# WUSTL ESE 589 - ESE589HW1-18 (3 pages)

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# ESE589HW1-18

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## ESE589HW1-18

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Pages:
3
School:
Washington University in St. Louis
Course:
Ese 589 - Biological Imaging Technology

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ESE 589 Spring 2018 Homework 1 Assigned February 6 2018 Due February 12 2018 Read Part I Basic Imaging Principles Chapters 1 2 and 3 in Medical Imaging Signals and Systems by Prince and Links Part II Radiography Chapters 4 5 and 6 in Medical Imaging Signals and Systems by Prince and Links Recommended Problems Do not hand in 1 Consider an unusual imaging system whose aperture consists of a set of pinholes on a rectangular grid spaced every 1 m in the x direction and every 2 m in the y direction There are 15 holes in each row x direction and 7 holes in each column y direction A mathematical model for the point spread function can be written in at least two ways as h x y 7 3 x k y 2l k 7 l 3 7 3 h x y x k y 2l k 7 l 3 a Compute the transfer function H u v for this aperture b Find an approximate expression for the bandwidths in each of the frequencies u and v conjugate to x and y Suppose this aperture is used in place of a pinhole in a pinhole camera so that the image on a focal plane at distance d from the aperture For an object at distance z in front of the aperture with source image s x y an approximate equation for the image i x y ignoring several geometric effects but accounting for image inversion is yz xz i x y h s d d d d Suppose that the source image is zero outside of some region s x y 0 for x 4 mm or y 8 mm In terms of the distance of the focal plane from the aperture d find the set of distances z such that the image in the focal plane i x y consists of 105 7 15 non overlapping copies of the source image j 2 u x v y 2 Let f x y e 0 0 and let s x y f x y cos 2 u0 x v0 y For each of these functions a state whether it is separable b find its periods and c find its Fourier transform x 2 y 2 Let h x y e be the point spread function for a linear shift invariant system d find the output of this system with input f x y and with input s x y 3 Consider a linear shift invariant imaging system with point spread function PSF 1 x2 y 2 h x y x2 y 2 0 a Find the FWHM of the

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