Synthetic Surfaces

Beside functions for analysis of measured data, Gwyddion provides several generators of artificial surfaces that can be used for testing or simulations also outside Gwyddion.

All the surface generators share a certain set of parameters, determining the dimensions and scales of the created surface and the random number generator controls. These parameters are described below, the parameters specific to each generator are described in the corresponding subsections.

Image parameters:

Horizontal, Vertical size

The horizontal and vertical resolution of the generated surface in pixels.

Square image

This option, when enabled, forces the horizontal and vertical resolution to be identical.

Width, Height

The horizontal and vertical physical dimensions of the generated surface in selected units. Note square pixels are assumed so, changing one causes the other to be recalculated.

Dimension, Value units

Units of the lateral dimensions (Width, Height) and of the values (heights). The units chosen here also determine the units of non-dimensionless parameters of the individual generators.

Like Current Channel

Clicking this button fills all the above parameters according to the current channel.

Note that while the units of values are updated, the value scale is defined by generator-specific parameters that might not be directly derivable from the statistical properties of the current channel. Hence these parameters are not recalculated.

Replace the current channel

This option has two effects. First, it causes the dimensions and scales to be automatically updated each time the function is used as if Like Current Channel was clicked. Second, it makes the generated surface replace the current channel instead of creating a new channel.

Random generator controls:

All generated surfaces are periodic (i.e. perfectly tilable).

Random seed

The random number generator seed. Choosing the same parameters and resolutions and the same random seed causes the same surface to be generated, even on different computers. Different seeds lead to different surfaces with the same overall characteristics given by the generator parameters.

New

Replaces the seed with a random number.

Randomize

Enabling this option makes the seed to be chosen randomly every time the generator is run. This permits to conveniently re-run the generator with a new seed simply by pressing Ctrl-F (see keyboard shortcuts).

Spectral

Spectral synthesis module creates randomly rough surfaces by constructing the Fourier transform of the surface according to specified parameters and then performing the inverse Fourier transform to obtain the real surface.

The Fourier image parameters define the shape of the PSDF, i.e. the Fourier coefficient modulus, the phases are chosen randomly. At present, all generated surfaces are isotropic, i.e. the PSDF is radially symmetric.

RMS

The root mean square value of the heights (or of the differences from the mean plane which, however, always is the z = 0 plane).

Minimum, maximum frequency

The minimum and maximum spatial frequency. Increasing the minimum frequency leads to “flattening” of the image, i.e. to removal of large features. Decreasing the maximum frequency limits the sharpness of the features.

Enable Gaussian multiplier

Enables the multiplication of the Fourier coefficients by a Gaussian function that in the real space corresponds to the convolution with a Gaussian.

Autocorrelation length

The autocorrelation length of the Gaussian (see section Statistical Analysis for the discussion of autocorrelation functions).

Enable power multiplier

Enables multiplication by factor proportional to 1/kp, where k is the spatial frequency and p is the power. This permits to generate various fractal surfaces.

Power

The power p.

Artificial surfaces generated by spectral synthesis: a narrow range of spatial frequencies (left), Gaussian random surface (centre) and a fractal surface generated with power multiplier of 1.5 (right).

Objects

The object placement method permits to create random surfaces composed of features of a particular shape. The algorithm is simple: the given number of objects is placed on random positions at the surface. For each object placed, the new heights are changed to max(z, z0 + h), where z is the current height at a particular pixel, h is the height of the object at this pixel (assuming a zero basis) and z0 is the current minimum height over the basis of the object being placed.

Shape

The shape (type) of placed objects. At present the possibilities include half-spheres, boxes, pyramids, tetrahedrons and some more weird shapes.

Coverage

The average number of times an object covers a pixel on the image. Coverage value of 1 means the surface would be exactly once covered by the objects provived that thay covered it uniformly. Larger values mean more layers of objects – and slower image generation.

Size

The object size, usually the side of a containing square.

Aspect Ratio

The ratio between the x and y dimensions of an object – with respect to same base proportions.

Changing the aspect ratio does not always imply mere geometrical scaling, e.g. objects called nuggets change between half-spheres and rods when the ratio is changed.

Height

A quantity proportional to the height of the object, normally the height of the highest point.

Checking Scales with size makes unperturbed heights to scale proportionally with object size. Otherwise the height is independent on size.

Orientation

The rotation of objects with respect to some base orientation, measured counterclockwise.

Each parameter can be randomized for individual objects, this is controlled by Variance. For multiplicative quantities (all except orientation), the distribution is log-normal with the RMS value of the logarithmed quantity given by Variance.

Artificial surfaces generated by object placement: spheres of varied size (left), narrow thatches of varied direction (centre), nuggets of varied aspect ratio (right).