Digital Radiography - Assessing Image Quality

Introduction

The Modulation Transfer Function (MTF) is a method of determining the response of an imaging system to different spatial frequencies in the images. Spatial frequency is generally expressed as cycles, or line pairs, per millimeter (lp/mm) in analog environments, but for digital systems, cycles per pixel (c/p) is more appropriate where sensor sizes vary from one detector to another. Two important parameters for determining the image quality in spatial domain are contrast and resolution. MTF is an equivalent term which is used to characterize the image in frequency domain. Generally, MTF for an imaging system is plotted as % amplitude against spatial frequency. At frequencies where the MTF of an imaging system is 100%, the object details are unattenuated and the image retains its full contrast. Similarly, at a MTF of 50%, the contrast of the imaging system is reduced by half of the original value. In imaging science, the MTF is usually normalized to 100% at very low frequencies. The focal spot of the radiographic unit is one of the most important parameters, because it influences the resolution of the image. There is a direct relationship between the focal spot and the MTF curve of a radiography system. For large focal spot x-ray machines, MTF values reach a minimum (i.e. zero) at comparative low spatial frequency and vice versa.

Theory

The frequency response function (MTF) of an X-ray machine with a square focal spot of dimension (a) can be represented by the following relationship

Here, d₁ is the source-to-object distance and d₂ is the object-to-film distance. The parameter “f” equals the spatial frequency of the sinusoidal object. The above equation is similar to an optical system because Fourier transformation of a slit with width ‘a’ is (sin πfa / πfa). The value of MTF function will be zero where frequency is such that the argument of sine function is equal to π or its multiples. If frequency is ‘f₀’, for the MTF to be zero,

The above equation shows that the maximum spatial frequency of the object (f₀) (i.e. the finest details of the object) is inversely proportional to the proportional focal spot size of the x-ray machine. MTF has a multiplicative property. In radiography, the effective MTF is the multiplication of the MTF of film and that of the focal spot.

Therefore, MTF(effective) = MTF(film) x MTF(focal spot)

In the case of industrial radiography, MTF of the focal spot is governed by focal spot dimension through geometric unsharpness. The MTF of film is determined from contact imaging for a particular type of radiation detector and it does not undergo maxima and minima, as seen in MTF of focal spot. Therefore, it is sufficient to work with MTF of focal spot in radiography application for a particular type of detector.