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ffortissimo: A Freeform Forward-Modeling Pipeline for High-Contrast Images of Circumstellar Disks Based on Automatic Differentiation

This paper introduces ffortissimo, a novel JAX-based forward-modeling pipeline that leverages automatic differentiation to perform freeform, pixel-based characterization of circumstellar disks in PSF-subtracted images, successfully recovering complex dust morphologies and scattering properties around HR 4796A while highlighting remaining challenges in noise artifact characterization for precision photometry.

Original authors: Jay K. Kueny, Joseph D. Long, Jared R. Males, Alycia J. Weinberger, Laird M. Close, Joshua Liberman, Sebastiaan Haffert, Eden McEwen, Maggie Y. Kautz, Olivier Guyon, Logan Pearce, Parker T. Johnson, K

Published 2026-06-23

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CC BY 4.0

Original authors: Jay K. Kueny, Joseph D. Long, Jared R. Males, Alycia J. Weinberger, Laird M. Close, Joshua Liberman, Sebastiaan Haffert, Eden McEwen, Maggie Y. Kautz, Olivier Guyon, Logan Pearce, Parker T. Johnson, Katie Twitchell, Jialin Li, Alex Hedglen, Avalon Gower, Warren Foster, Jhen Lumbres, Lauren Schatz

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 clear photo of a faint, dusty ring floating around a bright star. The problem is that the star is so blindingly bright that it creates a "glare" (like when you take a picture of a streetlight at night) that washes out the details of the dust ring. Astronomers use special software to subtract that glare, but the software is a bit clumsy: in trying to remove the star's light, it often accidentally smears or erases parts of the dust ring itself, especially the parts closest to the star.

This paper introduces a new tool called ffortissimo (a play on the musical term for "very loud," but here meaning "very strong" or "very free") to solve this problem. Here is how it works, explained simply:

The Old Way: Trying to Guess the Shape

Traditionally, astronomers tried to fix these blurry images by guessing what the dust ring should look like. They would assume the ring was a perfect circle or a simple oval with a specific mathematical shape. They would then tweak their guess until it matched the blurry photo.

The Flaw: Real dust rings are messy. They have gaps, bumps, and weird twists. If you force a messy ring to fit a perfect mathematical formula, you miss all the interesting details. It's like trying to describe a jagged mountain range by saying, "It's just a big hill."

The New Way: The "Pixel-by-Pixel" Detective

ffortissimo changes the game. Instead of guessing a shape, it treats every single tiny dot (pixel) in the image as a separate clue.

The Analogy: Imagine you are trying to reconstruct a shattered vase. The old method was to guess the vase's shape based on a few pieces and fill in the rest with clay. The ffortissimo method is like having a super-smart robot that looks at every single shard, figures out exactly where it belongs, and assembles the vase piece by piece, even if the final shape is weird or irregular.
How it learns: The tool uses a powerful computer technique called "automatic differentiation." Think of this as the tool having a "feeling" for how to improve the image. If a part of the image looks too dark, it knows to brighten that specific pixel. If a part looks too noisy, it knows to smooth it out. It does this millions of times per second, learning the true shape of the dust ring directly from the data, without forcing it into a pre-made box.

The "Magic" of Speed

Usually, doing this kind of detailed, pixel-by-pixel reconstruction takes a supercomputer days to calculate.

The Analogy: The authors built their tool using a special "engine" (called Jax) that runs on modern graphics cards (the same kind used for video games). This allows the tool to run 100 to 150 times faster than previous methods. It's like upgrading from a bicycle to a jet engine. What used to take a week now takes about an hour and a half.

What They Found

They tested this tool on the famous HR 4796A system, a young star surrounded by a bright dust ring.

Recovering the Lost: They showed that ffortissimo could recover parts of the dust ring that the old "glare-removal" software had accidentally erased. It successfully reconstructed the "forward-scattering" peak—a bright spot on the ring that usually gets wiped out by the glare subtraction.
Seeing the Invisible: Because the tool is so precise, it can actually "see" features smaller than the telescope's normal limit. It's like being able to read the fine print on a newspaper from a mile away because the tool knows exactly how the lens blurs the image and mathematically "un-blurs" it.
The Catch (Noise): The tool is very good at finding the dust, but it is also very good at finding "noise" (random static in the image). Sometimes, the tool gets confused and thinks a speck of noise is part of the dust ring. The authors admit that while the tool is powerful, it currently struggles to perfectly tell the difference between a real dust feature and a random glitch in the camera, especially very close to the bright star.

The Bottom Line

ffortissimo is a new, open-source tool that lets astronomers look at dusty rings around stars with much sharper eyes. Instead of forcing the universe to fit a simple math formula, it lets the data tell the story, revealing complex shapes and hidden details that were previously lost in the glare. However, users are warned to be careful: because the tool is so sensitive, it might sometimes "hallucinate" details that are actually just camera noise, so the results need to be checked carefully.

Technical Summary of "ffortissimo: A Freeform Forward-Modeling Pipeline for High-Contrast Images of Circumstellar Disks Based on Automatic Differentiation"

Problem Statement
Characterizing circumstellar disks via direct imaging is hindered by two primary challenges. First, traditional parametric modeling assumes dust density distributions follow fixed functional forms, which often fails to capture complex morphologies such as gaps, clumps, warps, and spirals. Second, standard high-contrast imaging post-processing techniques, specifically Angular Differential Imaging (ADI) paired with Karhunen-Loève Image Projection (KLIP), introduce artifacts. These algorithms inevitably subtract portions of the disk signal along with the stellar point-spread function (PSF) noise (self-subtraction), distorting the true morphology of faint structures, particularly at small angular separations and along the minor axis of inclined disks. This distortion complicates the accurate measurement of the dust Scattering Phase Function (SPF) and makes it difficult to infer the bulk composition of the scattering material.

Methodology
The authors introduce ffortissimo, a novel, open-source Python pipeline designed for pixel-based, freeform forward modeling of extended objects in KLIP-reduced images. The pipeline is built within the Jax framework, leveraging automatic differentiation ("autodiff") and GPU-accelerated array computations to enable efficient optimization.

The core workflow involves the following steps:

Forward Modeling Framework: The pipeline utilizes the DiskFM formalism (Mazoyer et al. 2020) to simulate the instrument response and PSF subtraction artifacts (self-subtraction and over-subtraction) on a synthetic disk model. This allows the model to be directly compared against the KLIP-reduced data.
Freeform Parameterization: Unlike traditional methods that fit a small set of geometric and physical parameters, ffortissimo treats every pixel within a Region of Interest (ROI) as an independent free parameter. This allows the model to learn the dust density and brightness distribution directly from the data without assuming a specific parametric shape.
Optimization: The pipeline employs the Adam optimizer to minimize a cost function defined by the residuals between the forward-modeled image and the observed KLIP-reduced image, normalized by an empirically measured noise map.
Regularization: To prevent the freeform model from overfitting noise (resulting in "gritty" artifacts) and to enforce physical smoothness, the authors implement a spatial frequency regularization scheme. This involves:
- Generating a reference disk model (using a simple parametric scattered-light model) to create a reference power spectrum template.
- Fitting an elliptical Gaussian window to this template to define expected spatial frequencies.
- Penalizing the freeform model's power spectrum if it exceeds this reference template during optimization.
Validation: The authors validate the regularization method by testing it on "diskless" background noise images and images with flipped or isotropic reference models to ensure the method does not bias the retrieved morphology toward the reference template.

Key Contributions

Development of ffortissimo: A fully differentiable, GPU-accelerated pipeline that performs pixel-by-pixel forward modeling of circumstellar disks, capable of handling the complex artifacts introduced by KLIP-ADI and KLIP-RDI.
Data-Driven SPF Retrieval: The ability to infer dust scattering properties and the Scattering Phase Function (SPF) directly from data, even through regions heavily affected by PSF subtraction artifacts (e.g., the minor axis of inclined disks), without relying on pre-supposed analytical SPF profiles like the Henyey-Greenstein function.
Computational Efficiency: By utilizing Jax and gradient descent, the pipeline achieves convergence speeds roughly 100–150 times faster than traditional Markov Chain Monte Carlo (MCMC) based DiskFM approaches, reducing convergence time from days to approximately 1.5 hours on a single NVIDIA H100 GPU.
Super-Resolution Potential: The framework demonstrates the ability to infer spatial features smaller than the telescope's diffraction limit (deconvolution) by optimizing a pre-convolution model, provided the signal-to-noise ratio is sufficient.

Results
The pipeline was tested on visible-light images of the HR 4796A circumstellar disk obtained with the MagAO-X instrument.

Morphological Recovery: The freeform models successfully recovered complex brightness distributions and asymmetries in the disk lobes that traditional parametric models failed to fit, resulting in significantly improved residuals.
SPF Extraction: The pipeline successfully retrieved the SPF across a wide range of scattering angles, including the forward-scattering peak at the minor axis, which is typically erased by KLIP-ADI. The extracted SPFs showed good agreement with those derived from parametric models using Legendre polynomials, particularly in the $z'$ -band.
Inject-and-Recover Tests: Using synthetic disks injected into "back-rotated" datasets, the authors demonstrated that ffortissimo can recover known SPFs and spatial features (such as nested ringlets with widths of $\sim$ 1 pixel) even in the presence of wind-driven halo (WDH) noise, though performance degrades in regions with severe noise artifacts.
Limitations Observed: The models were found to learn certain noise artifacts, specifically the wind-driven halo (WDH) and residual speckle noise at small angular separations, indicating that the current pipeline struggles to distinguish faint disk features from diffuse background noise in low signal-to-noise regimes.

Significance and Claims
The paper claims that ffortissimo offers a powerful tool for the morphological characterization of circumstellar disks, particularly for systems with complex geometries that defy simple parametric descriptions. By removing the assumption of a fixed parametric form, the method allows for a more direct retrieval of dust scattering properties and spatial structures.

However, the authors maintain a modest stance regarding the current precision of the method. They explicitly state that precision photometry using these freeform models is not yet advised due to remaining challenges in characterizing background noise, wind-driven halos, and speckles. The authors emphasize that while the pipeline can recover lost signals and sub-resolution features, the results should be treated with caution and cross-validated with other methods until a rigorous statistical framework for pixel-by-pixel variance is established. The primary value of the current work is presented as exploratory morphological characterization and the demonstration of a new, computationally efficient pathway for forward modeling high-contrast images.

The Old Way: Trying to Guess the Shape

The New Way: The "Pixel-by-Pixel" Detective

The "Magic" of Speed

What They Found

The Bottom Line

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