The autocorrelation function may be used for enhancing periodic structures and is also used in roughness analysis for extracting correlation length parameters. If the image is periodic the autocorrelation function will exhibit peaks with the same periodic length as the source image as shown in the below example
The Autocorrelation function is activated from ProcessingàAuto Correlation
Cross-correlation
The Cross-correlation function between two images can be obtained from an image secondary to the main image window by right-clicking on Cross Correlate with Main.
The correlation function formulas are shown in the reference guide.
Correlation averaging is a powerful tool for analyzing images and profile data containing repeated structures like atoms, molecules or calibration patterns. The technique can find all the repeated structures and add them so that an average image of the recurrent structure is obtained. In ideal situations the signal-to-noise-ratio can be improved by the square root of the number of additions. In contrast to other filtering techniques it will not filter specific frequencies but preserve all frequencies that are represented in the repeated structure. The following example is based on an STM image of Didodecyl-benzene molecules self-assembled on a graphite substrate.
Pressing the associated key 
starts the correlation averaging. If the zoom image is active SPIP will use this image as the structure that has to be recognized and averaged, otherwise SPIP automatically determines a suitable template based on unit cell detection. Let us assume you define the template by the rectangle marker tool 
:
The template will also be seen in the zoom window:
Start the correlation averaging by the toolkey or from the menu: Processing®Average®Marked Area, Correlation Averaging.
The process will create a cross correlation image displaying peaks associated with the individual areas matching the template. From the cross correlation peaks and the raw image the Average image together with the Standard deviation image are calculated. The latter will contains detailed information about the uniformity of the structures and noise in the instrument. Also, the standard deviation image may provide important information about structural uniformity, and for example reveal details on how self-assembled molecules are attached to a substrate. The SD Image shown below displays low SD values at the right part of the benzene rings indicating that this part of the molecule is the part most fixed to the substrate.
The same procedure can also be used for profiles as shown below. The first picture shows the original curve with the cursors set for marking the template defining the structure to search for. The distance between the cursors will define the final size of the average curve. You may also apply the curve zoom function for defining the template. The second curve below shows the average result.
