<title>Estimation of scene correlation lengths</title>

Abstract

Numerical estimates of correlation lengths occurring in natural and synthetically generated IR two-dimensional digital scenes, both below (BTH) and above (ATH) the horizon, are presented. Diagnostics and generation of synthetic scenes for arbitrary correlation length to pixel ratio are analyzed for their dependence on scene dimension. New equations, useful for estimating scene correlation lengths from the large and small correlation length components of a single cloud top altitude multiscale BTH broken cloud scene, are given. These equations are valid for a minus two exponent power-law Power Spectral Density (PSD) corresponding to a one-dimensional cut in the scene data. The physical components are defined by the intrinsic cloud top statistics, the edge statistics due to the jump in mean radiance from cloud top to ground, and the intrinsic ground statistics. Other power laws as well as integral- and micro- scales are considered. Footprint effects are included. The scene correlation length estimate is expected to be useful as a prediction tool and as a diagnostic where component radiance standard deviations and correlation lengths are known. The methodology is based on PSD and Auto Correlation Function (ACF) measurements. Implementation of scene analysis by statistical methods at Lockheed Palo Alto Research Laboratory (LPARL) is highly interactive and graphically oriented. A complete statistical analysis set includes hard copy scene imagery; radiance profiles; histogram; orthogonal, ensemble-averaged, one-dimensional PSDs and ACFs; and the estimation of correlation lengths. A typical set run time for a 512 by 512 pixel scene is ten minutes on a VAX Station 3200. The statistics of any rectangular local scene of arbitrary 2n dimension can be obtained also.