Basic Operations

Value-reading and basic geometrical operations represent the core of any data processing program. Gwyddion offers a wide set of functions for data scaling, rotation, resampling or profile extraction. This section describes these simple but essential functions.

Simple Image Operations

Most basic operations can be found in Data ProcessBasic Operations menu; some are also carried out by tools.

Scale

Data ProcessBasic OperationsScale

Resample the data to different pixel dimensions using the selected interpolation method.

Crop

The Crop tool can crop an image either in place or putting the result to a new image (with option Create new image). With Keep lateral offsets option enabled, the top left corner coordinates of the resulting image correspond to the top left corner of the selection, otherwise the top left corner coordinates are set to (0, 0).

Extend

Data ProcessBasic OperationsExtend

Extending is essentially the opposite of cropping. Of course, adding more real data around the image borders is only possible by measuring more data. So this function offers, instead, several simple artificial extension methods such as mirrored and unmirrored periodic continuation or repetition of boundary values.

Rotation

Rotation of data by 90 degrees or by user-specified amount is done using some of the rotate functions: Data ProcessBasic OperationsRotate Clockwise, Rotate Anticlockwise or Rotate. Rotation by 180° is equivalent to Flip Both.

Flip

Flip the data horizontally (i.e. about the vertical axis) and vertically (i.e. about the horizontal axis) with Data ProcessBasic OperationsFlip Horizontally and Flip Vertically, respectively.

Flip Both (Rotate by 180°)

Flip the data about the centre (i.e. about both axes) with Data ProcessBasic OperationsFlip Both.

Invert Value

Data ProcessBasic OperationsInvert Value

The inversion function inverts the data about the mean value, keeping the mean value unchanged.

Limit Range

Data ProcessBasic OperationsLimit Range

Data range can be limited by cutting values outside the specified range. The range can be set numerically or taken from the false color map range previously set using the Color range tool and it is also possible to cut off outliers farther than a chosen multiple of RMS from the mean value.

Square Samples

Data ProcessBasic OperationsSquare Samples

Upsample the data (along the axis with larger pixel size) to make pixels square. Most scans have pixels with 1:1 aspect ratio, therefore this function has no effect on them.

Tilt

Data ProcessBasic OperationsTilt

Tilt the data by a gradient or angle, specified numerically.

Dimensions and Units

Data ProcessBasic operationsDimensions and Units

Change physical dimensions, units or value scales and also lateral offsets. This is useful for the correction of raw data that have been imported with wrong physical scales or as a simple manual recalibration of dimensions and values.

Note

The settings are remembered between invocations. This allows repeating the same recalibration on multiple data. It also makes relatively easy to apply some rescaling from the last time even if you do not want to. When unsure, always start by pressing the Reset button to clear all the offsets and factors.

Reading Values

The simplest value reading method is to place the mouse cursor over the point you want to read value of. The coordinates and/or value is then displayed in the data window or graph window status bar.

Read Value Tool

The Read Value tool offers more value reading possibilities: it displays coordinates and values of the last point of the data window the mouse button was pressed. It can average the value from a circular neighbourhood around the selected point, this is controlled by option Averaging radius. When the radius is 1, the value of a single pixel is displayed (as the simplest method does). Button Set Zero shifts the surface to make the current z the new zero level.

Read Value can also display the inclination of the local facet or local surface curvature. Averaging radius again determines the radius of the area to use for the plane fit. Curvature in particular need relatively large areas to be reliable.

Inclinations

In all Gwyddion tools, facet and plane inclinations are displayed as the spherical angles (ϑφ) of the plane normal vector.

Angle ϑ is the angle between the upward direction and the normal, this means that ϑ = 0 for horizontal facets and it increases with the slope. It is always positive.

Angle φ is the counter-clockwise measured angle between axis x and the projection of the normal to the xy plane, as displayed on the following figure. For facets it means φ corresponds to the downward direction of the facet.

Measuring facet orientation

Surface facet (displayed blue) orientation measured as the counterclockwise angle from x-axis to the projection of facet normal vector n to xy plane.

Distance Tool

Distances and differences can be measured with the Distance tool. It displays the horizontal (Δx), vertical (Δy) and total planar (R) distances; the azimuth φ (measured identically to inclination φ ) and the endpoint value difference Δz for a set of lines selected on the data.

The distances can be copied to the clipboard or saved to a text file using the buttons below the list.

Distance tool dialog screenshot

Distance tool with three selected lines.

Profile Extraction

The Profile tool extracts profiles drawn and adjusted using mouse in the image, shown in a live preview in the dialog. Profiles can be of different thickness which means that more neighbour data perpendicular to profile direction are used for evaluation of one profile point for thicker profiles. This can be very useful for noise suppression while measuring regular objects.

After profiles are chosen, they can be extracted to graphs (separate or grouped in one Graph window) for further analysis using Graph functions.

Profile tool dialog screenshot

Profile tool with three extracted profiles and expanded options.

The profile curve is constructed from data sampled at regular intervals along the selected line. Values in points that do not lie exactly at pixel centres (which normally occurs for oblique lines) are interpolated using the chosen interpolation mode. Unless an explicit number of samples to take is set using the Fix res. option, the number of samples corresponds to the line length in pixels. This means that for purely horizontal or purely vertical lines no interpolation occurs.

Profile subpixel interpolation scheme

Illustration of data sampling in profile extraction for oblique lines. The figures on the left show the points along the line where the values are read for natural and very high resolution. The graphs on the right show the extracted values. Comparison of the natural and high resolution profiles taken with Round interpolation reveals that indeed natural-resolution curve points form a subset of the high-resolution points. The influence of the interpolation method on values taken in non-grid positions is demonstrated by the lower two graphs, comparing Round and Key interpolation at high resolution.

In the measurement of profiles across edges and steps, it is often important to choose the profile direction perpendicular to the edge. The buttons Improve Direction and Improve All can help with this. The first attempts to improve the orthogonality of the currently edited line, while the second tries to improve all selected lines. The line centres are preserved; only the directions of the profiles are adjusted. The automatic improvement is not infallible, but it usually works well for reasonably clean standalone edges.

Radial profiles

The standard profiles described above correspond to Linear profiles mode in the tool. It is also possible to extract angularly averaged shapes of symmetrical surface features, by selecting the Radial profiles mode. In this case the abscissa of the extracted graph is the distance from the centre instead of the distance along the line. The origin is in the centre of the selected line (and denoted with a tick).

Although the line can be adjusted manually, finding the best centre for the radial profile manually may be difficult. Therefore, the tool can perform the precise location of the best centre itself. You only need to select the line approximately and then press Symmetrize to adjust the currently edited line or Symmetrize All to adjust all lines. The lines will be shifted slightly to minimise the differences between line profiles taken in different directions from the centre.

Conversion to other data types

Function Data ProcessBasic OperationsVolumize creates volume data from an image. The height field is interpreted as the surface of a solid object, as usual in AFM. Voxels below the surface (inside the material) are filled with 1s while voxels above the surface (outside) are filled with 0s. The z-coordinate of the volume data therefore corresponds to the image values, while the volume data values are unitless.

Function Data ProcessBasic OperationsVolumize Layers creates volume data from a sequence of images. All images in the file must have the same dimensions. They are then treated as planes in the volume data that are created by stacking the images. The z-coordinate of the volume data therefore corresponds to the stack index (and can be specified in the dialogue), while the volume data values have the same units as the image data.

Function Data ProcessBasic OperationsXYZize creates XYZ data from an image. Each image pixel corresponds to one point in the created XYZ data. Therefore, the xy coordinates thus form a regular grid and all units are the same as for the image.