A Comparison of Methods to Measure the Modulation Transfer Function of Aerial Survey Lens Systems from the Image Structures

For the image quality analysis of photogrammetrical systems using the Modulation Transfer Function (MTF), the edge gradient analysis (EGA), using a Hanning function, and the grating pattern method are compared. Artificial edge and grating patterns were photographed from an airplane and were analyzed to determine the quality of the photogrammetric system. The pictures were scanned with a microdensitometer. For comparison with the artificial patterns, a natural roof edge was examined. Good agreement of all MTF measurements was found. Furthermore, the resolution found from MTF curves agreed well with the resolution obtained from three-bar 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. EDGE DIFFERENTIATION METHOD In linear space invariant systems the image obtained can be described by the convolution integral METHODS FOR DETERMINING THE MTF FROM AN EDGE IMAGE During the past 20 years different calculation methods for edge gradient analysis, EGA, have been developed Gones, 1967; Jones and Yeadon, 1969; Lei and Tiziani, 1986; Sievers, 1976). One method, based on the differentiation of the edge, has often been used for MTF determination. The OTF is determined from the Fourier transform of the spread function, obtained from differentiating the edge image. It can be called an indirect method. Recently, a direct method using a Hanning window was developed (Lei and Tiziani, 1986). The method is based on the Fourier spectrum amplitude ratio between the real and an ideal edge image. It can be called an edge spectrum ratio method. There are several other methods for EGA (Scott et aI., 1963). In the following only the differentiation method and the edge spectrum ratio method will be discussed. INTRODUCTION I N PHOTOGRAMMETRY the image quality of photographs is of great importance. With digital image processing the image quality can be improved under certain conditions. Flight conditions usually lead to reduced image quality (Holdermann, 1976). The optical transfer function (OTF) and especially the modulation transfer function (MTF) are useful techniques for measuring the image quality of photographs. The MTF is the result of -the contributions of the links in the image transfer forming chain, namely, the camera, the film, image motion (in systems without forward motion compensation, FMC), vibrations, and the atmosphere (Tiziani, 1977). Artificial or natural edges are used for the edge gradient analysis (EGA), and varying spatial frequency patterns are used for the grating pattern technique. The aim of this paper is to compare both methods and to test their reliability. Results are shown and discussed. Furthermore, the influence of linear image motion on image quality is examined. (4)