The CAKE Command

The CAKE command is so called, because it allows an arbitrary user ``cake'' of data to be defined, and integrated to one of a large choice of single and multiple scans.

When the CAKE command is first entered, an initial ``cake'' is defined. First the beam centre is defined in the same manner as the BEAM CENTRE command; see Section 11.4, Page . This is followed by graphical input for the STARTING AZIMUTH, END AZIMUTH, INNER LIMIT, and lastly the OUTER LIMIT. All these values expect the OUTER LIMIT have defaults which may be used instead, by clicking within the prompt boxes.

The defined ``cake'' or integration area, will be drawn on top of the image in inverse video. The CAKE sub-menu now appears. This is shown in Figure 40. If the CAKE sub-menu is exited, and re-entered within the same FIT2D session, the defined ``cake'' is remembered.

Figure 40: The CAKE Sub-Menu

The following commands are available:

EXIT: Exit CAKE sub-menu and return to calling menu.

INTEGRATE: Integrate currently defined ``cake'' region, with a choice of the number of azimuthal and radial/2-theta output pixels. This allows enormous flexibility in defining intensity versus azimuthal angle scans, $2\theta$ scans, multiple $2\theta$ scans, and polar transformations.

INNER RADIUS: Change inner radius/2-theta angle of the currently defined ``cake'' integration region.

ZOOM IN: Graphical region definition

?: List of available commands and short descriptions.

END AZIMUTH: Change end azimuth of the currently defined ``cake'' integration region.

OUTER RADIUS: Change outer radial/2-theta angle of the currently defined ``cake'' integration region.

Z-SCALING: Automatic or user control of intensity display range; see Section 5.3, Page .

HELP: Detailed help text

EXCHANGE: Swap current data with the ``memory''; see Section 5.2, Page .

START AZIMUTH: Change starting azimuthal angle of the currently defined ``cake'' integration region.

MASK: Mask or Un-mask data (masked pixels are not re-binned); see Section 5.7, Page .

BEAM CENTRE: Change beam centre, which defines the zero angle for integration; see Section 11.4, Page .

FULL: Set ROI to be all of the currently defined data.

UN-ZOOM: Zoom out to see more of the data

ASPECT RATIO: Control automatic correct aspect ratio (or not). After integration, the output is often highly non-square. For better display it is often better to set AUTOMATIC CORRECT ASPECT RATIO IMAGE DISPLAY to NO.

When a suitable ``cake'' has been defined and ``bad'' pixels masked out, the INTEGRATION command should be selected. The TYPE OF AZIMUTHAL/RADIAL OR 2-THETA TRANSFORM control form appears. An example is shown in Figure 41.

Figure 41: The TYPE OF AZIMUTHAL/RADIAL OR 2-THETA TRANSFORM Control Form

The following parameters may be controlled:

START AZIMUTH: Change starting azimuthal angle of the currently defined ``cake'' integration region.

END AZIMUTH: Change end azimuth of the currently defined ``cake'' integration region.

INNER RADIUS: Change inner radius/2-theta angle of the currently defined ``cake'' integration region.

OUTER RADIUS: Change outer radial/2-theta angle of the currently defined ``cake'' integration region.

SCAN TYPE: Allows one of 4 different types of integrated scans to be selected:

2-THETA: This is an equal angle scan, equivalent to a $2\theta$ scan on a powder diffractometer. The scale is in degrees.

Q-SPACE: This is similar to the 2-THETA scan, but the output elements are in equal Q-range bins. The scale is in inverse nanometres. The definition of Q is $(4\pi / \lambda) sin(2\theta / 2)$, where $2\theta$ is the angle of the scattering as recorded on the detector relative to the direct beam.

RADIAL: This is an equal radial distance element scan. The scale is in millimetres.

D-SPACINGS: This converts pixel angles to equivalent D-spacings and outputs an scan in equal D-spacing distance pixels.

AZIMUTH BINS: Number of bins in the output scan in the azimuthal sense. This may be increased up to the size of the program array in the second dimension.

RADIAL BINS: Number of bins in the output scan in the radial, $2\theta$, or Q-space sense. This may be increased up to the size of the program array in the first dimension.

CONSERVE INT.: NO means that the output intensities are normalised by the number of contributing pixels (although geometrical corrections may be applied). This is appropriate for producing the equivalent of a $2\theta$ scan, and for a Q-space scan, but does not converse total intensity. For applications which require integrated intensities to be conserved, this should be set to YES.

POLARISATION: YES to apply a polarisation correction to the intensities during the integration.

FACTOR: This is the polarisation factor which is used if the polarisation correction is applied.

The polarisation factor is defined as $(I_h - I_v) / (I_h + I_v)$, where $I_h$ is the horizontal component and $I_v$ is the vertical component. (Horizontal should normally correspond to the X-direction of the image.)

DISTANCE: The sample to detector distance in millimetres.

GEOMETRY COR.: YES corrects a flat ``scan'' to the equivalent of a $2\theta$ scan, or a Q-space scan. (CONSERVE INT. should be set to NO). These are the effect of change of distance and obliqueness at higher angles for the flat image plate compared to a detector on a $2\theta$ arm, always facing the sample.

By setting azimuthal bins to 1, a single 1-D radial/$2\theta$/Q-space scan can be obtained.

By setting the number of radial bins to 1, and selecting the ``cake'' as an annulus about a ring, or an arc peak, an integration of intensity versus azimuth may be obtained.

Leaving both these numbers greater than 1, a 2-D polar transform is obtained. In the output array the X-direction is used to store the radial/$2\theta$/Q-space bins and the Y-direction the azimuthal bins¹⁰.

An example of the result of such a transform is shown in Figure 42.

Figure 42: Example of a Polar Transform of a Powder Pattern

Here the powder rings have become straight lines, at equal $2\theta$ angle. Any wobble in the lines shows inaccuracy in the beam centre, or the detector tilt angles, or spatial distortion in the detector, or maybe deviatoric stress in the sample.

The black region at zero and low $2\theta$ is the beam-stop shadow, and the black regions at high $2\theta$ are area outside the rectangular input region.