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+ | # For this part, assume that the object is of constant density with <math>\mu(x,y)=\mu_0</math>. Then sketch a plot of <math>\hat{P}_n</math> versus the object thickness, <math>T_n</math>, in <math>mm</math>, for the <math>n^{th}</math> detector. Label key features of the curve such as its slope and intersection. |

## Revision as of 00:35, 7 July 2019

Communication, Networking, Signal and Image Processing (CS)

Question 5: Image Processing

August 2016 (Published on Jul 2019)

## Problem 1

- Calculate an expression for $ \lambda_n^c $, the X-ray energy corrected for the dark current.

$ \lambda_n^c=\lambda_n^b-\lambda_n^d $

- Calculate an expression for $ G_n $, the X-ray attenuation due to the object's presence.

$ G_n=-\mu(x,y_0+n*\Delta d)\lambda_n $

- Calculate an expression for $ \hat{P}_n $, an estimate of the integral intensity in terms of $ \lambda_n $, $ \lambda_n^b $, and $ \lambda_b^d $.

$ \lambda_n=(\lambda_n^b-\lambda_n^d)e^{-\int_0^x \mu(t)dt} \hat{P}_n=\int_0^x \mu(t)dt=-log\frac{\lambda_n}{\lambda_n^b-\lambda_n^d} $

- For this part, assume that the object is of constant density with $ \mu(x,y)=\mu_0 $. Then sketch a plot of $ \hat{P}_n $ versus the object thickness, $ T_n $, in $ mm $, for the $ n^{th} $ detector. Label key features of the curve such as its slope and intersection.