Common-Resolution Convolution Kernels for Space- and Ground-Based Telescopes

Abstract: Multi-wavelength study of extended astronomical objects requires combining images from instruments with differing point spread functions (PSFs). We describe the construction of convolution kernels that allow one to generate (multi-wavelength) images with a common PSF, thus preserving the colors of the astronomical sources. We generate convolution kernels for the cameras of the Spitzer Space Telescope, Herschel Space Observatory, Galaxy Evolution Explorer (GALEX), Wide-field Infrared Survey Explorer (WISE), ground-based optical telescopes (Moffat functions and sum of Gaussians), and Gaussian PSFs. These kernels allow the study of the Spectral Energy Distribution (SED) of extended objects, preserving the characteristic SED in each pixel. The convolution kernels and the IDL packages used to construct and use them are made publicly available.

• The paper introduces a method to construct convolution kernels that harmonize diverse telescope PSFs to a common resolution for consistent multiwavelength comparison.
• The methodology employs Fourier transform-based filtering to correct and standardize PSFs, ensuring minimal negative artifacts while preserving intrinsic colors.
• Performance metrics like the integral D and W₋ confirm that the kernels effectively improve image alignment, enhancing spectral energy distribution analyses.

Common-Resolution Convolution Kernels: A Methodological Synopsis

The paper entitled "Common-Resolution Convolution Kernels for Space- and Ground-Based Telescopes" introduces a methodology to harmonize the resolution of images obtained from various telescopes. This is a critical procedure for multiwavelength studies, which require consistent comparison of data across different instruments with varied point-spread functions (PSFs).

Construction and Purpose

The primary objective is to construct convolution kernels that standardize images to a common PSF. The focus is on enabling the maintenance of intrinsic source colors in multiwavelength observations. The paper outlines the construction of kernels for several astronomical instruments including space-based observatories (Spitzer, Herschel, GALEX, WISE), ground-based optical telescopes, and theoretical Gaussian PSFs. The provided kernels are instrumental in aligning image resolutions, thus facilitating accurate spectral energy distribution (SED) analysis of extended astronomical objects.

Methodology

The construction process involves a sequence of steps beginning with the correction of missing data and resampling of PSFs to a common pixel scale. The PSFs are then subjected to a rotational symmetry analogy, centered, and adjusted for size consistency. A critical component is the determination of the Fourier transform of the PSF, followed by a filtering approach to eliminate high-frequency noise artifacts before inversion to real space for kernel construction.

Performance Evaluation

Kernel performance is assessed by metrics such as the integral $D$, measuring the deviation between the target and convolved PSFs, and $W_{-}$, evaluating negative excursions in the kernel that could lead to undesired artifacts. The majority of constructed kernels exhibit performance substantially within acceptable limits, enabling secure use in transforming images from various instruments to a common target PSF.

Applications and Implications

The paper's contributions are significant for the astrophysical community, as evidenced by detailed performance assessments demonstrating negligible artifact introduction in transformed images. The kernels are particularly advantageous for aligning images from the Spitzer and Herschel Space Telescopes with varying resolutions, enhancing their utility in unified data analysis approaches.

Moreover, the paper provides guidelines on creating custom kernels, empowering researchers to extend the framework to new telescopic datasets as future PSF characterizations emerge. This facilitates continuous integration of developing telescopic data into coherent analysis pipelines.

Future Prospect

The methodology paves the way for enriched, consistent astrophysical analyses across diverse datasets. Enhanced image register harmonization could potentially allow for more intricate scientific investigations into cosmic phenomena, leveraging synergistic multi-instrument insights into the behavior of astronomical objects over a broad spectrum of wavelengths. As imaging technology continues to advance, the development of robust convolution kernel libraries will be indispensable to extracting maximal value from multi-modal astronomical data sets.

In summary, the paper delivers a comprehensive framework for constructing effective convolution kernels, significantly advancing the field’s capability to achieve consistent and color-preserving multiwavelength astronomical investigations.