Reference no: EM131845035

Question: 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:

f(x) = (1/(√2Πσ)) e^{-(x - μ)2/2σ2}

(a) If f(x) represents a probability density function on the domain (-∞ to +∞) show that μ is the mean value and σ is the standard deviation.

(b) Show algebraically that the full-width-at-half-maximum (FWHM) for a Gaussian point spread function is:

FWHM = 2√(2ln(2)σ)