Spherical Crystal Projection

For the Crystal Spectrometer Imaging Model, a series of rays are projected from each pixel in the detector grid onto the surface of a curved crystal. The rays are reflected off the crystal surface then must pass through an aperture and intersect the plasma in order to contribute to the total intensity at the detector. For each detector pixel, the range of angles over which the rays hit the crystal surface determines the photon energy range detected (via. Bragg diffraction).

Controls for the crystal spectrometer calculation can be accessed from Detector settings by selecting Crystal spectrometer for the projection type. The following figure shows the crystal spectrometer user interface controls for an example calculation:

The top part of the widget contains settings for the crystal properties, and geometry of the spectrometer (Coordinate values are in the same frame of reference as the source plasma) :

Spectrometer type - type of curvature of the crystal used for the spectrometer. Currently convex, spherical, toroidal, elliptical and transmission crystal options are available.
Crystal curvature - radius of curvature of the crystal surface. Note that it is possible to approximate a flat crystal by using a large value for the curvature.
Crystal lattice spacing - 2d lattice spacing for the crystal. One of several crystals can be selected from the combo box or a specific value may be entered.
Central Bragg angle - the angle between a ray incident from the ‘source position’ coordinate and the crystal surface at the center of the crystal.
Crystal reflectivity - clicking the ‘Crystal Reflectivity’ checkbox will switch on the crystal response function during the calculation. The integrated reflectivity function for the crystal can be specified by clicking the ‘Set Table Values’ button and entering a 2-column table of numbers (integrated reflectivity in radians as a function of photon energy in eV).
Source position - position which the spectrometer is aligned to.
Crystal position - position of the center of the crystal surface.
Plasma-slit distance, crystal-detector distance - distance from plasma to slit, crystal to detector.

The lower part of the widget has a several settings for controlling the number of divisions used to divide the crystal, slit and detector surface. Each grid is divided into a user specified number of horizontal and vertical pixels. The number of horizontal pixels used for the slit determines how well the angular width of the plasma source is resolved by each crystal surface element. Since each crystal surface element diffracts a range of photon energies, the number of crystal surface points in the horizontal direction determines how well the spectral distribution of the source is resolved at the detector.

Some ‘rule of thumb’ guidelines to help choose grid values for crystal spectrometer settings can be given as follows:

The horizontal spacing of the aperture grid should be sufficiently fine so that each crystal surface element has at least several rays that intersect the plasma.
The vertical size of the crystal elements should be less than the vertical size of the aperture, to avoid introducing artifacts in the detector image.
The number of horizontal crystal pixels should be chosen so that the range of diffracted photon energies from each surface element is small enough to give the required spectral resolution.
To save calculation time, a single vertical pixel can be used for the detector and crystal grids if the plasma is uniform or if only the spectral information is of interest.

Interpolation

During the detector calculation, each crystal surface element can be further sub-divided into a rectangular grid to effectively greatly increase the number of surface elements with minimal additional computational overhead. The angle resolved specific intensity is assumed to be uniform across each surface element, whilst the ray tracing calculation of the intensity contributions to the detector image is carried out using the sub-divided grid.

Viewing the spectrometer setup

A 3-dimensional view of the crystal, slit, and detector positions can be accessed via the Detector-Target orientation tool from the Display menu. The slit aperture is shown by a blue rectangle, the crystal by a light gray surface and the detector by a dark gray rectangle - see figure below. A series of white lines extending from the spectrometer ‘source position’ coordinate to each point on the crystal surface grid, and reflected off onto the detector plane are also shown. These can be used as a guide to check whether the sizes of the slit, crystal surface and detector are appropriate for rays from the source to propagate to the detector surface via the crystal. In addition to rotating and zooming, the view can also be translated by clicking and dragging with the middle mouse button (or scroll wheel).

Detector Setup: Crystal Spectrometer Imaging Model

Interpolation

Viewing the spectrometer setup