Automatic MTF measurement through a least square method

Abstract

The Modulation Transfer Function (MTF) is a major parameter for high resolution optical remote sensing systems, indicating how spatial frequencies are transmitted and weakened by the imaging global chain. Assessing MTF is thus a very important task during both the in-flight commissioning period and the routine monitoring phases. Classical in flight MTF measurement methods are based upon devoted well known patterns such as knife edge patterns. These techniques induce heavy constraints upon satellite payload programming taking into account nebulosity conditions and pattern ground maintenance. Moreover, for high MTF systems, MTF assessment proves to be difficult because the point spread function has a too reduced extension. Another solution consists in taking two images of the same scene, one in a high resolution mode and the other one in a lower resolution mode. When the resolution ratio is high enough (typically higher then 3), it is possible to simulate the lower resolution image through convolution with a filter and undersampling. The least square method consists in an iterative process, according to which the convolution filter evolves in order to minimize a least square criterion measuring the difference between the simulation and the low resolution image. Once the process has converged, taking the Fourier Transform of the convolution filter gives an estimation of the ratio between low resolution image MTF versus high resolution image MTF. This method may be successfully applied to remote sensing systems such as Quickbird, Ikonos, SPOT5 and future PLEIADES-HR to assess MTF in the multispectral mode. The goal of this paper is to present the MTF assessment method, the way it was validated through simulations and its application within SPOT5 context.