 Linear imaging systems Imaging system requirement The object and image spaces can have different scales Object space ( r ) image space ( r’ ) PHYS 6720 - Lecture V 6 V-1 Linear imaging systems Imaging system requirement The object and image spaces share the same real space but still use different symbols to separate them out Object space ( r ) image space ( r’ )
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2 PHYS 6720 - Lecture V 7 V-1 Linear imaging systems Dimensionality of r and r Æ 1D spaces: signals are function of one spatial coordinate (e.g., infinitely large grating of black-white stripes, linear array detectors). Æ 2D spaces: signals are functions of two spatial coordinates (e.g., all conventional films or panel detectors). Æ 3D spaces: signals are functions of three spatial coordinates (through reconstruction). PHYS 6720 - Lecture V 8 V-1 Linear imaging systems Linear imaging systems Let I( r )=input signal for an object, I’( r ’)=output signal for an image, then an imaging system can be described mathematically as a mapping functional H: I’( r ’)=H{I( r )}. If the following relation is true aI’ 1 ( r ’)+bI’ 2 ( r ’)=H{aI 1 ( r )+ bI 2 ( r )} , where a and b are scalar constants, then the imaging system is defined as linear V-1 Linear imaging systems Why do we like linear systems? Æ If linear, it can be proved that the mapping functional H must be a convolution operator: I’( r ’) = h( r’ , r ) I( r ) where h is also called a system response function. Æ For a linear system with a given h function, any output can be predicted from the input signal. (' ,)() hI d rr r r A.C. Kak, M. Slaney, “Principles of computerized tomographic imaging”, (IEEE Press, 1988) (pdf file is available at: http://www.slaney.org/pct/ ) PHYS 6720 - Lecture V 10 V-1 Linear imaging systems Spatial invariant systems If an imaging system with object and image spaces have the same scale and is spatial invariant, then h( r’ , r )=h( r’ - r ) Imaging System PHYS 6720 - Lecture V 11 V-1 Linear imaging systems Magnification For a 2D linear imaging system, a magnification M is defined through a scaling relation:
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6720 Lecture 5_imaging systems - Lecture V 1 2 3 4 5...

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