What is interpolation?
Interpolation is the process of estimating unknown values that fall between known values.
In this example, a straight line passes through two points of known value. You can estimate the point of unknown value because it appears to be midway between the other two points. The interpolated value of the middle point could be 9.5.
Spatial interpolation calculates an unknown value from a set of sample points with known values that are distributed across an area. The distance from the cell with unknown value to the sample cells contributes to its final value estimation.
The unknown value of the cell is based on the values of the sample points as well as the cell's relative distance from those sample points.
You can use spatial interpolation to create an entire surface from just a small number of sample points; however, more sample points are better if you want a detailed surface.
In general, sample points should be well-distributed throughout the study area. Some areas, however, may require a cluster of sample points because the phenomenon is transitioning or concentrating in that location. For example, trying to determine the size and shape of a hill might require a cluster of samples, whereas the relatively flat surface of the surrounding plain might require only a few.
Whether you are concerned with the amount of rainfall, concentrations of pollution, or the differences in elevation, it is impossible to measure these phenomena at every point within a geographic area. You can, however, obtain a sample of measurements from various locations within the study area, then, using those samples, make inferences about the entire geographic area. Interpolation is the process that enables you to make such an inference.
The primary assumption of spatial interpolation is that points near each other are more alike than those farther away; therefore, any location's values should be estimated based on the values of points nearby.
Interpolating the sample points' values creates a surface. As with all of the cells, the unknown value of the light-blue cell in the center will be estimated based on values of the surrounding sample points.
With spatial interpolation, your goal is to create a surface that models the sampled phenomenon in the best possible way. To do this, you start with a set of known measurements and, using an interpolation method, estimate the unknown values for the area. You then make adjustments to the surface by limiting the size of the sample and controlling the influence the sample points have on the estimated values.