AC05
Interferometric imaging from wave delay to EHT data
A distant telescope pair measures one striped pattern across the sky. Derive that measurement, turn it with Earth, and learn what a triangle preserves when station phases drift. Then reconstruct a saved synthetic sky and fit a measured EHT triangle with its own calibration limits.
Concept
How scattered telescopes make an image
A telescope pair measures one pattern across the sky. Many directions and Earth’s rotation turn those patterns into an image.
L1
From wave delay to complex visibility
Derive a telescope pair’s Fourier measurement, fix its sign and units, and calculate the visibility of a point and a double source.
L2
Earth rotation and closure phase
Project real station separations onto the sky, count independent measurements, and derive the phase combination that cancels station errors.
L3
Dirty beams and nonunique images
Derive the dirty image, distinguish flux per beam from flux per pixel, and reconstruct one saved signal set with two explicit priors.
Tutorial
Fit a real EHT closure triangle
Reproduce a measured M87 closure phase from pinned EHT data, then fit several source models that explain the same three amplitudes and one angle.
Paper guide
Read EHT imaging and dynamic priors
Read fixed EHT imaging figures, distinguish measured data from synthetic tests, and trace how spatial and temporal priors affect reconstruction.
The browser reconstructs a finite-pixel synthetic sky from saved complex signals and a separate ideal calibrator. The measured EHT tutorial fits amplitudes and closure phase. The final guide follows fixed paper figures through calibration, synthetic tests and spatial or temporal priors.
Sources and calculation scope
- NRAO Essential Radio Astronomy, Chapter 3, aperture synthesis
The narrow-field Fourier relation and Earth-rotation synthesis, especially equations 3.180–3.200. The browser uses a spherical Earth, a single wavelength and a finite pixel sky.
- EHT 2019-D01-01 M87 data release, pinned commit 27ae76a
Actual EHT-HOPS SR1 network-calibrated Stokes I from 10 April 2017, low band, 227.0707 GHz. The tutorial preserves the publisher CSV and selects one simultaneous AA–AZ–LM triangle. The repository licenses data under PDDL 1.0.
- EHT Collaboration, First M87 Results IV, arXiv:1906.11241v1
Fixed version of the 2019 imaging paper, DOI 10.3847/2041-8213/ab0e85. Read Figures 1, 3, 5 and 7, the station-gain equation 7, regularized imaging equation 14, and Appendix A. Figures remain with the publisher and authors; this guide links to them.
- Johnson et al., Dynamical Imaging with Interferometry, arXiv:1711.01286v1
Fixed 3 November 2017 version, DOI 10.3847/1538-4357/aa97dd. Sections 2.3–3 and equation 3 explain temporal regularization; Figures 7–10 use simulated black-hole observations. Figure 12 uses real 7 mm VLBA M87 data across epochs.