[Paper Review] A 3D Drizzle Algorithm for JWST and Practical Application to the MIRI Medium Resolution Spectrometer

David R. Law, J. Morrison+5 more|arXiv (Cornell University)|Jun 8, 2023

Atmospheric Ozone and ClimateEarth and Planetary Sciences3 citations

TL;DR

This paper presents a 3D drizzle algorithm for constructing spectral cubes from JWST's MIRI Medium Resolution Spectrometer (MIRI MRS) and NIRSpec IFU data by computing volumetric overlaps between detector pixels and cube voxels. By decoupling spatial and spectral overlap calculations, the method achieves near-ideal spectrophotometric fidelity (0.03% loss) while enabling efficient pipeline implementation, with key findings showing that 4-point dithering and aperture radii ≥1.5×PSF FWHM reduce resampling artifacts to <1% and that covariance correction factors of 1.5–3 are needed for accurate spectral variance estimation.

ABSTRACT

We describe an algorithm for application of the classic `drizzle' technique to produce 3d spectral cubes using data obtained from the slicer-type integral field unit (IFU) spectrometers on board the James Webb Space Telescope. This algorithm relies upon the computation of overlapping volume elements (composed of two spatial dimensions and one spectral dimension) between the 2d detector pixels and the 3d data cube voxels, and is greatly simplified by treating the spatial and spectral overlaps separately at the cost of just 0.03% in spectrophotometric fidelity. We provide a matrix-based formalism for the computation of spectral radiance, variance, and covariance from arbitrarily dithered data and comment on the performance of this algorithm for the Mid-Infrared Instrument's Medium Resolution IFU Spectrometer (MIRI MRS). We derive a series of simplified scaling relations to account for covariance between cube spaxels in spectra extracted from such cubes, finding multiplicative factors ranging from 1.5 to 3 depending on the wavelength range and kind of data cubes produced. Finally, we discuss how undersampling produces periodic amplitude modulations in the extracted spectra in addition to those naturally produced by fringing within the instrument; reducing such undersampling artifacts below 1% requires a 4-point dithering strategy and spectral extraction radii of 1.5 times the PSF FWHM or greater.

Motivation & Objective

• To develop a computationally efficient 3D drizzle algorithm for JWST's slicer-type IFU spectrometers, specifically MIRI MRS and NIRSpec.
• To address the challenge of spectrophotometric fidelity and computational tractability in constructing 3D spectral cubes from dithered, irregularly sampled 2D detector data.
• To quantify and correct for covariance between spaxels in the final data cubes, which distorts variance estimates in extracted 1D spectra.
• To analyze the impact of severe spatial and spectral undersampling (factor ~2) on spectral cube quality and to provide mitigation strategies.
• To provide practical recommendations for observing and data analysis to minimize resampling artifacts in extracted spectra.

Proposed method

• The algorithm computes volumetric overlap between 2D detector pixels and 3D data cube voxels, treating spatial and spectral overlaps separately to reduce computational cost.
• It uses a matrix-based formalism to compute spectral radiance, variance, and covariance from dithered observations, enabling accurate statistical propagation through the resampling process.
• The method employs a pre-compiled C-based implementation to achieve performance scalability for pipeline use.
• It derives scaling factors to correct for covariance between spaxels in extracted 1D spectra, with values ranging from 1.5 to 3 depending on wavelength and cube sampling.
• The algorithm is validated using real MIRI MRS data, including observations of the bright star 16CygB, to assess artifact amplitudes and dithering effectiveness.
• It incorporates a 4-point dithering strategy and aperture radius thresholds (≥1.5×PSF FWHM) to suppress periodic undersampling artifacts.

Experimental results

Research questions

• RQ1 How can the classic 2D drizzle technique be extended to 3D for IFU spectroscopy on JWST’s MIRI MRS and NIRSpec instruments with minimal loss in spectrophotometric accuracy?
• RQ2 What is the impact of spatial and spectral undersampling on spectral cube quality, and how can it be mitigated through observing strategy?
• RQ3 How does covariance between spaxels in the final data cube affect the variance of extracted 1D spectra, and what corrections are needed?
• RQ4 What dithering pattern and spectral aperture radius are required to reduce resampling artifacts to below 1% in extracted spectra?
• RQ5 What computational optimizations enable efficient pipeline implementation of 3D drizzle for large-scale JWST data processing?

Key findings

• The 3D drizzle algorithm achieves 0.03% loss in spectrophotometric fidelity by decoupling spatial and spectral overlap computations, enabling efficient pipeline use with minimal accuracy cost.
• Covariance between spaxels in MIRI MRS data cubes necessitates correction factors of 1.5 to 3 for accurate variance estimation in extracted 1D spectra, depending on wavelength and aperture size.
• Without mitigation, severe undersampling (factor ~2) introduces periodic amplitude modulations of up to 20% in extracted spectra.
• A 4-point dithering pattern reduces resampling artifacts to below 5%, and further reduction to less than 1% requires spectral extraction apertures of at least 1.5 times the PSF FWHM.
• The resampling noise in preview cubes (calwebb_spec2) is higher than in final cubes (calwebb_spec3), which combine multiple dithered exposures.
• The algorithm enables accurate variance propagation through a matrix formalism, though the full covariance matrix remains intractable for practical use.