## Str (Texture aspect ratio)

Str is a measure of uniformity of the surface texture. The value is obtained by dividing the horizontal distance in the direction in which the auto-correlation function decays to the value[s] (0.2 by default) the fastest (equivalent to Sal) by the horizontal distance in the direction of the slowest decay of auto-correlation function to the value[s].

Auto-correlation function

In image processing, an auto-correlation function is a measure of the matching ratio between an image rendered in different coordinates and the original image.

The auto-correlation function used for the calculation of Sal and Str is as follows:

The following explains this function by using the X direction only for simplicity.

Suppose that there is a data of a height difference as shown below.

The auto-correlation of this data is represented by the following shape:

Simply speaking, an auto-correlation function determines the overlapping area of the data of different height data and the original height data.

(Yellow areas in the figure below.)

When the difference is small, the overlapping area is large and so as the auto-correlation value.

When the difference is large, the overlapping area is small and so as the auto-correlation value.

A steep height difference decreases an auto-correlation immediately because even a small difference causes a great change in the shape.

A gradual height difference decreases an auto-correlation slowly because the shape does not change until the difference becomes large.

Since Sal determines the distance at which the auto-correlation decreases the fastest, it can be used for the judgment of whether there is a point at which the surface height changes abruptly.

Since Str determines the ratio of distances at which the auto-correlation decreases the fastest and slowest, it can be used for the judgment of the presence of lay.