Infrared Power Spectral Density Diurnal Variations And Clutter Rejection Scaling Laws For Focal Plane Arrays

Abstract

The diurnally varying IR imagery obtained from different field of view (FOV) is studied for the purpose of Wiener's whitening technique to be implemented in the image domain for real time clutter rejection. The measured power spectral density (PSD) on a focal plane arrays (FPA) is derived in terms of the propagation of the correlation of the ground irradiance lλ(e): PSD(k) = , where λ is the IR wavelength, eo is an arbitrary point within the downward FOV, the angular brackets denote an ensemble average, and H is the height above the ground. A combined measure of both dynamic ranges and resolution line pairs that can explain the thermal contrast and the diurnal variations is derived from Rayleigh's visibility V(r ) by means of Taylor series expansion and logarithmic derivative of the measured temperature fluctuation correlation function C(r )= , such that V(r ) = (r /2)•(d log C(r )/dr ). The measured PSD(k ) at FPA reveals systematically a diurnal trend of the power law variation of all FOV sceneries, |k |-D-1 where D = 0, 1, 2, 3. Consequently Wigner distribution W( k ,x 0) is introduced to generalize the Wiener PSD(k) to include the nonstationary FOV ye. Spatiotemporal filtering for clutter-rejection is a Wiener and Wigner whitening procedure in the sense of whitening in matching with the FOV. Analytical scaling laws of clutter leakage ≈en/1D+1 useful for FPA designs have been derived in terms of a step size FPA resolution parameter e=kcxs/2, the filter differencing order n, and a projected ground correlation length L at the FPA l=(D0H|λR2L, where k c is the optical cutoff frequency (D0/λf 0), expressed in terms of the lens aperture D0, the focal length f 0, and the pixel separation distance xs, and the slant range R. Finally, the optical bench flight scene simulator is implemented using stationary scene input at a fixed FOV, and the optical flow on the moving platform FPA is derived. An apparent scene velocity along the radial direction / from a fixed point (x0,y0) on EPA is generated from a stationary input scene, on the FPA v (x ,y )=(f0H/R2)Ul sin[(x-x0)2+ (y-y0)2)1/2]where U is the platform velocity component in parallel to the ground.© (1986) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.