In this paper we investigate methods to solve the inverse problem for the optical occulation measurements from a planet-orbiting satellite. Our emphasis is on the stellar occultation technique which offers a promising method to monitor the global vertical distributions of the crucial trace gases like ozone in the Earth's stratosphere. The occulation measurement principle is self-calibrating because the star (or Sun) signal is also measured when the light is not attenuated by the atmosphere. This feature is crucial in developing the long-term space-borne monitoring systems of the Earth's trace gases. The inverse problem for an occultation measurement can be divided into a spectral inversion part and into a spatial inversion part. In the former problem we aim at finding the tangential column densities of the different gases which are involved in the attenuating of the starlight traversing through the atmosphere onto our detector. In the latter part we bring together measurements from different altitudes and geogrphaical locations to construct the global distributions of the trace gases in the Earth's atmosphere. This paper deals with the first problem; the second problem will be treated in a subsequent paper. ¿American Geophysical Union 1993