Rikkyo University

Astronomical space X-ray satellites, starting with the U.S. Uhuru in 1970, have contributed to the advancement of space X-ray observations, including the launch of six X-ray satellites in Japan. By observing the universe in X-rays, we can study high-energy cosmic phenomena that are invisible to the human eye. With high-resolution instruments capable of observing cosmic X-rays, we can study a range of phenomena, including very dense celestial bodies such as black holes and neutron stars, as well as phenomena known as supernova explosions that occur at the end of the lives of massive stars. These observations help unravel the mysteries of the hot and unknown universe.

Among these X-ray satellites, Chandra, which has been operational since its launch in 1999 and continues to operate as of 2023, has the highest spatial resolution (0.5 arcseconds) of any X-ray satellite. Its exceptional capabilities have provided insights into various high-energy physical phenomena, including the time evolution of supernova remnants. However, the focusing device (X-ray telescope) that directly affects X-ray vision becomes less efficient at accurately focusing the image as we move away from the optical axis. The deviation of the image from the ideal point image is known as the point-spread function (PSF). Figure 2 shows the shape of the PSF at different locations based on simulated measurements using the observed image of the Cassiopeia A supernova remnant from Chandra in 2004 as the background. As the distance from the optical axis increases, the focusing power decreases and the PSF spreads wider. In other words, the observed image is not an accurate representation of the true celestial object, but rather a result of viewing it through lenses with varying focusing powers at different locations.

In order to obtain the true image of celestial objects, it is crucial to effectively correct for the variations in focusing power caused by the direction of light incidence. One commonly used technique for this purpose is image deconvolution. It involves comparing the observed image with the PSF obtained by simulation or other means, and mathematically processing the PSF to correct for its effects and estimate the true and sharp image. In astronomy, Richardson-Lucy (RL) deconvolution is often used. The RL method, developed by Richardson (1972) and Lucy (1974), uses iterative processing based on Bayesian estimation to estimate the true sharp image. When applying the deconvolution method in practice, it is common to use a single PSF for each observed image. However, relying on a single PSF alone is not sufficient to achieve highly accurate deconvolution for all observed images from Chandra. As a result, we have developed a method that incorporates the position dependence of the PSF into the existing deconvolution technique. This approach allows us to effectively compensate for image distortions at different positions and accurately estimate the true representation of celestial objects.

In this study, we have developed a new method based on the RL method to incorporate position-dependent PSFs with into the calculations. We thoroughly examined the computational approach of the RL method and implemented improvements to efficiently integrate multiple PSFs into the calculation process. However, we encountered computational limitations when directly preparing PSFs for every pixel in the entire set of observed images. To address this, we devised a strategy to switch PSFs at regular intervals, to achieve faster computation. Additionally, we developed a proprietary correction method to mitigate the artificial generation of artificial lines at transition points, which can arise from variations in brightness. These advancements have enabled us to successfully implement the RL method with position-dependent PSFs for the complete spatial coverage of Chandra observations within a practical computational time frame.

As a proof of principle for our developed proprietary method, we applied it to the supernova remnant Cassiopeia A. Figure 1 (left) shows the observed image from Chandra, while Figure 1 (right) shows the result after applying our method. In the region where the image blur is more pronounced towards the right, our method enhances fine structures, resulting in a clearer image. We have illustrated this difference using monochromatic images in Figure 3. Thus, for the first time in the world, we have successfully applied our deconvolution method to the Cassiopeia A supernova remnant, suppressing the effects of the spatially-variant PSF and obtaining a clear image for the entire range of observations compared to previous methods.

We have developed a deconvolution method that can be applied to the entire set of Chandra observations, and we have demonstrated its principles by applying it to the supernova remnant Cassiopeia A. Given that Chandra has been observing for about 20 years, this method has great potential for various applications, such as studying the spatiotemporal evolution of celestial objects, discovering unknown structures, and obtaining highly accurate measurements of motion. By improving the visual acuity of X-ray observations through this method, we expect to expand the range of our ability to observe the universe at multiple wavelengths, including radio and visible light observations.

This research was supported by the Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research. Specifically, it was funded by the Challenging Exploratory Research (Pioneer) JP20K20527"Development of Ultra-Low Temperature Compton Camera for Precision X-ray Spectroscopic Polarimetry" (Principal Investigator: Shinya Yamada), the Grants-in-Aid for Scientific Research (B) JP22H01272"Formation of the Radio Nebula W50 by the SS433 Jet and Elucidation of the Gamma-Ray Emission Mechanism" (Research Collaborator: Shinya Yamada), and the Grants-in-Aid for and the Grants-in-Aid for Scientific Research (B) JP20H01941"Elucidation of the State Transition Processes in Active Galactic Nuclei Based on Radiative Magnetohydrodynamic Simulations" (Research Collaborator: Shinya Yamada).