is organized into eight steps (major subroutines) which are called in succession by the main program. Information is exchanged between the steps by files (see Table 1), which allows the repetition of selected steps with a different set of input parameters without rerunning the whole program. The files generated by XDS
are either ASCII-type files that can be inspected and modified using a text editor or binary control images saved as a byte-offset variant of the CBFlib format (Bernstein & Hammersley, 2005
; Bernstein & Ellis, 2005
). Such images are indicated by the file-name extension .cbf
and can be looked at using the open-source program XDS-Viewer
written by Michael Hoffer.
Information exchange between program steps of XDS
All files have a fixed name defined by XDS, which makes it mandatory to process each data set in a newly created directory in order to avoid name clashes. Clearly, one should not run more than one XDS job at a time in the same directory. Output files affected by rerunning selected steps (see Table 1) should also first be given another name if their original contents are meant to be saved.
Data processing begins by copying an appropriate input file into the new directory. Input-file templates are provided with the XDS package for a number of frequently used data-collection facilities. The copied input file must be renamed XDS.INP and edited to provide the correct parameter values for the actual data-collection experiment. All parameters in XDS.INP are named by keywords containing an equals sign as the last character and many of them will be mentioned here in context in order to clarify their meaning. Execution of XDS (JOB=XDS) invokes each of the eight program steps as described below. The results and diagnostics from each step are saved in files with the extension .LP attached to the program-step name. These files should always be studied carefully to see whether processing was satisfactory or, in the case of failure, to find out what could have gone wrong.
This program step calculates a lookup table of additive spatial corrections at each detector pixel which is stored in the files X-CORRECTIONS.cbf, Y-CORRECTIONS.cbf. Often, the data images have already been corrected for geometrical distortions, in which case XYCORR produces tables of zeros.
For spiral read-out imaging-plate detectors the small corrections resulting from radial (ROFF=) and tangential (TOFF=) offset errors of the scanner are computed.
For some multiwire and CCD detectors that deliver geometrically distorted images, corrections are derived from a calibration image (BRASS_PLATE_IMAGE=file name). This image displays the response to a brass plate containing a regular grid of holes which is mounted in front of the detector and illuminated by an X-ray point source. Clearly, the source must be placed exactly at the location to be occupied by the crystal during the actual data collection, as photons emanating from the calibration source are meant to simulate all possible diffracted beam directions. For visual control, spots that have been located and accepted from the brass-plate image by XYCORR are marked in the file FRAME.cbf.
The following problems can be encountered in this step.
- (i) A misplaced calibration source can lead to an incorrect lookup table, impairing the correct prediction of the observed diffraction pattern in subsequent program steps.
- (ii) An underexposed calibration image can result in an incomplete and unreliable list of calibration spots.
INIT determines three lookup tables, saved as the files BLANK.cbf, GAIN.cbf and BKGINIT.cbf, that are required by the subsequent processing steps for classifying pixels in the data images as background or belonging to a diffraction spot (‘strong’ pixels). These tables should be inspected with the XDS-Viewer program.
BLANK.cbf contains a lookup table of the detector noise. It is determined from a specific image recorded in the absence of X-rays (DARK_CURRENT_IMAGE=) or is assumed to be a constant derived from the mean recorded value in each corner of the data images.
GAIN.cbf codes for the expected variation of the pixel contents in the background region of a data image. The variance of the contents of a pixel in the background region is GAIN·(pixel contents − detector noise). The variance is determined from the scatter of pixel values within a rectangular box (NBX=, NBY=) of size (2·NBX + 1)·(2·NBY + 1) centred at each image pixel in succession. The table GAIN.cbf is used to distinguish background pixels from ‘strong’ pixels that are part of a diffraction spot.
BKGINIT.cbf estimates the initial background at each pixel from a few data images specified by the input parameter BACKGROUND_RANGE=. The lookup table is obtained by adding the X-ray background from each image. Shaded regions on the detector (i.e. from the beamstop), pixels outside a user-defined circular region (TRUSTED_REGION=) or pixels with an undefined spatial correction value are classified as untrustworthy and marked by −3.
The following problem can be encountered in this step. Some detectors with insufficient protection from electromagnetic pulses may generate badly spoiled images whose inclusion leads to a completely wrong X-ray background table. These images can be identified in INIT.LP by their unexpected high mean pixel contents and this step should be repeated with a different set of images.
locates strong diffraction spots occurring in a subset of the data images and saves their centroids in the file SPOT.XDS
. The data subset is defined by contiguous image number ranges, where each range is specified by the keyword SPOT_RANGE=. As described in Kabsch (2010
), spots are defined as sets of ‘strong’ pixels that are adjacent in three dimensions. The classification of ‘strong’ pixels is controlled by the decision constants STRONG_PIXEL= and BACKGROUND_PIXEL=. If the total number of ‘strong’ pixels occurring in the specified data images exceeds the upper limit as given by the input parameter MAXIMUM_NUMBER_OF_STRONG_PIXELS=, the weaker ones are discarded. A spot is accepted if it contains a minimum number of ‘strong’ pixels (MINIMUM_NUMBER_OF_PIXELS_IN_A_SPOT=) and if the spot centroid is sufficiently close to the location of the strongest pixel in the spot (SPOT_MAXIMUM-CENTROID=).
The following problem can be encountered in this step. Sharp edges such as ice rings in the images can lead to an excessive number of ‘strong’ pixels being erroneously classified as contributing to diffraction spots. These aliens could prevent IDXREF from recognizing the crystal lattice.
IDXREF uses the initial parameters describing the diffraction experiment as provided by XDS.INP and the observed centroids of the spots from the file SPOT.XDS to find the orientation, metric and symmetry of the crystal lattice and refines all or a specified subset of these parameters [input parameter REFINE(IDXREF)=] . On return, the complete set of parameters are saved in the file XPARM.XDS and the original file SPOT.XDS is replaced by a file of identical name, now with indices attached to each observed spot. Spots not belonging to the crystal lattice are given indices 0, 0, 0. XDS considers the run to be successful if the coordinates of at least 70% of the given spots can be explained with reasonable accuracy (input parameter MAXIMUM_ERROR_OF_SPOT_POSITION=); otherwise, XDS will stop with an error message. Alien spots often arise because of the presence of ice or small satellite crystals and continuation of data processing may still be meaningful. In this case, XDS is called again with an explicit list of the subsequent steps specified in XDS.INP (input parameter JOB=DEFPIX XPLAN INTEGRATE CORRECT).
uses the methods described in Kabsch (1993
) to determine a crystal lattice that explains the observed locations of the diffraction spots listed in the file SPOT.XDS
. Firstly, a reciprocal-lattice vector referring to the unrotated crystal is computed from each observed spot centroid. Differences between any two reciprocal-lattice vectors that are above a specified minimal length (SEPMIN=) are accumulated in a three-dimensional histogram. These difference vectors will form clusters in the histogram, since there are many different pairs of reciprocal-lattice vectors of nearly identical vector difference. The clusters are found as maxima in the smoothed histogram (CLUSTER_RADIUS=) and a basis of three linearly independent cluster vectors is selected that allows all other cluster vectors to be expressed as nearly integral multiples of small magnitude with respect to this basis. The basis vectors and the 60 most populated clusters with attached indices are listed in IDXREF.LP
. If many of the indices deviate significantly from integral values, the program is unable to find a reasonable lattice basis and all further processing will be meaningless.
If the space group and unit-cell parameters are specified, a reduced cell is derived and the reciprocal-basis vectors found above are reinterpreted accordingly; otherwise, a reduced cell is determined directly from the reciprocal basis. The parameters of the reduced cell, the coordinates of the reciprocal-basis vectors and their indices with respect to the reduced cell are reported.
Based on the orientation and metric of the reduced cell now available, IDXREF
indexes up to 3000 of the strongest spots using the local-indexing method. This method considers each spot as a node of a tree and identifies the largest subtree of nodes which can be assigned reliable indices. The number of reflections in the ten largest subtrees is reported and usually shows a dominant first tree corresponding to a single lattice, whereas alien spots are found in small subtrees. Reflections in the largest subtree are used for initial refinement of the basis vectors of the reduced cell, the incident-beam wavevector and the origin of the detector, which is the point in the detector plane nearest to the crystal. Experience has shown that the detector origin and the direction of the incident beam are often specified with insufficient accuracy, which could easily lead to a misindexing of the reflections by a constant offset. For this reason, IDXREF
considers alternative choices for the index origin and reports their likelihood of being correct. The parameters controlling the local indexing are INDEX_ERROR=, INDEX_MAGNITUDE=, INDEX_QUALITY= (corresponding to
, ϕ and 1 − min
in Kabsch, 2010
) and INDEX_ORIGIN=h
, which is added to the indices of all reflections in the tree. After initial refinement based on the reflections in the largest subtree, all spots which can now be indexed are included. Usually, the detector distance and the direction of the rotation axis are not refined, but if the spots were extracted from images covering a large range of total crystal rotation then better results are obtained by including these parameters in the refinement [REFINE(IDXREF)=] .
The refined metric parameters of the reduced cell are used to test each of the 44 possible lattice types as described in Kabsch (2010
). For each lattice type, IDXREF
reports the likelihood of its being correct and the conventional unit-cell parameters. The program step concludes with an overview of possible lattice symmetries, but makes no automatic decision for the space group. If the crystal symmetry is unknown, XDS
will continue data processing with the crystal being described by its reduced-cell basis vectors and triclinic symmetry. Space-group assignment is postponed to the last program step, CORRECT
, when integrated intensities are available.
The following problems can be encountered in this step.
- (i) The indices of many difference-vector clusters deviate significantly from integral values. This can be caused by incorrect input parameters, such as rotation axis, oscillation angle or detector position, by a large fraction of alien spots in SPOT.XDS, by placing the detector too close to the crystal or by an inappropriate choice of the parameters SEPMIN= and CLUSTER_RADIUS= in densely populated images.
- (ii) Indexing and refinement is unsatisfactory despite well indexed difference-vector clusters. This is probably caused by the selection of an incorrect index origin and IDXREF should be rerun with plausible alternatives for INDEX_ORIGIN= after a visual check of a data image with XDS-Viewer.
- (iii) Despite successful indexing and refinement, IDXREF stops with the error message INSUFFICIENT PERCENTAGE OF INDEXED REFLECTIONS, complaining that less than 70% of the given spots could be explained. Alien spots often arise because of the presence of ice or small satellite crystals and continuation of data processing may still be meaningful. To continue data processing, just specify the missing processing steps in XDS.INP by JOB=DEFPIX XPLAN INTEGRATE CORRECT and call XDS again.
DEFPIX recognizes regions in the initial background table (file BKGINIT.cbf) that are obscured by intruding hardware and marks the shaded pixels as untrusted. In addition, pixels that are outside a user-defined resolution range (INCLUDE_RESOLUTION_RANGE=) are marked and eliminated from the trusted region. The marked background table that is thus obtained is saved in the file BKGPIX.cbf which is needed by the subsequent program steps. To recognize the obscured regions in the initial background, DEFPIX generates a control image (file ABS.cbf) that contains values of around 10 000 for unshaded pixels and lower values for shaded pixels. The classification of the pixels into reliable and untrusted pixels is based on the two input parameters VALUE_RANGE_FOR_TRUSTED_DETECTOR_PIXELS= (default 6000 30 000) and INCLUDE_RESOLUTION_RANGE= (default 20.0 0.0). Pixels in the table ABS.cbf with a value outside the ranges specified by the two parameters are marked unreliable (by −3) in the background table BKGPIX.cbf.
The following problem can be encountered in this step. If the parameter VALUE_RANGE_FOR_TRUSTED_DETECTOR_PIXELS= specifies a value range that is too narrow, ‘good’ regions will erroneously be excluded from the trusted detector region. Check BKGPIX.cbf with the XDS-Viewer program and if necessary repeat the DEFPIX step with more appropriate values.
XPLAN supports the planning of data collection. It is based upon information provided by the input files XPARM.XDS and BKGPIX.cbf, both of which become available on processing a few test images with XDS. XPLAN estimates the completeness of new reflection data expected to be collected for each given starting angle and total crystal rotation and reports the results for a number of selected resolution shells in the file XPLAN.LP. To minimize the recollection of data, the name of a file containing already measured reflections can be provided by the input parameter REFERENCE_DATA_SET=.
The following problems can be encountered in this step.
- (i) Incorrect results may occur for some space groups, i.e. P42, if the unit cell determined by XDS from processing a few test images implicates reflection indices that are inconsistent with those from the reference data set. However, the correct cell choice can be found by using the old data as a reference and repeating CORRECT with the appropriate reindexing transformation, followed by copying GXPARM.XDS to XPARM.XDS. The same applies if IDXREF was run for an unknown space group and then reindexed in CORRECT.
- (ii) XPLAN ignores potential reflection overlap owing to the finite oscillation range covered by each image.
INTEGRATE determines the intensity of each reflection predicted to occur in the rotation data images (DATA_RANGE=) and saves the results in the file INTEGRATE.HKL.
The diffraction parameters needed to predict the reflection positions are initially provided by the file XPARM.XDS. These parameters are either kept constant or refined periodically using strong diffraction spots encountered in the data images. Whether refinement should be carried out at all and which parameters are to be refined can be specified by the user [input parameter REFINE(INTEGRATE)=]. The centroids of the strong spots in the data images are computed from pixels that exceed the background by a given multiple of standard deviations (input parameters SIGNAL_PIXEL=, BACKGROUND_PIXEL=). Strong spots are used in the refinement if their centroids are reasonably close to their calculated position (input parameter MAXIMUM_ERROR_OF_SPOT_POSITION=).
For determination of the intensity, approximate values describing the extension and the form of the diffraction spot must be specified. The shapes of all spots become very similar when the contents of each of their contributing image pixels is mapped onto a three-dimensional coordinate system, specific for each reflection, which has its origin on the surface of the Ewald sphere at the terminus of the diffracted beam wavevector (see Kabsch, 2010
). The transformed spot can roughly be described as a Gaussian involving two parameters: the standard deviations of the reflecting range σM
(input parameter REFLECTING_RANGE_E.S.D.=σM
) and the beam divergence σD
(input parameter BEAM_DIVERGENCE_E.S.D.=σD
). This leads to an integration region around the spot that is defined by the parameters δM
(REFLECTING_RANGE=) and δD
(BEAM_DIVERGENCE=), which are typically chosen to be 6–10 times larger than σM
, respectively. Appropriate values for these parameters are determined automatically by XDS
); the user has the option to override the automatic assignments.
Integration is carried out by a two-step procedure. In the first pass, spot templates are generated by superimposing the profiles of strong reflections after their mapping to the Ewald sphere. Grid points with a value above a minimum percentage of the maximum in the template (parameter CUT=) are marked for inclusion in the final integration. To allow for variations in their shape, profile templates are generated from reflections located at nine regions of equal size covering the detector surface and additional sets of nine to cover equally sized (parameter DELPHI=) batches of images. The actual integration is carried out in the second pass by profile fitting with respect to the spot shape determined in the first pass. Incomplete reflections below a minimum percentage of the observed reflection intensity (parameter MINPK=) will be discarded. Otherwise, the missing intensity is estimated from the learned reflection profiles.
On return from the INTEGRATE step, all spots expected to occur in the last data image are encircled and the modified image is saved as the file FRAME.cbf for inspection.
The following problems can be encountered in this step.
- (i) Off-centred profiles indicate incorrectly predicted reflection positions by using the parameters provided by the file XPARM.XDS (i.e. misindexing by using a wrong origin of the indices), crystal slippage or change in the incident-beam direction.
- (ii) Profiles extending to the borders of the box indicate too-small values of the parameters BEAM_DIVERGENCE= or REFLECTING_RANGE=. This leads to incorrect integrated intensities because of truncated reflection profiles and unreliable background determination.
- (iii) Display of the file FRAME.cbf shows spots which are not encircled. If these unexpected reflections are not close to the spindle and are not ice reflections, then it is likely that the parameters provided by the file XPARM.XDS are wrong.
applies correction factors to the intensities and standard deviations of all reflections found in the file INTEGRATE.HKL
, determines the space group if unknown and refines the unit-cell parameters, reports the quality and completeness of the data set and saves the final integrated intensities in the file XDS_ASCII.HKL
. Some of the employed algorithms are new and are described in Kabsch (2010
accepts reflections from the file INTEGRATE.HKL
- (i) recorded (parameter MINPK=) on specified images (parameter DATA_RANGE=);
- (ii) within a given resolution range (parameter INCLUDE_RESOLUTION_RANGE=);
- (iii) outside ice rings (parameter EXCLUDE_RESOLUTION_RANGE=);
- (iv) not overloaded (parameter OVERLOAD=); and
- (v) not marked for exclusion in the file REMOVE.HKL.
Thus, the user has the option to exclude unreliable reflections from the final data set by repeating the CORRECT step with appropriate parameter values.
The intensities of the accepted reflections are first corrected for effects arising from polarization of the incident beam (parameters FRACTION_OF_POLARIZATION=, POLARIZATION_PLANE_NORMAL=) and absorption effects (parameters AIR=, SILICON=, SENSOR_THICKNESS=) arising from differences in path lengths of the diffracted beam. These corrections do not depend on knowledge of the space group.
The integrated intensities of the reflections in the file INTEGRATE.HKL may or may not have been indexed in the correct space group; for the purpose of integration, it is important only that all reflections occurring in the data images have been indexed with respect to some unit-cell basis and that their locations on the images were hit exactly. The correct reflection indices in the true space group are always a linear transformation of the original indices used in INTEGRATE.HKL. All lattices consistent with the locations of the reflections saved in INTEGRATE.HKL (decision parameters MAX_CELL_AXIS_ERROR=, MAX_CELL_ANGLE_ERROR=) and their corresponding linear transformations are printed to provide a useful overview similar to that shown in IDXREF.LP.
If the space group is not specified, XDS
proposes one of the enantiomorphous space groups without screw axes that is compatible with the observed lattice symmetry and explains the intensities of a subset of the reflections (parameter TEST_RESOLUTION_RANGE=) at an acceptable R
(Diederichs & Karplus, 1997
; Weiss, 2001
) using a minimum number of unique reflections. The criteria for an acceptable R
are controlled by the decision parameters MIN_RFL_Rmeas= and MAX_FAC_Rmeas=.
The user can always override the automatic decisions by specifying the correct space-group number (parameter SPACE_GROUP_NUMBER=) and unit-cell parameters (parameter UNIT_CELL_CONSTANTS=) in XDS.INP
and repeating the CORRECT
step. This provides a simple way to rename orthorhombic unit-cell parameters, which often becomes necessary if screw axes are present. In addition, the user has the option to specify the following in XDS.INP
- (i) a reference data set (parameter REFERENCE_DATA_SET=),
- (ii) a reindexing transformation (parameter REIDX=) and
- (iii) three basis vectors if known from processing a previous data set taken at the same crystal orientation in a multi-wavelength experiment (parameters UNIT_CELL_A-AXIS=, UNIT_CELL_B-AXIS=, UNIT_CELL_C-AXIS=).
The possibility of comparing the new data with a reference data set is particularly useful for resolving the issue of alternative settings of polar or rhombohedral cells (such as P4, P6 and R3). Also, reference data are quite useful for recognizing misindexing or for testing potential heavy-atom derivatives.
For refinement of the unit-cell parameters [parameter REFINE(CORRECT)=], CORRECT uses a subset of the accepted reflections whose observed centroid is sufficiently close to the predicted spot position (parameter MAXIMUM_ERROR_OF_SPOT_POSITION=). The refined set of parameters is saved in the file GXPARM.XDS, which has an identical layout to the file XPARM.XDS produced by IDXREF. If the crystal has not slipped during data collection, these parameters are quite accurate.
Other correction factors (parameter CORRECTIONS=) which partially compensate for radiation damage, absorption effects and variations in the sensitivity of the detector surface are determined from the symmetry-equivalent reflections usually found in the data images. The corrections are chosen such that the integrated intensities of symmetry-equivalent reflections come out as similar as possible. The user may control application of the various corrections by specifying the parameter CORRECTIONS= by a combination of the keywords DECAY MODULATION ABSORPTION. Whether Friedel pairs are considered as symmetry-equivalent reflections in the calculation of the correction factors depends on the values of the two parameters STRICT_ABSORPTION_CORRECTION= and FRIEDEL’S_LAW=. The number of correction factors is controlled by the input parameters MINIMUM_I/SIGMA=, NBATCH= and REFLECTIONS/CORRECTION_FACTOR=.
The residual scatter in intensity of symmetry-equivalent reflections is used to estimate their standard deviations. Here, the initial estimate v
0(I) (obtained from the INTEGRATE step) for the variance of the reflection intensity I is replaced by v(I) = a[v
0(I) + bI
2]. The two constants a and b are chosen to minimize discrepancies between v(I) and the variance estimated from sample statistics of symmetry-related reflections. Based on the more realistic error estimates for the intensities, outliers are recognized by comparison with other symmetry-equivalent reflections. These outliers are included in the main output file XDS_ASCII.HKL, in which they are marked by a negative sign attached to the estimated standard deviations of their intensity. Classification of a reflection as a misfit is controlled by a decision constant which has the default value of WFAC1=1.5. Specification of a lower value such as WFAC1=1.0 by the user will lead to an increasing number of misfits and lower R factors as outliers are not included in the reported statistics.
Data quality as a function of resolution is described by the agreement of intensities of symmetry-related reflections and quantified by the R
and the more robust indicator R
(Diederichs & Karplus, 1997
; Weiss, 2001
). These R
factors as well as the intensities of all reflections with indices of type h
0 and 00l
and those expected to be systematically absent provide important information for identification of the correct space group. Clearly, large R
factors or many rejected reflections or large observed intensities for reflections that are expected to be systematically absent suggest that the assumed space group or indexing is incorrect. The presence or absence of anomalous scatterers is specified by the parameter FRIEDEL’S_LAW=. Finally, CORRECT
analyzes the distribution of reflection intensities as a function of their resolution and reports outliers from the Wilson plot. Often, these aliens arise from ice rings in the data images. To suppress the unwanted reflections from the final output file XDS_ASCII.HKL
, the user copies them to a file named REMOVE.HKL
in the current directory and repeats the CORRECT
The following problems can be encountered in this step.
- (i) Incomplete data sets may lead to wrong conclusions about the space group, as some of its symmetry operators might not be involved in the R-factor calculations.
- (ii) Often, the CORRECT step is repeated several times. It should be remembered that XDS overwrites earlier versions of the output files XDS_ASCII.HKL, GXPARM.XDS