This paper presents new techniques for adaptive spatial binning of Integral-Field Spectroscopic (IFS) data to achieve a constant signal-to-noise ratio (S/N) per bin. These methods are essential for the proper analysis of IFS observations and can also be applied to standard photometric imagery or other two-dimensional data. The study focuses on the Sa galaxy NGC 2273, using the panoramic IFS SAURON to test various binning schemes. The goal is to bin the data such that the average S/N per spectral element is 50.
The paper discusses the challenges of spatially resolved astronomical observations, where S/N varies significantly across the detector elements. Two types of averaging processes are possible: smoothing and binning. While smoothing increases local S/N by correlating neighboring data, binning groups and averages data, resulting in sparser sampling and fewer final data points. Binning is more suitable for precise error management and when the number of data points matters.
The paper introduces two methods for 2D binning: the Quadtree method and Voronoi tessellations. The Quadtree method partitions the region into axis-aligned squares, but it has limitations, such as unavoidable S/N spread and non-square bins at the edges. Voronoi tessellations, on the other hand, naturally satisfy the topological requirement and can be tailored to meet the morphological and uniformity requirements by appropriately distributing the Voronoi generators.
The paper presents a modified Lloyd algorithm for generating Centroidal Voronoi Tessellations (CVTs) that produce bins with equal mass according to a density function. This method is applied to the SAURON data of NGC 2273, resulting in bins with a low S/N scatter (RMS ~3%). The algorithm is robust and can handle both large and small bins, with small bins consisting of only a few pixels.
The paper concludes that adaptive 2D binning is essential for the analysis of IFS data and can be extended to three dimensions. The methods described are applicable to various datasets, including stellar proper motions observations and N-body simulations. The software implementing these methods is available for use. The study demonstrates that adaptive binning can achieve a constant S/N per bin, ensuring reliable and unbiased analysis of IFS data.This paper presents new techniques for adaptive spatial binning of Integral-Field Spectroscopic (IFS) data to achieve a constant signal-to-noise ratio (S/N) per bin. These methods are essential for the proper analysis of IFS observations and can also be applied to standard photometric imagery or other two-dimensional data. The study focuses on the Sa galaxy NGC 2273, using the panoramic IFS SAURON to test various binning schemes. The goal is to bin the data such that the average S/N per spectral element is 50.
The paper discusses the challenges of spatially resolved astronomical observations, where S/N varies significantly across the detector elements. Two types of averaging processes are possible: smoothing and binning. While smoothing increases local S/N by correlating neighboring data, binning groups and averages data, resulting in sparser sampling and fewer final data points. Binning is more suitable for precise error management and when the number of data points matters.
The paper introduces two methods for 2D binning: the Quadtree method and Voronoi tessellations. The Quadtree method partitions the region into axis-aligned squares, but it has limitations, such as unavoidable S/N spread and non-square bins at the edges. Voronoi tessellations, on the other hand, naturally satisfy the topological requirement and can be tailored to meet the morphological and uniformity requirements by appropriately distributing the Voronoi generators.
The paper presents a modified Lloyd algorithm for generating Centroidal Voronoi Tessellations (CVTs) that produce bins with equal mass according to a density function. This method is applied to the SAURON data of NGC 2273, resulting in bins with a low S/N scatter (RMS ~3%). The algorithm is robust and can handle both large and small bins, with small bins consisting of only a few pixels.
The paper concludes that adaptive 2D binning is essential for the analysis of IFS data and can be extended to three dimensions. The methods described are applicable to various datasets, including stellar proper motions observations and N-body simulations. The software implementing these methods is available for use. The study demonstrates that adaptive binning can achieve a constant S/N per bin, ensuring reliable and unbiased analysis of IFS data.