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data-md-toggle=toc type=checkbox id=__toc > <label class="md-nav__link md-nav__link--active" for=__toc > CPU-side crystallographic data analysis (Jungfraujoch) </label> <a href="#" class="md-nav__link md-nav__link--active">CPU-side crystallographic data analysis (Jungfraujoch)</a> <nav class="md-nav md-nav--secondary"> <ul class=md-nav__list data-md-scrollfix=""> </ul> </nav> <ul class=md-nav__list > <li class=md-nav__item > <a href="#references" class=md-nav__link >References</a> <li class=md-nav__item > <a href="#geometry-reciprocal-space-mapping-and-basic-quantities" class=md-nav__link >1. 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href="python_client/docs/DefaultApi.html#deactivate-post" class=md-nav__link ><strong>deactivate_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#detector-status-get" class=md-nav__link ><strong>detector_status_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#fpga-status-get" class=md-nav__link ><strong>fpga_status_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#image-buffer-clear-post" class=md-nav__link ><strong>image_buffer_clear_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#image-buffer-image-cbor-get" class=md-nav__link ><strong>image_buffer_image_cbor_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#image-buffer-image-jpeg-get" class=md-nav__link ><strong>image_buffer_image_jpeg_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#image-buffer-image-tiff-get" class=md-nav__link ><strong>image_buffer_image_tiff_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#image-buffer-start-cbor-get" class=md-nav__link ><strong>image_buffer_start_cbor_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#image-buffer-status-get" class=md-nav__link ><strong>image_buffer_status_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#image-pusher-status-get" class=md-nav__link ><strong>image_pusher_status_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#initialize-post" class=md-nav__link ><strong>initialize_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#pedestal-post" class=md-nav__link ><strong>pedestal_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#preview-pedestal-tiff-get" class=md-nav__link ><strong>preview_pedestal_tiff_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#preview-plot-bin-get" class=md-nav__link ><strong>preview_plot_bin_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#preview-plot-get" class=md-nav__link ><strong>preview_plot_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#result-scan-get" class=md-nav__link ><strong>result_scan_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#start-post" class=md-nav__link ><strong>start_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#statistics-calibration-get" class=md-nav__link ><strong>statistics_calibration_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#statistics-data-collection-get" class=md-nav__link ><strong>statistics_data_collection_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#statistics-get" class=md-nav__link ><strong>statistics_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#status-get" class=md-nav__link ><strong>status_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#trigger-post" class=md-nav__link ><strong>trigger_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#version-get" class=md-nav__link ><strong>version_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#wait-till-done-post" class=md-nav__link ><strong>wait_till_done_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#wait-until-running-post" class=md-nav__link ><strong>wait_until_running_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#xfel-event-code-get" class=md-nav__link ><strong>xfel_event_code_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#xfel-pulse-id-get" class=md-nav__link ><strong>xfel_pulse_id_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/AzimIntSettings.html" class=md-nav__link >AzimIntSettings</a> <li class=md-nav__item > <a href="python_client/docs/BrokerStatus.html" class=md-nav__link >BrokerStatus</a> <li class=md-nav__item > <a href="python_client/docs/CalibrationStatisticsInner.html" class=md-nav__link >CalibrationStatisticsInner</a> <li class=md-nav__item > <a href="python_client/docs/ColorScale.html" class=md-nav__link >ColorScale</a> <li class=md-nav__item > <a href="python_client/docs/DarkMaskSettings.html" class=md-nav__link >DarkMaskSettings</a> <li class=md-nav__item > <a href="python_client/docs/DatasetSettings.html" class=md-nav__link >DatasetSettings</a> <li class=md-nav__item > <a href="python_client/docs/DatasetSettingsSmargon.html" class=md-nav__link >DatasetSettingsSmargon</a> <li class=md-nav__item > <a href="python_client/docs/DatasetSettingsUnitCell.html" class=md-nav__link >DatasetSettingsUnitCell</a> <li class=md-nav__item > <a href="python_client/docs/DatasetSettingsXrayFluorescenceSpectrum.html" class=md-nav__link >DatasetSettingsXrayFluorescenceSpectrum</a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html" class=md-nav__link >jfjoch_client.DefaultApi</a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#cancel-post" class=md-nav__link ><strong>cancel_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-azim-int-get" class=md-nav__link ><strong>config_azim_int_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-azim-int-put" class=md-nav__link ><strong>config_azim_int_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-dark-mask-get" class=md-nav__link ><strong>config_dark_mask_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-dark-mask-put" class=md-nav__link ><strong>config_dark_mask_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-detector-get" class=md-nav__link ><strong>config_detector_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-detector-put" class=md-nav__link ><strong>config_detector_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-file-writer-get" class=md-nav__link ><strong>config_file_writer_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-file-writer-put" class=md-nav__link ><strong>config_file_writer_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-image-format-conversion-post" class=md-nav__link ><strong>config_image_format_conversion_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-image-format-get" class=md-nav__link ><strong>config_image_format_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-image-format-put" class=md-nav__link ><strong>config_image_format_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-image-format-raw-post" class=md-nav__link ><strong>config_image_format_raw_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-indexing-get" class=md-nav__link ><strong>config_indexing_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-indexing-put" class=md-nav__link ><strong>config_indexing_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-instrument-get" class=md-nav__link ><strong>config_instrument_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-instrument-put" class=md-nav__link ><strong>config_instrument_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-internal-generator-image-put" class=md-nav__link ><strong>config_internal_generator_image_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-internal-generator-image-tiff-put" class=md-nav__link ><strong>config_internal_generator_image_tiff_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-mask-get" class=md-nav__link ><strong>config_mask_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-mask-tiff-get" class=md-nav__link ><strong>config_mask_tiff_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-roi-get" class=md-nav__link ><strong>config_roi_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-roi-put" class=md-nav__link ><strong>config_roi_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-select-detector-get" class=md-nav__link ><strong>config_select_detector_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-select-detector-put" class=md-nav__link ><strong>config_select_detector_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-spot-finding-get" class=md-nav__link ><strong>config_spot_finding_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-spot-finding-put" class=md-nav__link ><strong>config_spot_finding_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-user-mask-get" class=md-nav__link ><strong>config_user_mask_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-user-mask-put" class=md-nav__link ><strong>config_user_mask_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-user-mask-tiff-get" class=md-nav__link ><strong>config_user_mask_tiff_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-user-mask-tiff-put" class=md-nav__link ><strong>config_user_mask_tiff_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-zeromq-metadata-get" class=md-nav__link ><strong>config_zeromq_metadata_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-zeromq-metadata-put" class=md-nav__link ><strong>config_zeromq_metadata_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-zeromq-preview-get" class=md-nav__link ><strong>config_zeromq_preview_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#config-zeromq-preview-put" class=md-nav__link ><strong>config_zeromq_preview_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#deactivate-post" class=md-nav__link ><strong>deactivate_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#detector-status-get" class=md-nav__link ><strong>detector_status_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#fpga-status-get" class=md-nav__link ><strong>fpga_status_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#image-buffer-clear-post" class=md-nav__link ><strong>image_buffer_clear_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#image-buffer-image-cbor-get" class=md-nav__link ><strong>image_buffer_image_cbor_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#image-buffer-image-jpeg-get" class=md-nav__link ><strong>image_buffer_image_jpeg_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#image-buffer-image-tiff-get" class=md-nav__link ><strong>image_buffer_image_tiff_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#image-buffer-start-cbor-get" class=md-nav__link ><strong>image_buffer_start_cbor_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#image-buffer-status-get" class=md-nav__link ><strong>image_buffer_status_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#image-pusher-status-get" class=md-nav__link ><strong>image_pusher_status_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#initialize-post" class=md-nav__link ><strong>initialize_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#pedestal-post" class=md-nav__link ><strong>pedestal_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#preview-pedestal-tiff-get" class=md-nav__link ><strong>preview_pedestal_tiff_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#preview-plot-bin-get" class=md-nav__link ><strong>preview_plot_bin_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#preview-plot-get" class=md-nav__link ><strong>preview_plot_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#result-scan-get" class=md-nav__link ><strong>result_scan_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#start-post" class=md-nav__link ><strong>start_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#statistics-calibration-get" class=md-nav__link ><strong>statistics_calibration_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#statistics-data-collection-get" class=md-nav__link ><strong>statistics_data_collection_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#statistics-get" class=md-nav__link ><strong>statistics_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#status-get" class=md-nav__link ><strong>status_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#trigger-post" class=md-nav__link ><strong>trigger_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#version-get" class=md-nav__link ><strong>version_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#wait-till-done-post" class=md-nav__link ><strong>wait_till_done_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#wait-until-running-post" class=md-nav__link ><strong>wait_until_running_post</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#xfel-event-code-get" class=md-nav__link ><strong>xfel_event_code_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/DefaultApi.html#xfel-pulse-id-get" class=md-nav__link ><strong>xfel_pulse_id_get</strong></a> <li class=md-nav__item > <a href="python_client/docs/Detector.html" class=md-nav__link >Detector</a> <li class=md-nav__item > <a href="python_client/docs/DetectorList.html" class=md-nav__link >DetectorList</a> <li class=md-nav__item > <a href="python_client/docs/DetectorListDetectorsInner.html" class=md-nav__link >DetectorListDetectorsInner</a> <li class=md-nav__item > <a href="python_client/docs/DetectorListElement.html" class=md-nav__link >DetectorListElement</a> <li class=md-nav__item > <a href="python_client/docs/DetectorModule.html" class=md-nav__link >DetectorModule</a> <li class=md-nav__item > <a href="python_client/docs/DetectorModuleDirection.html" class=md-nav__link >DetectorModuleDirection</a> <li class=md-nav__item > <a href="python_client/docs/DetectorPowerState.html" class=md-nav__link >DetectorPowerState</a> <li class=md-nav__item > <a href="python_client/docs/DetectorSelection.html" class=md-nav__link >DetectorSelection</a> <li class=md-nav__item > <a href="python_client/docs/DetectorSettings.html" class=md-nav__link >DetectorSettings</a> <li class=md-nav__item > <a href="python_client/docs/DetectorState.html" class=md-nav__link >DetectorState</a> <li class=md-nav__item > <a href="python_client/docs/DetectorStatus.html" class=md-nav__link >DetectorStatus</a> <li class=md-nav__item > <a href="python_client/docs/DetectorTiming.html" class=md-nav__link >DetectorTiming</a> <li class=md-nav__item > <a href="python_client/docs/DetectorType.html" class=md-nav__link >DetectorType</a> <li class=md-nav__item > <a href="python_client/docs/ErrorMessage.html" class=md-nav__link >ErrorMessage</a> <li class=md-nav__item > <a href="python_client/docs/FileWriterFormat.html" class=md-nav__link >FileWriterFormat</a> <li class=md-nav__item > <a href="python_client/docs/FileWriterSettings.html" class=md-nav__link >FileWriterSettings</a> <li class=md-nav__item > <a href="python_client/docs/FpgaStatusInner.html" class=md-nav__link >FpgaStatusInner</a> <li class=md-nav__item > <a href="python_client/docs/GeomRefinementAlgorithm.html" class=md-nav__link >GeomRefinementAlgorithm</a> <li class=md-nav__item > <a href="python_client/docs/GridPlot.html" class=md-nav__link >GridPlot</a> <li class=md-nav__item > <a href="python_client/docs/GridPlots.html" class=md-nav__link >GridPlots</a> <li class=md-nav__item > <a href="python_client/docs/GridScan.html" class=md-nav__link >GridScan</a> <li class=md-nav__item > <a href="python_client/docs/GridScanResult.html" class=md-nav__link >GridScanResult</a> <li class=md-nav__item > <a href="python_client/docs/GridScanResultImagesInner.html" class=md-nav__link >GridScanResultImagesInner</a> <li class=md-nav__item > <a href="python_client/docs/ImageBufferStatus.html" class=md-nav__link >ImageBufferStatus</a> <li class=md-nav__item > <a href="python_client/docs/ImageFormatSettings.html" class=md-nav__link >ImageFormatSettings</a> <li class=md-nav__item > <a href="python_client/docs/ImagePusherStatus.html" class=md-nav__link >ImagePusherStatus</a> <li class=md-nav__item > <a href="python_client/docs/ImagePusherType.html" class=md-nav__link >ImagePusherType</a> <li class=md-nav__item > <a href="python_client/docs/IndexingAlgorithm.html" class=md-nav__link >IndexingAlgorithm</a> <li class=md-nav__item > <a href="python_client/docs/IndexingSettings.html" class=md-nav__link >IndexingSettings</a> <li class=md-nav__item > <a href="python_client/docs/InstrumentMetadata.html" class=md-nav__link >InstrumentMetadata</a> <li class=md-nav__item > <a href="python_client/docs/JfjochBrokerApi.html" class=md-nav__link >jfjoch_client.JfjochBrokerApi</a> <li class=md-nav__item > <a href="python_client/docs/JfjochBrokerApi.html#config-zeromq-metadata-put" class=md-nav__link ><strong>config_zeromq_metadata_put</strong></a> <li class=md-nav__item > <a href="python_client/docs/JfjochSettings.html" class=md-nav__link >JfjochSettings</a> <li class=md-nav__item > <a href="python_client/docs/JfjochSettingsSsl.html" class=md-nav__link >JfjochSettingsSsl</a> <li class=md-nav__item > <a href="python_client/docs/JfjochStatistics.html" class=md-nav__link >JfjochStatistics</a> <li class=md-nav__item > <a href="python_client/docs/MeasurementStatistics.html" class=md-nav__link >MeasurementStatistics</a> <li class=md-nav__item > <a href="python_client/docs/PcieDevicesInner.html" class=md-nav__link >PcieDevicesInner</a> <li class=md-nav__item > <a href="python_client/docs/PixelMaskStatistics.html" class=md-nav__link >PixelMaskStatistics</a> <li class=md-nav__item > <a href="python_client/docs/Plot.html" class=md-nav__link >Plot</a> <li class=md-nav__item > <a href="python_client/docs/PlotTypeEnum.html" class=md-nav__link >PlotTypeEnum</a> <li class=md-nav__item > <a href="python_client/docs/PlotUnitX.html" class=md-nav__link >PlotUnitX</a> <li class=md-nav__item > <a href="python_client/docs/Plots.html" class=md-nav__link >Plots</a> <li class=md-nav__item > <a href="python_client/docs/PreviewSettings.html" class=md-nav__link >PreviewSettings</a> <li class=md-nav__item > <a href="python_client/docs/RoiAzimList.html" class=md-nav__link >RoiAzimList</a> <li class=md-nav__item > <a href="python_client/docs/RoiAzimuthal.html" class=md-nav__link >RoiAzimuthal</a> <li class=md-nav__item > <a href="python_client/docs/RoiBox.html" class=md-nav__link >RoiBox</a> <li class=md-nav__item > <a href="python_client/docs/RoiBoxList.html" class=md-nav__link >RoiBoxList</a> <li class=md-nav__item > <a href="python_client/docs/RoiCircle.html" class=md-nav__link >RoiCircle</a> <li class=md-nav__item > <a href="python_client/docs/RoiCircleList.html" class=md-nav__link >RoiCircleList</a> <li class=md-nav__item > <a href="python_client/docs/RoiDefinitions.html" class=md-nav__link >RoiDefinitions</a> <li class=md-nav__item > <a href="python_client/docs/RotationAxis.html" class=md-nav__link >RotationAxis</a> <li class=md-nav__item > <a href="python_client/docs/ScanResult.html" class=md-nav__link >ScanResult</a> <li class=md-nav__item > <a href="python_client/docs/ScanResultImagesInner.html" class=md-nav__link >ScanResultImagesInner</a> <li class=md-nav__item > <a href="python_client/docs/SpotFindingSettings.html" class=md-nav__link >SpotFindingSettings</a> <li class=md-nav__item > <a href="python_client/docs/StandardDetectorGeometry.html" class=md-nav__link >StandardDetectorGeometry</a> <li class=md-nav__item > <a href="python_client/docs/TcpSettings.html" class=md-nav__link >TcpSettings</a> <li class=md-nav__item > <a href="python_client/docs/UnitCell.html" class=md-nav__link >UnitCell</a> <li class=md-nav__item > <a href="python_client/docs/ZeromqMetadataSettings.html" class=md-nav__link >ZeromqMetadataSettings</a> <li class=md-nav__item > <a href="python_client/docs/ZeromqPreviewSettings.html" class=md-nav__link >ZeromqPreviewSettings</a> <li class=md-nav__item > <a href="python_client/docs/ZeromqSettings.html" class=md-nav__link >ZeromqSettings</a> </ul> </nav> </div> </div> </div> <div class="md-sidebar md-sidebar--secondary" data-md-component=toc > <div class=md-sidebar__scrollwrap > <div class=md-sidebar__inner > <nav class="md-nav md-nav--secondary"> <ul class=md-nav__list data-md-scrollfix=""> </ul> </nav> </div> </div> </div> <div class=md-content > <article class="md-content__inner md-typeset" role=main > <section class="tex2jax_ignore mathjax_ignore" id=cpu-side-crystallographic-data-analysis-jungfraujoch > <h1 id=cpu-data-analysis--page-root >CPU-side crystallographic data analysis (Jungfraujoch)<a class=headerlink href="#cpu-data-analysis--page-root" title="Link to this heading">¶</a></h1> <p>This document describes the crystallographic algorithms implemented in Jungfraujoch for <strong>CPU</strong>- and <strong>GPU</strong>-side real‑time and near‑real‑time data analysis.</p> <p><strong>Scope.</strong> The pipeline covered here comprises:</p> <ol class="arabic simple"> <li><p>geometry mapping and corrections,</p> <li><p>azimuthal integration (powder/radial profiles),</p> <li><p>Bragg spot finding (strong pixels → connected components → spot descriptors),</p> <li><p>indexing (still and rotation modes),</p> <li><p>Bravais lattice / centering inference,</p> <li><p>geometry and lattice refinement,</p> <li><p>reflection prediction (still and rotation),</p> <li><p>Bragg integration by either 2D summation or reference-driven profile fitting,</p> <li><p>scaling and merging,</p> <li><p>merge-level error modelling and outlier rejection,</p> <li><p>auxiliary statistics (Wilson plot, ⟨I/σ(I)⟩, CC1/2, CCref).</p> </ol> <section id=references > <h2 id=references >References<a class=headerlink href="#references" title="Link to this heading">¶</a></h2> <p>The methods are inspired and reuising solutions implemented in:</p> <ul class=simple > <li><p>W. Kabsch, “XDS”, <em>Acta Cryst.</em> <strong>D66</strong> (2010), 125–132 and related XDS papers (rotation geometry, partiality, scaling concepts).</p> <li><p>W. Kabsch, “Integration, scaling, space-group assignment and post-refinement”, <em>Acta Cryst.</em> <strong>D66</strong> (2010), 133–144 (mosaicity/partiality likelihood treatment; notation such as ζ and rotation factors).</p> <li><p>T. A. White et al., CrystFEL method papers (spot finding, three‑ring integration, serial/still diffraction processing concepts).</p> <li><p>J. Kieffer & J. P. Wright, “PyFAI: a Python library for high performance azimuthal integration on GPU”, <em>Powder Diffraction</em> <strong>28</strong> (2013), S339-S350 (detector geometry definition, azimuthal integration)</p> <li><p>H. Powell, “The Rossmann Fourier autoindexing algorithm in MOSFLM”, <em>Acta Cryst.</em> <strong>D55</strong> (1999), 1690-1695 (FFT indexing) (list is not exhaustive)</p> </ul> </section> <section id=geometry-reciprocal-space-mapping-and-basic-quantities > <h2 id=geometry-reciprocal-space-mapping-and-basic-quantities >1. Geometry, reciprocal-space mapping, and basic quantities<a class=headerlink href="#geometry-reciprocal-space-mapping-and-basic-quantities" title="Link to this heading">¶</a></h2> <section id=coordinate-conventions > <h3 id=coordinate-conventions >1.1 Coordinate conventions<a class=headerlink href="#coordinate-conventions" title="Link to this heading">¶</a></h3> <p>For a pixel coordinate <span class="math notranslate nohighlight">\((x,y)\)</span> (in pixels), Jungfraujoch converts to a laboratory direction vector via:</p> <ol class="arabic simple"> <li><p>shift by direct-beam position <span class="math notranslate nohighlight">\((x_\mathrm{beam}, y_\mathrm{beam})\)</span>,</p> <li><p>scale by pixel size <span class="math notranslate nohighlight">\(p\)</span> (mm),</p> <li><p>set detector distance <span class="math notranslate nohighlight">\(D\)</span> (mm),</p> <li><p>apply detector orientation rotation <span class="math notranslate nohighlight">\(R_\mathrm{det}\)</span> (PyFAI-like parameterization).</p> </ol> <p>The unnormalized detector coordinate (mm) is: <span class="math notranslate nohighlight">\( \mathbf{r}_\mathrm{det}(x,y) = \begin{pmatrix} (x-x_\mathrm{beam})p\\ (y-y_\mathrm{beam})p\\ D \end{pmatrix}. \)</span></p> <p>The lab-frame vector is: <span class="math notranslate nohighlight">\( \mathbf{r}_\mathrm{lab} = R_\mathrm{det}\,\mathbf{r}_\mathrm{det}. \)</span></p> <p>Let the incident wavevector magnitude be <span class="math notranslate nohighlight">\(k = 1/\lambda\)</span> in Å<span class="math notranslate nohighlight">\(^{-1}\)</span>, and define: <span class="math notranslate nohighlight">\( \mathbf{S}_0 = (0,0,k). \)</span></p> <p>The <strong>reciprocal-space scattering vector</strong> associated with pixel <span class="math notranslate nohighlight">\((x,y)\)</span> is: <span class="math notranslate nohighlight">\( \mathbf{s}(x,y) = k\,\frac{\mathbf{r}_\mathrm{lab}}{\lVert \mathbf{r}_\mathrm{lab}\rVert} - \mathbf{S}_0. \)</span></p> <p>This <span class="math notranslate nohighlight">\(\mathbf{s}\)</span> is the fundamental quantity used for spot finding (resolution filters), indexing, and refinement.</p> </section> <section id=two-theta-azimuth-resolution-and-q > <h3 id=two-theta-azimuth-resolution-and-q >1.2 Two-theta, azimuth, resolution and <span class="math notranslate nohighlight">\(q\)</span><a class=headerlink href="#two-theta-azimuth-resolution-and-q" title="Link to this heading">¶</a></h3> <p>The scattering angle <span class="math notranslate nohighlight">\(2\theta\)</span> is computed from <span class="math notranslate nohighlight">\(\mathbf{r}_\mathrm{lab}\)</span> via: <span class="math notranslate nohighlight">\( 2\theta = \arctan\!\left(\frac{\sqrt{x_\mathrm{lab}^2 + y_\mathrm{lab}^2}}{z_\mathrm{lab}}\right). \)</span></p> <p>Resolution (Å) at a pixel is: <span class="math notranslate nohighlight">\( d = \frac{\lambda}{2\sin(\theta)} = \frac{\lambda}{2\sin(2\theta/2)}. \)</span></p> <p>The magnitude <span class="math notranslate nohighlight">\(q = 2\pi/d\)</span> is used for radial binning and ice-ring handling.</p> </section> <section id=distance-from-the-ewald-sphere > <h3 id=distance-from-the-ewald-sphere >1.3 Distance from the Ewald sphere<a class=headerlink href="#distance-from-the-ewald-sphere" title="Link to this heading">¶</a></h3> <p>For a reciprocal lattice point <span class="math notranslate nohighlight">\(\mathbf{p}\)</span> (Å<span class="math notranslate nohighlight">\(^{-1}\)</span>), define: <span class="math notranslate nohighlight">\( \Delta_\mathrm{Ewald}(\mathbf{p}) = \lVert \mathbf{p} + \mathbf{S}_0\rVert - k. \)</span> Jungfraujoch uses <span class="math notranslate nohighlight">\(|\Delta_\mathrm{Ewald}|\)</span> as an operational proxy for excitation error. This appears in:</p> <ul class=simple > <li><p>still prediction (accept if <span class="math notranslate nohighlight">\(|\Delta_\mathrm{Ewald}|\le \Delta_\mathrm{cut}\)</span>),</p> <li><p>profile radius estimation (see §7.1),</p> <li><p>still partiality option in scaling/merging (§9.3).</p> </ul> </section> </section> <hr class=docutils /> <section id=azimuthal-integration-radial-profiles > <h2 id=azimuthal-integration-radial-profiles >2. Azimuthal integration (radial profiles)<a class=headerlink href="#azimuthal-integration-radial-profiles" title="Link to this heading">¶</a></h2> <p>Azimuthal integration produces a 1D radial profile <span class="math notranslate nohighlight">\(I(q)\)</span> or <span class="math notranslate nohighlight">\(I(d)\)</span> by histogramming pixels into radial bins. Pixels are <strong>not split</strong> across bins; each pixel contributes wholly to a single bin.</p> <section id=histogram-estimator > <h3 id=histogram-estimator >2.1 Histogram estimator<a class=headerlink href="#histogram-estimator" title="Link to this heading">¶</a></h3> <p>Let bin index <span class="math notranslate nohighlight">\(b(x,y)\in\{0,\dots,B-1\}\)</span> be precomputed from <span class="math notranslate nohighlight">\(q(x,y)\)</span> (or equivalently from <span class="math notranslate nohighlight">\(d(x,y)\)</span>). For each bin <span class="math notranslate nohighlight">\(b\)</span>:</p> <ul class=simple > <li><p>accumulate corrected intensity: <span class="math notranslate nohighlight">\( S_b = \sum_{(x,y):\,b(x,y)=b} I(x,y)\,C(x,y), \)</span></p> <li><p>and count: <span class="math notranslate nohighlight">\( N_b = \#\{(x,y):\,b(x,y)=b \text{ and pixel is valid}\}. \)</span></p> </ul> <p>A simple mean profile is then <span class="math notranslate nohighlight">\( \bar{I}_b = S_b / N_b\)</span> (when <span class="math notranslate nohighlight">\(N_b>0\)</span>). Invalid pixels (masked, saturated, detector error codes) are excluded.</p> </section> <section id=corrections-applied > <h3 id=corrections-applied >2.2 Corrections applied<a class=headerlink href="#corrections-applied" title="Link to this heading">¶</a></h3> <p>Two standard corrections are available:</p> <p><strong>(i) Solid angle / geometric correction.</strong> A commonly used approximation for flat detectors gives a <span class="math notranslate nohighlight">\(\cos^3(2\theta)\)</span> factor: <span class="math notranslate nohighlight">\( C_\Omega(2\theta) = \cos^3(2\theta). \)</span></p> <p><strong>(ii) Polarization correction.</strong> With polarization coefficient <span class="math notranslate nohighlight">\(P\)</span> (beamline dependent) and azimuth <span class="math notranslate nohighlight">\(\phi\)</span>: <span class="math notranslate nohighlight">\( C_\mathrm{pol}(2\theta,\phi) = \frac{1}{2}\left(1+\cos^2(2\theta) - P\cos(2\phi)\left(1-\cos^2(2\theta)\right)\right), \)</span> applied as a divisor to intensities (i.e. scale by <span class="math notranslate nohighlight">\(1/C_\mathrm{pol}\)</span>) when enabled.</p> </section> <section id=background-estimate-for-profiles > <h3 id=background-estimate-for-profiles >2.3 Background estimate for profiles<a class=headerlink href="#background-estimate-for-profiles" title="Link to this heading">¶</a></h3> <p>A background estimate is derived from the integrated profile using the azimuthal integration settings (details depend on the configured estimator). This background is used for monitoring and diagnostics; it is <strong>not</strong> the same as local Bragg-spot background used in summation integration (§8).</p> </section> </section> <hr class=docutils /> <section id=spot-finding-strong-pixels-bragg-spots > <h2 id=spot-finding-strong-pixels-bragg-spots >3. Spot finding (strong pixels → Bragg spots)<a class=headerlink href="#spot-finding-strong-pixels-bragg-spots" title="Link to this heading">¶</a></h2> <p>Spot finding is a two-stage process:</p> <ol class="arabic simple"> <li><p><strong>Strong-pixel selection</strong> using intensity and/or local signal-to-noise criteria.</p> <li><p><strong>Connected-component labeling (CCL)</strong> to group strong pixels into candidate spots, followed by spot-level filtering and feature extraction.</p> </ol> <section id=strong-pixel-detection-by-local-statistics > <h3 id=strong-pixel-detection-by-local-statistics >3.1 Strong-pixel detection by local statistics<a class=headerlink href="#strong-pixel-detection-by-local-statistics" title="Link to this heading">¶</a></h3> <p>For each pixel <span class="math notranslate nohighlight">\(i\)</span> with value <span class="math notranslate nohighlight">\(v_i\)</span>, consider a square window (nominally <span class="math notranslate nohighlight">\(31\times 31\)</span> pixels) around it. Let the window contain <span class="math notranslate nohighlight">\(n\)</span> valid pixels (excluding masked/bad/saturated), and define: <span class="math notranslate nohighlight">\( \Sigma = \sum v,\qquad \Sigma_2 = \sum v^2. \)</span></p> <p>To avoid biasing the local statistics by the test pixel itself, Jungfraujoch evaluates the pixel against the window with the pixel removed: <span class="math notranslate nohighlight">\( \Sigma' = \Sigma - v_i,\quad \Sigma_2' = \Sigma_2 - v_i^2,\quad n' = n-1. \)</span></p> <p>A variance-like quantity proportional to <span class="math notranslate nohighlight">\(n'^2\)</span> is formed: <span class="math notranslate nohighlight">\( V = n'\Sigma_2' - (\Sigma')^2, \)</span> and the deviation-from-mean quantity: <span class="math notranslate nohighlight">\( \Delta = v_i n' - \Sigma'. \)</span></p> <p>A pixel is considered strong if:</p> <ul class=simple > <li><p>it is above a photon/count threshold, and</p> <li><p><span class="math notranslate nohighlight">\(\Delta>0\)</span>, and</p> <li><p>the squared deviation exceeds a scaled variance: <span class="math notranslate nohighlight">\( \Delta^2 > V\cdot T^2, \)</span> where <span class="math notranslate nohighlight">\(T\)</span> is the configured signal-to-noise threshold.</p> </ul> <p>This is equivalent to a local z-score criterion but implemented in integer arithmetic to be robust and fast.</p> <p>Special cases:</p> <ul class=simple > <li><p>saturated pixels can be forced to “strong” (useful for detecting overloaded Bragg spots),</p> <li><p>invalid pixels are never strong.</p> </ul> </section> <section id=resolution-and-ice-ring-handling > <h3 id=resolution-and-ice-ring-handling >3.2 Resolution and ice-ring handling<a class=headerlink href="#resolution-and-ice-ring-handling" title="Link to this heading">¶</a></h3> <p>Spot finding can be restricted to a resolution range <span class="math notranslate nohighlight">\([d_\mathrm{high}, d_\mathrm{low}]\)</span> by masking pixels outside the range. Optionally, pixels in identified ice-ring regions can be tagged so that subsequent indexing/refinement may include or exclude them (see §4 and §6).</p> <p>A single per-image <strong>ice-ring score</strong> is derived from the azimuthally-integrated radial profile: for each hexagonal-ice powder ring (positions <span class="math notranslate nohighlight">\(d\)</span> from Moreau <em>et al.</em>, Acta Cryst D77, 2021), the profile intensity at the ring is divided by a smooth background estimated from the <em>whole</em> profile — a running median of the non-ice bins, interpolated under each ring — and the strongest ring’s ratio is reported (1 = no ice, <span class="math notranslate nohighlight">\(>1\)</span> = ice above background). A whole-profile background is used rather than a couple of adjacent shoulder bins so the estimate is robust to the radial binning: at a coarse Q-spacing a local shoulder can be only ~1 bin and would double-count the ring’s own edge (offline processing defaults to a fine 0.01 1/Å spacing, <code class="docutils literal notranslate"><span class=pre >--azim-q-spacing</span></code>, so the rings are well resolved). (A significance/z-score was considered but is uninformative here: with many photons any real ice ring is highly significant, so the discriminating quantity is the ice <em>magnitude</em>, i.e. this ratio.) It is stored per image (<code class="docutils literal notranslate"><span class=pre >ice_ring_score</span></code>, HDF5 <code class="docutils literal notranslate"><span class=pre >/entry/MX/iceRingScore</span></code>) as a monitoring quantity, distinct from the merge-time ice masking, which is data-driven from the per-ring merged CC1/2.</p> <p>A further optional safeguard removes isolated high-resolution “spur” spots by detecting large gaps in <span class="math notranslate nohighlight">\(1/d\)</span> (or <span class="math notranslate nohighlight">\(q\)</span>) space and discarding spots beyond the gap. This is intended for macromolecular diffraction where edge-of-detector backgrounds can be extremely low.</p> </section> <section id=connected-component-labeling-ccl > <h3 id=connected-component-labeling-ccl >3.3 Connected-component labeling (CCL)<a class=headerlink href="#connected-component-labeling-ccl" title="Link to this heading">¶</a></h3> <p>Strong pixels are grouped into connected components (adjacent strong pixels) using a CCL algorithm. Each component yields a candidate spot with:</p> <ul class=simple > <li><p>centroid <span class="math notranslate nohighlight">\((x,y)\)</span> (often intensity-weighted),</p> <li><p>pixel count (spot size),</p> <li><p>integrated spot intensity proxy (sum of pixel values),</p> <li><p>resolution <span class="math notranslate nohighlight">\(d\)</span> at the centroid (or mean over pixels),</p> <li><p>and quality flags (e.g. ice-ring classification).</p> </ul> <p>Spot-level filters include minimum/maximum pixel count and resolution limits.</p> </section> </section> <hr class=docutils /> <section id=indexing-overview > <h2 id=indexing-overview >4. Indexing overview<a class=headerlink href="#indexing-overview" title="Link to this heading">¶</a></h2> <p>Indexing maps observed reciprocal-space vectors <span class="math notranslate nohighlight">\(\mathbf{s}_i\)</span> to a lattice such that: <span class="math notranslate nohighlight">\( \mathbf{s}_i \approx h_i\mathbf{a}^* + k_i\mathbf{b}^* + l_i\mathbf{c}^*, \)</span> with integer <span class="math notranslate nohighlight">\((h_i,k_i,l_i)\)</span>.</p> <p>Jungfraujoch supports two complementary indexing strategies:</p> <ol class="arabic simple"> <li><p><strong>FFT-based indexing</strong> (Rossmann-type): does not require an a priori unit cell; suitable for unknown samples.</p> <li><p><strong>Fast-feedback indexing</strong> (TORO-like): requires an approximate unit cell; optimized for speed and feedback.</p> </ol> <p>Both feed into a common robust refinement/selection stage which maximizes the number of inliers under an indexing tolerance.</p> <section id=indexed-spot-decision-inlier-test > <h3 id=indexed-spot-decision-inlier-test >4.1 Indexed-spot decision (inlier test)<a class=headerlink href="#indexed-spot-decision-inlier-test" title="Link to this heading">¶</a></h3> <p>Given a trial lattice with direct basis vectors <span class="math notranslate nohighlight">\(\mathbf{a},\mathbf{b},\mathbf{c}\)</span> (used here as reciprocal-space dot-test vectors), fractional indices are estimated by: <span class="math notranslate nohighlight">\( h_f = \mathbf{s}\cdot\mathbf{a},\quad k_f = \mathbf{s}\cdot\mathbf{b},\quad l_f = \mathbf{s}\cdot\mathbf{c}. \)</span> Let <span class="math notranslate nohighlight">\((h,k,l)=(\mathrm{round}(h_f),\mathrm{round}(k_f),\mathrm{round}(l_f))\)</span> and define the fractional residual: <span class="math notranslate nohighlight">\( \delta^2 = (h_f-h)^2 + (k_f-k)^2 + (l_f-l)^2. \)</span> A spot is indexed if <span class="math notranslate nohighlight">\(\delta^2 \le \tau^2\)</span>, where <span class="math notranslate nohighlight">\(\tau\)</span> is the configured tolerance.</p> <p>For indexed spots, the reciprocal lattice point <span class="math notranslate nohighlight">\(\mathbf{p} = h\mathbf{a}^*+k\mathbf{b}^*+l\mathbf{c}^*\)</span> is used to compute <span class="math notranslate nohighlight">\(\Delta_\mathrm{Ewald}(\mathbf{p})\)</span> (stored as a diagnostic and later used in profile-radius estimation).</p> </section> </section> <hr class=docutils /> <section id=fft-indexing-unknown-unit-cell > <h2 id=fft-indexing-unknown-unit-cell >5. FFT indexing (unknown unit cell)<a class=headerlink href="#fft-indexing-unknown-unit-cell" title="Link to this heading">¶</a></h2> <p>FFT indexing follows a classical approach: detect dominant periodicities by projecting reciprocal-space points onto many directions and Fourier transforming the resulting 1D histograms.</p> <section id=directional-projections-and-histograms > <h3 id=directional-projections-and-histograms >5.1 Directional projections and histograms<a class=headerlink href="#directional-projections-and-histograms" title="Link to this heading">¶</a></h3> <p>Choose a set of unit vectors <span class="math notranslate nohighlight">\(\{\mathbf{u}_d\}\)</span> on a half-sphere (a near-uniform distribution generated via a golden-angle construction). For each direction <span class="math notranslate nohighlight">\(d\)</span>, form a histogram in the scalar projection: <span class="math notranslate nohighlight">\( t_{id} = \left|\mathbf{u}_d\cdot \mathbf{s}_i\right|. \)</span></p> <p>Bin width is chosen approximately as: <span class="math notranslate nohighlight">\( \Delta t \approx \frac{1}{2 L_\mathrm{max}}, \)</span> where <span class="math notranslate nohighlight">\(L_\mathrm{max}\)</span> is the maximum expected real-space unit-cell edge (Å). The histogram extent is tied to the maximum <span class="math notranslate nohighlight">\(q\)</span> used (set by a high-resolution cutoff for indexing).</p> </section> <section id=fft-peak-picking-and-candidate-vectors > <h3 id=fft-peak-picking-and-candidate-vectors >5.2 FFT peak picking and candidate vectors<a class=headerlink href="#fft-peak-picking-and-candidate-vectors" title="Link to this heading">¶</a></h3> <p>For each direction, the FFT magnitude spectrum is computed; peaks correspond to periodicities along <span class="math notranslate nohighlight">\(\mathbf{u}_d\)</span>. Each direction yields a candidate real-space length <span class="math notranslate nohighlight">\(L\)</span> with maximum spectral magnitude (subject to <span class="math notranslate nohighlight">\(L\ge L_\mathrm{min}\)</span>).</p> <p>Candidate vectors are <span class="math notranslate nohighlight">\(\mathbf{v}_d = L_d\,\mathbf{u}_d\)</span>.</p> <p>A collinearity filter removes nearly parallel vectors (e.g. within 5°) and attempts to resolve harmonic ambiguity: shorter “fundamental” vectors may be preferred over longer harmonics if their peak magnitude is sufficiently strong relative to the dominant peak.</p> </section> <section id=lattice-reduction-and-cell-candidates > <h3 id=lattice-reduction-and-cell-candidates >5.3 Lattice reduction and cell candidates<a class=headerlink href="#lattice-reduction-and-cell-candidates" title="Link to this heading">¶</a></h3> <p>Triples of candidate vectors are combined to form candidate bases <span class="math notranslate nohighlight">\((\mathbf{A},\mathbf{B},\mathbf{C})\)</span>. A simple reduction is applied: <span class="math notranslate nohighlight">\( \mathbf{B} \leftarrow \mathbf{B} - \mathrm{round}\!\left(\frac{\mathbf{B}\cdot\mathbf{A}}{\mathbf{A}\cdot\mathbf{A}}\right)\mathbf{A}, \)</span> $ \mathbf{C} \leftarrow \mathbf{C} - \mathrm{round}!\left(\frac{\mathbf{C}\cdot\mathbf{A}}{\mathbf{A}\cdot\mathbf{A}}\right)\mathbf{A}</p> <ul class=simple > <li><p>\mathrm{round}!\left(\frac{\mathbf{C}\cdot\mathbf{B}}{\mathbf{B}\cdot\mathbf{B}}\right)\mathbf{B}. $</p> </ul> <p>Candidates are filtered by allowed length and angle ranges.</p> </section> <section id=robust-refinement-and-best-cell-selection > <h3 id=robust-refinement-and-best-cell-selection >5.4 Robust refinement and best-cell selection<a class=headerlink href="#robust-refinement-and-best-cell-selection" title="Link to this heading">¶</a></h3> <p>Candidate bases are refined against observed spots using an iterative inlier‑focused least‑squares procedure (trimmed/contracting threshold). The output cell is chosen to:</p> <ol class="arabic simple"> <li><p>maximize the number of indexed spots under the tolerance <span class="math notranslate nohighlight">\(\tau\)</span>, and</p> <li><p>break ties by a refined score (smaller residual threshold/score is preferred).</p> </ol> <p>An optional reference unit cell (if supplied) restricts acceptance to cells within a relative distance tolerance in edge lengths (permutation-invariant).</p> </section> </section> <hr class=docutils /> <section id=bravais-lattice-centering-inference-lattice-search > <h2 id=bravais-lattice-centering-inference-lattice-search >6. Bravais lattice / centering inference (“lattice search”)<a class=headerlink href="#bravais-lattice-centering-inference-lattice-search" title="Link to this heading">¶</a></h2> <p>If the space group is supplied by the user, its lattice constraints are assumed for refinement and subsequent processing.</p> <p>If not, Jungfraujoch attempts to infer the most plausible Bravais lattice type from the metric tensor after Niggli reduction:</p> <ol class="arabic simple"> <li><p><strong>Niggli reduction</strong> is performed to obtain a reduced cell in <span class="math notranslate nohighlight">\(G^6\)</span> representation (Gruber vector).</p> <li><p>The reduced cell is compared against a list of Niggli classes corresponding to Bravais lattices and centerings.</p> <li><p>The highest-symmetry class that matches within tolerances is selected (relative metric tolerance and angular tolerance).</p> </ol> <p>The output includes:</p> <ul class=simple > <li><p>a conventional cell,</p> <li><p>crystal system (triclinic, monoclinic, …),</p> <li><p>centering symbol <span class="math notranslate nohighlight">\(P, A, B, C, I, F, R\)</span>.</p> </ul> <p>This stage provides centering information used for systematic absences in prediction (§7.3) and for reporting.</p> <p><strong>Note.</strong> In ambiguous or special cases, forcing space group to <span class="math notranslate nohighlight">\(P1\)</span> (no symmetry assumptions) is recommended.</p> </section> <hr class=docutils /> <section id=geometry-and-lattice-refinement > <h2 id=geometry-and-lattice-refinement >7. Geometry and lattice refinement<a class=headerlink href="#geometry-and-lattice-refinement" title="Link to this heading">¶</a></h2> <p>Refinement adjusts experimental geometry and crystal parameters to minimize discrepancies between observed spot reciprocal vectors and those predicted by a lattice model with integer indices.</p> <section id=parameterization > <h3 id=parameterization >7.1 Parameterization<a class=headerlink href="#parameterization" title="Link to this heading">¶</a></h3> <p>The refinement jointly optimizes, depending on mode and constraints:</p> <ul class=simple > <li><p>beam center <span class="math notranslate nohighlight">\((x_\mathrm{beam}, y_\mathrm{beam})\)</span>,</p> <li><p>detector distance <span class="math notranslate nohighlight">\(D\)</span>,</p> <li><p>detector tilt angles (two-angle model; third rotation often held at 0),</p> <li><p>rotation axis direction (for rotation datasets),</p> <li><p>crystal orientation (a global rotation),</p> <li><p>unit-cell parameters, with constraints determined by inferred crystal system.</p> </ul> <p>For higher symmetries, constraints are enforced, e.g.</p> <ul class=simple > <li><p>cubic: <span class="math notranslate nohighlight">\(a=b=c,\ \alpha=\beta=\gamma=90^\circ\)</span>,</p> <li><p>tetragonal: <span class="math notranslate nohighlight">\(a=b\)</span>,</p> <li><p>hexagonal: <span class="math notranslate nohighlight">\(a=b,\ \gamma=120^\circ\)</span>,</p> <li><p>monoclinic (unique axis <span class="math notranslate nohighlight">\(b\)</span>): <span class="math notranslate nohighlight">\(\alpha=\gamma=90^\circ\)</span>, <span class="math notranslate nohighlight">\(\beta\)</span> refined.</p> </ul> </section> <section id=residuals-and-objective > <h3 id=residuals-and-objective >7.2 Residuals and objective<a class=headerlink href="#residuals-and-objective" title="Link to this heading">¶</a></h3> <p>For each indexed spot assigned integer <span class="math notranslate nohighlight">\((h,k,l)\)</span>, compute:</p> <ul class=simple > <li><p>observed reciprocal vector <span class="math notranslate nohighlight">\(\mathbf{s}_\mathrm{obs}\)</span> from its detector position and current geometry,</p> <li><p>predicted reciprocal vector <span class="math notranslate nohighlight">\(\mathbf{s}_\mathrm{pred}(h,k,l;\ \text{lattice params})\)</span>.</p> </ul> <p>Residual is: <span class="math notranslate nohighlight">\( \mathbf{r} = \mathbf{s}_\mathrm{obs} - \mathbf{s}_\mathrm{pred}. \)</span></p> <p>A non-linear least squares solver minimizes <span class="math notranslate nohighlight">\(\sum \|\mathbf{r}\|^2\)</span> over all selected inlier spots.</p> </section> <section id=rotation-datasets-bringing-observations-to-a-common-reference-frame > <h3 id=rotation-datasets-bringing-observations-to-a-common-reference-frame >7.3 Rotation datasets: bringing observations to a common reference frame<a class=headerlink href="#rotation-datasets-bringing-observations-to-a-common-reference-frame" title="Link to this heading">¶</a></h3> <p>For oscillation/rotation data, each image corresponds to a rotation angle <span class="math notranslate nohighlight">\(\phi\)</span> about an axis <span class="math notranslate nohighlight">\(\mathbf{m}_2\)</span>. Observed reciprocal vectors are rotated “back to start” so that all images are refined in a single reference crystal frame: <span class="math notranslate nohighlight">\( \mathbf{s}_\mathrm{obs,ref} = R(\phi)\,\mathbf{s}_\mathrm{obs}, \)</span> with <span class="math notranslate nohighlight">\(R(\phi)\)</span> constructed from the axis-angle representation of the goniometer model.</p> </section> <section id=multi-stage-tightening-of-inlier-tolerance > <h3 id=multi-stage-tightening-of-inlier-tolerance >7.4 Multi-stage tightening of inlier tolerance<a class=headerlink href="#multi-stage-tightening-of-inlier-tolerance" title="Link to this heading">¶</a></h3> <p>Refinement is performed in stages with decreasing acceptance tolerance for including reflections (e.g. from coarse to fine), which stabilizes convergence when starting from imperfect indexing and approximate geometry.</p> </section> </section> <hr class=docutils /> <section id=bragg-integration > <h2 id=bragg-integration >9. Bragg integration<a class=headerlink href="#bragg-integration" title="Link to this heading">¶</a></h2> <p>Jungfraujoch predicts reflection positions for integration by enumerating Miller indices within a resolution cutoff and accepting those that satisfy a diffraction condition model.</p> <section id=enumerating-reciprocal-lattice-points > <h3 id=enumerating-reciprocal-lattice-points >8.1 Enumerating reciprocal lattice points<a class=headerlink href="#enumerating-reciprocal-lattice-points" title="Link to this heading">¶</a></h3> <p>For a maximum resolution <span class="math notranslate nohighlight">\(d_\mathrm{min}\)</span>, accept <span class="math notranslate nohighlight">\((h,k,l)\)</span> such that: <span class="math notranslate nohighlight">\( \lVert \mathbf{p}(h,k,l)\rVert^2 = \lVert h\mathbf{a}^* + k\mathbf{b}^* + l\mathbf{c}^*\rVert^2 \le \left(\frac{1}{d_\mathrm{min}}\right)^2. \)</span></p> </section> <section id=still-prediction-excitation-error-cutoff > <h3 id=still-prediction-excitation-error-cutoff >8.2 Still prediction (excitation-error cutoff)<a class=headerlink href="#still-prediction-excitation-error-cutoff" title="Link to this heading">¶</a></h3> <p>For still images, the diffracting condition is approximated by an excitation-error cutoff: <span class="math notranslate nohighlight">\( \left|\Delta_\mathrm{Ewald}(\mathbf{p})\right| \le \Delta_\mathrm{cut}. \)</span> Accepted reflections are projected to the detector by intersecting the diffracted direction <span class="math notranslate nohighlight">\(\mathbf{S}=\mathbf{S}_0+\mathbf{p}\)</span> with the detector plane, using the current geometry.</p> </section> <section id=rotation-prediction-laue-equation-partiality-model > <h3 id=rotation-prediction-laue-equation-partiality-model >8.3 Rotation prediction (Laue equation + partiality model)<a class=headerlink href="#rotation-prediction-laue-equation-partiality-model" title="Link to this heading">¶</a></h3> <p>For rotation/oscillation datasets, Jungfraujoch solves for rotation angles <span class="math notranslate nohighlight">\(\phi\)</span> where the rotated reciprocal lattice point satisfies the Ewald-sphere condition. In an XDS-like notation, define:</p> <ul class=simple > <li><p>rotation axis unit vector <span class="math notranslate nohighlight">\(\mathbf{m}_2\)</span>,</p> <li><p><span class="math notranslate nohighlight">\(\mathbf{S}_0\)</span> incident vector,</p> <li><p><span class="math notranslate nohighlight">\(\mathbf{S}(\phi)=\mathbf{S}_0+\mathbf{p}(\phi)\)</span>.</p> </ul> <p>A key quantity is: <span class="math notranslate nohighlight">\( \zeta = \left|\mathbf{m}_2\cdot \mathbf{e}_1\right|,\quad \mathbf{e}_1 = \frac{\mathbf{S}\times \mathbf{S}_0}{\lVert \mathbf{S}\times \mathbf{S}_0\rVert}, \)</span> which also appears in XDS as the Lorentz component linked to the rotation axis.</p> <p>A Gaussian mosaicity model yields a partiality fraction over an oscillation width <span class="math notranslate nohighlight">\(\Delta\phi\)</span>:</p> <p><span class="math notranslate nohighlight">\( P(\phi;\sigma_M,\zeta,\Delta\phi) = \frac{1}{2}\left[\mathrm{erf}\!\left(\frac{\phi+\Delta\phi/2}{\sqrt{2}\,\sigma_M/\zeta}\right) - \mathrm{erf}\!\left(\frac{\phi-\Delta\phi/2}{\sqrt{2}\,\sigma_M/\zeta}\right)\right], \)</span></p> <p>with mosaicity <span class="math notranslate nohighlight">\(\sigma_M\)</span> in radians.</p> <p>Reflections are predicted if they meet minimum <span class="math notranslate nohighlight">\(\zeta\)</span> and mosaicity-window criteria, and their predicted detector coordinates fall on the active detector area.</p> </section> <section id=systematic-absences-centering > <h3 id=systematic-absences-centering >8.4 Systematic absences (centering)<a class=headerlink href="#systematic-absences-centering" title="Link to this heading">¶</a></h3> <p>Systematic absences are applied at least at the centering level (prior to full space-group symmetry). For centering symbol <span class="math notranslate nohighlight">\(C\)</span>:</p> <ul class=simple > <li><p><span class="math notranslate nohighlight">\(I\)</span>: absent if <span class="math notranslate nohighlight">\(h+k+l\)</span> odd,</p> <li><p><span class="math notranslate nohighlight">\(A\)</span>: absent if <span class="math notranslate nohighlight">\(k+l\)</span> odd,</p> <li><p><span class="math notranslate nohighlight">\(B\)</span>: absent if <span class="math notranslate nohighlight">\(h+l\)</span> odd,</p> <li><p><span class="math notranslate nohighlight">\(C\)</span>: absent if <span class="math notranslate nohighlight">\(h+k\)</span> odd,</p> <li><p><span class="math notranslate nohighlight">\(F\)</span>: absent if any of <span class="math notranslate nohighlight">\(h+k, h+l, k+l\)</span> is odd,</p> <li><p><span class="math notranslate nohighlight">\(R\)</span>: absent if <span class="math notranslate nohighlight">\((-h+k+l)\bmod 3 \ne 0\)</span>,</p> <li><p><span class="math notranslate nohighlight">\(P\)</span>: no centering absences.</p> </ul> </section> </section> <hr class=docutils /> <section id=d-bragg-integration-profile-fitting-over-a-three-ring-roi > <h2 id=d-bragg-integration-profile-fitting-over-a-three-ring-roi >9. 2D Bragg integration (profile fitting over a three-ring ROI)<a class=headerlink href="#d-bragg-integration-profile-fitting-over-a-three-ring-roi" title="Link to this heading">¶</a></h2> <p>Jungfraujoch integrates each predicted reflection in the detector plane over a CrystFEL-inspired “three-ring” region of interest (§9.1). The <strong>default</strong> extraction is <strong>profile fitting</strong> (Kabsch; §9.3), which weights each pixel by a fitted spot profile and so recovers weak reflections far better than plain summation; plain box summation (§9.2) is retained as the seed for the profile and as a fallback. Both methods share the same ROI and background model, and emit the same per-reflection <span class="math notranslate nohighlight">\((I,\sigma,\text{partiality},d)\)</span>, so scaling, the rotation combine (§10.6) and merging consume either unchanged.</p> <section id=regions-of-interest > <h3 id=regions-of-interest >9.1 Regions of interest<a class=headerlink href="#regions-of-interest" title="Link to this heading">¶</a></h3> <p>For each predicted reflection at <span class="math notranslate nohighlight">\((x_p,y_p)\)</span>, define three radii:</p> <ul class=simple > <li><p><span class="math notranslate nohighlight">\(r_1\)</span>: inner signal radius,</p> <li><p><span class="math notranslate nohighlight">\(r_2\)</span>: inner background radius,</p> <li><p><span class="math notranslate nohighlight">\(r_3\)</span>: outer background radius.</p> </ul> <p>Pixels are classified by their squared distance <span class="math notranslate nohighlight">\(r^2=(x-x_p)^2+(y-y_p)^2\)</span>:</p> <ul class=simple > <li><p><strong>signal region:</strong> <span class="math notranslate nohighlight">\(r^2 < r_1^2\)</span>,</p> <li><p><strong>background annulus:</strong> <span class="math notranslate nohighlight">\(r_2^2 \le r^2 < r_3^2\)</span>.</p> </ul> <p>Invalid pixels (masked/bad/saturated) are excluded from both sums.</p> </section> <section id=box-summation-seed-and-fallback > <h3 id=box-summation-seed-and-fallback >9.2 Box summation (seed and fallback)<a class=headerlink href="#box-summation-seed-and-fallback" title="Link to this heading">¶</a></h3> <p>Let:</p> <ul class=simple > <li><p><span class="math notranslate nohighlight">\(S = \sum I(x,y)\)</span> over signal pixels,</p> <li><p><span class="math notranslate nohighlight">\(n_S\)</span> = number of valid signal pixels,</p> <li><p><span class="math notranslate nohighlight">\(B = \sum I(x,y)\)</span> over background pixels,</p> <li><p><span class="math notranslate nohighlight">\(n_B\)</span> = number of valid background pixels.</p> </ul> <p>Background per pixel and integrated intensity: <span class="math notranslate nohighlight">\( \hat{b} = \frac{B}{n_B},\qquad \hat{I} = S - n_S \hat{b}, \)</span> with a Poisson-like uncertainty <span class="math notranslate nohighlight">\(\sigma(\hat{I})\approx\sqrt{S}\)</span> (floored at 1). A reflection is accepted as “observed” only if all signal pixels were valid and <span class="math notranslate nohighlight">\(n_B\)</span> exceeds a minimum. This box sum is the classical estimator; it is used directly with <code class="docutils literal notranslate"><span class=pre >--integrator</span> <span class=pre >boxsum</span></code>, and otherwise seeds the profile fit below.</p> <p>The background mean is computed with a single <strong>high-outlier reject</strong> (drop ring pixels above <span class="math notranslate nohighlight">\(\hat{b}+3\sqrt{\hat{b}}\)</span>, recompute): a bandwidth-streaked high-resolution spot or a close neighbour can leak into the ring and bias the mean high, over-subtracting and driving weak high-resolution intensities negative. A clean Poisson background is essentially unchanged by the cut.</p> </section> <section id=profile-fitted-extraction-default > <h3 id=profile-fitted-extraction-default >9.3 Profile-fitted extraction (default)<a class=headerlink href="#profile-fitted-extraction-default" title="Link to this heading">¶</a></h3> <p>A fixed signal disk captures a <em>width-dependent</em> fraction of each spot, which puts a multiplicative floor on the per-observation precision of strong reflections and weights weak reflections poorly. Profile fitting removes this by extracting each intensity against a fitted spot shape, without needing reference intensities. Per frame:</p> <ol class="arabic simple"> <li><p><strong>Seed.</strong> Box-sum every reflection (§9.2) to get a rough intensity and observed centroid, and select strong spots (significance <span class="math notranslate nohighlight">\(\ge 5\)</span>).</p> <li><p><strong>Build the profile.</strong> From the strong spots, form a profile <strong>per resolution shell</strong>: an isotropic Gaussian of the measured second moment (the default), or an empirical averaged grid. The width is shell-dependent because spot size grows with resolution; the intrinsic spot is essentially round in the detector plane (per-detector-region and crystal-anisotropy profiles were evaluated and add nothing — the real crystal anisotropy lives in the discarded rocking direction). When a finite energy bandwidth is set, however, it smears each spot <strong>radially</strong> by <span class="math notranslate nohighlight">\(\sigma_\mathrm{bw}=\text{bandwidth}\cdot R_\mathrm{px}\)</span> (distance from the beam centre, large at high resolution), turning high-resolution spots into radial streaks. There the profile is elongated <em>only along the radial direction</em> per reflection (<span class="math notranslate nohighlight">\(\sigma^2_\mathrm{radial}=\sigma^2_\mathrm{intrinsic}+\sigma_\mathrm{bw}^2\)</span>, tangential unchanged) on a grid grown to hold the streak, capturing it without the tangential background an isotropic widening would add.</p> <li><p><strong>Fit (Kabsch).</strong> With profile <span class="math notranslate nohighlight">\(P\)</span>, background <span class="math notranslate nohighlight">\(B\)</span> and the shell variance model, the intensity and its uncertainty are <span class="math notranslate nohighlight">\( I = \frac{\sum P\,(c-B)/v}{\sum P^2/v},\qquad \sigma = \sqrt{\frac{1}{\sum P^2/v}},\qquad v = B + \max(I,0)\,P, \)</span> where <span class="math notranslate nohighlight">\(c\)</span> is the pixel value and the de-biased variance <span class="math notranslate nohighlight">\(v\)</span> (background plus model signal, rather than the down-fluctuating observed count) is iterated. The rotation/excitation partiality is carried exactly as in the box-sum path.</p> </ol> <p>The integrator is selected by <code class="docutils literal notranslate"><span class=pre >--integrator</span> <span class=pre >boxsum|gaussian|empirical</span></code> (default <code class="docutils literal notranslate"><span class=pre >gaussian</span></code>).</p> </section> <section id=lorentzpolarization-factor-handling > <h3 id=lorentzpolarization-factor-handling >9.4 Lorentz–polarization factor handling<a class=headerlink href="#lorentzpolarization-factor-handling" title="Link to this heading">¶</a></h3> <p>For integrated reflections, polarization correction can be applied as a multiplicative correction to the reflection scale via the geometry-based polarization term (§2.2). A Lorentz-like factor is carried as <code class="docutils literal notranslate"><span class=pre >rlp</span></code> in predictions, and used during scaling/merging (§10).</p> </section> </section> <hr class=docutils /> <section id=scaling-and-merging > <h2 id=scaling-and-merging >10. Scaling and merging<a class=headerlink href="#scaling-and-merging" title="Link to this heading">¶</a></h2> <p>After per-image integration, Jungfraujoch scales observations and merges them into unique reflections. The design is intentionally compatible with XDS/XSCALE concepts, while supporting both still and rotation partiality models.</p> <section id=observation-model > <h3 id=observation-model >10.1 Observation model<a class=headerlink href="#observation-model" title="Link to this heading">¶</a></h3> <p>For an observation <span class="math notranslate nohighlight">\(j\)</span> of a unique reflection <span class="math notranslate nohighlight">\(h\)</span> on image (or image group) <span class="math notranslate nohighlight">\(i\)</span>, the predicted measured intensity is modeled as: <span class="math notranslate nohighlight">\( I_{ij} \approx G_i \, L_{ij}\, P_{ij}\, I_h, \)</span> where:</p> <ul class=simple > <li><p><span class="math notranslate nohighlight">\(G_i\)</span> is the image scale factor,</p> <li><p><span class="math notranslate nohighlight">\(L_{ij}\)</span> is a Lorentz-like / geometry factor (stored as <code class="docutils literal notranslate"><span class=pre >rlp</span></code> or derived),</p> <li><p><span class="math notranslate nohighlight">\(P_{ij}\)</span> is a partiality term (model-dependent),</p> <li><p><span class="math notranslate nohighlight">\(I_h\)</span> is the merged (true) intensity parameter for that unique reflection.</p> </ul> <p>A least-squares objective is minimized: <span class="math notranslate nohighlight">\( \sum_{ij} \left(\frac{I_{ij}^{\mathrm{pred}} - I_{ij}^{\mathrm{obs}}}{\sigma_{ij}}\right)^2 \)</span> with regularization on <span class="math notranslate nohighlight">\(G_i\)</span> and optional smoothness constraints (particularly meaningful for rotation series).</p> </section> <section id=partiality-models-available > <h3 id=partiality-models-available >10.2 Partiality models available<a class=headerlink href="#partiality-models-available" title="Link to this heading">¶</a></h3> <p>Jungfraujoch supports several partiality choices:</p> <ol class="arabic simple"> <li><p><strong>Rotation partiality</strong> (XDS-like; see §8.3): <span class="math notranslate nohighlight">\( P_{ij} = \frac{1}{2}\left[ \mathrm{erf}\!\left(\frac{\Delta\phi_{ij}+\Delta\phi/2}{\sqrt{2}\,\sigma_{M,i}/\zeta_{ij}}\right) - \mathrm{erf}\!\left(\frac{\Delta\phi_{ij}-\Delta\phi/2}{\sqrt{2}\,\sigma_{M,i}/\zeta_{ij}}\right) \right]. \)</span> Mosaicity <span class="math notranslate nohighlight">\(\sigma_{M,i}\)</span> can be refined per image group with bounds.</p> <li><p><strong>Still partiality</strong> (excitation-error proxy): <span class="math notranslate nohighlight">\( P_{ij} = \exp\!\left(-\frac{\Delta_\mathrm{Ewald}^2}{R_i^2}\right), \)</span> where <span class="math notranslate nohighlight">\(R_i^2\)</span> is a refined width parameter (bounded).</p> <li><p><strong>Unity</strong>: <span class="math notranslate nohighlight">\(P_{ij}=1\)</span>.</p> <li><p><strong>Fixed</strong>: use the per-reflection partiality carried from prediction.</p> </ol> <p>Reflections below a minimum partiality can be rejected from merging to avoid unstable corrections.</p> </section> <section id=regularization-and-smoothness > <h3 id=regularization-and-smoothness >10.3 Regularization and smoothness<a class=headerlink href="#regularization-and-smoothness" title="Link to this heading">¶</a></h3> <p>To stabilize scale determination, a weak prior <span class="math notranslate nohighlight">\(G_i\approx 1\)</span> is used. For rotation datasets, optional smoothness encourages slowly varying scales and mosaicity: <span class="math notranslate nohighlight">\( \log G_{i-1} - 2\log G_i + \log G_{i+1} \approx 0, \)</span> (and similarly for mosaicity), reflecting the expectation of gradual changes during a rotation scan.</p> </section> <section id=merging-estimator > <h3 id=merging-estimator >10.4 Merging estimator<a class=headerlink href="#merging-estimator" title="Link to this heading">¶</a></h3> <p>After refinement, corrected observations are formed: <span class="math notranslate nohighlight">\( I^{\mathrm{corr}}_{ij} = \frac{I^{\mathrm{obs}}_{ij}}{G_i L_{ij} P_{ij}},\qquad \sigma^{\mathrm{corr}}_{ij} = \frac{\sigma^{\mathrm{obs}}_{ij}}{G_i L_{ij} P_{ij}}. \)</span></p> <p>Unique intensities are merged by inverse-variance weighted mean: <span class="math notranslate nohighlight">\( I_h = \frac{\sum_j w_j I^{\mathrm{corr}}_{ij}}{\sum_j w_j},\qquad w_j = \frac{1}{(\sigma^{\mathrm{corr}}_{ij})^2}. \)</span></p> <p>An internal-consistency term can inflate uncertainties when multiple observations are present, in the spirit of XSCALE.</p> </section> <section id=merging-statistics > <h3 id=merging-statistics >10.5 Merging statistics<a class=headerlink href="#merging-statistics" title="Link to this heading">¶</a></h3> <p>Per-shell and overall merging statistics are computed on corrected intensities, including:</p> <ul class=simple > <li><p>number of observations,</p> <li><p>number of unique reflections,</p> <li><p>mean <span class="math notranslate nohighlight">\(I/\sigma(I)\)</span>,</p> <li><p>an R<span class="math notranslate nohighlight">\(_\mathrm{meas}\)</span>-like quantity derived from within‑HKL deviations (shell-binned).</p> </ul> <p>Completeness requires enumeration of possible reflections given a unit cell and symmetry; where this is not fully available, completeness may be reported as 0 or omitted.</p> </section> <section id=rotation-datasets-combining-partials-into-fulls-3d-integration > <h3 id=rotation-datasets-combining-partials-into-fulls-3d-integration >10.6 Rotation datasets: combining partials into fulls (3D integration)<a class=headerlink href="#rotation-datasets-combining-partials-into-fulls-3d-integration" title="Link to this heading">¶</a></h3> <p>In a rotation scan a reflection is recorded as a series of <em>partials</em> spread across the frames its rocking curve crosses. Merging those partials directly would force the merge error model to absorb the rocking-curve slicing as if it were measurement noise, capping the achievable <span class="math notranslate nohighlight">\(I/\sigma\)</span>. For rotation data Jungfraujoch instead <strong>combines</strong> each reflection’s partials into a single <em>full</em> intensity first, then scales and merges the fulls — a 3D integration over the rocking curve.</p> <p>The combine groups each reflection’s partials into rocking events (contiguous runs of frames) and reduces each event to one full:</p> <ul class=simple > <li><p><strong>De-biased weighted sum.</strong> Partials are combined by inverse-variance weighting, where each partial’s variance is its background-noise component plus the <em>model</em> signal shared across the event (Kabsch profile-fit form). Using the shared model signal rather than the individual down-fluctuating intensity stops weak partials from being over-weighted, which would otherwise inflate the merged error model. The weights depend on the full, so the estimate is iterated.</p> <li><p><strong>Captured fraction.</strong> The partiality summed over the event, <span class="math notranslate nohighlight">\(f=\min(1,\sum_j p_j)\)</span>, measures how completely the rocking curve was sampled; it replaces a per-partial minimum-partiality cut, because an event seen over only a few percent of its curve is unreliable however many frames it spans.</p> <li><p><strong>Capture-aware uncertainty.</strong> A full captured incompletely (<span class="math notranslate nohighlight">\(f<1\)</span>) is extrapolated and biased high. The unobserved fraction is charged as an extra systematic uncertainty, <span class="math notranslate nohighlight">\(\sigma^2 \leftarrow \sigma^2 + \big(c\,(1-f)\,I\big)^2\)</span>, so the merge down-weights these extrapolated fulls and the error model treats their scatter as expected. It is enabled by default for the rotation path.</p> </ul> <p>The fulls are then re-scaled in the XDS sense — a per-image scale refit directly on the complete reflections under the unity partiality model — and merged (§10.4). Because every merged observation is now a counting-statistics-limited full rather than a partiality-divided slice, the error model reaches a far higher asymptotic <span class="math notranslate nohighlight">\(I/\sigma\)</span>.</p> </section> </section> <hr class=docutils /> <section id=mosaicity-and-profile-radius-monitoring > <h2 id=mosaicity-and-profile-radius-monitoring >11. Mosaicity and “profile radius” monitoring<a class=headerlink href="#mosaicity-and-profile-radius-monitoring" title="Link to this heading">¶</a></h2> <section id=profile-radius-intrinsic-excitation-error-width > <h3 id=profile-radius-intrinsic-excitation-error-width >11.1 Profile radius (intrinsic excitation-error width)<a class=headerlink href="#profile-radius-intrinsic-excitation-error-width" title="Link to this heading">¶</a></h3> <p>The “profile radius” is the intrinsic angular width of a reflection — crystal mosaicity plus beam divergence — estimated from the spread of <span class="math notranslate nohighlight">\(\Delta_\mathrm{Ewald}\)</span> over indexed spots, <span class="math notranslate nohighlight">\( R \approx \sqrt{\tfrac{1}{N}\sum_i \Delta_{\mathrm{Ewald},i}^2}. \)</span> When the beam has a finite energy bandwidth, that bandwidth smears each reflection radially by <span class="math notranslate nohighlight">\(\sigma_\mathrm{bw}\approx \mathrm{bandwidth}\cdot\lambda/2d^2\)</span> (largest at high resolution), which also broadens the measured <span class="math notranslate nohighlight">\(\Delta_\mathrm{Ewald}\)</span> spread. Since prediction re-applies the bandwidth term per reflection (§8.2), this contribution is deconvolved from the estimate — <span class="math notranslate nohighlight">\(R^2 = \langle\Delta_\mathrm{Ewald}^2\rangle - \langle\sigma_\mathrm{bw}^2\rangle\)</span> — so that <span class="math notranslate nohighlight">\(R\)</span> is the intrinsic width and bandwidth is not double-counted. Still predictions use an excitation-error cutoff proportional to <span class="math notranslate nohighlight">\(R\)</span>.</p> </section> <section id=mosaicity-from-rotation-data > <h3 id=mosaicity-from-rotation-data >11.2 Mosaicity from rotation data<a class=headerlink href="#mosaicity-from-rotation-data" title="Link to this heading">¶</a></h3> <p>For rotation data the mosaicity <span class="math notranslate nohighlight">\(\sigma_M\)</span> is estimated by maximum likelihood from the rocking offsets <span class="math notranslate nohighlight">\(\tau\)</span> of indexed spots, using the XDS reflection-fraction model <span class="math notranslate nohighlight">\(R(\tau;\sigma_M/\zeta)\)</span> (Kabsch 2010): each spot’s exact Bragg angle is located near its frame, <span class="math notranslate nohighlight">\(\zeta\)</span> (the rotation-axis Lorentz component) is computed, and <span class="math notranslate nohighlight">\(\sigma_M\)</span> is chosen to maximize <span class="math notranslate nohighlight">\(\sum_i \log R(\tau_i;\sigma_M/\zeta_i)\)</span>.</p> <p>The <span class="math notranslate nohighlight">\(\phi\)</span> search window for the Bragg angle is set <strong>wider than the oscillation</strong>, so that reflections recorded at large rocking offset are included. These tail reflections carry most of the information about the mosaic width; a window limited to the oscillation range would truncate the <span class="math notranslate nohighlight">\(\tau\)</span> distribution and bias <span class="math notranslate nohighlight">\(\sigma_M\)</span> low.</p> <p>The estimated mosaicity feeds the rotation prediction (how many frames each reflection spans, §8.3) and the rotation partiality (§10.2). It is <strong>held fixed during scaling</strong>: in the per-image scale fit the mosaicity is degenerate with the scale <span class="math notranslate nohighlight">\(G\)</span> (both rescale the predicted intensity), so refining it there is unstable. A correct mosaicity matters because it controls both how much of each rocking curve is captured and the partiality used to form fulls (§10.6); too small a value truncates the captured curve and over-peaks the partiality, degrading the combined fulls.</p> </section> </section> <hr class=docutils /> <section id=wilson-statistics-and-frenchwilson-treatment > <h2 id=wilson-statistics-and-frenchwilson-treatment >12. Wilson statistics and French–Wilson treatment<a class=headerlink href="#wilson-statistics-and-frenchwilson-treatment" title="Link to this heading">¶</a></h2> <section id=per-shell-i-i > <h3 id=per-shell-i-i >12.1 Per-shell ⟨I/σ(I)⟩<a class=headerlink href="#per-shell-i-i" title="Link to this heading">¶</a></h3> <p>For monitoring integration quality, Jungfraujoch reports mean <span class="math notranslate nohighlight">\(\langle I/\sigma(I)\rangle\)</span> in a fixed number of resolution shells. Shelling is performed in <span class="math notranslate nohighlight">\(1/d^2\)</span> space (typical of crystallographic practice).</p> </section> <section id=wilson-plot-b-factor-proxy > <h3 id=wilson-plot-b-factor-proxy >12.2 Wilson plot (B-factor proxy)<a class=headerlink href="#wilson-plot-b-factor-proxy" title="Link to this heading">¶</a></h3> <p>A Wilson-type analysis is computed by binning intensities by resolution and fitting: <span class="math notranslate nohighlight">\( \langle I\rangle \propto \exp\!\left(-\frac{B}{2}\frac{1}{d^2}\right), \)</span> i.e. <span class="math notranslate nohighlight">\( \log \langle I\rangle = \mathrm{const} - \frac{B}{2}\left(\frac{1}{d^2}\right). \)</span> A linear regression of <span class="math notranslate nohighlight">\(\log\langle I\rangle\)</span> vs <span class="math notranslate nohighlight">\(1/d^2\)</span> provides an estimate of <span class="math notranslate nohighlight">\(B\)</span>, subject to basic quality checks (e.g. <span class="math notranslate nohighlight">\(R^2\)</span> threshold).</p> </section> <section id=frenchwilson-posterior-expectation-of-i-and-f > <h3 id=frenchwilson-posterior-expectation-of-i-and-f >12.3 French–Wilson (posterior expectation of I and |F|)<a class=headerlink href="#frenchwilson-posterior-expectation-of-i-and-f" title="Link to this heading">¶</a></h3> <p>To mitigate negative intensities and obtain physically meaningful amplitudes, Jungfraujoch implements a French–Wilson style Bayesian treatment using per-shell mean intensity as a prior scale.</p> <p>For each merged observation <span class="math notranslate nohighlight">\(I_\mathrm{obs}\)</span> with uncertainty <span class="math notranslate nohighlight">\(\sigma\)</span>, the posterior over true intensity <span class="math notranslate nohighlight">\(I\ge 0\)</span> is: <span class="math notranslate nohighlight">\( p(I\mid I_\mathrm{obs}) \propto p(I)\,\exp\!\left(-\frac{(I_\mathrm{obs}-I)^2}{2\sigma^2}\right), \)</span> with priors differing between acentric and centric cases (standard Wilson distributions).</p> <p>Numerical quadrature over a scaled intensity variable is used to compute posterior moments:</p> <ul class=simple > <li><p><span class="math notranslate nohighlight">\(\langle I\rangle\)</span>,</p> <li><p><span class="math notranslate nohighlight">\(\langle |F|\rangle = \langle \sqrt{I}\rangle\)</span>, and an amplitude uncertainty estimate via: <span class="math notranslate nohighlight">\( \sigma_F \approx \sqrt{\langle I\rangle - \langle |F|\rangle^2}. \)</span></p> </ul> </section> </section> <hr class=docutils /> <section id=practical-notes-and-limitations > <h2 id=practical-notes-and-limitations >13. Practical notes and limitations<a class=headerlink href="#practical-notes-and-limitations" title="Link to this heading">¶</a></h2> <ul class=simple > <li><p><strong>Bragg integration is profile-fitted by default</strong> (per-shell Gaussian profile, Kabsch extraction; §9.3), with plain box summation available as a fallback (<code class="docutils literal notranslate"><span class=pre >--integrator</span> <span class=pre >boxsum</span></code>). The profiles are built per frame from that frame’s strong spots, which suits fast-feedback and serial/streaming use; a profile shared across many frames (as in full offline workflows) is not currently formed.</p> <li><p><strong>Space-group symmetry</strong> beyond centering absences is not necessarily enforced during prediction/integration unless the space group is supplied and used downstream.</p> <li><p><strong>Resolution masking and ice rings</strong> are controllable; including ice-ring spots in indexing can improve robustness for some samples but may bias refinement in others.</p> <li><p><strong>Rotation vs still modes</strong> differ substantially in prediction and scaling because partiality is angle-driven in rotation data and excitation-error-driven in still data.</p> </ul> </section> </section> </article> </div> </div> </main> </div> <footer class=md-footer > <div class=md-footer-nav > <nav class="md-footer-nav__inner md-grid"> <a href=DETECTOR_GEOMETRY.html title="Detector geometry" class="md-flex md-footer-nav__link md-footer-nav__link--prev" rel=prev > <div class="md-flex__cell md-flex__cell--shrink"> <i class="md-icon md-icon--arrow-back md-footer-nav__button"></i> </div> <div class="md-flex__cell md-flex__cell--stretch md-footer-nav__title"> <span class=md-flex__ellipsis > <span class=md-footer-nav__direction > "Previous" </span> Detector geometry </span> </div> </a> <a href=OPENAPI.html title=OpenAPI class="md-flex md-footer-nav__link md-footer-nav__link--next" rel=next > <div class="md-flex__cell md-flex__cell--stretch md-footer-nav__title"><span class=md-flex__ellipsis > <span class=md-footer-nav__direction > "Next" </span> OpenAPI </span> </div> <div class="md-flex__cell md-flex__cell--shrink"><i class="md-icon md-icon--arrow-forward md-footer-nav__button"></i> </div> </a> </nav> </div> <div class="md-footer-meta md-typeset"> <div class="md-footer-meta__inner md-grid"> <div class=md-footer-copyright > <div class=md-footer-copyright__highlight > © Copyright 2024, Paul Scherrer Institute. </div> Created using <a href="http://www.sphinx-doc.org/">Sphinx</a> 8.1.3. and <a href="https://github.com/bashtage/sphinx-material/">Material for Sphinx</a> </div> </div> </div> </footer> <script src="_static/javascripts/application.js"></script> <script>app.initialize({version: "1.0.4", url: {base: ".."}})</script> |