GRAPHICAL DISPLAY OF THREE-DIMENSIONAL (3-D) INTENSITY DATA FROM SINGLE-CRYSTAL REFLECTIONS

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GRAPHICAL DISPLAY OF THREE-DIMENSIONAL (3-D) INTENSITY DATA FROM SINGLE-CRYSTAL

REFLECTIONS

M. Pilotti, G. Mcintyre

To cite this version:

M. Pilotti, G. Mcintyre. GRAPHICAL DISPLAY OF THREE-DIMENSIONAL (3-D) INTENSITY

DATA FROM SINGLE-CRYSTAL REFLECTIONS. Journal de Physique Colloques, 1986, 47 (C5),

pp.C5-183-C5-187. �10.1051/jphyscol:1986524�. �jpa-00225841�

JOURNAL DE PHYSIQUE

Colloque C5, supplbment au no 8, Tome 47, aoat 1986

GRAPHICAL DISPLAY OF THREE-DIMENSIONAL (3-D) INTENSITY DATA FROM SINGLE-CRYSTAL REFLECTIONS

M.U.

and G.J. McINTYRE

Institut Laue-Langevin,

Grenoble Cedex, France

R6umb - Un programme elhentaire pour la visualisation et la manipulation des Z x tri-dimensionnels de donndes des pics de diffraction issus dlun monocristal sur un terminal graphique de type Evans et Sutherland PS300 est ddcrit. La superposition des enveloppes dlint&ration ou celle des

ellipsoides de resolution des algorithmes de traitement des donnges permet lldvaluation de l1ef f icaci te' des algori thmes. Quelques exemples montrant les possibilitds de diagnostic rapide de ce programme sont donnb.

Abstract - A simple program to display and manipulate 3-D arrays of counts of single-crystal diffraction reflections on an Evans and Sutherland PS300 graphics display is described. Superposition of integration envelopes or resolution ellipsoids from data-reduction algorithms allows assessment of the effectiveness of the algorithms. Some examples illustrating the diagnostic applications of the program are given.

I - INTRODUCTION

A dif fractometer equipped with a 2-D position-sensitiv6 detector may routinely collect a 3-D array of sampling counts for each reflection from a single crystal.

Various algorithms have been devised to take advantage of the three dimensionality of the data in order to optimize the estimate of the integrated intensity of the

reflection with respect to both the precision and the accuracy (see ref. 1 for a review of algorithms for neutron-diffraction data). The essential aim of most algorithms is to construct the 3-D contour of smallest volume that separates the.

counts in the reflection from the counts in the background, for example, by prior calculation of the resolution function, or by statistical analysis of the histogram of counts. The application of similar algorithms to single-counter data can be readily verified by inspection of the 1-D scan profile. Verification of the effectiveness of algorithms for position-sensitive detector data, however, is hindered by the difficulty of graphically displaying the intensity variation within the 3-D array of counts. Nevertheless such display is necessary for,

(a) development of the algorithms and associated software, (b) assessment of crystal quality at the start of an experiment,

(c) assessment of the suitability of a particular algorithm to a particular experiment, and

(d) inspection of reflections that have been flagged as abnormal by the algorithms.

In this paper we describe the display options and some diagnostic applications of RFLBOX, a simple program that we are developing to display and manipulate images of single-crystal reflections on an Evans and Sutherland PS300 graphics display.

(')present address : School of Chemistry. University of Briatol. Cantocks Close. GB-Bcistol BSB ITS.

Great-Britain

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986524

C5-184

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I1 - HARDWARE DESCRIPTION

In our installation the PS300 may be controlled by any one of a number of Digital Equipment VAX 11/750 computers, running under the VMS operating system. The computer is connected to the Motorola MC68000 graphic control microprocessor of the PS300 via a 9600-baud RS-232 serial interface. Our display system also includes a 19-inch colour calligraphic screen, 1 megabyte of dual-access memory, 12 function keys on the PS300 keyboard, 8 programmable control dials (function dials) and a data tablet.

A detailed description of the display system is given in the Evans and Sutherland PS300 Documentation Set (also see ref. 2).

I11 - SOFTWARE DESCRIPTION

The program RFLBOX is written in the VAX implementation of Fortran 77. The display of the data is made partly via calls to the Graphics Support Routines library of the PS300 and partly via the PS300 Command Language. These form a background object which is transferred to the PS300 for display and manipulation.

The integration envelope or resolution ellipsoid, being a (mostly smooth) surface, is well suited to repesentation by the wire-frame contouring frequently used to display electron scattering density in macromolecular model-building programs. On the other hand we have chosen to display all the counts in the data array as individual points, rather than by an adaption of wire-frame contouring, for two reasons. First, the dual aims of inspection of the reflection itself and evaluation of the suitability of a particular algorithm mean that we must be careful not to bias the display of the data by our expectations of the 3-D shape of the reflection, especially since these expectations may also be premises of the data reduction algorithm. Secondly, the visual contrast between the data and the integration envelope is enhanced if they are displayed in different ways.

To display simultaneously all the counts from a complete scan would in many cases be impractical. Therefore we display only the counts observed in a box placed about each reflection. The units along the three perpendicular box edges correspond to two perpendicular dimensions of a 2-D position-sensitive detector and the rotation angle of the crystal. Since the resolution conditions will in general change from one reflection to the next, even within the same scan, the dimensions of the box are variable.

The counts are represented on the display by a 3-D grid of points whose colours are varied from blue to red and whose luminosities are increased on a natural logarithmic scale of the count intensities. The colour and intensity variation gives an

immediate impression of the locations of the reflection peaks, while the logarithmic scale aids identification of anomalies in the reflection tails. We have found that with a five-fold division of the count intensity scale the displayed image gives a quick impression of the count distribution without being too confusing. Further subdivision of the scale may be acceptable for slowly varying distributions but the display is then often too cluttered in colour for the weaker reflections which have larger relative variations in the counts of neighbouring points. Table 1 gives the count scale and the corresponding colours and display intensities that we have found give a satisfactory representation of a 3-D reflection. The lowest intensity division contains mainly bickground counts and it is usually the most populated level. To avoid the peaks being masked by the background the colours and display intensities were chosen so that the points in this level are barely visible on the screen when all levels are displayed.

Superimposed on the array of counts is the ellipsoid that delimits the peak from the background. In the examples of Section IV the parameters of the ellipsoid have been determined by the algorithm of Wilkinson and Khamis / 3 / . A satisfactory impression of the extent and orientation of the ellipsoid is obtained by drawing the

cross-section of the ellipse in planes perpendicular to each major axis at the three points that divide the axis into four equal parts. Irregularly shaped integration envelopes could be included in a similar manner.

For detailed inspection of the distribution, the different intensity levels and the

ellipsoid are connected to separate function keys on the PS300 keyboard which permits

Count

1 to exp(Im/5)

Colour Display Intensity

blue 0.45

exp(Im/5) to exp(21m/5) cyan 0.70 exp(21m/5) to exp(31m/5) magenta 0.79 exp(31m/5) to exp(41m/5) green 0.85

exp(41m/5) to exp(Im) red 1.00

Table 1. - The count ranges and corresponding colours and display

intensities. I is the natural logarithm of the maximum count in the array.

The box surrounNing the array of counts is displayed with intensity 0.50, and the ellipsoid with intensity 1.0.

any level, or the ellipsoid, to be selectively switched on and off. Display of the lowest level on its own may reveal features in the background, such as planes of weak powder scattering. The object may be rotated, translated and scaled in real time by use of the function dials. In addition the ellipsoid may be made to blink at a user-controlled rate. Rotation of the image while the ellipsoid blinks allows ready verification that the integration envelope encompasses the counts above background.

Several reflections from one scan may be displayed simultaneously to allow checking of reflection overlap both in the count data and in the integration. Plot fifes to draw the displayed image on a digital plotter may also be created.

IV - PERFORMANCE

EXAMPLES

The PS300 can display up to about 50,000 vectors at a refresh rate of 30Hz without obvious flickering. Thus if all points are displayed the count array is limited to, for example, 30

30 x 50 points. Larger arrays can be inspected with some intensity levels switched off. The main rate-determining step in the present program is the calculation of the coordinates of each count and the allocation of the count to the vectar list to be displayed. The calculation for the 37,200 points in the full display corresponding to Fig. 1 required 100 seconds CPU time on a VAX 11/750.

Significant reduction of this time should be possible.

Figs. 1 and 2, which were obtained with the plot option, illustrate the diagnostic possibilities of the program. These scans were made on the multidetector

diffractometer D19a at the I.L.L. /4/. The detector is a gas-filled 2-D multi-wire proportional counter, 8 cm wide and curved along its height of 128 cm /5/. The data displayed at each step of the crystal rotation about the vertical instrument axis are the counts observed at the intersections of the horizontal anodes and the vertically curved cathodes. The anode and cathode spacings are 2.54 mm and 5.00 mm

respectively; the sample to detector distance is appoximately 1160 mm. Fig. 1 emphasizes that the display axes correspond not to reciprocal axes but to angles in instrumental space; two axes being nearly equivalent to polar angles on the Ewald sphere, and the third axis being the crystal rotation. The intersection of a reciprocal lattice line with the Ewald sphere is a curve in these axes.

Future improvements to be made to the program include;

(a) on-line modification of the integration envelope or ellipsoid parameters together with integration of the reflection intensity,

(b) on-line variation of the count intensity scale

(c) 9-space mapping via the cursor and data tablet to aid identification of satellite reflections, and

(d) optional smoothing of the data to improve the display of weak broad scattering

such as powder lines.

JOURNAL

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Fig. 1 - A stereographic plot of six adjacent 1 0 R reflections from a crystal of phenylquinhydrone. For clarity only the points in the strongest and the

next-to-weakest intensity levels are shown. The reciprocal lattice line lies

parallel to the rotation axis so that all six reflections may be observed with a

position-sensitive detector in a scan only fractionally longer than a scan for just

one reflection. The integration ellipsoids are clearly appropriate for the strong

reflections, but the ellipsoids interpolated for the two weak reflections (in the

centre of the figure) are slightly misoriented. This misorientation, which is due to

errors in the interpolation procedure, went undetected until the reflections were

inspected with RFLBOX. It can also be seen that the dimensions of the shell in which

background for a particular reflection is determined must be carefully chosen to

avoid contamination from neighbouring reflections.

Fig. 2.

A stereographic plot of a weak protein reflection which has nearly the same Bragg angle as a parasitic powder line from the aluminium heat shield of the cryostat. Only the points in the strongest and third-strongest intensity levels are displayed. The observation of such contaminated distributions led to improvements in the data-reduction algorithm, first to detect contaminated reflections, and then to l'subtract" the parasitic powder scattering from the distribution before integration of the intensity.

We thank Mr. Adrian Perkins for programming advice, and Drs. Sax Mason and Robert Stansfield for constructive criticism of the displayed images.

REFERENCES

/1/ Stansfield, R. F. D. and McIntyre, G. J., Neutron Scattering in the 'Nineties, Julich, January 1985, IAEA-CN-46/64, pp 191-198-

/2/ Pflugrath, J. W., Saper, M. A. and Ouiocho, F. A., Methods and A lications &

Crystallo ra hic Com utin (Ball, S. R. and Ashida, T. ---Clare- Oxford, 1$83Ppp 3 ' &

/3/ Wilkinson, C. and Khamis, H. W., Position-Sensitive Detection of Thermal Neutrons, (Convert, P. and Forsyth, J. B., Eds.), Academic Press, N& -983 pp

?ca=33K

/4/ Thomas, M., Stansfield, R. F. D., Berneron, M., Filhol, A., Greenwood, G., Jacobe, J., Feltin, D. and Mason, S. A., Position-Sensitive Detection of Thermal Neutrons, (Convert, P. and Forsyth, J. B., Eds.), Academic Press, New Z r m pp

- -

-

/5/ Jacobe, J., Feltin, D., Rambaud, A,, Ratel, F., Gamon, M. and Pernock, J. B.,

Position-Sensitive Detection of Thermal Neutrons, (Convert, P. and Forsyth, J. B.,

Eds.

, Academic Press, New ~ o i % , m p - n § .