A method for producing an earth observation image of a region by means of a radar having a synthetic aperture and a phase-controlled array antenna which is composed of individual antennas and has an azimuth pivot angle range that can be achieved by a steering angle, wherein each individual antenna has an element factor describing the individual antenna gain as a function of the spatial angle, and the array antenna has an array factor which describes the array antenna gain resulting from the arrangement and the number of individual antennas as a function of the spatial angle, wherein the array antenna gain has a plurality of main maxima which are substantially equally large, but which are, with regard to the total gain resulting from the element factor and the array antenna gain, attenuated towards increasing steering angles, wherein in the method - the earth observation image is produced on the basis of a multi-look processing, i.e. on the basis of the processing of an overall acquisition of a region which is composed of a plurality of partial acquisitions of the region (so-called looks) produced by illumination across respective different viewing angle ranges, wherein the partial acquisitions are respectively filtered out of the overall acquisition, wherein - portions of the synthetic aperture having, at particular viewing angles, a signal-to-noise ratio which is smaller than a predeterminable limit value, are made usable by a signal-to-noise-dependent summation of the individual looks, wherein the summation either - is derived, independent of the location, directly from the azimuth antenna pattern by a normalized correction of the antenna pattern in the individual looks, wherein, first, the antenna pattern is corrected and then a normalization is carried out in each look such that at a particular azimuth angle or, if the operation is carried out in the spectrum, at a particular azimuth frequency specific to each look the product of inverse antenna pattern and normalization in each look results in a value of one, or - is carried out in a location-dependent manner by a signal-to-noise-dependent weighting of the looks which is different at each pixel position, wherein the weighting function is produced according to desired optimization criteria. - the earth observation image is produced on the basis of a multi-look processing, i.e. on the basis of the processing of an overall acquisition of a region which is composed of a plurality of partial acquisitions of the region (so-called looks) produced by illumination across respective different viewing angle ranges, wherein the partial acquisitions are respectively filtered out of the overall acquisition, wherein - portions of the synthetic aperture having, at particular viewing angles, a signal-to-noise ratio which is smaller than a predeterminable limit value, are made usable by a signal-to-noise-dependent summation of the individual looks, wherein the summation either - is derived, independent of the location, directly from the azimuth antenna pattern by a normalized correction of the antenna pattern in the individual looks, wherein, first, the antenna pattern is corrected and then a normalization is carried out in each look such that at a particular azimuth angle or, if the operation is carried out in the spectrum, at a particular azimuth frequency specific to each look the product of inverse antenna pattern and normalization in each look results in a value of one, or - is carried out in a location-dependent manner by a signal-to-noise-dependent weighting of the looks which is different at each pixel position, wherein the weighting function is produced according to desired optimization criteria. - is derived, independent of the location, directly from the azimuth antenna pattern by a normalized correction of the antenna pattern in the individual looks, wherein, first, the antenna pattern is corrected and then a normalization is carried out in each look such that at a particular azimuth angle or, if the operation is carried out in the spectrum, at a particular azimuth frequency specific to each look the product of inverse antenna pattern and normalization in each look results in a value of one, or - is carried out in a location-dependent manner by a signal-to-noise-dependent weighting of the looks which is different at each pixel position, wherein the weighting function is produced according to desired optimization criteria.