Patent Application
20150016594
1. Field of the Invention
This invention relates generally to the field of X-ray diffraction and, more specifically, to the analysis of single-crystal specimen using an active pixel array sensor.
2. Description of the Related Art
Single-crystal X-ray diffraction (SC-XRD) is a method for determining the three-dimensional atomic structure of a crystalline compound. A single-crystal specimen of the compound is irradiated with monochromatic X-ray radiation from different directions, some of which is diffracted in specific patterns and detected by an active pixel sensor. The structural information of the specimen is determined from the geometry and relative intensities of these diffraction patterns. The intensities are integrated from the pixels in the active pixel array sensor images.
A typical laboratory system 100 for performing single-crystal diffraction experiments normally consists of five components as shown in
The goniometer 110 allows the crystal sample 112 to be rotated around several axes. Precise crystallography requires that the sample crystal 112 be aligned to the center of the goniometer 110 and maintained in that center when rotated around the goniometer rotational axes during data collection. During exposure, the sample (a single crystal of the compound of interest) is rotated in the X-ray beam 108 through a precise angular range with a precise angular velocity. The purpose of this rotation is to predictably bring Bragg reflections into constructive interference with the incident beam 108. During this time, called the charge integration time, the pixels of the sensor receive and integrate the X-ray signals.
Active pixel array sensors used in SC-XRD may include CMOS or CCD imagers. While effective, sensors such as these are often subject to pixel defects. The affected pixels may be permanently dark (i.e., “dead pixels”), permanently bright (i.e., “hot pixels”), or they may exhibit other behavior that prevents an accurate signal from being detected at these pixel locations. As such, to maintain an accurate signal detection, diffraction intensities that overlap with defective pixels must either be rejected, or estimated values must be in place of a useful response from the defective pixels.
Most established methods for pixel defect correction use nearby good pixels to determine replacement pixel values. In the simplest case, the replacement pixel value is copied from one of the neighboring pixels. More sophisticated approaches use linear or higher order interpolation across neighbors on both sides of the defective pixels and in one or two dimensions. In most cases the corrected pixel values are good enough to be inconspicuous to the human eye but, in the case of single-crystal X-ray diffraction images, they seldom pass the scrutiny of a numerical analysis. The affected intensities are often trapped as outliers and need to be rejected from the data. Moreover, if they remain undetected, they can negatively influence the result of the structure analysis.
In accordance with the present invention, a method is provided for correcting erroneous intensity measurements caused by defective pixels of the detector of a single-crystal X-ray diffraction system in which diffraction images are collected from a plurality of different scan angles for a crystal mounted in the system. From the diffraction images, reflection positions on the detector are predicted using an orientation matrix established for the crystal. A three-dimensional observed profile is then constructed for each reflection. This profile is indicative of pixel intensity relative to scan angle for detector pixels falling within the predicted reflection position on the detector. A learned “model” profile is also constructed as an average of the normalized profile data from a plurality of reflection profiles, and a defective pixel list for the system is provided that is indicative of the location of defective pixels in the detector. For each reflection under examination, the defective pixel list is then compared with the observed profile for that reflection to determine components of that observed profile that are affected by a defective pixel, and those components are replaced with corresponding components from the model profile.
The method may also involve the step of rejecting a reflection from the system output data if too much of the reflection data is affected by one or more defective pixels. In such a case, after replacing components of an observed profile with corresponding components from the model profile, a determination is made as to what percentage of an overall intensity represented by that observed profile is attributable to the components that were replaced. If that percentage exceeds a predetermined value, the reflection is then omitted from the output data. The exact percentage may vary depending on the application but, in an exemplary embodiment, a value of twenty-five percent is used.
In one embodiment, the model profile is updated during the correction process. In this embodiment, when a reflection under examination is found to have no components that are affected by a defective pixel, a determination is made as to whether the reflection is a “strong” reflection, that is, whether it has an intensity above a certain threshold. If so, the data from that reflection is used to update the model profile.
The invention also encompasses variations on how to construct the model profile. In one embodiment, the model profile is constructed using data from substantially all of the observed profiles for reflections having a minimum intensity. In an alternative embodiment, however, a different model profile is constructed for each of the reflections. In this embodiment, the detector surface is divided into a predetermined number of different detection regions, and the model profile for a given reflection comprises a weighted average of normalized data from a plurality of regional model profiles, each of which is associated with a different one of the detector regions and each of which is constructed as an average of the normalized profile data from observed profiles of reflections falling within its respective detector region. In an exemplary embodiment, there are nine detector regions, each having the same area, although a different number of detector regions and relative sizes may also be used. The calculation of the weighted average of the regional profile data may also vary depending on the application. For example, the weighted average may be such that the data from a given regional profile is weighted as a function of the distance from a predicted centroid of the reflection to a center of the region with which that regional profile is associated.
A method according to the present invention may also include the determination of an integrated intensity value for each reflection by calculating a summation of components of the observed profile for that reflection. Different methods of making this determination are anticipated herein and, in one embodiment, the integrated intensity value for a given reflection includes calculating a weighted sum of components of the observed profile for that reflection and the corresponding components of the model profile. However, other methods may also be used.
The present invention provides a correction of errors resulting from defective pixels in the active pixel array sensor of a single-crystal X-ray diffraction system. The steps of a method according to an exemplary embodiment of the invention are shown in the flow diagram of
Using the data from the images, the positions of the reflections on the detector surface may be predicted (step 202) using the orientation matrix and other data, such as the location of the detector and its angular orientation. The determination of an orientation matrix is known in the art, and provides information regarding the orientation of the crystal and the geometry of its lattice. Thus, a set of predictions is made so that, for different scan angles, the expected location of a reflection on the detector, and therefore which pixels will be illuminated by the reflection, is identified.
In step 204 of
In order to minimize sampling error, a convolver is applied to each background-subtracted image pixel before distributing its intensity over the profile grid points within the range of the convolver. The optimal convolver size is determined from the relative sizes of the XYZ pixels in image space versus the grid size in profile space. However, when an image pixel is entered into a profile, its intensity is conserved. That is, the sum of the profile values increases by exactly the value of the image pixel, although the pixel may contribute to several profile points. By default, the size of a profile in the present embodiment is 9×9×9, although those skilled in the art will understand that other magnitudes may also be chosen.
In addition to the observed reflection profiles, a normalized learned “model” profile for a specific reflection is computed as a weighted average of a number of different observed profiles. For example, in a first embodiment, there is a single model profile that is constructed using all of the shape-adjusted observed profiles of strong reflections, i.e., reflections having an intensity above a particular magnitude. Thus, for each of these strong reflections, the observed profile data is adjusted spatially to account for any shape variations relative to the other reflection profiles, and is normalized and averaged with the profile data of the other reflections. In this way, the model profile represents an average intensity distribution (in the three-dimensional profile space) of all of the reflections. This model profile will be used subsequently to correct for profile data of specific observed reflection profiles that have been compromised by one or more defective pixels.
In an alternative embodiment, multiple model profiles may be constructed relative to different regions of the detector. For example, the detector surface may be divided into nine different regions of equal area, and a model profile constructed for each of the regions, although those skilled in the art will recognize that different numbers of detector regions may also be chosen. These regional model profiles are constructed in the same manner as for the single model profile embodiment discussed above, except that each uses only reflection data that originates in the region of the detector that it represents. The model profiles are used for replacing voxels of specific observed reflection profiles that are compromised by defective pixels but, for a given reflection, the normalized model profile used is calculated as a weighted average of normalized model profiles from the different detector regions, where the weight is a function of the distance from the predicted reflection centroid to the center of each region.
In each of the aforementioned embodiments, the model profile may be constructed during an initial run prior to the process of correcting the reflection data. However, as discussed below, the model profile may also be modified during the process of collecting the reflection data and doing the correction. In such a case, the model profile would typically start as an ideal Gaussian profile and, before the main integration starts, a number of preliminary integration passes would be conducted to “seed” the model profile with information. Then, during the subsequent integration and pixel correction steps, the model profile is improved by adding data from strong reflections that are uncompromised by the influence of defective pixels.
For doing pixel correction according to the present invention, the observed profile for a given reflection is used together with a defective pixel list that is built from tests applied to the detector itself. These tests are conducted prior to any crystal examination, and may be part of the factory calibration process. Methods for finding defective pixels are known in the art. One method involves exposing the entire detector and taking a series of images of increasing intensity to the point of approaching saturation. An intensity curve is then fit to each pixel to find which of them has a defective response.
Referring again to
If the reflection being examined overlaps with any defective pixels, the voxels that are affected are replaced with data from the model profile (step 216), either as originally built, or as updated in step 214. The model profile may be derived from all of the observed reflection profile data, or it may be based on a weighted average of multiple model profiles from different detector regions, as discussed above.
After replacing the affected voxels in the observed reflection profile, a determination is made as to what percentage of the intensity was considered to be “defective” due to the influence of a defective pixel. The total intensity from all voxels and the intensity from all defective voxels are summed, respectively (step 218), and if the total intensity of defective voxels is less than or equal to 25% of the total intensity of voxels in that learned model profile (step 220), the reflection is output (step 222). If the total intensity of defective voxels is greater than 25%, the reflection is rejected (step 224). The method then proceeds to the observed profile for the next reflection (step 226), and the evaluation process recommences.
In the present embodiment, reflections are integrated using data from the observed profiles of the reflections, including voxels that have been replaced to compensate for the effect of a defective pixel. Before starting integration, a user enters estimates of the size in X, Y and Z of a “nominal” spot. These size estimates are used to define an ellipsoid around each predicted spot position to define the volume (a parallelepiped, referred to as the “integration box”) over which observed reflection profiles are accumulated. Input X, Y and Z size estimates are typically refined in preliminary passes through the first few images before integration.
The integrated intensity is determined for every reflection profile by two different techniques: simple summation and least-squares (LS) profile fitting. In both cases, the summation volume used, that is the voxels that will be included in the summation, is determined from the observed profile. In particular, a cross-section of the observed profile having an intensity at a certain minimum percentage of that of the profile peak intensity (4% in the present embodiment) serves as the footprint for the reflection, i.e., the area on the detector from which pixels are summed. From this the voxels that correspond to this detector area may be determined, and are considered to make up the summation volume. In the case of simple summation, the integrated intensity is computed by summing those pixels in the reflection's observed profile that lie within the summation volume. By using the inverse of the operation described above for populating the voxels in the observed profile with pixel intensities it is possible to go from “profile space” back to “detector space” to find the relevant detector pixels. In the case of LS fitting, the integration is also over the summation volume, but the LS-fit intensity involves a weighted sum of the observed profile and the model profile at the reflection's centroid position. That is, the footprint is determined as described above, but instead of simply summing the pixels inside this footprint, the model profile is scaled to best fit the intensities of the pixels inside the footprint, and the voxel intensities of that scaled profile are then summed to form the “LS-fit intensity.” The final integrated intensity is then determined as a weighted sum of the LS-fit intensity and the simple summation.
Those skilled in the art will understand that the steps of the different embodiments of the invention described herein will typically be performed by a data processor as part of a sampling and data collection procedure. Thus, once the system is set up with the desired criteria, and a sample crystal properly located therein, the system can typically perform the data collection and integration process without the need for manual intervention by a user.
