Quantifying and containing the curse of high resolution coronal imaging

Abstract

Abstract. Future missions such as Solar Orbiter (SO), InterHelioprobe, or Solar Probe aim at approaching the Sun closer than ever before, with on board some high resolution imagers (HRI) having a subsecond cadence and a pixel area of about (80 km) 2 at the Sun during perihelion. In order to guarantee their scientific success, it is necessary to evaluate if the photon counts available at these resolution and cadence will provide a sufficient signal-to-noise ratio (SNR).For example, if the inhomogeneities in the Quiet Sun emission prevail at higher resolution, one may hope to locally have more photon counts than in the case of a uniform source. It is relevant to quantify how inhomogeneous the quiet corona will be for a pixel pitch that is about 20 times smaller than in the case of SoHO/EIT, and 5 times smaller than TRACE.We perform a first step in this direction by analyzing and characterizing the spatial intermittency of Quiet Sun images thanks to a multifractal analysis. We identify the parameters that specify the scale-invariance behavior. This identification allows next to select a family of multifractal processes, namely the Compound Poisson Cascades, that can synthesize artificial images having some of the scale-invariance properties observed on the recorded images.The prevalence of self-similarity in Quiet Sun coronal images makes it relevant to study the ratio between the SNR present at SoHO/EIT images and in coarsened images. SoHO/EIT images thus play the role of "high resolution" images, whereas the "low-resolution" coarsened images are rebinned so as to simulate a smaller angular resolution and/or a larger distance to the Sun. For a fixed difference in angular resolution and in Spacecraft-Sun distance, we determine the proportion of pixels having a SNR preserved at high resolution given a particular increase in effective area. If scaleinvariance continues to prevail at smaller scales, the concluCorrespondence to: V. Delouille (v.delouille@oma.be) sion reached with SoHO/EIT images can be transposed to the situation where the resolution is increased from SoHO/EIT to SO/HRI resolution at perihelion.

Scale invariant images in astronomy through the lens of multifractal modeling

“…To reach order statistics larger than two, we performed a wavelet based multifractal analysis. We found reasonable multiscaling power-law behaviors of structure functions S(q, j) computed as empirical moments of order q of the Daubechies' wavelet coefficient modulus [2,10]:…”

“…where H 0.6, q * + 2.25 and T = 0.85 [2]. A quantitative validation of this model is provided by a multifractal analysis which yields the same multiscaling exponents for both the model and the data.…”

“…Then the fractional integration yields the field I characterized by ζ(q) = qH + τ (q). See [2,4] for a detailed presentation.…”

“…This scale invariance can be characterized using the multiscaling exponents. We have shown that a multifractal model involving compound Poisson cascades is able to generate images having the same multifractal parameters as the original observations [2]. Other approaches involving multifractal analysis were presented to study coherent magnetic structures (active regions) [3].…”

Virtual resolution enhancement of scale invariant textured images using stochastic processes

“…This consistency is defined by two requirements: the preservation of scale invariance properties of the initial image (statistical consistency) and a zoom out to the initial resolution must yield the original image back (physical consistency). One application domain is in solar physics where current observations are 1024×1024 images at resolution 1800km (E.I.Telescope onboard SOHO) [3]. Therefore, physicists are considering the design of a new spatial telescope with a much better resolution of 80km which is about 25 times finer than that of EIT.…”