Jungfraujoch/docs/DETECTOR_GEOMETRY.md

# Detector geometry

At the moment Jungfraujoch supports solely flat detectors. The default option is to place modules in their actual location
relative to the detector frame. It is not recommended to place detector modules stacked.

The simplest case is a detector perpendicular to the beam. In this case it is enough to provide beam center, detector distance
and wavelength. 

For a more complex case, one can provide the detector tilt in the PyFAI convention.
This convention uses Point Of Nominal Interaction (PONI) definition. Beam X and Y would correspond to the location on the detector,
where beam from the sample is perpendicular to the detector surface and not to the actual direct beam location. Then tilt of the detector
is defined with three rotation angles: `rot1` (rotating detector right), `rot2` (rotating detector downwards), `rot3` (rotating detector clockwise). 
See [PyFAI documentation](https://pyfai.readthedocs.io/en/stable/) for more details.

## What a pixel coordinate means: (0, 0) is the centre of the first pixel

Pixel coordinates in Jungfraujoch and Rugnux are **0-based and pixel-centred**: an integer coordinate
is the *centre* of that pixel, so pixel *i* covers [*i* − 0.5, *i* + 0.5) and the sensor spans
−0.5 … width − 0.5. A beam centre of 948.0 × 546.0 sits in the middle of pixel [546][948], not on any
of its corners; 948.5 is the boundary between pixel 948 and 949.

This holds throughout the code: spot and reflection centroids are intensity-weighted sums of the
integer pixel indices, the resolution and azimuthal-bin maps evaluate pixel (col, row) at exactly
(col, row), and a fractional coordinate is turned back into a pixel index by rounding, not by
truncation. The same convention applies to every coordinate the system exposes — the beam centre
(`beam_x_pxl`/`beam_y_pxl` in the API and broker configuration, `--beam-x`/`--beam-y` in Rugnux,
`beam_center_x`/`beam_center_y` in NXmx and in the CBOR stream), the spot and predicted-reflection
positions written to HDF5, and the PONI reported by `--mode calibration`.

Other programs place the origin differently, and the difference is worth half a pixel — enough to
matter when a geometry is copied between programs and then refined:

| Convention | Beam centre equivalent to our *x* = 948.0 |
|---|---|
| Jungfraujoch, Rugnux | 948.0 |
| XDS (`ORGX`/`ORGY`) | 949.0 — also pixel-centred, but pixels are numbered from 1 |
| Measured from the edge of the sensor, in length units — pyFAI (`Poni2`, fast axis), DIALS/dxtbx | (948.0 + 0.5) × pixel size, because the centre of pixel *i* is at (*i* + 0.5) × pixel size from the edge |
| pyFAI `Poni1` (slow axis) | (height − 1 − *y* + 0.5) × pixel size — pyFAI measures the slow axis from the opposite edge, and the `.poni` declares `orientation: 2` to say so |

The `.poni` file written by `rugnux --mode calibration` is in pyFAI's frame and so already carries
that half pixel; the pixel values the same run reports are ours. `Rot3` in that file is our rot3
negated and turned by 180°: the half turn sets the azimuthal reference, because pyFAI's in-plane axes
are the negatives of ours. It leaves 2θ untouched, so it moves only the azimuth.

## Inside: two axis vectors; outside: rot1/rot2/rot3

Internally the detector plane is one orthogonal matrix whose columns are the **fast axis** (the
laboratory direction of a +1 column step), the **slow axis** (+1 row step) and the **normal** (the
sample→PONI direction). Every geometry calculation — resolution, azimuth, polarization, prediction,
refinement — is that matrix applied to the offset of a pixel from the PONI.

`rot1`/`rot2`/`rot3` remain the way the tilt is stated from outside, and the two views convert both
ways: `R = Rz(-rot3)·Rx(-rot2)·Ry(+rot1)` in the internal frame, and back from the columns as

```
rot2 = asin(-slow.z)         rot1 = atan2(-fast.z, normal.z)         rot3 = atan2(slow.x, slow.y)
```

with `rot2` in [-90°, 90°]. The angles are what is stored and what is written out, so a geometry
given as angles comes back exactly as it was given.

## What a miniCBF header states about the mounting

A PILATUS miniCBF gives the geometry twice. The `# ` lines every writer produces carry the distance, the
beam centre and the angles; some beamlines then append a CBF template block holding a full **imgCIF axis
table**, which states the laboratory direction of the image's fast and slow pixel directions, of the base
goniometer axis, and of a 2theta arm where there is one. Where that table is present it is read, in
preference to any assumption - it is the same information NXmx puts in `fast_pixel_direction` /
`slow_pixel_direction` and the goniometer `vector`, in the form this format states it.

imgCIF's laboratory frame has Z from the sample towards the source and Y opposite gravity, so it differs
from the internal frame by a half turn about x - a rotation, not a mirror, so an axis carried through it
turns the same way by the same angle.

There are two things a header can state that an assumption gets wrong by 90 degrees — an error no
refinement recovers, and one the run's axis-sign rescue cannot reach either, a quarter turn not
being a sign:

* the image mounted a quarter turn round, so its columns run vertically;
* a spindle that turns about the **vertical** rather than the horizontal.

Where a header carries no axis table, a `+SLOW` on its `# Oscillation_axis` line still says the spindle
runs along the image's slow direction rather than its fast one. The axis *name* on that line is not
usable - one header says `X.CW +SLOW` where its own table says the axis is Y - but the direction token is,
and on the header that states both they agree.

## A detector swung out on a 2theta arm

Chemical crystallography reaches high angle by swinging the detector out on a 2theta arm rather than by
moving it closer. The arm turns the detector about the sample, so it changes nothing else: the distance
is still measured along the detector normal, and the beam centre is still the point of normal incidence,
which is where the arm's own axis meets the detector and does not move. The swing is therefore exactly a
PONI rotation, and the direct beam is what moves - by `distance * tan(2theta)`, off the beam centre and
often off the detector altogether.

Nothing has to be given for this: Rugnux takes it from the file. An NXmx master states the detector's
position as a `depends_on` chain of transformations, and the arm is one rotation in that chain - so the
chain is followed, rather than a field of one particular name being looked for. A PILATUS miniCBF states
it as `# Detector_2theta`, which turns about the same axis as the base spindle, the two being one axis on
the four-circle geometry those headers describe.

## Mirrored and quarter-turned detectors

On top of the continuous tilt the detector setup carries a **discrete image orientation**: whether the
stored image is mirrored in Y, and how many multiples of 90° about the beam it is turned by. It is
applied to the offset from the PONI before the tilt.

The distinction matters because these two operations are exact pixel remappings — an image can be
shown the right way up without resampling anything — while an arbitrary in-plane rotation cannot.
`rot3` is therefore reserved for the genuinely arbitrary part: an in-plane angle is **never**
decomposed into a quarter turn plus a residual, and the discrete part is set only where something
states it (the detector configuration, `--detector-mirror-y` / `--detector-quarter-turns`, or the
value a Jungfraujoch-written file records).

Both operations leave the distance from the PONI unchanged, so resolution, the solid-angle correction
and anything else that needs only a radius are unaffected by them. Polarization *is* affected, and
correctly so: it is computed from the azimuth in the **laboratory**, and what these operations change
is which pixel index lands at which laboratory azimuth.

This is a different setting from `mirror_y` in the JSON configuration file (described below), which flips the
**module layout** while the image is being assembled and so decides what the stored pixels are. The
discrete image orientation changes no pixel at all.

## Macromolecular crystallography convention for the vertical direction
One place of confusion is the convention to have point (0,0) of the detector in the top left corner of the detector,
with Y values increasing downwards. This is also consistent with computer image formats.

However, other techniques (as well as internal operation of PSI X-ray detectors) might follow a convention where point (0,0)
is in the bottom left corner and Y values increase upwards. Such a convention is used, for example, by PyFAI.

In general, the convention is controlled in Jungfraujoch with a setting in the JSON configuration file, which allows the detector to be mirrored in Y.

The convention in use is worth checking whenever a geometry is carried between programs.