faradaydreams 0.0.3

Faraday Rotation Recovery using Convex Optimization

Faraday-Dreams

New developments that allow correction for channel averaging when reconstructing broad band polarimetric signals.

This code is built using Optimus Primal to apply convex optimization algorithms in deniosing.

Requirements

• Python 3.8
• Optimus Primal
• PyNUFFT when using the NUFFT algorithm (Optional)

Install

You can install from the master branch

pip install git+https://github.com/Luke-Pratley/Faraday-Dreams.git@master#egg=faradaydreams

or from a frozen version at pypi

pip install faradaydreams

Related Publications

• Removing non-physical structure in fitted Faraday rotated signals: non-parametric QU-fitting, PASA (Accepted), L. Pratley and M. Johnston-Hollitt, and B. M. Gaensler, 2021
• Wide-band Rotation Measure Synthesis, ApJ, L. Pratley, M. Johnston-Hollitt, 2020

Basic example for 1d spectrum

We can import a simple solver using the following command

import faradaydreams.recover_faraday_spectra as recover_faraday_spectra

We can define a dictionary with variables such as the tolerance for convergence tol, the maximum number of iterations iter, and if we wish to enforce that $\lambda^2 \leq 0$ has zero flux project_positive_lambda2. We expect the Faraday depth signal to be complex valued, so the real and positivity constraints are False.

options = {
    'tol': 1e-5,
    'iter': 50000,
    'update_iter': 1000,
    'record_iters': False,
    'real': False,
    'positivity': False,
    'project_positive_lambda2': False
}

Below we pass data to the solver which returns a dictionary with processed result. We pass in the Stokes Q and U spectra and their associated errors in Jy. We provide the channel frequencies (in Hz) and with channel_width=None we do not correct for channel averaging, if we pass the array of channel widths in Hz it will try to do a correction.

The size of a Faraday width pixel is chosen to be dphi=15 rad/m^2 and we choose the spectrum to span Nphi=320 pixels across centred at 0 rad/m^2. We choose not to scale the uncertainty on the measurements that we wish to fit the solution with sigma_factor=1. beta=1e-2 is the step size for the minimization, and 1e-0 to 1e-3 normally works well.

results = recover_faraday_spectra.recover_1d_faraday_spectrum(
    Q=data['Q'],
    U=data['U'],
    error_Q=data['e_Q'],
    error_U=data['e_U'],
    freq=freq,
    dphi=15,
    Nphi=320,
    sigma_factor=1,
    beta=1e-2,
    options=options,
    channel_widths=None)     

The returned dictionary has the form

    return {
        "solution": solution,
        "phi": phi,
        "y_solution": y_model,
        "solution_lambda2": model_lambda2,
        "measurements": y,
        "measurements_residuals": y - m_op.dir_op(solution) / weights,
        "measurements_lambda2": lambda2,
        "measurements_weights": weights,
        "measurements_sigma": sigma
    }

where we can plot the solution results['solution'] against results['phi']. results['y_solution'] is the same signal in lambda^2 coordinates results['solution_lambda2']. The original measurements results['measurements'] and the residuals of the solution results['measurements_residuals'] are also returned.

Look in the examples directory for a fully working example in the form of a python notebook.