Synthetic Data Generation Pipeline

• Synthetic Data Generation Pipelines are computational frameworks that replicate real-world observational processes by simulating key statistical and instrumental effects.
• They integrate end-to-end steps—from model ingestion and Fourier transformation to applying realistic corruptions like tropospheric delays, noise, and pointing errors—mirroring standard VLBI calibration.
• These pipelines enable rigorous benchmarking of imaging algorithms and inform instrument design through quantitative metrics such as cross-correlation fidelity.

Synthetic data generation pipelines are computational frameworks designed to produce artificial datasets that faithfully replicate key statistical, structural, and application-dependent properties of target domains. In high-precision fields such as radio astronomy, realistic synthetic observations enable rigorous testing of instrument capabilities, calibration and imaging algorithms, observational strategies, and physical models. A paradigmatic example is the SYMBA (SYnthetic Measurement creator for long Baseline Arrays) pipeline, which generates end-to-end simulated Very Long Baseline Interferometry (VLBI) data—including realistic observational corruptions and full calibration sequences—allowing for robust benchmarking and methodology development in interferometric imaging.

1. End-to-End Pipeline Structure and Objectives

The SYMBA pipeline is architected to mimic the full radio interferometric observation and data reduction process, starting from theoretical source models and culminating in calibrated visibility data ready for imaging. Its design explicitly integrates every key observational stage:

• Model Ingestion: Accepts 2D/3D source models in FITS or ASCII format, including static or time-dependent emissions, supporting both total intensity (Stokes I) and full polarization scenarios.
• Fourier Transformation: Simulates the propagation of sky brightness to the interferometer’s $uv$-plane via Fourier transforms, mapping the model to baseline-sampled visibilities using the intended observation schedule or custom $uv$-coverages (potentially VEX-derived).
• Application of Corruptions: Physical and instrumental effects are systematically imposed:
  • Tropospheric absorption and delay (mean opacity and phase turbulence, via the radiative transfer equation $dI_\nu/ds = \epsilon_\nu - \kappa_\nu I_\nu$ and Kolmogorov-type turbulence structure functions).
  • Receiver chain noise (from system equivalent flux density, SEFD).
  • Pointing errors (with primary beam attenuation quantified via exponential beam response functions).
  • Gain fluctuations, quantization inefficiencies, and polarization leakage.
• Calibration Sequence: Synthetic visibilities are cleaned using a CASA-based calibration workflow (rPICARD), sequentially performing fringe fitting, amplitude calibration, and network calibration analogously to real EHT data reduction.
• Optional Imaging: Regularized maximum likelihood algorithms (RML), e.g., the eht-imaging package, reconstruct images for quantitative comparison.
• Control and Reproducibility: A master ASCII configuration file fully describes schedules, array geometry, hardware parameters, weather, and source model, ensuring total experiment documentation and reproducibility.

This end-to-end coupling provides a comprehensive testbed in which theoretical models, experimental designs, and calibration strategies can be validated under known, controlled conditions.

2. Physical and Instrumental Corruption Modeling

A distinguishing feature of SYMBA is its physically motivated modeling of propagation effects and systematics:

• Mean Tropospheric Effects:
  • Opacity and phase delays are computed by integrating the radiative transfer equation with emission ($\epsilon_\nu$) and absorption ($\kappa_\nu$) coefficients, connected via Kirchhoff's law ($\epsilon_\nu/\kappa_\nu = B_\nu(T)$).
• Atmospheric Turbulence:
  • Phase structure function is modeled as $D_\phi(r) = \mu (r/r_0)^\beta$ (with $\beta = 5/3$ for Kolmogorov turbulence), yielding spatial and temporal coherence metrics ($t_c \simeq r_0/v$ for velocity $v$).
• Receiver Noise:
  • For a baseline $mn$, the noise standard deviation is $$\sigma_{mn} = ( \eta_Q \sqrt{ (SEFD_m \cdot SEFD_n) / (2\,\Delta\nu\,t_{int} )} )^{-1}$$, factoring quantization efficiency ($\eta_Q$), bandwidth, and integration time.
• Pointing Error Attenuation:
  • Beam response to pointing offsets is quantified as $$Z_{\text{obs}}/Z_{\text{true}} = \exp[ -8\log^2 2 \cdot ((\rho_m/P_{FWHM_m})^2 + (\rho_n/P_{FWHM_n})^2) ]$$.
• Gain/Polarization Leakage:
  • Amplitude and phase gains, as well as D-term (leakage) corruptions, are introduced to reflect calibration imperfections.

This explicit physics-based layering distinguishes data generated by SYMBA from toy models or oversimplified data simulations, providing a platform for detailed failure case analysis in calibration and imaging.

3. Calibration and Imaging Pipeline

Following corruption, the simulated raw visibility data replicate all non-idealities encountered in real observations. SYMBA then applies a full VLBI calibration pipeline, closely mirroring standard practice:

• Fringe Fitting: Recovers station-based phase, delay, and rate offsets (Schwab-Cotton algorithmic family) to correct atmospheric and instrumental phase errors.
• A Priori Amplitude Calibration: System temperature and opacity corrections recalibrate the flux density scale, referencing both measured and simulated opacities.
• Network Calibration: For stations with redundant baselines (e.g., ALMA/APEX, SMA/JCMT), network-based gain corrections further stabilize the array.
• Data Averaging and Export: Calibrated data are averaged and written out in standard formats (UVFITS), ready for robust imaging with closure-only or self-calibration routines.

This sequence ensures that synthetic datasets not only look like real VLBI data in terms of corruption, but also provide an equally challenging testbed for calibration algorithms, enabling systematic studies of sensitivity to weather, station additions, and calibration systematics.

4. Quantitative Assessment and Scientific Studies

SYMBA facilitates precise, quantitative studies of instrument and algorithmic performance:

Assessment Type	Description	Metric and Analysis
Case: Point Source	Visualizes effects of individual corruptions; demonstrates calibration efficacy	Phase/amplitude vs. time traces
Model Imaging (Crescent, GRMHD)	Assesses image reconstruction fidelity in the presence of realistic corruptions	Image cross-correlation $\rho_{NX}$
Weather Impact	Quantifies effects of increased PWV, reduced $t_c$, and pointing error	Data loss, degraded $\rho_{NX}$
Array Expansion	Simulates the effect of new stations on $uv$-coverage and resolution	Shift in $\rho_{NX}$ curves

The normalized cross-correlation metric

$$\rho_{NX}(X,Y) = \frac{1}{N} \sum_{i} \frac{(X_i - \langle X \rangle)(Y_i - \langle Y \rangle)}{\sigma_X \sigma_Y}$$

is used to quantify fidelity of reconstructed images as a function of beam size, array configuration, and calibration regime. This enables operationally meaningful, beam-matched fidelity assessment—critical for separating model distinguishability from reconstruction limitations.

5. Model Discrimination and Future Array Design

Case studies on different physically motivated models (e.g., thermal-jet vs. $\kappa$-jet GRMHD simulations) highlight how improved $uv$-coverage and calibration can allow robust discrimination in real-world data:

• The thermal-jet model yields a thinner, symmetric ring, while the $\kappa$-jet model introduces pronounced knots and extended jet features.
• With future arrays (expanded EHT), image fidelity gains enable detection of subtle morphological distinctions, as made evident by sharper cross-correlation peaks and increased dynamic range in reconstructions.

This supports data-driven instrument design, enabling predictions of the scientific returns from array upgrades in advance of costly deployments.

6. Practical and Community Impact

SYMBA has been used to:

• Validate observational strategies (array configuration, weather tolerance, scan design) prior to expensive observing campaigns.
• Benchmark calibration and imaging pipelines, both through visual inspection and formal metrics such as the cross-correlation $\rho_{NX}$.
• Quantify the impact of additional array elements and environmental parameters on attainable science goals (e.g., black hole shadow imaging, jet structure retrieval).
• Serve as a tool for the wider community to test modeling, calibration, and imaging algorithms against physically realistic, reproducible synthetic datasets.

This enables the broader VLBI and astrophysics community to bridge the gap between theoretical simulations and observational capabilities with unprecedented rigor.

7. Conclusions

The SYMBA synthetic data generation pipeline exemplifies a physically grounded, operationally faithful approach to end-to-end radio interferometric data simulation. By coupling advanced model ingestion, explicit corruption modeling, and a standard calibration workflow, SYMBA produces datasets suitable for detailed analysis of instrument and algorithm performance under controlled conditions. Strong, quantitative results demonstrate that after full calibration, key source structure can be robustly recovered (subject to limitations set by weather, array design, and calibration quality), and that fidelity metrics can guide both modeling and future instrument design. This closes the loop between theory, algorithm engineering, and observational practice in contemporary radio astronomy, providing a reference architecture for synthetic pipeline development in other scientific disciplines (Roelofs et al., 2020).