🔭 astrophysics

A Point-Spread Function for the Extreme Ultraviolet High-Resolution Imager on board Solar Orbiter

This paper presents a comprehensive point-spread function for Solar Orbiter's HRIEUV instrument that quantifies light redistribution caused by diffraction and scattering, enabling image deconvolution that significantly enhances photometric accuracy, dynamic range, and contrast for scientific analysis.

Original authors: Stefan J. Hofmeister, Emil Kraaikamp, Sergei Shestov, Luca Teriaca, Alexandros Koukras, Cis Verbeeck, Frederic Auchere, Daniel W. Savin, Michael Hahn, David Berghmans

Published 2026-05-05

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CC BY 4.0

Original authors: Stefan J. Hofmeister, Emil Kraaikamp, Sergei Shestov, Luca Teriaca, Alexandros Koukras, Cis Verbeeck, Frederic Auchere, Daniel W. Savin, Michael Hahn, David Berghmans

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine trying to take a crystal-clear photo of a distant city at night, but your camera lens is covered in a fine layer of dust and has a tiny, intricate spiderweb stuck right in front of it. When you snap the picture, the bright lights of the city don't just stay sharp; they smear out, creating a hazy glow that washes out the dark shadows and blurs the details.

This is exactly the problem scientists faced with the HRIEUV, a high-resolution camera on the Solar Orbiter spacecraft. This camera takes pictures of the Sun in extreme ultraviolet light (a type of light our eyes can't see). The researchers found that the camera's "lens" (which is actually a complex system of mirrors and filters) was scattering and bending a massive amount of sunlight, making the images look fuzzy and washing out the contrast between bright and dark areas.

Here is the story of how they fixed it, explained simply:

The Problem: The "Hazy" Sun

The paper explains that when light enters the camera, it hits two main troublemakers:

The Spiderwebs (Diffraction): The filters that let light in are held up by tiny metal grids (meshes) and support structures that look like spiderwebs. As light passes through these grids, it bends and creates a star-like pattern of streaks and rings.
The Dust (Diffuse Scattering): The mirrors inside the camera aren't perfectly smooth; they have microscopic bumps (roughness). When light hits these bumps, it scatters in all directions, like light hitting a frosted glass window. This creates a general "fog" over the entire image.

The scientists calculated that 57% of the sunlight hitting the camera was being messed up by these two effects. Instead of landing exactly where it was supposed to, over half the light was being redistributed, making bright spots dimmer and dark spots brighter, effectively ruining the picture's clarity.

The Solution: The "Digital Eraser"

To fix this, the team didn't build a new camera; they built a mathematical "map" of the mess, called a Point-Spread Function (PSF). Think of the PSF as a detailed instruction manual that says, "If a photon of light lands here, it actually came from there, and it got smeared by this specific pattern."

Once they had this map, they could use a process called deconvolution. Imagine you have a blurry photo of a face. If you know exactly how the blur happened (e.g., "the camera moved 2 pixels to the left"), you can use math to reverse the motion and sharpen the face back to its original state. That is what they did with the Sun.

How They Made the Map

They couldn't just look at the Sun to figure out the blur, because the Sun is always bright. They needed a way to see the "fog" without the "lights."

They used a rare event: Mercury's Transit.
On January 3, 2023, the planet Mercury passed directly in front of the Sun. To the camera, Mercury looked like a tiny, perfectly black dot blocking the light.

The Trick: Inside that tiny black dot, there should be zero light. But because of the camera's "fog" (scattering), the black dot wasn't actually black; it was filled with light leaking in from the bright Sun around it.
The Detective Work: By measuring exactly how much light was leaking into Mercury's shadow, the scientists could reverse-engineer the "fog." They watched Mercury move across the Sun, sampling the light leakage from different distances and angles. This allowed them to build a complete map of how the camera scatters light.

They also used blueprints of the camera to calculate the "spiderweb" effect mathematically, confirming their observations.

The Result: A Sharper Sun

Once they applied their new "digital eraser" (the PSF) to the images, the results were dramatic:

Bright things got brighter: The intense, active areas of the Sun became up to 40% brighter in the corrected images.
Dark things got darker: The quiet, dark areas became up to 85% darker.
Details popped out: The "fog" was removed, revealing sharp, crisp details in the solar loops and structures that were previously hidden.

Why It Matters

The paper concludes that by understanding and correcting for these optical imperfections, scientists can now see the Sun with much greater precision. It's like cleaning a dirty window: the view outside hasn't changed, but now you can finally see the details clearly. This allows for much better scientific analysis of solar activity, helping us understand our star better.

In short: The camera had a dirty lens and a spiderweb in front of it. The scientists figured out exactly how the dirt and web distorted the light, and then used math to clean the picture up, revealing a much sharper view of the Sun.

Technical Summary: A Point-Spread Function for the Extreme Ultraviolet High-Resolution Imager on board Solar Orbiter

Problem Statement
The Extreme Ultraviolet High-Resolution Imager (HRIEUV) on board the Solar Orbiter observes the Sun at 174 Å. Like many instruments operating at these wavelengths, HRIEUV suffers from significant instrumental light redistribution caused by diffraction and scattering. This redistribution degrades image resolution and dynamic contrast, obscuring faint structures and reducing photometric accuracy. The light redistribution arises from two primary sources: (1) diffraction caused by the mechanical mountings and mesh grids supporting the entrance and filter-wheel filters, and (2) diffuse scattering resulting from the micro-roughness of the telescope mirrors. Without a precise characterization of the Point-Spread Function (PSF), these instrumental effects cannot be corrected, limiting the scientific utility of the observations.

Methodology
The authors derive the HRIEUV PSF by combining theoretical modeling of diffraction with empirical calibration of diffuse scattering using Mercury transit observations from January 3, 2023.

Diffraction Modeling: The diffraction component was derived from the instrument's mechanical drawings. Due to computational constraints preventing full two-dimensional Fresnel propagation (which would require ~12 TB of memory), the authors employed a "simplified-combined" approach. This method models diffraction from the entrance filter using Fraunhofer propagation from the entrance pupil to the detector and calculates diffraction from the filter-wheel mesh using an analytical far-field solution. These individual patterns are convolved to form the total diffraction PSF. One-dimensional Fresnel modeling was used to validate that this simplification yields results consistent with full near-field propagation within the resolution of the detector pixels.
Diffuse Scattering Calibration: The diffuse scattering component was calibrated using 126 images of the Mercury transit. The methodology utilizes a semi-blind inversion algorithm (based on Hofmeister et al. 2022) that reconstructs the spatial profile of scattered light. By analyzing the intensities within the occulted pixels of Mercury—where the true solar intensity is zero but scattered light from the surrounding disk is present—the authors solved for the PSF coefficients.
- The inversion incorporated the known diffraction PSF as a fixed component.
- The diffuse scattering component was spatially discretized into concentric shells.
- An iterative process was used: deconvolving images with the current PSF estimate, setting occulted pixels to zero to approximate the true image, and refitting the PSF coefficients.
- To prevent overfitting and ensure robustness, the diffuse PSF was parameterized using a "softened power law" ( $f_{psfS}(\Delta r) = a / (b + \Delta r)^c$ ).
- Uncertainty was assessed via cross-validation and bootstrapping, and robustness was tested against potential anisotropies and dark-current calibration errors.

Key Contributions and Results

Quantification of Light Redistribution: The study determines that 56.6% of the incoming light is redistributed over the detector. Specifically, approximately 26.4% is diffracted (predominantly by the entrance-filter mesh and mounting), and 41.1% is diffusely scattered (likely due to mirror micro-roughness).
PSF Characterization:
- Diffraction: The diffraction pattern is dominated by the entrance-filter mesh, creating directional peaks with a spacing of 5.74 pixels. The entrance-filter mounting contributes to the PSF core, while the filter-wheel mesh contributes primarily to short-range diffraction.
- Diffuse Scattering: The diffuse component is well-described by a softened power law. It scatters 41% of the light across the detector, with the intensity decreasing steeply with distance.
Validation: The derived PSF was validated against solar flare observations and the Mercury transit data. Simulations using the combined PSF successfully reproduced the observed intensity distributions along diffraction arms and within Mercury's shadow, with errors generally within ±4% (reaching up to 13% in specific detector positions).
Image Correction: Applying deconvolution (using the Richardson-Lucy algorithm) with the derived PSF significantly improves image quality. The authors report that correcting for these effects increases the intensity of bright structures by up to 40% and decreases the intensity of dark structures by up to 85%, thereby enhancing dynamic range and contrast.

Significance and Claims
The paper claims that the derived PSF provides a quantitative description of the instrumental effects affecting HRIEUV, enabling the correction of images for scattered and diffracted light. The authors emphasize that this correction substantially enhances the dynamic range and contrast of observations, facilitating more precise scientific analysis.

The study also offers insights into instrument design, noting that while the filter-wheel mesh is in the near-field of the detector, the analytical far-field solution provides a sufficient approximation for the resulting diffraction pattern given the detector's pixel size. Furthermore, the comparison with the Atmospheric Imaging Assembly (AIA) highlights that while HRIEUV scatters a larger fraction of light than AIA, it does so over shorter angular distances, which may be beneficial for off-limb observations. The authors conclude that the derived PSF should be regarded as a detector-averaged representation, as small spatial variations in the PSF or residual intensity gradients could not be definitively distinguished from the data. The PSF and associated deconvolution tools are made available for the community to improve the photometric accuracy and sharpness of HRIEUV data.

The Problem: The "Hazy" Sun

The Solution: The "Digital Eraser"

How They Made the Map

The Result: A Sharper Sun

Why It Matters

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