5 General remarks and conclusion

The principal component analysis is very sensitive to spectral shape. For this reason, the spectrum must not present strong variations, as those due for example, to ice absorption bands occurring in the near infrared region, otherwise the result will be mainly driven by these spectral features. The most suitable spectral window for enhancement purposes is the visible because the spectra of planetary bodies present a smooth increase in reflectance toward longer wavelengths with some small absorption, generally close to $0.8 - 1\ \mu$m. Far from being complete, in the following we want to indicate a possible extension of the sharpening technique to space born imaging spectrometers. Unlike with ground-based telescopes, for which atmospheric seeing is the major source of image degradation, pointing errors are the dominant source for diffraction-limited telescopes in space. Pointing systems have a large number of random, and systematic errors. Cross track, along track, encoder errors, control law parameters (pole, zero for DC systems), gear periodicities, mount models (e.g., flexure, mirror sag/slip) and others (Brown 1993). Pointing errors distribute the light from a point source over a larger area and reduce the intensity of the image peak, which is to say its Strehl ratio. The Strehl ratio is the ratio of the intensity of the actual image peak to that of the theoretically perfect image for that system. An optical system is commonly called "diffraction limited" if its Strehl ratio is greater than 0.8. For example, for an optically perfect Hubble Space Telescope, the pointing errors should not be more than a few milliarcseconds in order to maintain diffraction limited quality in the ultraviolet (Brown 1993). Therefore, the technique illustrated above could also be used to mitigate the jitter effects on hyperspectral images. Although we have developed this method having in mind planetary applications, it could also be applied to CCD multispectral images (e.g. the classical U, B, V, I filters). However, as already mentioned in the second section, the result should be less impressive, due to the small number of spectral bands compared to what is achievable with imaging spectroscopy.

Acknowledgements

We are particularly grateful to the support staff and telescope operators of the Sierra Nevada Observatory. Without their help the observations described in the paper would not have been possible. We specially thank Dr. J.L. Moreno and Dr. J. Rodriguez of Institute of Astrophysics of Andalucia for their continuous assistance. The help of Mrs. S. Zampieri and Mr. R. Perciballi in the manuscript preparation is also gratefully acknowledged. Funding were provided by ASI and CSIC grants.