In the coming decade, the Roman Space Telescope will map the universe’s invisible skeleton by chasing faint distortions in the shapes of distant galaxies. But turning that subtle signal into trustworthy cosmology hinges on one stubborn detail: the telescope’s eye, the Point Spread Function or PSF. The PSF tells you how a point of light from the sky gets smeared into the detector, a fingerprint of the optics, detectors, and geometry of a telescope. If you don’t know that fingerprint with astonishing precision, the shapes you measure will be off, and the cosmic conclusions you draw will drift off target.
The study led by Federico Berlfein at Carnegie Mellon University’s McWilliams Center for Cosmology and Astrophysics (with colleagues including Rachel Mandelbaum, Xiangchong Li, Tianqing Zhang, Scott Dodelson, and Katarina Markovic) dives into a hidden complication: the PSF changes with wavelength, and stars and galaxies glow with different spectral energy distributions (SEDs). In Roman’s near-infrared world, chromatic differences can bias weak-lensing measurements if the PSF is modeled using stars but applied to galaxies with different colors. Berlfein and colleagues built Roman-like image simulations using realistic galaxy and star catalogs and then ran thousands of simulated galaxies through a shear-measurement pipeline. They then tested two families of mitigations: a PSF-level correction rooted in the SED slope differences, and two practical estimation routes—an analytic color-based approach and a self-organizing-map (SOM) machine-learning approach.
The punchline is candid and important: chromatic biases are real and sizable enough to demand calibration for Roman’s precise weak-lensing program. But the researchers don’t stop at the warning. They sketch and test viable correction strategies that could keep Roman on track, especially for its four typical weak-lensing bands and its widest, deepest filter. The work is a concrete reminder that as we chase fainter signals, tiny color-dependent quirks of our instrument become major players in the game of cosmic inference.
What Chromatic PSF Means for Cosmic Shear
In a diffraction-limited, space-based telescope like Roman, the PSF grows with wavelength. The absence of atmosphere makes the optics cleaner, but it also makes the wavelength dependence of the PSF more pronounced. That seems like a nerdy footnote until you realize that galaxy shapes—your primary signal in cosmic shear—are smeared by that PSF in a color-dependent way. Stars, which astronomers use to measure the PSF, have their own color fingerprints. Galaxies, which you actually want to weigh in on cosmic shear, do not share those fingerprints. So the PSF you derive from stars is not perfectly the PSF that acts on galaxies, and that mismatch introduces a chromatic bias into shear estimates.
To formalize the problem, the authors describe the measured shear as a linear function of the true shear, with a multiplicative bias m and an additive bias c. Those biases hide in the affects of how the PSF size and shape translate into ellipticity measurements. In Roman’s lexicon, the key filters are the four weak-lensing bands—Y106, J129, H158, F184—and the wide filter W146. Because the PSF is wavelength-dependent, and because SEDs differ between stars and galaxies (and can even vary within a single galaxy due to color gradients), the effective PSF for stars and for galaxies can diverge in systematic ways. Berlfein and team quantify exactly how big those divergences can be and how they propagate into the cosmic-shear signal.
At the core is the idea of an effective PSF: PSFeff, o(x,y) is the wavelength-integrated PSF weighted by the filter’s throughput F(λ) and the object’s SED S_o(λ). When you model PSF from stars but measure galaxies that have different SEDs, you’re effectively applying PSFeff,★ instead of PSFeff,g. The authors cast the difference as a sum of image-based basis functions, B_n, each scaled by coefficients ΔS_n that capture how the star-galaxy SED mismatch shifts the PSF. Leading order terms often capture most of the effect, especially in narrower filters, but broader bands can demand higher-order terms because galaxy SEDs aren’t perfectly linear across wide wavelength ranges. This is the mathematical backbone of their chromatic-corrective strategy: if you know the PSF’s wavelength behavior and the SED slopes, you can neutralize the bias at the PSF level, before it corrupts shear measurements.
As a practical matter, Roman’s scenario is especially favorable for PSF work: space means stable optics, precise ray-tracing PSF models, and clean, repeatable images. The authors leverage GalSim and the official Roman PSF package to generate realistic, oversampled images of stars and galaxies, then measure shear with a method that operates cleanly on these noiseless, controlled simulations. The punchline from this section is simple: the chromatic effect exists, and its fingerprint is predictable enough that a PSF-level correction can be designed to remove it—at least in principle and in controlled tests.
What the Simulations Reveal About Biases
The team built two realistic extragalactic catalogs—cosmoDC2 and Diffsky—and paired them with a stellar catalog drawn from Rubin-Roman simulations. They simulated 10,000 galaxies per run and 400,000 stars to represent a typical setup, across Roman’s WL bands and the wide filter. The results are sobering but also instructive: when you average across all galaxies, the chromatic PSF biases push the multiplicative shear bias m to about 0.2% in the four weak-lensing bands and to roughly 2% in the wide filter. In plain terms, the wide filter is an order of magnitude more sensitive to these chromatic quirks. In individual redshift slices, the biases can reach 0.4–0.9% for the WL bands and 3–6% for the wide filter. On the additive side, the WL bands stay within the broader allowable budgets, but the wide filter can exceed the total systematic budget in some scales.
Crucially, the biases are remarkably robust across the two galaxy catalogs they tested. Diffsky and cosmoDC2 tell a consistent story: the chromatic PSF effect is not a quirky artifact of a single SED library but a real risk tied to how stars and galaxies differ in color. The authors also quantify color-gradient effects—second-order chromatic terms that arise when a galaxy’s bulge and disk host different SEDs. For the four WL bands, these color-gradient biases stay below the most stringent Roman requirements. The wide filter, however, shows more variability between catalogs and can push biases toward the edge of, or beyond, tolerances. That signals a cautionary note: broad-band, high-SNR science may demand more complex corrections than the narrower bands.
Beyond the sheer numbers, the paper emphasizes a practical truth: the chromatic biases do not vanish with more photons or with better optics; they shift with wavelength in a way that interacts with galaxy colors in nontrivial ways. The team frames these biases not as a singular endgame but as a structured problem you can attack with a PSF-level correction, interval-by-interval calibration, and careful use of realistic SEDs. In their own words (paraphrased): the bias is real, but it can be understood and controlled if you treat the PSF and the SED as a coupled, learnable system rather than as an afterthought tacked onto a standard shear pipeline.
Mitigating Chromatic Biases at the PSF Level
The authors propose and test a PSF-centered mitigation strategy that hinges on a simple but powerful idea: if you can express the PSF’s chromatic error as a linear combination of fixed, wavelength-agnostic images B_n, then the galaxy-specific color information reduces to a small set of coefficients ΔS_n. The leading term, ΔS_1 B_1(x,y), captures the bulk of the chromatic PSF bias in many cases. The practical upshot is that you can correct the PSF itself, rather than trying to repair the galaxy shapes after the fact. The authors formalize this with a Taylor expansion around the filter’s effective wavelength, identify the B_n basis, and show how the slope differences between star and galaxy SEDs map into a few coefficients that determine the PSF correction needed for each galaxy.
In a perfect, no-noise world, applying the leading-order correction using the true ΔS_1 for each galaxy brings the multiplicative biases down to the most stringent Roman requirements for all WL bands. The wide filter, though, stubbornly resists a one-term fix; it often requires including second-order terms in the SED expansion. This is the practical ceiling: narrow bands tolerate a clean, first-order correction; a wide band demands a more elaborate, higher-order treatment, or perhaps a more constrained scientific use of that band.
Two realistic routes to estimate the needed ΔS_1 coefficients form the heart of the practical implementation. The first is an analytic, color-based estimator that uses a galaxy’s fluxes in adjacent filters to infer its SED slope inside the band of interest. The second is a machine-learning approach using self-organizing maps (SOMs) trained on combined LSST-Roman colors to predict per-galaxy SED slopes. The authors don’t claim one method to be universally best; instead, they show that each method has tradeoffs that depend on how well the SED library represents real galaxies and on how accurately you can infer the galaxy’s color behavior from photometry alone.
Practical Implementation and What Really Works
The paper digs into two practical implementations for ΔS_1: the analytic method using adjacent filters (for H158 the neighbors J129 and F184 are used) and the SOM-based method trained on nine-color spaces combining LSST and Roman photometry. They evaluate how well these estimators predict the true ΔS_1 and then test how well the resulting corrections suppress the measured shear biases in simulated images. The results are nuanced and instructive.
For the four WL bands, applying a per-galaxy correction using the true ΔS_1 virtually eliminates the stringent multiplicative bias, showing the first-order correction can be enough when the SED slope is known exactly. Using the average ΔS_1 across all galaxies or across redshift bins works well to meet a relaxed requirement, but can fail in certain redshift bins or when one uses a particularly nonlinear galaxy population (as in the Diffsky catalog). The SOM approach, while more complex to deploy, tends to perform better in the Diffsky case, especially when corrections are applied per galaxy; it remains broadly effective in the cosmoDC2 case, though it can struggle if the training set isn’t representative of the observed galaxies. The analytic estimator, by contrast, is more sensitive to how linear the galaxy SED is within the filter pair, and can stumble when galaxies show nonlinearity in color across adjacent bands.
When the authors turned to the wide W146 filter, the story got tougher. The first-order correction often fails to meet even the relaxed m < 0.001 target in several redshift slices, and using a second-order polynomial for the SED did not reliably fix the problem. In other words, broad-band corrections are inherently more fragile: you need a more faithful description of the galaxy SED inside the band, which may demand higher-order terms or richer spectral information than practical photometry alone can provide. The color-gradient tests—galaxy color variations inside a galaxy’s own light distribution—also matter, but for the WL bands they stay small; for the wide filter they can become non-negligible. The upshot is clear: a robust chromatic PSF correction pathway is essential for the WL bands, and the wide filter will require especially careful, perhaps multi-pronged, strategies to keep biases in check.
What This Means for Roman and the Era of Precision Cosmology
Put bluntly: chromatic PSF biases are not an aesthetic concern. They are a practical obstacle that could limit Roman’s ability to extract precise cosmological information from weak lensing if left uncorrected. The authors’ results quantify the stakes: biases on the order of 0.2% in the WL bands and around 2% in the wide filter aren’t just small—these numbers sit at the heart of the systematic budgets for Roman. In the worst redshift slices, biases can swell to nearly 1% in the WL bands and up to several percent in the wide band. At stake is the fidelity of measurements of the matter distribution and the growth of structure, which feed into the science goals of constraining dark energy, neutrino masses, and the physics of gravity on cosmic scales.
The research doesn’t stop at diagnosing the problem. It lays out a practical framework for mitigation that is broadly applicable to space-based weak-lensing missions, and it invites the broader cosmology community to invest in SED-aware PSF modeling. The two mitigation avenues—analytic slope-based corrections and SOM-based corrections—offer complementary paths, each with caveats tied to the quality and representativeness of spectral libraries and training data. The work also foregrounds a critical truth about next-generation surveys: as statistical precision climbs, systematics that were once negligible can become dominant. Chromatic PSF effects are a vivid example of that shift, pushing the field to develop calibration strategies that are as sophisticated as the instruments themselves.
Beyond Roman, the study resonates with the broader plan of the precision-cosmology era, where surveys like Euclid and LSST are already knitting together multi-wavelength data streams. The authors’ emphasis on PSF-level corrections and SED-based mitigation could inform cross-survey calibration, helping ensure that future cosmic-shear measurements from different telescopes remain on a coherent, bias-controlled footing. And the work speaks to a practical lesson for instrument designers and data analysts alike: the most robust corrections come from marrying physically grounded models (the PSF’s wavelength behavior) with empirical, data-driven estimates of galaxy colors and SED slopes.
As the Roman HLWAS concept evolves, the authors suggest that real-world implementation will need to grapple with additional complexities—noise, image coaddition from many exposures, and the inevitable mismatch between simulated catalogs and the real universe. Yet the core message is already actionable: build a chromatic-aware PSF model, calibrate it with a realistic SED-informed framework, and you can keep Roman’s weak-lensing science on track. It’s a reminder that the border between instrumentation and cosmology is not a line but a seam—a place where color, light, and physics intersect to reveal the shape of the cosmos.
