The Earth's thermosphere and ionosphere constitute a dynamic system that varies daily in response to energy inputs from above and from below. This system can exhibit a significant response within an hour to changes in those inputs, as plasma and fluid processes compete to control its temperature, composition, and structure. Within this system, short wavelength solar radiation and charged particles from the magnetosphere deposit energy, and waves propagating from the lower atmosphere dissipate. Understanding the global-scale response of the thermosphere-ionosphere (T-I) system to these drivers is essential to advanc- ing our physical understanding of coupling between the space environment and the Earth's atmosphere. Previous missions have successfully determined how the "climate" of the T-I system responds. The Global-scale Observations of the Limb and Disk (GOLD) mission will determine how the "weather" of the T-I responds, taking the next step in understanding the coupling between the space environment and the Earth's atmosphere. Operating in geostationary orbit, the GOLD imaging spectrograph will measure the Earth's emissions from 132 to 162 nm. These measurements will be used image two critical variables-thermospheric temperature and composition, near 160 km-on the dayside disk at half-hour time scales. At night they will be used to image the evolution of the low latitude ionosphere in the same regions that were observed earlier during the day. Due to the geostationary orbit being used the mission observes the same hemisphere repeatedly, allowing the unambiguous separation of spatial and temporal variability over the Americas.

Most authors include a paraxial (small-angle) limitation in their discussion of diffracted wave fields. This paraxial limitation severely limits the conditions under which diffraction behavior is adequately described. A linear systems approach to modeling nonparaxial scalar diffraction theory is developed by normalization of the spatial variables by the wavelength of light and by recognition that the reciprocal variables in Fourier transform space are the direction cosines of the propagation vectors of the resulting angular spectrum of plane waves. It is then shown that wide-angle scalar diffraction phenomena are shift invariant with respect to changes in the incident angle only in direction cosine space. Furthermore, it is the diffracted radiance (not the intensity or the irradiance) that is shift invariant in direction cosine space. This realization greatly extends the range of parameters over which simple Fourier techniques can be used to make accurate calculations concerning wide-angle diffraction phenomena. Diffraction-grating behavior and surface-scattering effects are two diffraction phenomena that are not limited to the paraxial region and benefit greatly from this new development.

Scattering effects from microtopographic surface roughness are merely nonparaxial diffraction phenomena resulting from random phase variations in the reflected or transmitted wavefront. Rayleigh-Rice, Beckmann-Kirchhoff. or Harvey-Shack surface scatter theories are commonly used to predict surface scatter effects. Smooth-surface and/or paraxial approximations have severely limited the range of applicability of each of the above theoretical treatments. A recent linear systems formulation of nonparaxial scalar diffraction theory applied to surface scatter phenomena resulted first in an empirically modified Beckmann-Kirchhoff surface scatter model, then a generalized Harvey-Shack theory that produces accurate results for rougher surfaces than the Rayleigh-Rice theory and for larger incident and scattered angles than the classical Beckmann-Kirchhoff and the original Harvey-Shack theories. These new developments simplify the analysis and understanding of nonintuitive scattering behavior from rough surfaces illuminated at arbitrary incident angles.

Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 08/13/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Abstract. Surface scatter effects from residual optical fabrication errors can severely degrade optical performance. The total integrated scatter (TIS) from a given mirror surface is determined by the ratio of the spatial frequency band-limited "relevant" root-mean-square surface roughness to the wavelength of light. For short-wavelength (extreme-ultraviolet/x-ray) applications, even state-of-the-art optical surfaces can scatter a significant fraction of the total reflected light. In this paper we first discuss how to calculate the band-limited relevant roughness from surface metrology data, then present parametric plots of the TIS for optical surfaces with arbitrary roughness, surface correlation widths, and incident angles. Surfaces with both Gaussian and ABC or K -correlation power spectral density functions have been modeled. These parametric TIS predictions provide insight that is useful in determining realistic optical fabrication tolerances necessary to satisfy specific optical performance requirements.

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