1. Assume that we’ve taken a radiograph of a small circular plastic object from which we have made the following relative exposure measurements along a line including the object:
359, 376, 421, 424, 394, 371, 423, 349, 399, 346, 482, 476, 498, 501, 528, 449, 501, 530, 525, 439, 502, 467, 521, 520, 523, 479, 528, 529, 476, 523, 430, 392, 439, 390, 429, 439, 387, 380, 420, 429
(a) Make a graph of these values as a function of position.
(b) Calculate contrast, noise, and the signal-to-noise ratio.
In each case define all terms and describe how you determined each value.
2. Assume that a point spread function is described by the following Gaussian function:
(a) If f(x) represents a probability density function on the domain (- to +) show that is the mean value and is the standard deviation.
(b) Show algebraically that the full-width-at-half-maximum (FWHM) for a Gaussian point spread function is:
( )
e
x
xf 2
2
2
2
1)( σ
µ
σπ
−−
=
()
e
x
xf
2
2
2
2
1
)(
s
m
sp
--
=
s)2ln(22=FWHM