Euclid VI. NISP-P optical ghosts

1. Problem Statement

The Euclid space mission's Near-Infrared Spectrometer and Photometer (NISP) instrument is designed to deliver high-precision photometry in three bands ($Y_E$, $J_E$, $H_E$). However, the optical path contains several elements (dichroic beamsplitter, bandpass filters, lenses) that introduce parasitic reflections, known as optical ghosts.

These ghosts manifest as defocused, offset images of bright stars on the Focal Plane Array (FPA). If unmasked, these artifacts contaminate the photometry of fainter sources, violating the mission's requirement for relative photometric errors below 1.5%. Specifically, the paper addresses two dominant types of ghosts in the NISP photometric (NISP-P) data:

• Dichroic Ghosts: Caused by internal double-reflections within the telescope's dichroic beamsplitter.
• Filter Ghosts: Caused by internal double-reflections within the NISP fore-optics bandpass filters.

Unlike the VIS instrument, where ghosts are nearly normal to the filter surface, NISP's off-axis design results in oblique angles of incidence (AOIs), causing significant displacement and complex morphological variations across the detector field.

2. Methodology

Data Sources

The authors utilized processed NISP-P data from the Performance Verification (PV) phase, prior to the first partial decontamination (March 2024). The dataset included:

• 3,270 images containing 6,023 instances of suitably bright stars.
• Sources included the self-calibration field near the North Ecliptic Pole, Hubble Space Telescope CALSPEC white dwarf observations, and various survey validation fields (e.g., CDFS, COSMOS, EDF-N/S).
• Bright stars were identified using 2MASS ($J < 8$) and Gaia magnitudes were transformed to the Euclid system for consistency.

Detection Algorithm

A custom automated pipeline was developed to detect and characterize ghosts:

1. Source Identification: Bright stars were located, and their positions converted to FPA coordinates.
2. Cutout Generation: $60 \times 60$ pixel cutouts (for dichroic ghosts) and $80 \times 80$ pixel cutouts (for filter ghosts) were generated around predicted ghost locations.
3. Background Subtraction: A low-resolution background map was created using super-pixels and median filtering to remove local variations.
4. Edge Detection: The Canny filter was applied to the cutouts to identify edges.
5. Shape Fitting:
   • Dichroic Ghosts: A Circular Hough Transformation was used to detect the ring shape, as these ghosts are relatively circular and constant in size.
   • Filter Ghosts: Due to their elliptical and field-dependent nature, an Elliptical Hough Transformation was employed. A Gaussian fit to the radial profile was used to estimate the initial radius for the Hough search.
6. Modeling: The detected positions, radii, and shapes were used to build 2D polynomial models describing the ghost behavior across the FPA.

Modeling Approach

• Offsets: The displacement between the source star and the ghost center was modeled using 3rd-order polynomials in FPA coordinates ($Y_{MOSA}, Z_{MOSA}$).
• Masking Radius: The radius required to mask the ghost ($R_{mask}$) was determined by calculating the flux profile and finding where it drops below the allowed contamination threshold ($0.0866 \, e^- \text{pixel}^{-1}$). This was fitted as a power law: $R_{mask} = R_0 m^\Gamma$, where $m$ is the source magnitude.
• Shape (Filter Ghosts): The elongation (major/minor axis ratio) and orientation were modeled using 2nd-order polynomials to account for field-dependent distortion.

3. Key Contributions

• Automated Detection Pipeline: Development of a robust algorithm using Canny edge detection and Hough transformations to automatically identify and characterize optical ghosts in large datasets.
• Comprehensive Parametric Models:
  • Dichroic Ghosts: Defined as having a "doubled-ringed doughnut" shape with a constant radius dependent only on source magnitude.
  • Filter Ghosts: Defined as having a "thin ring with a central cusp" that varies significantly in shape (circular to elliptical), orientation, and offset depending on the FPA position and filter wavelength.
• Masking Criteria: Established specific magnitude limits ($m_{min}$) and radius relations for masking. Only stars brighter than $\sim 9–11$ magnitudes produce ghosts requiring masking.
• Validation: Confirmed that the models derived from PV data remained stable after the March 2024 decontamination event, ensuring no significant optical shifts occurred.

4. Key Results

Dichroic Ghosts

• Offset: Ranges from 3 to 6 mm (167–335 pixels) across the FPA. The offset is well-modeled by 3rd-order polynomials.
• Shape: Consistently circular with a "doughnut" morphology; minimal variation across the field.
• Masking Radius: Depends on source magnitude, ranging from 21 to 34 pixels.
• Brightness: Peak flux ratios are $\sim 5.7–8.3 \times 10^{-9}$ (an order of magnitude fainter than ground-test predictions).

Filter Ghosts

• Offset: Highly variable, ranging from 1 to 17 mm (56–949 pixels). The offset pattern is radially symmetric but centered off the FPA center (approx. $Y_{MOSA} = -10$ mm).
• Shape: Highly field-dependent. Near the center, they are circular; toward the corners, they become elongated (up to a 1.22 ratio) and exhibit a "bird-like" cusp due to the spherical convexity of the filter entrance surface.
• Masking Radius: The minor axis ranges from 23 to 45 pixels based on magnitude; the major axis is scaled by the position-dependent elongation model.
• Brightness: Peak flux ratios are $\sim 4.6–13 \times 10^{-9}$.

Impact on Data

• Masking Threshold: Ghosts from stars fainter than $m \approx 9–11$ (depending on the filter) are negligible and do not require masking.
• Area Loss: For the Q1 data release, the total area lost due to masking ghosts, persistence, saturated stars, and other defects is ~4% (ranging 2–10% depending on stellar density). This is well within the mission's 12% error budget for lost area.

5. Significance

This paper provides the essential technical framework for the Euclid Quick Data Release (Q1) and future data processing. By accurately modeling and masking these optical ghosts, the Euclid Collaboration ensures:

1. Photometric Purity: Prevents contamination of faint source photometry by bright star artifacts, crucial for weak lensing and galaxy clustering studies.
2. Pipeline Robustness: The polynomial models allow the NIR pipeline to dynamically predict and mask ghosts for any observation, independent of detector gaps or specific field positions.
3. Optical Performance Validation: The results confirm that the NISP instrument performs better than ground-test predictions regarding ghost brightness, validating the optical design and coating quality.

The models and coefficients (provided in the paper's Appendices) are now standard components of the Euclid data processing chain, ensuring the scientific integrity of the mission's wide survey. Future data releases will refine these models as more data becomes available, though significant changes due to optical aging are not expected.