An overview of the Raster Interpolation toolset 

Release 9.3
Last modified January 23, 2009 
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Visiting every location in a study area to measure the height, magnitude, or concentration of a phenomenon is usually difficult or expensive. Instead, you can measure the phenomenon at strategically dispersed sample locations, and predicted values can be assigned to all other locations. Input points can be randomly or regularly spaced or based on some sampling scheme.
Surface interpolation functions create a continuous (or prediction) surface from sampled point values. The continuous surface representation of a raster dataset represents height, concentration, or magnitude (for example, elevation, pollution, or noise). Surface interpolation functions make predictions from sample measurements for all locations in a raster dataset, whether a measurement has been taken at the location or not. There are a variety of ways to derive a prediction for each location; each method is referred to as a model. With each model, there are different assumptions made of the data, and certain models are more applicable for specific data (for example, one model may account for local variation better than another). Each model produces predictions using different calculations.
The Inverse Distance Weighted (IDW) and Spline methods are referred to as deterministic interpolation methods because they assign values to locations based on the surrounding measured values and on specified mathematical formulas that determine the smoothness of the resulting surface. A second family of interpolation methods consists of geostatistical methods (such as Kriging), which are based on statistical models that include autocorrelation (the statistical relationship among the measured points). Because of this, not only do geostatistical techniques have the capability of producing a prediction surface, but they can also provide some measure of the certainty or accuracy of the predictions.
Learn more about surfaces and surface models.
Learn more about discrete vs. continuous features.
Learn more about functional surfaces.
Learn more about surface continuity.
The following table lists tools in the Interpolation toolset with a brief description of each. The Interpolation tools are generally divided into deterministic and geostatistical methods. IDW, Spline, and Trend are deterministic and Kriging is a geostatistical method. Topo To Raster and Topo To Raster By File use an interpolation method designed for creating continuous surfaces from contour lines; the method contains properties favorable for creating surfaces for hydrologic analysis.
Tool  Description 
IDW  Interpolates a surface from points using an inverse distance weighted technique 
Kriging  Interpolates a grid from a set of points using kriging 
Natural Neighbor  Interpolates a surface from points using a natural neighbor technique 
Spline  Interpolates a surface from points using a minimum curvature spline technique 
Topo to Raster  Interpolates a hydrologically correct surface from point, line, and polygon data 
Topo to Raster by File  Interpolates a hydrologically correct surface from point, line, and polygon data by using parameters specified in a file 
Trend  Interpolates a surface from points using a trend technique 