Subtracting the coronagraphic point spread function (PSF) is essential to achieving the greatest possible imaging contrast between a bright target and faint astrophysical signals with small angular separations. 

See also: NIRCam Coronagraphic Imaging , JWST High-Contrast Imaging

The purpose of PSF subtraction is to achieve limiting contrast between a bright host (e.g., star, AGN) and the faintest detectable astrophysical signal or "companion" in its vicinity.  (See HCI NIRCam Limiting Contrast for more information.)  The companion may be an extended source (e.g., a circumstellar disk), a jet, or a point source (e.g., an exoplanet).

PSF reference images are usually obtained immediately before or after the host observation so that phase differences in the imaged wavefronts are negligible.  The optimal reference PSF may be a composite of multiple reference images obtained after changing the observatory's pointing (offset) or axial orientation (roll).  Once obtained, this optimal reference PSF image is scaled in intensity and then subtracted from the host images.

The most critical and consequential step in the processing of NIRCam coronagraphic images is subtracting the wing of the point spread function (PSF) of the host target centered behind a coronagraphic occulting mask (occulter).

Currently, NIRCam supports three PSF subtraction strategies, each with its own pointing operations, which vary in complexity and performance.

1. In the simple "reference star differential imaging" (RDI) strategy, coronagraphic images are obtained for both the host and reference targets. The reference image is scaled and subtracted from the host image to reveal any companion features, which are now as free as possible of residual light from the host. 
   
   
2. The "angular differential imaging" (ADI) or "roll subtraction" strategy is self-referenced, involving only the host target. Two coronagraphic images are obtained that differ only in a small (5°–10°) roll maneuver, which must be sufficient to fully separate the 2 positions of the companion-feature image.  Observatory roll maneuvers are restricted to ±5°, and observation planning is supported by the JWST Coronagraphic Visibility Tool.
   
   
3. The "small grid dither" (SGD) RDI strategy involves a mini-library of PSF reference images, obtained in a 3-, 5-, or 9-point patterns of precise subpixel offsets ("dithers").  The mini-library is thus a collection of slightly varying reference images caused by the small offsets relative to the nominal occulter position.  Because the span of each SGD pattern is larger than the expected error in the target acquisition position, the optimal reference PSF for subtraction is a careful interpolation of the mini-library of reference images.  A variety of algorithms are available to perform the optimal subtraction, such as PCA (Principal Component Analysis performed by the level 3 data pipeline), KLIP (Karhunen-Loève Image Projection), or LOCI (Locally Optimized Combination of Images).

References

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Carter, A., et al. 2023, ApJ Letters, 951, 1 
The JWST Early Release Science Program for Direct Observations of Exoplanetary Systems I: High Contrast Imaging of the Exoplanet HIP 65426 b from 2-16  μm

Girard, J. H., et al., 2022 (Commissioning, # 1441), SPIE, 121803Q
JWST/NIRCam Coronagraphy: commissioning and first on-sky results

Kammerer, J., et al., 2022 (Commissioning), SPIE, 121803N
Performance of near-infrared high-contrast imaging methods with JWST from commissioning

Perrin, M., et al. 2018, SPIE, 1069809
Updated Optical Modeling of JWST Coronagraph Performance, Stability, and Strategies

Perrin, M. et al. 2013, JWST-STScI-003472
Sample Target Acquisition Scenarios for JWST

Soummer, R. et al. 2012, SPIE, 91433V 
Small-grid dithering strategy for improved coronagraphic performance with JWST

Stark, C. et al. 2016, JWST-STScI-004707
How to Implement a JWST Coronagraphic Observation Sequence in APT