Modulation transfer function obtained from image structures

Abstract

A new and relatively simple method for edge gradient analysis (EGA) has been developed to determine the modulation transfer function (MTF) of photogrammetrical systems. The MTF can be calculated as the ratio of the amplitude of those frequencies present in the original edge to the amplitude of the same frequency in the scanned edge image. Thus a differentiation of the edge scan - as usually implemented - is not necessary. In order to avoid a division by zero we multiplied the edge images by the so called Hanning function before performing the Fourier analysis. From the point of noise sensitivity the method using a Hanning window is advantageous in comparison to the edge differentiation method. The edge gradient analysis method and the grating pattern method are compared. Artificial edge, natural roof edge, and grating patterns were used to determine the quality of the photogrammetrical system. Good agreement of all MTF measurements was found. Furthermore, the resolution found from MTF curves agreed well with the resolution obtained from threebar targets. Generally, the MTF curves obtained from patterns in the flight direction were lower than the MTF's perpendicular to the flight direction due to airplane movement. The influence of linear image motion and its compensation was examined and is discussed. Furthermore, the longitudinal motion of the object as defect of focus is studied analytically and experimentally for a close range.