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Build the transmitted region

Region is the region a chopper train transmits, exactly — a union of convex polygons in (inverse velocity, emission time).

Build one

Start from the rectangle your source draws from, and transmit it through the train:

from chopcal.lib import Region

# the rectangle the source draws from: wavelengths in AA, then emission time in s
source = Region.from_wavelengths(0.4, 45.0, 0.0, 3e-3)
region = source.transmit(train)

print(len(region), 'polygon(s)')
print(region.wavelength_ranges())
print(f'acceptance {region.area / source.area:.6e}')

1 polygon(s)
[(1.1458362867034736, 3.0515432206219723)]
acceptance 3.929119e-03

Region.from_wavelengths(low, high, time_minimum, time_range) takes angstrom and seconds; Region.rectangle takes inverse velocity directly if you have it.

For the six BIFROST discs the answer is one polygon of five vertices. That is the whole transmitted phase space of the instrument.

Why it is exact

A neutron emitted at inverse velocity a and time t reaches path L at t + L*a, so a disc open on [lower, upper] accepts

lower <= t + L*a <= upper

a slab between two parallel lines. A train's acceptance is an intersection of unions of such slabs, and intersection distributes over union — so the exact region is a union of convex pieces, one per choice of which opening and which turn of each disc a neutron goes through. Nothing is approximated and nothing is quantised.

Read the pieces

for polygon in region.polygons:
    print(len(polygon), 'vertices, area', polygon.area)
    for inverse_velocity, time in polygon.vertices:
        print(f'  {inverse_velocity:.6e} s/m at {time * 1e3:.4f} ms')

Each Polygon has vertices, area and contains. The vertices are the disc edges, at the precision of a double.

Because the pieces are disjoint — two turns of one disc cannot both pass the same neutron — region.area is a plain sum, with no inclusion-exclusion.

Ask about one neutron

centre = region.polygons[0].vertices[0]
print(region.contains(*centre))            # a vertex is on the boundary, so inside
print(region.contains(5e-3, 1e-3))         # far outside

The boundary counts as inside.

Reuse the source rectangle

transmit answers a question; it does not consume the region it was asked of.

# `transmit` answers a question; it does not consume the rectangle
without_bandwidth = source.transmit(train[:4])
print(len(source), len(region), len(without_bandwidth))

1 1 1

So one rectangle can be transmitted through several trains, or through prefixes of one, to see which discs are doing the cutting.

Write it out

data = region.to_dict(sampled=source)
print(sorted(data))
print(data['acceptance'])
# region.write_json('region.json', sampled=source)   # the same thing, on disk

region.to_dict(sampled=source) gives plain data; region.write_json(path, sampled=source) writes the same thing to a file — byte for byte what the Polygon_ESS_butterfly McStas component writes beside its data. Every number carries enough digits to read back bit-exact, and the file is a few hundred bytes where a mask of any useful resolution is megabytes.

sampled is what sets the acceptance; without it both it and acceptance are null.

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