A New Method of Deriving Doppler Velocities for Solar Orbiter SPICE

This paper presents a follow-up to previous work on correcting PSF-induced Doppler artifacts in observations by the SPICE spectrograph on Solar Orbiter. In a previous paper, we demonstrated correction of these artifacts in the $y-λ$ plane with PSF Regularization, treating the forward problem with a method based on large sparse matrix inversion. It has since been found that similar apparent artifacts are also present in the $x-λ$ direction, i.e., across adjacent slit positions. This is difficult (although not impossible) to correct with the previous matrix inversion method due to the time variation between slit positions. We have therefore devised a new method which addresses both $x-λ$ and $y-λ$ artifacts simultaneously by applying wavelength dependent shifts at each $x-y$ plane of the spectral cube. This paper demonstrates the SPICE data issue, describes the new method, and shows a comparison with the previous one. We explore the time variation of the correction parameters for the SPICE data and show a clear orbit dependence. The results of the method are significantly higher quality derived Doppler signals, which we estimate at less than $\sim$ 5 km/s uncertainty for brighter lines in the absence of other systematics. Furthermore, we show the new SPICE polar observation results as a demonstration. The correction codes are written in Python, publicly available on GitHub, and can be directly applied to SPICE level 2 datasets.

💡 Research Summary

This paper addresses a long‑standing problem in Solar Orbiter’s SPICE EUV slit‑scanning spectrograph: artificial Doppler‑shift patterns caused by a tilted point‑spread function (PSF). In the earlier work (Plowman et al. 2023, “Paper I”), the authors identified a PSF tilt in the y‑λ plane that leaked light from bright features into neighboring spatial pixels at shifted wavelengths, producing characteristic red‑blue lobes in Doppler maps. They corrected this effect with a large‑scale sparse‑matrix inversion that effectively de‑convolved the PSF and then re‑applied a nominal PSF (the “PSF regularization” method).

Subsequent analysis revealed that a similar artifact also appears in the x‑λ direction, i.e., across adjacent slit positions built up during the raster scan. Because the raster is performed over time, each x‑slice samples a slightly different solar scene, violating the assumption of a static source that underlies the matrix‑inversion approach. Moreover, the time‑varying nature of the PSF makes a full three‑dimensional (x, y, λ) de‑convolution computationally prohibitive.

The authors therefore propose a much simpler, computationally cheap correction that simultaneously removes both x‑λ and y‑λ tilts. The key observation is that the tilt manifests as a wavelength‑dependent spatial shift. For each wavelength slice λk, the x‑y coordinates (xi, yj) are shifted to (xi + Δx·(λk‑λ0), yj + Δy·(λk‑λ0)), where λ0 is a reference wavelength (typically the centre of the spectral window) and Δx, Δy are constant coefficients describing the linear shift per unit wavelength. Using SciPy’s RegularGridInterpolator, the entire spectral cube is re‑interpolated onto these new coordinates, effectively “skew‑correcting” the data.

After the skew correction, the authors fit spectral lines in each pixel. Because each line’s centre may be displaced by Δλ relative to λ0, a final “de‑warping” step applies the inverse shift (‑Δx·Δλ, ‑Δy·Δλ) to the fitted line parameters. This restores the line profiles to their true spatial locations. The algorithm requires only two free parameters, which can be found by a brute‑force search over a modest parameter grid; the search takes minutes on a single CPU.

Advantages of the new method are: (1) negligible computational cost compared with the sparse‑matrix approach; (2) minimal sensitivity to temporal variations between raster steps, since the correction is applied per wavelength slice rather than assuming a static source; (3) ease of parameter optimisation, enabling routine application to large SPICE data sets. The primary trade‑off is a modest loss of spatial resolution (≈1 pixel, about a factor of 1.5) due to the interpolation steps, and the lack of any resolution enhancement that the PSF‑regularization method could provide.

The authors validate the technique by comparing SPICE Doppler maps before and after correction, and against co‑observations with IRIS. The characteristic artificial lobes disappear, and the corrected maps agree better with IRIS than the previous method, especially when both x‑ and y‑shifts are applied. They also demonstrate the method on a polar observation, showing high‑quality Doppler velocities with estimated uncertainties below ~5 km s⁻¹ for bright lines, assuming no other systematic errors.

A further result is the discovery that the shift parameters Δx and Δy vary systematically with Solar Orbiter’s orbital phase, indicating a thermal or mechanical origin (likely related to the scanning mirror upstream of the slit). This orbit‑dependence suggests that a time‑dependent calibration could be built into the pipeline.

All correction code is written in Python, released publicly on GitHub, and can be applied directly to SPICE level‑2 products. In summary, the wavelength‑dependent shift correction provides a fast, robust, and accurate means to mitigate PSF‑induced Doppler artifacts in SPICE data, enabling the mission’s primary science goals—elemental abundance and solar‑wind source diagnostics—to be pursued with reliable velocity measurements.