[Paper Review] Broadband Fizeau Interferometers for Astrophysics

Siddharth Savyasachi Malu, Peter Timbie|arXiv (Cornell University)|Jun 30, 2010

Astronomy and Astrophysical Research1 references3 citations

TL;DR

This paper proposes sub-band splitting in broadband Fizeau interferometers to overcome fringe smearing in wideband measurements, enabling high-fidelity visibility reconstruction across frequency sub-bands. By modeling detector outputs as sums of sub-band visibilities modulated by fringes, the method allows simultaneous imaging and visibility measurement with reduced systematic leakage, particularly beneficial for detecting faint CMB B-mode polarization signals.

ABSTRACT

Measurements of the 2.7 K cosmic microwave background (CMB) radiation now provide the most stringent constraints on cosmological models. The power spectra of the temperature anisotropies and the $E$-mode polarization of the CMB are explained well by the inflationary paradigm. The next generation of CMB experiments aim at providing the most direct evidence for inflation through the detection of $B$-modes in the CMB polarization, presumed to have been caused by gravitational waves generated during the inflationary epoch around $10^{-34}$s. The $B$-mode polarization signals are very small ($\leq$10$^{-8}$K) compared with the temperature anisotropies ($\sim 10^{-4}$K). Systematic effects in CMB telescopes can cause leakage from temperature anisotropy into polarization. Bolometric interferometry (BI) is a novel approach to measuring this small signal with lower leakage. If BI can be made to work over wide bandwidth ($\sim20-30\%$) it can provide similar sensitivity to imagers. Subdividing the frequency passband of a Fizeau interferometer would mitigate the problem of `fringe smearing.' Furthermore, the approach should allow simultaneous measurements in image space and visibility space. For subdividing the frequency passsband (`sub-band splitting' henceforth), we write an expression for the output from every baseline at every detector in the focal plane as a sum of visibilities in different frequency sub-bands. For operating the interferometer simultaneously as an imager, we write the output as two integrals over the sky and the focal plane, with all the phase differences accounted for.}{The sub-band splitting method described here is general and can be applied to broad-band Fizeau interferometers across the electromagnetic spectrum. Applications to CMB measurements and to long-baseline optical interferometry are promising.

Motivation & Objective

• Address the challenge of fringe smearing in broadband Fizeau interferometers, which degrades u-v plane resolution and sensitivity.
• Overcome limitations of conventional heterodyne interferometers in handling large bandwidths and numerous baselines.
• Enable high-sensitivity, low-systematic measurements of the cosmic microwave background (CMB), especially for detecting faint B-mode polarization.
• Develop a method to simultaneously measure visibilities and reconstruct images using a single Fizeau interferometric system.
• Provide a general framework applicable across the electromagnetic spectrum, with specific relevance to CMB and optical interferometry.

Proposed method

• Model the output of each detector in the focal plane as a sum of visibility contributions from multiple frequency sub-bands.
• Express the detector signal as an integral over the detector area, incorporating both the sky visibility and the fringe pattern at each sub-band frequency.
• Account for finite detector size by averaging the fringe pattern over the detector’s effective collecting area, assuming phase variation is negligible across the detector.
• Formulate a system of equations (Eq. 17) relating observed outputs to sub-band visibilities and fringe phases, enabling inversion to recover visibility spectra.
• Utilize phase modulators (as in Hyland et al. 2009; Charlassier et al. 2009) to enable full baseline coverage and visibility measurement in a Fizeau configuration.
• Leverage the natural imaging capability of Fizeau interferometry by combining visibility and image space measurements through dual-path signal processing.

Experimental results

Research questions

• RQ1 How can fringe smearing in broadband Fizeau interferometers be mitigated to preserve u-v plane resolution and sensitivity?
• RQ2 Can sub-band splitting enable accurate reconstruction of visibility spectra without requiring narrowband filters or complex spectral calibration?
• RQ3 To what extent can a Fizeau interferometer simultaneously perform imaging and visibility measurement with minimal resource overhead?
• RQ4 How does sub-band splitting reduce systematic leakage from temperature anisotropies into CMB polarization signals?
• RQ5 What is the theoretical and practical feasibility of extending this method to long-baseline optical and millimeter-wave interferometry?

Key findings

• Sub-band splitting effectively separates visibility contributions across frequency sub-bands, enabling high-fidelity reconstruction of visibilities despite broadband operation.
• The method allows the recovery of 2m visibility components (real and imaginary parts for m sub-bands) from a system with m frequency channels and baseline pairs.
• By assuming negligible phase variation across a detector’s area, the system of equations (Eq. 17) becomes solvable for sub-band visibilities, enabling practical implementation.
• The Fizeau interferometer with sub-band splitting naturally supports simultaneous imaging and visibility measurement, as shown in Appendix A.
• The technique is general and applicable across the electromagnetic spectrum, with demonstrated relevance to CMB experiments like QUBIC.
• The approach mitigates systematic effects such as leakage from temperature anisotropies into polarization, which is critical for detecting sub-nK B-mode signals.