Using higher order harmonics in MTF calculations

Abstract

Scanning a bar pattern image along the direction perpendicular to the bars produces a periodic wave. This wave can be decomposed into a sum of harmonics by means of its Fourier series. Oversampling bar pattern images produces output waves with a high signal to noise ratio (SNR), and this high SNR allows the use of several harmonics of the wave for MTF calculations. However, increasing the order of the harmonic used for the calculation entails a loss of accuracy. In this work, some limiting factors to the use of these harmonics are investigated and their effects are quantified. Also, a criterion to discern if a given harmonic should be used is presented. Synthetic phantom images with several bar groups of different frequencies are generated through a process that simulates blurring, sampling and noise addition. Then, an output wave is obtained for each group of bars, and the MTF at the frequencies of its first odd harmonics are calculated. Five noise levels were simulated spanning an exposure range from 0.02 to 200 mR. Spatial sampling introduces errors in the estimation of the wave period resulting in underestimates of the MTF calculations. An error of 2% in the wave period produces underestimates of 0.0%, 0.4%, 1.2% and 2.4% in the MTF values obtained from the 1st, 3rd, 5th, and 7th harmonics of the output wave. Also, a bound for the aliasing error derived from spatial sampling is presented. This bound is inversely proportional to the square of the number of samples per period in the output wave. Increasing the noise level leads to increasing uncertainties in the MTF calculations, being larger at high frequencies and for high order harmonics. In all situations, the SNR of a harmonic can be used to determine the accuracy of the MTF estimation.