This paper presents a convergent weighted-averaging interpolation scheme designed to enhance the detail in the analysis of randomly spaced atmospheric data. The scheme is based on the Fourier integral representation, assuming that atmospheric variables can be represented as the sum of an infinite number of independent waves. The practical limitations include the need for reasonably uniform data distribution and accurate data, with the effect of inaccuracies controlled by stopping the convergence process before significant amplification. The scheme has been tested on 500-mb height data over the United States, producing results comparable to manual analysis. Further tests on sea level pressure data and regional airways data demonstrate its applicability to mesoscale wavelengths. The paper discusses the development of the interpolation scheme, including the definition of a smoothed function and the weight factor, and presents experimental results showing the effectiveness of the method in recovering lost details through iterative interpolation. The conclusions highlight the advantages of the scheme, such as computational simplicity and the ability to handle non-uniform data distributions, while also noting practical limitations and suggestions for future improvements.This paper presents a convergent weighted-averaging interpolation scheme designed to enhance the detail in the analysis of randomly spaced atmospheric data. The scheme is based on the Fourier integral representation, assuming that atmospheric variables can be represented as the sum of an infinite number of independent waves. The practical limitations include the need for reasonably uniform data distribution and accurate data, with the effect of inaccuracies controlled by stopping the convergence process before significant amplification. The scheme has been tested on 500-mb height data over the United States, producing results comparable to manual analysis. Further tests on sea level pressure data and regional airways data demonstrate its applicability to mesoscale wavelengths. The paper discusses the development of the interpolation scheme, including the definition of a smoothed function and the weight factor, and presents experimental results showing the effectiveness of the method in recovering lost details through iterative interpolation. The conclusions highlight the advantages of the scheme, such as computational simplicity and the ability to handle non-uniform data distributions, while also noting practical limitations and suggestions for future improvements.