leonarski_fandClaude Opus 5
efa8ab1221
A photon entering a flat sensor at an angle alpha to its normal crosses t/cos(alpha) of material instead of t, so the absorbed fraction rises toward the detector edge. The correction is QE(0)/QE(alpha) taken on the diffracted-beam direction against the detector normal, not on the scattering angle, so it follows a tilted or swung-out detector rather than assuming the two coincide. On an untilted detector this is a function of |s| alone: it is 99.7% a Wilson B offset and cancels exactly within a resolution shell, so merged protein data barely moves and no gain is claimed. It stops cancelling the moment the detector is tilted, because the incidence angle then acquires an azimuthal dependence: on a 30 degree swung-out geometry at 18 keV the within-shell spread reaches 21% median and 31% peak, and the anisotropy tensor moves with it. Attenuation lengths are the tabulated NIST coefficients rather than a wavelength-cubed approximation, which is within 0.2% for silicon above 10 keV but wrong for CdTe by a factor of two, and by six above the cadmium K edge. Photoelectric branching cancels in the ratio; K-fluorescence escape is not modelled, and the header says so. The correction self-disables where the physics makes it meaningless - an opaque sensor - so it needs no flag and is exactly neutral on all long-wavelength data and on thick CdTe. That also makes it a no-op on a file that stores its sensor thickness in the wrong unit, of which the corpus holds one. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01EFEJG6WBQv8th4UJFNe53N
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# Acknowledgements
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Citation: F. Leonarski, M. Bruckner, C. Lopez-Cuenca, A. Mozzanica, H.-C. Stadler, Z. Matej, A. Castellane, B. Mesnet, J. Wojdyla, B. Schmitt and M. Wang "Jungfraujoch: hardware-accelerated data-acquisition system for kilohertz pixel-array X-ray detectors" (2023), J. Synchrotron Rad., 30, 227-234 [doi:10.1107/S1600577522010268](https://doi.org/10.1107/S1600577522010268).
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The project is supported by :
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* Innosuisse via Innovation Project "NextGenDCU high data rate acquisition system for X-ray detectors in structural biology applications" (101.535.1 IP-ENG; Apr 2023 - Sep 2025).
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* ETH Domain via Open Research Data Contribute project (Jan - Dec 2023)
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* AMD University Program with donation of licenses of Ethernet IP cores and Vivado software
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Decoding bitshuffle+LZ4 images on the GPU, rather than decompressing them on the host and uploading
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the result, follows Jon Wright (ESRF): "Experiences with GPU decompression for bitshuffle + LZ4
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data", HDF5 User Group meeting (2021), and [bslz4decoders](https://github.com/jonwright/bslz4decoders).
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The CUDA kernels in Jungfraujoch are its own, but the approach is his.
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Spot extraction groups strong pixels into spots with the sparse connected-component labelling of the
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ACTS traccc project: P. Gessinger, H. M. Gray, A. Krasznahorkay, C. Leggett, J. Niermann,
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A. Salzburger, S. N. Swatman and B. Yeo, "traccc: GPU track reconstruction library for HEP
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experiments" (2025), [arXiv:2505.22822](https://arxiv.org/abs/2505.22822);
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[traccc](https://github.com/acts-project/traccc). The CPU spot extractor adapts its SparseCCL source,
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and the CUDA spot extractor follows the design of its GPU counterpart - a backward-neighbour graph
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over a sorted hit list, resolved by a parallel union-find. traccc is MPL-2.0; see
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[THIRD_PARTY_NOTICES.md](THIRD_PARTY_NOTICES.md). The SparseCCL algorithm itself is A. Hennequin,
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B. Couturier, V. V. Gligorov and L. Lacassagne, "SparseCCL: Connected Components Labeling and
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Analysis for sparse images" (2019), DASIP 2019, 65-70
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[doi:10.1109/DASIP48288.2019.9049184](https://doi.org/10.1109/DASIP48288.2019.9049184).
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This software uses Viridis, Magma and Inferno colormaps from Matplotlib under its BSD-compatible license
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## Public diffraction data used for testing
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In addition to in-house datasets collected at SLS 2.0, Jungfraujoch is tested against public
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diffraction data collected on other people's beamlines, on detectors and in file formats we do not
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produce ourselves - most of it at other facilities, a few sets at the Swiss Light Source but not by
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this system. That data was collected and published by other people. Every dataset used, the DOI to
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cite for it, and the deposition it belongs to are listed in
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[EXTERNAL_TEST_DATA](EXTERNAL_TEST_DATA.md); we thank the depositors, and the repositories that make
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the data findable and citable.
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**[IRRMC](https://proteindiffraction.org/)**, the Integrated Resource for Reproducibility in
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Macromolecular Crystallography (Minor lab, University of Virginia), is the source of most of them.
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IRRMC releases its data under CC0 and asks that the DOI of the dataset be cited; those DOIs are in
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the table. M. Grabowski, K. M. Langner, M. Cymborowski, P. J. Porebski, P. Sroka, H. Zheng,
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D. R. Cooper, M. D. Zimmerman, M.-A. Elsliger, S. K. Burley and W. Minor, "A public database of
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macromolecular diffraction experiments" (2016), Acta Cryst. D72, 1181-1193
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[doi:10.1107/S2059798316014716](https://doi.org/10.1107/S2059798316014716); M. Grabowski,
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M. Cymborowski, P. J. Porebski, T. Osinski, I. G. Shabalin, D. R. Cooper and W. Minor, "The
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Integrated Resource for Reproducibility in Macromolecular Crystallography: Experiences of the first
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four years" (2019), Struct. Dyn. 6, 064301
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[doi:10.1063/1.5128672](https://doi.org/10.1063/1.5128672).
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**[SBGrid Data Bank](https://data.sbgrid.org/)** supplied eighteen of the datasets. P. A. Meyer,
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S. Socias, J. Key, E. Ransey, E. C. Tjon, A. Buschiazzo et al., "Data publication with the
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structural biology data grid supports live analysis" (2016), Nat. Commun. 7, 10882
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[doi:10.1038/ncomms10882](https://doi.org/10.1038/ncomms10882).
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**[Zenodo](https://zenodo.org/)** hosts sixteen, deposited there directly by the groups that
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collected them. European Organization for Nuclear Research and OpenAIRE, "Zenodo" (2013), CERN
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[doi:10.25495/7GXK-RD71](https://doi.org/10.25495/7GXK-RD71). Three of those datasets were
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published as IUCrData Raw Data Letters; the letters are cited on the
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[EXTERNAL_TEST_DATA](EXTERNAL_TEST_DATA.md) page, beside the datasets they describe.
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**[MXRDR](https://mxrdr.icm.edu.pl/)**, the Macromolecular Xtallography Raw Data Repository
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(ICM, University of Warsaw), supplied four, released under CC0 with the dataset DOI to be cited;
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those DOIs (`10.18150/…`, `10.60884/…`) are in the table.
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**The [ESRF data portal](https://data.esrf.fr/)** supplied one, released under CC BY 4.0 under the
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ESRF data policy with the dataset DOI (`10.15151/…`) to be cited.
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The beamline, resolution, space group and unit cell quoted for each dataset are the values
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deposited with the corresponding PDB entry, read from the RCSB PDB data API. H. M. Berman,
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J. Westbrook, Z. Feng, G. Gilliland, T. N. Bhat, H. Weissig, I. N. Shindyalov and P. E. Bourne,
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"The Protein Data Bank" (2000), Nucleic Acids Res. 28, 235-242
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[doi:10.1093/nar/28.1.235](https://doi.org/10.1093/nar/28.1.235).
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## File formats read from a published specification
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**CBF / imgCIF** - the native miniCBF reader implements the `x-CBF_BYTE_OFFSET` compression scheme
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and reads the imgCIF `_axis` table (the laboratory directions of the image's fast and slow pixel
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directions, of the goniometer axes and of a 2theta arm) from the specification alone; no CBFlib or
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other CBF code is used, so there is no licence obligation, only this credit.
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H. J. Bernstein and A. P. Hammersley, "Specification of the Crystallographic Binary File
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(CBF/imgCIF)" (2006), International Tables for Crystallography Vol. G, 37-43
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[doi:10.1107/97809553602060000729](https://doi.org/10.1107/97809553602060000729);
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A. P. Hammersley, H. J. Bernstein and J. D. Westbrook, "Image dictionary (imgCIF)" (2006),
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International Tables for Crystallography Vol. G, 444-458
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[doi:10.1107/97809553602060000746](https://doi.org/10.1107/97809553602060000746).
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## Crystallographic methods adopted from other packages
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The analysis pipeline reimplements methods first published, and in most cases first implemented, by
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other crystallographic software. The code below is Jungfraujoch's own; the methods are theirs, and
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are acknowledged here. Where a package's source was consulted this is said explicitly. None of these
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packages is linked or vendored, with the single exception of GEMMI (see
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[THIRD_PARTY_NOTICES.md](THIRD_PARTY_NOTICES.md)).
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**[XDS](https://xds.mr.mpg.de/)** — rotation geometry and notation, the reciprocal Lorentz and
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partiality treatment, the maximum-likelihood mosaicity estimate, the `MINPK` criterion for rejecting
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a reflection whose predicted profile is not cleanly its own, the intensity-based test for a
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centred lattice, and the scaling correction surfaces indexed by image number and detector region. W. Kabsch, "XDS" (2010), Acta Cryst. D66, 125-132
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[doi:10.1107/S0907444909047337](https://doi.org/10.1107/S0907444909047337); W. Kabsch, "Integration,
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scaling, space-group assignment and post-refinement" (2010), Acta Cryst. D66, 133-144
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[doi:10.1107/S0907444909047374](https://doi.org/10.1107/S0907444909047374).
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**Profile fitting** with reweighted, de-biased variances is the Kabsch/Otwinowski iteration, from the
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second XDS paper above and from Z. Otwinowski and W. Minor, "Processing of X-ray diffraction data
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collected in oscillation mode" (1997), Methods Enzymol. 276, 307-326
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[doi:10.1016/S0076-6879(97)76066-X](https://doi.org/10.1016/S0076-6879%2897%2976066-X).
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**The two-dimensional integration architecture** — integrating each image in the detector plane
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and only afterwards assembling a reflection's partials into a full across images, as against
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three-dimensional profile fitting through the image stack — is the architecture of DENZO/SCALEPACK
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and MOSFLM, and it is the one rugnux's rotation pipeline follows (per-image profile-fitted
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integration, then partials combined into fulls; §9 and §10.6 of the analysis reference). The
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Otwinowski & Minor citation above and the MOSFLM citations below carry the credit for the paradigm
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as well as for the specifics taken from each.
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**[DIALS](https://dials.github.io/)** — the resolution cutoff from the CC1/2 fall-off, per-observation
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outlier rejection at merge, the scaling error model, and the treatment of a reflection whose
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background is contaminated. Its published behaviour, and in places its source, settled several
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choices here. G. Winter, D. G. Waterman, J. M. Parkhurst et al., "DIALS: implementation and
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evaluation of a new integration package" (2018), Acta Cryst. D74, 85-97
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[doi:10.1107/S2059798317017235](https://doi.org/10.1107/S2059798317017235); D. G. Waterman,
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G. Winter, R. J. Gildea et al., "Diffraction-geometry refinement in the DIALS framework" (2016),
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Acta Cryst. D72, 558-575 [doi:10.1107/S2059798316002187](https://doi.org/10.1107/S2059798316002187);
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J. Beilsten-Edmands, G. Winter, R. Gildea et al., "Scaling diffraction data in the DIALS software
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package: algorithms and new approaches for multi-crystal scaling" (2020), Acta Cryst. D76, 385-399
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[doi:10.1107/S2059798320003198](https://doi.org/10.1107/S2059798320003198); J. M. Parkhurst,
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G. Winter, D. G. Waterman et al., "Robust background modelling in DIALS" (2016), J. Appl. Cryst. 49,
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1912-1921 [doi:10.1107/S1600576716013595](https://doi.org/10.1107/S1600576716013595).
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**[POINTLESS](https://www.ccp4.ac.uk/)** (CCP4) — the space-group search. Stage A scores each
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candidate rotation operator by the correlation of I(h) with I(Rh) on **resolution-normalised**
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intensities (E²), as POINTLESS does — both arms of a symmetry pair sit at the same |s|, so on raw
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intensities the resolution fall-off is variance shared between them and lifts a false operator's
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correlation as much as a true one's; the screw-axis test scores a
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predicted-absent class against the rest of its own axial row rather than against a global mean or a
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fixed cut, and lets confidence fall away with the number of axial reflections instead of refusing
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below a count. P. Evans, "Scaling and assessment of data quality" (2006), Acta Cryst. D62, 72-82
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[doi:10.1107/S0907444905036693](https://doi.org/10.1107/S0907444905036693); P. R. Evans, "An
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introduction to data reduction: space-group determination, scaling and intensity statistics" (2011),
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Acta Cryst. D67, 282-292 [doi:10.1107/S090744491003982X](https://doi.org/10.1107/S090744491003982X);
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P. R. Evans and G. N. Murshudov, "How good are my data and what is the resolution?" (2013), Acta
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Cryst. D69, 1204-1214 [doi:10.1107/S0907444913000061](https://doi.org/10.1107/S0907444913000061);
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J. Agirre, M. Atanasova, H. Bagdonas et al., "The CCP4 suite: integrative software for macromolecular
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crystallography" (2023), Acta Cryst. D79, 449-461
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[doi:10.1107/S2059798323003595](https://doi.org/10.1107/S2059798323003595).
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**[MOSFLM](https://www.mrc-lmb.cam.ac.uk/mosflm/)** — the Rossmann FFT autoindexing algorithm and
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post-refinement practice, including which parameters are safe to refine per image and which must be
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refined over a wedge. The autoindexing algorithm itself — projecting the reciprocal-space points
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onto many directions and Fourier-transforming the 1D projection histograms — is I. Steller,
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R. Bolotovsky and M. G. Rossmann, "An algorithm for automatic indexing of oscillation images using
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Fourier analysis" (1997), J. Appl. Cryst. 30, 1036-1040
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[doi:10.1107/S0021889897008777](https://doi.org/10.1107/S0021889897008777); MOSFLM is the
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implementation whose practice is followed. A. G. W. Leslie and H. R. Powell, "Processing diffraction data with MOSFLM"
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(2007), in *Evolving Methods for Macromolecular Crystallography*, NATO Science Series II, vol. 245,
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41-51 [doi:10.1007/978-1-4020-6316-9_4](https://doi.org/10.1007/978-1-4020-6316-9_4);
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T. G. G. Battye, L. Kontogiannis, O. Johnson, H. R. Powell and A. G. W. Leslie, "iMOSFLM: a new
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graphical interface for diffraction-image processing with MOSFLM" (2011), Acta Cryst. D67, 271-281
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[doi:10.1107/S0907444910048675](https://doi.org/10.1107/S0907444910048675); H. R. Powell,
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T. G. G. Battye, L. Kontogiannis, O. Johnson and A. G. W. Leslie, "Integrating macromolecular X-ray
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diffraction data with the graphical user interface iMosflm" (2017), Nat. Protoc. 12, 1310-1325
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[doi:10.1038/nprot.2017.037](https://doi.org/10.1038/nprot.2017.037).
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**[CrystFEL](https://www.desy.de/~twhite/crystfel/)** — spot finding, the three-ring integration
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region, the serial/stills processing model, and the per-frame indexing acceptance test
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(`indexing_peak_check()` in `peaks.c`). T. A. White, R. A. Kirian, A. V. Martin, A. Aquila, K. Nass,
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A. Barty and H. N. Chapman, "CrystFEL: a software suite for snapshot serial crystallography" (2012),
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J. Appl. Cryst. 45, 335-341 [doi:10.1107/S0021889812002312](https://doi.org/10.1107/S0021889812002312).
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The self-calibrating spot finder's per-resolution-ring background statistics, with the Bragg peaks
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excluded by iterated clipping, follow Cheetah's peakfinder8: A. Barty, R. A. Kirian,
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F. R. N. C. Maia, M. Hantke, C. H. Yoon, T. A. White and H. N. Chapman, "Cheetah: software for
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high-throughput reduction and analysis of serial femtosecond X-ray diffraction data" (2014),
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J. Appl. Cryst. 47, 1118-1131
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[doi:10.1107/S1600576714007626](https://doi.org/10.1107/S1600576714007626).
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**[fast-feedback-indexer](https://github.com/paulscherrerinstitute/fast-feedback-indexer)** — the
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known-cell indexer for serial stills (`-X ffbidx`) is PSI's fast-feedback-indexer library, linked at
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build time (BSD-3-Clause; see [THIRD_PARTY_NOTICES.md](THIRD_PARTY_NOTICES.md)), which implements
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the TORO algorithm: P. Gasparotto, L. Barba, H.-C. Stadler, G. Assmann, H. Mendonça, A. W. Ashton,
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M. Janousch, F. Leonarski and B. Béjar, "TORO Indexer: a PyTorch-based indexing algorithm for
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kilohertz serial crystallography" (2024), J. Appl. Cryst. 57, 931-944
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[doi:10.1107/S1600576724003182](https://doi.org/10.1107/S1600576724003182).
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**[GEMMI](https://github.com/project-gemmi/gemmi)** — symmetry operations, unit-cell and
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structure-factor machinery, and MTZ / XDS_ASCII I/O. Vendored in `gemmi_gph/`, so it also carries a
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licence obligation. M. Wojdyr, "GEMMI: A library for structural biology" (2022), J. Open Source
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Softw. 7, 4200 [doi:10.21105/joss.04200](https://doi.org/10.21105/joss.04200).
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**Křivý & Gruber's Niggli reduction, and the lattice-character table** — the reduction that puts
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every candidate cell in a comparable form is I. Křivý and B. Gruber, "A unified algorithm for
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determining the reduced (Niggli) cell" (1976), Acta Cryst. A32, 297-298
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[doi:10.1107/S0567739476000636](https://doi.org/10.1107/S0567739476000636), used through GEMMI's
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implementation; the table of lattice characters that maps a reduced cell to Bravais lattices and
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centrings follows International Tables for Crystallography Vol. A, Table 9.2.5.1.
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**Grosse-Kunstleve, Sauter & Adams's numerically stable cell reduction** - the magnitude-scaled
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tolerance that decides the sign of a structurally-zero scalar product, and with it the Niggli type a
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reduced cell is presented in. R. W. Grosse-Kunstleve, N. K. Sauter and P. D. Adams, "Numerically
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stable algorithms for the computation of reduced unit cells" (2004), Acta Cryst. A60, 1-6
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[doi:10.1107/S010876730302186X](https://doi.org/10.1107/S010876730302186X).
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**Le Page's metric-symmetry search** - the obliquity of each of the 81 candidate two-folds of a
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reduced cell, which is what tells a run that its lattice metric hosts more rotational symmetry than
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the group its intensities supported, and the derivation of the conventional axes from that
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rotation group, which is what the run then offers to the space-group search as a second lattice
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candidate. The two-fold search is used through GEMMI's implementation of it. Y. Le Page, "The
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derivation of the axes of the conventional unit cell from the dimensions of the Buerger-reduced
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cell" (1982), J. Appl. Cryst. 15, 255-259
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[doi:10.1107/S0021889882011959](https://doi.org/10.1107/S0021889882011959).
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**Hexagonal-ice ring positions** — the eleven ring $d$ spacings from 3.895 to 1.522 Å that the
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ice-ring score, the ice-ring flagging and the ice calibrant are all built on are taken from the
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measurements of, not enumerated from a cell. D. W. Moreau, H. Atakisi and R. E. Thorne, "Ice in
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biomolecular cryocrystallography" (2021), Acta Cryst. D77, 540-554
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[doi:10.1107/S2059798321001170](https://doi.org/10.1107/S2059798321001170).
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That list ends at 1.522 Å by its own scope, so the eight bands below it are calculated here rather
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than taken from anyone: ice Ih structure factors on the oxygen sublattice, kept where they reach 3% of
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the strongest line, which reproduces the eleven measured positions exactly. The lattice constants are
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Röttger and co-workers'. K. Röttger, A. Endriss, J. Ihringer, S. Doyle and W. F. Kuhs, "Lattice
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constants and thermal expansion of H2O and D2O ice Ih between 10 and 265 K" (1994), Acta Cryst. B50,
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644-648 [doi:10.1107/S0108768194004933](https://doi.org/10.1107/S0108768194004933).
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**The twinning L test** is Padilla and Yeates's: pairing each acentric reflection with a
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symmetry-independent neighbour and reading the first and second moments of
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L = (I1−I2)/(I1+I2) against their untwinned and perfect-twin values. J. E. Padilla and
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T. O. Yeates, "A statistic for local intensity differences: robustness to anisotropy and
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pseudo-centering and utility for detecting twinning" (2003), Acta Cryst. D59, 1124-1130
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[doi:10.1107/S0907444903007947](https://doi.org/10.1107/S0907444903007947).
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**Diffraction anisotropy** — the description of the overall fall-off by a single anisotropic
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displacement tensor, its symmetry constraints, and the fact that only its deviatoric part is
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determined (the isotropic part being degenerate with the overall scale) are Sheriff and Hendrickson's.
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The estimator fits that tensor to the observed intensity distribution, taking sigma(I) into account,
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in the sense of Popov and Bourenkov. The directional diffraction limits - <I/sigma(I)> in a cone about
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each principal direction, and the reporting of the anisotropic deltaB as the range of the principal
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components - follow AIMLESS. rugnux reports these; it corrects no intensity and removes no reflection
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on a directional criterion. S. Sheriff and W. A. Hendrickson, "Description of overall anisotropy in
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diffraction from macromolecular crystals" (1987), Acta Cryst. A43, 118-121
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[doi:10.1107/S010876738709977X](https://doi.org/10.1107/S010876738709977X); A. N. Popov and
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G. P. Bourenkov, "Choice of data-collection parameters based on statistic modelling" (2003), Acta
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Cryst. D59, 1145-1153 [doi:10.1107/S0907444903008163](https://doi.org/10.1107/S0907444903008163);
|
||
P. R. Evans and G. N. Murshudov, "How good are my data and what is the resolution?" (2013), Acta
|
||
Cryst. D69, 1204-1214 [doi:10.1107/S0907444913000061](https://doi.org/10.1107/S0907444913000061).
|
||
|
||
**[ANODE](https://doi.org/10.1107/S0021889811041768)** — reading the anomalous difference map at the
|
||
atoms of a supplied model and reporting the strongest sites by name, instead of searching the map for
|
||
blobs. The map itself is the textbook anomalous difference Fourier; what is taken from ANODE is that
|
||
reading: A. Thorn and G. M. Sheldrick, "ANODE: anomalous and heavy-atom density calculation" (2011),
|
||
J. Appl. Cryst. 44, 1285-1287
|
||
[doi:10.1107/S0021889811041768](https://doi.org/10.1107/S0021889811041768).
|
||
|
||
**sigma_A map coefficients** — the maps written by `--model` are weighted by a maximum-likelihood
|
||
sigma_A estimated per resolution shell, giving 2mFo-DFc and mFo-DFc rather than 2Fo-Fc and Fo-Fc.
|
||
What is taken is the formalism itself: the Rice and Woolfson likelihoods of |Fo| given |Fc| and
|
||
sigma_A, the figure of merit m and the scale D that follow from it, and the result that the
|
||
bias-corrected coefficient is 2mFo-DFc for an acentric reflection and mFo for a centric one.
|
||
R. J. Read, "Improved Fourier coefficients for maps using phases from partial structures with
|
||
errors" (1986), Acta Cryst. A42, 140-149
|
||
[doi:10.1107/S0108767386099622](https://doi.org/10.1107/S0108767386099622).
|
||
|
||
**Uniform random rotations** — the null a supplied model is scored against re-orients that model at
|
||
random about its own centroid, and the rotations are drawn uniformly from SO(3) through a uniform
|
||
random unit quaternion. K. Shoemake, "Uniform Random Rotations", in *Graphics Gems III*, ed. D. Kirk,
|
||
Academic Press (1992), 124-132 (no DOI).
|
||
|
||
**Data-quality statistics** follow the established conventions rather than any one program: R_meas
|
||
and R_pim, CC1/2 and CC\*, and the reporting of I/sigma(I). K. Diederichs and P. A. Karplus, "Improved
|
||
R-factors for diffraction data analysis in macromolecular crystallography" (1997), Nat. Struct. Biol.
|
||
4, 269-275 [doi:10.1038/nsb0497-269](https://doi.org/10.1038/nsb0497-269); P. A. Karplus and
|
||
K. Diederichs, "Linking crystallographic model and data quality" (2012), Science 336, 1030-1033
|
||
[doi:10.1126/science.1218231](https://doi.org/10.1126/science.1218231); K. Diederichs and
|
||
P. A. Karplus, "Better models by discarding data?" (2013), Acta Cryst. D69, 1215-1222
|
||
[doi:10.1107/S0907444913001121](https://doi.org/10.1107/S0907444913001121).
|
||
|
||
**Uncertainty conventions** follow the IUCr Commission on Crystallographic Nomenclature:
|
||
D. Schwarzenbach, S. C. Abrahams, H. D. Flack et al., "Statistical descriptors in crystallography:
|
||
Report of the IUCr Subcommittee on Statistical Descriptors" (1989), Acta Cryst. A45, 63-75
|
||
[doi:10.1107/S0108767388009596](https://doi.org/10.1107/S0108767388009596); D. Schwarzenbach,
|
||
S. C. Abrahams, H. D. Flack, E. Prince and A. J. C. Wilson, "Statistical descriptors in
|
||
crystallography. II. Report of a Working Group on Expression of Uncertainty in Measurement" (1995),
|
||
Acta Cryst. A51, 565-569 [doi:10.1107/S0108767395002340](https://doi.org/10.1107/S0108767395002340).
|
||
|
||
**Sensor absorption at oblique incidence** — the angle-dependent quantum efficiency of a flat
|
||
sensor, and the radial parallax variance that comes from the same integral, are the Beer-Lambert law
|
||
taken along a ray that crosses t/cos(alpha) of sensor and converts at a random depth. The
|
||
attenuation coefficients are the NIST tabulation: J. H. Hubbell and S. M. Seltzer, "Tables of X-Ray
|
||
Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients from 1 keV to 20 MeV for
|
||
Elements Z = 1 to 92 and 48 Additional Substances of Dosimetric Interest" (1995, data updated 2004),
|
||
NIST Standard Reference Database 126
|
||
[doi:10.18434/T4D01F](https://doi.org/10.18434/T4D01F).
|