Stray Light Correction for the Helioseismic and Magnetic Imager

TL;DR

This work develops a stray-light correction for the HMI by modeling the PSF as an Airy core convolved with a Lorentzian, parameterized and constrained using Venus and lunar transit observations in combination with ground-based calibrations. The PSF is deconvolved from full-disk images via the Richardson-Lucy algorithm, producing daily full-disk corrected data at 45 s and 720 s cadences that improve granulation contrast, brighten bright features, and elevate plage magnetic-field strengths, while partially correcting convective blueshift. The corrected data yield largely consistent local helioseismic inferences with the original data, except in sunspot regions where deviations appear; the cleaned data products (_dcon and _dconS) are now available in JSOC and recommended for improved photometric accuracy, feature tracking, and cross-instrument co-alignment. Overall, the methodology provides a robust, physically-motivated stray-light correction that enhances the scientific utility and interpretability of HMI imagery and derived products.

Abstract

We report a point spread function (PSF) and deconvolution procedure to remove stray light from the Helioseismic and Magnetic Imager (HMI) data. Pre-launch calibration observations, post-launch Venus transit and lunar transit data were used to develop the PSF and evaluate how well it reproduced the observed scattering. The PSF reported differs from previous stray light removal efforts since we do not use Gaussians as the central mathematical component. Instead, we use a Lorenztian convolved with an Airy function. In 2018, the HMI team began providing full-disk, stray-light-corrected data daily. Intensity, Doppler, magnetogram, and vector magnetic field data are provided. The deconvolution uses a Richardson-Lucy algorithm and takes less than one second per full-disk image. The results, on average, show decreases in umbral continuum intensity, a doubling of the granulation intensity contrast, increases in the total field strength, most notably in plage by $\sim$1.4--2.5 the original value, and a partial correction for the convective blueshift. Local helioseismology analyses using corrected data yield results that are consistent with those from uncorrected data, with only negligible differences, except in sunspot regions. The new data are found in JSOC with names similar to the original but with the qualifying term '$\_dcon$' or '$\_dconS$' appended, denoting whether the deconvolution was applied to the filtergrams or Stokes images. The HMI team recommends using the corrected data for improved visual clarity, more accurate irradiance reconstruction, better co-alignment with high-resolution data, reduced errors in tracking algorithms, and improved magnetic field strengths.

Figures (14)

• Figure 1: Several MTFs are shown as a function of spatial frequency. The $+$ symbols represent the average of three pre-launch (i.e. ground-based) observations during instrument calibration, as reported in wachter:2012 text and in their Figure 3. The ideal MTF, described by Equation \ref{['Eq-8']}, is plotted as a solid line while the ideal MTF multiplied by exponentials with $\gamma$ values of 2.5 and 4.5 are also plotted as dotted and dash lines, since these two curves bracket the pre-launch observations that are shown as symbols.
• Figure 2: A single filtergram image from the HMI side camera taken during the transit of Venus on 2012.06.06 at 02:04 UT is shown with pixels labelled on the x and y axis. Several sunspots are visible as well as the disk of Venus. A blank image with the same radius and center with limb darkening was generated with a circle of zeroes in the position of Venus. The blank image represented a solar image without any scattered light; the light level off the limb and within the disk of Venus is zero. A guess PSF was convolved with the blank image to estimate the scattered light distribution in a forward modeling process. This process was iterated until the result of the forward model best matched the observed image.
• Figure 3: The disk of Venus is shown with the observed and forward modeled light level contours overplotted. The observed contours appear as irregular circles, while the forward-modeled contours are smooth circles. The forward model uses a disk of zeros placed within a limb-darkened solar disk that is convolved with the PSF. The azimuthal asymmetry is apparent. We do not include an azimuthal dependence in the form of the PSF even though it is known to exist.
• Figure 4: The scattered light levels dependence on $\gamma$, $c$, and $\zeta$ as shown in Equations 9-10. The azimuthally averaged, normalized intensity observed in the disk of Venus (black line) is plotted on logarithmic scale as a function of pixels from the center of Venus in the top two plots and from the lunar edge during a lunar eclipse in the bottom panel. Forward modeled intensities are calculated by convolving a PSF with artificial data and light levels for different values of $\gamma$ (top left), $c$ (top right) and $\zeta$ (bottom). For the top left panel, $c$ and $\zeta$ are 0. For the top right and lower panels, a $\gamma$ of 4.5 is used, and a $c$ of 2$\times$10$^{-9}$ is used for the lower panel. Less light is scattered into the center of Venus with increasing values of $\gamma$ since the FWHM of its corresponding Lorentzian is proportional to $\frac{1}{\gamma}$. The c value is a constant multiplied by exponential term and simply raises the light level far away from any source.
• Figure 5: Comparisons are shown for the true continuum from 2022.12.31 06:00 UT (NOAA 13179, HARP 8927) with the plot on the left showing image data for the original (upper, left) and deconvolved data (lower, right). Scatter plots of the true continuum values are shown with the original versus deconvolved data for the 200 $\times$ 200 pixel region for active region and penumbra pixels (middle) and quiet-Sun pixels (right). The slope value, m, is shown in the panel as corresponding to a linear fit (blue) with a unity line (red) for context.