🔭 astrophysics

Impact of Charge Transfer Inefficiency on transit light-curves: A correction strategy for PLATO

This paper presents a correction strategy for Charge Transfer Inefficiency (CTI) in the PLATO mission that utilizes a calibrated model based on PLATOSim simulations to reduce CTI-induced transit depth biases from 4% to 0.06%, thereby ensuring the mission meets its required accuracy for detecting Earth-sized exoplanets.

Original authors: Shaunak Mishra, Reza Samadi, Diane Bérard

Published 2026-03-18

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CC BY 4.0

Original authors: Shaunak Mishra, Reza Samadi, Diane Bérard

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 you are trying to take a perfectly clear, high-definition photograph of a tiny, dim star in a crowded city at night. You want to spot a tiny planet passing in front of that star—a "transit"—which would look like a tiny, fleeting shadow. To do this, your camera needs to be incredibly precise.

Now, imagine that your camera sensor (the part that catches the light) has been sitting in space for years, bombarded by invisible cosmic rays. These rays have damaged the sensor, creating tiny, invisible "potholes" or "traps" in the silicon.

The Problem: The "Sticky Floor" Effect

When the camera tries to move the image data from the sensor to the computer (a process called "transferring charge"), these potholes act like sticky spots on a floor. As the data "walks" across the sensor, some of it gets stuck in the potholes.

Later, the potholes let the data go, but not in the right place. It's like walking across a sticky floor, dropping a few marbles, and then having them roll out from under your feet after you've already left the room.

In the world of astronomy, this causes two bad things:

The Peak Gets Flattened: The brightest part of the star's image loses some of its "marbles" (electrons), making the star look slightly dimmer than it really is.
The Tail: The marbles that were dropped and released later create a faint "tail" or smear behind the star.

For the PLATO mission (a European space telescope launching soon to find Earth-like planets), this is a disaster. If the camera thinks a star is slightly dimmer because of these sticky potholes, it might calculate that the planet blocking the star is bigger than it actually is. The mission requires a precision of 2% to find Earth-sized planets, but this "sticky floor" effect could introduce an error of nearly 4%, ruining the mission's ability to find habitable worlds.

The Solution: The "Smart Janitor" Strategy

The authors of this paper, S. Mishra and colleagues, developed a clever way to fix this. They didn't just try to patch the potholes; they built a mathematical "Smart Janitor" to clean up the data after it's taken.

Here is how their strategy works, broken down into simple steps:

1. Mapping the Potholes (Calibration)
First, they needed to know exactly where the potholes were and how "sticky" they were. They realized the damage wasn't random; it was worse at the edges of the camera sensor (like how the corners of a room get more dust).

The Analogy: Imagine the camera sensor is a giant dance floor. The center is clean, but the corners are covered in gum. The team created a map showing exactly how much gum is in every square inch of the floor.

2. The "Overscan" Test
To figure out how sticky the gum is, they looked at the "overscan" area of the camera. This is a fake, empty row of pixels at the edge of the sensor that doesn't take pictures but catches the "dropped marbles" (the sticky charge) that fell off the real image.

The Analogy: It's like watching where the marbles roll off the edge of the table to guess how sticky the table surface is. By analyzing this "trash," they could calculate the exact release time of the traps (how long it takes for the gum to let go).

3. The Correction Algorithm (The Fix)
Once they had their map of the potholes and the stickiness levels, they wrote a computer program to reverse the damage.

The Analogy: Imagine you have a blurry photo where the subject looks dim and has a ghostly tail. The computer program looks at the "gum map," calculates exactly how many marbles were stolen from the star, and adds them back in. It also subtracts the ghostly tail. It's like using a photo-editing tool, but instead of just guessing, it uses a precise physics model to restore the original image.

The Results: A Clean Slate

The team tested this on simulated data representing the worst-case scenario: an 8-year mission where the camera is very damaged.

Before the fix: The error was 3.95%. This was too high; the mission would have failed to meet its scientific goals.
After the fix: The error dropped to 0.06%.

This is a massive improvement. It means the "Smart Janitor" successfully cleaned up the data, bringing the precision well within the mission's strict requirements.

Why This Matters

This paper is a blueprint for the future. Even though it focuses on the PLATO mission, the method they developed can be used for any space telescope that uses digital cameras. It proves that even if space radiation damages our instruments, we can use smart math and calibration to "heal" the data and ensure we don't miss the discovery of a new Earth.

In short: Space radiation makes camera sensors sticky, distorting our view of the universe. These scientists built a mathematical "eraser" that cleans up the distortion, ensuring we can still find tiny, Earth-like planets with perfect clarity.

1. Problem Statement

The PLATO (PLAnetary Transits and Oscillations of stars) mission, scheduled for launch in 2026, aims to detect Earth-sized exoplanets orbiting solar-type stars with a radius measurement accuracy better than 2%. A critical threat to this precision is Charge Transfer Inefficiency (CTI), a degradation mechanism in Charge-Coupled Devices (CCDs) caused by radiation damage in the space environment.

Mechanism: Radiation creates charge-trapping sites in the silicon lattice. During charge transfer (readout), electrons are intermittently captured and released with a delay.
Consequence: This causes "charge trailing," where flux is lost from the source and redistributed into subsequent pixels (smearing). This distorts light curves and introduces a systematic bias in measured transit depths.
The Challenge: Previous correction methods (e.g., for Euclid) often assumed uniform trap density. However, PLATO's radiation analysis indicates that trap density varies spatially (increasing with radial distance from the optical center). Ignoring this spatial variation risks failing to meet the mission's strict 2% accuracy budget. The study quantifies this bias and proposes a novel correction strategy.

2. Methodology

The authors developed a comprehensive calibration and correction pipeline using simulated data generated by PLATOSim. The methodology is divided into three main phases:

A. CTI Modeling and Simulation

Charge Density Model (CDM): The study utilizes the CDM based on Shockley–Read–Hall theory to simulate charge capture and release.
Spatial Variation: Unlike standard models assuming uniform trap density, this work incorporates an axisymmetric radial dependence derived from PLATO radiation maps (OHB System AG, 2024). Trap density is modeled as a quadratic function of the normalized radial distance ( $R_{norm}$ ) from the focal plane center.
Simulation Setup: Light curves for Earth- and Jupiter-sized planets were simulated under various mission durations (4 and 8 years) and stellar magnitudes ( $m_V = 9, 11, 13$ ). Three specific CCD positions were tested: low trap density (bottom-left), intermediate (top-left), and high trap density (top-right).

B. Calibration Strategy (Three-Step Process)

The calibration aims to derive the parameters needed for correction using full-frame images acquired at the start of each quarter:

Initial Release Time Estimation: The parallel overscan signal (virtual rows beyond the physical sensor) is fitted with a multi-exponential decay function to identify the number of trap species and estimate their initial release times ( $\tau_{r,k}$ ).
Smearing Removal: A column-wise least-squares fit using an exponential-plus-constant function is applied to model and subtract the smearing contribution from the image.
Iterative Joint Calibration: An iterative algorithm combining the Extended Pixel Edge Response (EPER) method and the Massey et al. (2014) CTI correction algorithm is used. This step simultaneously refines:
- Polynomial coefficients ( $a_{p,k}$ ) describing the spatial trap density distribution.
- The well-fill power-law index ( $\beta$ ).
- The release times ( $\tau_{r,k}$ ).

C. Correction Strategy

Imagette Correction: For the small 6×6 pixel "imagettes" transmitted to the ground, the correction uses the calibrated spatial trap density map.
History Dependency: To account for charges deferred from sources read out before the target imagette, the algorithm utilizes the full-frame flux distribution from the beginning of the quarter.
Algorithm: An iterative inversion scheme (adapted from Massey et al.) is applied column-by-column to reconstruct the CTI-free signal.

3. Key Contributions

Quantification of Bias: The paper provides the first quantitative demonstration of CTI's impact on exoplanet transit measurements, showing that uncorrected CTI can induce a bias of up to ~4% in transit depth, which alone would consume the entire 2% accuracy budget for radius measurement.
Spatially Varying Trap Model: The authors successfully extended the CDM to handle non-uniform, radially dependent trap densities, a critical advancement over previous uniform models.
Integrated Calibration Pipeline: The development of a three-stage calibration strategy that derives spatial trap density maps, release times, and the well-fill index from simulated overscan data.
Correction Validation: A robust correction scheme that reduces the CTI-induced bias to negligible levels, validated through Monte Carlo simulations to assess error propagation.

4. Results

Bias Quantification: In the worst-case scenario (8-year mission, high trap density zone, $m_V=11$ ), CTI induced a transit depth bias of 3.95% (approx. 4.18 ppm). This corresponds to a 1.98% bias in the planet-to-star radius ratio, effectively exhausting the mission's error budget.
Trap Species Analysis: The study found that the fastest trap species contribute negligibly to the bias. The bias is primarily driven by the third (intermediate) and fourth (slow) trap species.
Correction Performance:
- The proposed correction strategy reduced the residual bias from 3.95% to 0.06%.
- This represents a 98.61% improvement, bringing the measurement well within PLATO's accuracy requirements.
- The correction remained effective across different mission durations (4 vs. 8 years) and stellar magnitudes.
Parameter Recovery: The iterative calibration successfully recovered the polynomial coefficients for trap density and the release times with high accuracy, particularly for the slow-trapping species that dominate the bias.

5. Significance and Limitations

Significance:
This work is critical for the success of the PLATO mission. It proves that without a specific correction strategy accounting for spatial trap variations, the mission cannot achieve its primary science goal of characterizing Earth-sized planets. The developed framework provides a generalizable solution for any future space mission using CCDs in high-radiation environments.

Limitations and Future Work:

Full-Frame Requirement: The current correction relies on full-frame images (available only at the start of quarters) to model the charge history. During regular operations, only small imagettes are transmitted, making in-flight correction for these specific targets challenging without ground-based reconstruction.
Drift Coupling: The simulation assumed ideal de-trending of stellar drift. In reality, the coupling between CTI and stellar drift on the focal plane may leave residuals.
PSF Fitting: The study used aperture photometry. Future work must validate the correction efficiency using PSF-fitting photometry, which is necessary for crowded fields.
Capture Cross-Sections: The capture cross-sections ( $\sigma_k$ ) were fixed based on literature values, as the EPER method cannot derive them. Future work may need to employ the First Pixel Response (FPR) method.

In conclusion, the authors have successfully demonstrated a viable path to mitigate CTI effects for PLATO, ensuring that the mission can meet its rigorous scientific requirements for detecting and characterizing potentially habitable exoplanets.