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.
The horizontal and vertical resolution of the generated surface in pixels.
This option, when enabled, forces the horizontal and vertical resolution to be identical.
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.
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.
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.
This option has two effects. First, it causes the dimensions and scales to be automatically set to those of the current channel. Second, it makes the generated surface replace the current channel instead of creating a new channel.
This option has two effects. First, it causes the dimensions and scales to be automatically set to those of the current channel. Second, it makes the generator to start from the surface contained in the current channel and modify it instead of starting from a flat surface. Note this does not affect whether the result actually goes to the current channel or a new channel is created.
Random generator controls:
The random number generator seed. Choosing the same parameters and resolutions and the same random seed leads to the same surface, even on different computers. Different seeds lead to different surfaces with the same overall characteristics given by the generator parameters.
Replaces the seed with a random number.
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 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 generated surfaces are periodic (i.e. perfectly tilable).
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.
The root mean square value of the heights (or of the differences from the mean plane which, however, always is the z = 0 plane). Button Like Current Channel sets the RMS value to those of the current channel.
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.
Enables the multiplication of the Fourier coefficients by a Gaussian function that in the real space corresponds to the convolution with a Gaussian.
Enables the multiplication of the Fourier coefficients by a function proportional to 1/(1 + k2T2)3/4, where T is the autocorrelation length. So, the factor itself is not actually Lorentzian but it corresponds to Lorentzian one-dimensional power spectrum density which in turn corresponds to exponential autocorrelation function (see section Statistical Analysis for the discussion of autocorrelation functions). This factor decreases relatively slowly so the finite resolution plays usually a larger role than in the case of Gaussian.
The autocorrelation length of the Gaussian or Lorentzian factors (see section Statistical Analysis for the discussion of autocorrelation functions).
Enables multiplication of Fourier coefficients by factor proportional to 1/kp, where k is the spatial frequency and p is the power. This permits to generate various fractal surfaces.
The power p.
The object placement method permits to create random surfaces composed of features of a specific 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 specific 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. The algorithm considers the horizontal plane to be filled with identical copies of the surface, hence, the generated surfaces are also periodic (i.e. perfectly tilable).
The shape (type) of placed objects. At present the possibilities include half-spheres, boxes, pyramids, tetrahedrons and some more weird shapes.
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 assuming that they covered it uniformly. Larger values mean more layers of objects – and slower image generation.
The lateral object size, usually the side of a containing square.
The ratio between the x and y dimensions of an object – with respect to some default 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.
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.
Button Like Current Channel sets the height value to a value based on the RMS of the current channel.
The rotation of objects with respect to some base orientation, measured counterclockwise.
The shapes can be truncated at a certain height, enabling creation of truncated cones, pyramids, etc. The truncation height is given as a proportion to the total object height. Unity means the shape is not truncated, zero would mean complete removal of the object.
Each parameter can be randomized for individual objects, this is controlled by Variance. For multiplicative quantities (all except orientation and truncation), the distribution is log-normal with the RMS value of the logarithmed quantity given by Variance.
Random uncorrelated point noise is generated independently in each pixel. Several distributions are available.
The distribution of the noise value. The possibilities include Gaussian, exponential, uniform and triangular distributions.
The noise can be generated as symmetrical or one-sided. The mean value of the distribution of a symmetrical noise is zero, i.e. the mean value of data does not change when a symmetrical noise is added. One-sided noise only increases (if positive) or decreases (if negative) the data values.
Root mean square value of the noise distribution. More precisely, it is the RMS of the corresponding symmetrical distribution in the case the distribution is one-sided.
Line noise represents noise with non-negligible duration that leads to typical steps or scars (also called strokes) in the direction of the fast scanning axis. Parameters Distribution, Direction and RMS have the same meaning as in Point noise. Other parameters control the lateral characteristics of the noise.
Two basic line defect types are available: steps and scars. Steps represent abrupt changes in the value that continue to the end of the scan (or until another step occurs). Scars are changes of the value with a finite duration, i.e. the values return to the original level after some time.
Steps have the following parameters:
Average number of defects per scan line, including any dead time (as determined by parameter Within line).
Fraction of the time to scan one line that corresponds to actual data acquisition. The rest of time is a dead time. Value 1 means there is no dead time, i.e. all steps occur within the image. Value 0 means the data acquisition time is negligible to the total line scan time, consequently, steps only occur between lines.
For cumulative steps the random step value is always added to the current value offset; for non-cumulative steps the new value offset is directly equal to the random step value.
Scars have the following parameters:
The fraction of the the image covered by defect if they did not overlap. Since the defect may overlap coverage value of 1.0 does not mean the image is covered completely.
Scar length in pixels.
Variance of the scar length, see Objects for description of variances.
Regular geometrical patterns represent surfaces often encountered in microscopy as standards or testing samples such as ridges, steps or holes. Each type of pattern has its own set of geometrical parameters determining the shape and dimensions of various part of the pattern. Each parameter has a variance control, similar to Object synthesis, that permits to make the pattern irregular in some aspects.
The placement of the pattern in the horizontal plane is controlled by parameters in tab Placement, common to all pattern types:
The rotation of the pattern with respect to some base orientation, measured counterclockwise.
This tab also contains the deformation parameters. While enabling the variation of geometrical parameters makes the generated surface somewhat irregular the shape of its features is maintained. Deformation is a complementary method to introduce irregularity, specifically by distorting the pattern in the xy plane. It has two parameters:
The magnitude of the lateral deformation. It is a relative numerical quantity essentially determining how far the deformation can reach.
The characteristic size of the deformations. It describes not how far the features are moved but how sharply or slowly the deformation itself changes within the horizontal plane.