Reference Differential Imaging (RDI)

• Reference Differential Imaging (RDI) is a high-contrast imaging technique that models the stellar PSF using reference stars instead of the target’s own sequence.
• It minimizes self-subtraction and enhances the detection of close-in companions and extended circumstellar structures compared to ADI.
• RDI leverages methods like PCA/KLIP, LOCI, and constrained variants with carefully selected reference libraries to optimize PSF subtraction.

Reference Differential Imaging (RDI) is a post-processing strategy in high-contrast imaging in which the stellar point-spread function (PSF) and quasi-static speckle field of a science target are modeled from images of other stars rather than from the target sequence itself. In the common decomposition $X = I + A$, where $I$ is the stellar PSF plus speckle field and $A$ is the astrophysical signal, RDI seeks a reference-based approximation to $I$ so that subtraction leaves planets, circumstellar disks, or other faint structures with substantially less ADI-type self-subtraction, especially at small angular separations and for extended emission (Ruane et al., 2019). In current practice, RDI spans direct reference subtraction, PCA/KLIP and LOCI-like estimators, archive-scale reference-library selection, constrained and hybrid ADI-RDI variants, and instrument-specific observing modes on Keck/NIRC2, VLT/SPHERE, HST/WFC3, JWST/NIRCam simulations, and SCALES spectroscopy (Xie et al., 2022).

1. Core principle and relation to ADI

In its basic form, RDI uses a library of reference images $\mathcal{R} = \{R_1,\ldots,R_N\}$ that contain only stellar residuals to model the stellar component of a science image and subtract it. Ruane et al. formulate the science image as $X = I + A$, then approximate the stellar term with a reference-derived basis,

$$I \approx \sum_{k=1}^K \langle X, Z^{(k)} \rangle Z^{(k)},$$

where the $Z^{(k)}$ are basis images obtained from reference frames and $K$ is the number of components retained (Ruane et al., 2019).

This differs operationally from Angular Differential Imaging (ADI), which uses the target’s own time series and field rotation to separate quasi-static speckles from astrophysical sources. ADI is effective when the companion or disk moves sufficiently on the detector, but it suffers from self-subtraction at small separations and for extended structures. In the Keck/NIRC2 vortex survey, the median parallactic-angle rotation was $11.1^\circ$, and for the typical rotation of the dataset ($I$0) RDI provided gains over ADI for angular separations smaller than $I$1 (Xuan et al., 2018). The same geometric issue is more severe for nearly pole-on or rotationally symmetric disks, for which classical ADI can completely self-subtract the signal (Stasevic et al., 3 Sep 2025).

A common misconception is that RDI is simply “ADI without rotation.” In practice, the distinction is more specific. RDI does not rely on angular or spectral diversity, so it does not inherit the ADI mechanism that attenuates sources because they appear in the reference set. That property makes RDI especially attractive for close-in companions, faint disks, and datasets with limited field rotation. At the same time, later developments show that standard RDI can still oversubtract circumstellar light if the PSF model is optimized directly on image regions containing astrophysical signal (Lawson et al., 2022).

2. Reference libraries and PSF modeling strategies

The simplest RDI implementation is direct subtraction of a matched reference PSF. In the SCALES medium-spectral-resolution simulations, the residual at wavelength channel $I$2 and parallactic angle $I$3 is written

$I$4

with the reference PSF assumed identical to the science PSF in the absence of the planet (Desai et al., 2023). In that study, no PCA was applied; planet extraction was achieved only by subtracting the reference PSF from the science image at each parallactic angle.

A more common formulation builds the PSF model as the best linear combination of reference images. In the SPHERE four-quadrant phase-mask experiment on HR 4796, the best linear combination of the reference images that reproduces each target image was determined with a $I$5 criterion inside $I$6 mas, excluding an ellipse around the disk so that circumstellar flux did not bias the optimization (Galicher et al., 2024). LOCI-like and PCA/KLIP formulations are standard in archive-scale RDI on Keck, SPHERE, HST, and JWST simulations.

Reference selection is itself a primary part of the method. Ruane et al. compared mean square error (MSE), Pearson correlation coefficient (PCC), and structural similarity index metric (SSIM) to rank reference frames and found that pre-selection of frames improved the detection significance of point sources by up to a factor of $I$7, with SSIM performing slightly better than MSE or PCC for their data (Ruane et al., 2019). In Super-RDI for Keck/NIRC2, five similarity metrics were evaluated—MSE, PCC, SSIM, FLSI, and CLSI—and synthetic companion injection-recovery tests showed that MSE-based frame selection combined with KLIP using $I$8–$I$9 frames and $A$0 principal components yielded the highest average S/N (Sanghi et al., 2024). For SPHERE/IRDIS disk reductions, PCC-only libraries achieved the best mean contrast overall, while a “mixed” library assembled from multiple observational parameters produced the best average disk S/N and the smallest deviation from the best contrast of each target (Stasevic et al., 3 Sep 2025).

The resulting picture is that RDI is not a single subtraction rule but a family of estimators whose performance depends jointly on the library, the selection metric, the PSF model class, and the optimization region.

3. Performance regime: separation, rotation, and library size

The best-quantified RDI/ADI crossover is from the Keck/NIRC2 vortex performance study. There, the critical parallactic-angle rotation $A$1 separating the RDI-dominated and ADI-dominated regimes follows a power law with separation,

$A$2

and if the slope is forced to $A$3, the corresponding characteristic displacement is $A$4 (Xuan et al., 2018). Operationally, if the total rotation is below $A$5, RDI outperforms ADI; above it, ADI outperforms RDI.

Archive-scale SPHERE/IRDIS RDI reaches a similar conclusion but with a different transition radius. Using a master H23 reference library of about $A$6 images per band from $A$7 observations, RDI was found to outperform ADI at small angular separations ($A$8) if the observing conditions were around the median conditions of the master reference library. On average, the gain was $A$9 mag over ADI at $I$0 separation under median conditions, and the optimal per-frame reference-library size plateaued at about $I$1–$I$2 high-correlation images (Xie et al., 2022). The same study showed that enlarging the master library from $I$3 observations to the full $I$4 observations improved the RDI contrast at $I$5 by about $I$6 mag.

Super-RDI on Keck/NIRC2 generalized this strategy to a $I$7-frame multi-year library. For the typical parallactic-angle rotation of that dataset ($I$8), Super-RDI performed better than a widely used implementation of ADI at separations $I$9, with an average gain of $\mathcal{R} = \{R_1,\ldots,R_N\}$0 mag in contrast at $\mathcal{R} = \{R_1,\ldots,R_N\}$1 and $\mathcal{R} = \{R_1,\ldots,R_N\}$2 mag at $\mathcal{R} = \{R_1,\ldots,R_N\}$3 (Sanghi et al., 2024). The performance improvement in separation space relative to earlier Keck/NIRC2 RDI work was attributed to increasing the PSF library size while carefully selecting reference frames.

These results suggest a consistent empirical regime. RDI becomes increasingly favorable when the science program emphasizes small inner working angles, modest field rotation, and well-matched reference libraries. ADI regains the advantage when field rotation is large enough that self-subtraction is weak and the target sequence itself provides the best-correlated reference set.

4. Extended structures, disks, and advanced variants

RDI is especially important for extended circumstellar emission because ADI can severely distort or erase such structures. Ruane et al. showed that RDI allowed accurate mapping of scattered-light distributions without self-subtraction artifacts in MWC 758 and 2MASS J16042165-2130284, whereas ADI either sharpened features artificially or completely self-subtracted the nearly symmetric disk (Ruane et al., 2019). In the SPHERE/IRDIS archival census, RDI resolved $\mathcal{R} = \{R_1,\ldots,R_N\}$4 disks in total intensity—$\mathcal{R} = \{R_1,\ldots,R_N\}$5 planet-forming disks and $\mathcal{R} = \{R_1,\ldots,R_N\}$6 debris disks—and $\mathcal{R} = \{R_1,\ldots,R_N\}$7 of them were detected only with RDI (Xie et al., 2022).

Because standard RDI can still oversubtract disk flux, several constrained variants have been developed. Constrained RDI reformulates the subtraction as

$\mathcal{R} = \{R_1,\ldots,R_N\}$8

where $\mathcal{R} = \{R_1,\ldots,R_N\}$9 is an estimate of the circumstellar signal and $X = I + A$0 is the RDI PSF model operator (Lawson et al., 2022). In PI-constrained RDI, $X = I + A$1 is derived from polarized intensity data; in model-constrained RDI, it is derived from a disk model. On Subaru/SCExAO–CHARIS data, PI-constrained RDI yielded an oversubtraction-free detection of the AB Aurigae disk in total intensity and decisively recovered the spectral signature of AB Aurigae b. In JWST/NIRCam simulations, model-constrained RDI outperformed both classical RDI and KLIP RDI at small separations in the inner belt region of HD 10647 (Lawson et al., 2022).

A distinct analytical branch is Karhunen–Loève Data Imputation (DIKL), introduced specifically for RDI. DIKL partitions each image into an anchor matrix $X = I + A$2, containing only speckle-dominated pixels, and a boat matrix $X = I + A$3, covering the full region to be cleaned. The KL transform is computed only on the anchor region, and the resulting coefficients are transferred to the boat region, so astrophysical signal in the boat region does not drive the fit (Ren, 2023). Relative to iterative DI-sNMF, DIKL achieved similar-quality RDI results with roughly $X = I + A$4 times lower computational cost, and the authors reported disk morphology and surface brightness agreement with DI-sNMF to within $X = I + A$5 in disk regions (Ren, 2023).

Hybrid methods then combine ADI and RDI explicitly. In ARDI with iterative PCA, the PCA basis is built on the concatenation of reference frames and the science cube after subtraction of the current disk estimate. Across synthetic tests and real protoplanetary disks, ARDI with IPCA improved the quality of recovered disk images and the sensitivity to planets embedded in disks compared to ADI or RDI individually, especially when structures were highly ambiguous for ADI and the quality of the reference frames was suboptimal for RDI (Juillard et al., 2024).

5. Observing modes and instrument-specific realizations

RDI has increasingly shaped observing strategy rather than only post-processing. On VLT/SPHERE, the star-hopping mode was designed to acquire a reference star within minutes of the science target and then alternate between them with only $X = I + A$6 minute of overhead per hop. In the HR 8799 campaign, the reference star was chosen to have $X = I + A$7 mag and to lie within $X = I + A$8–$X = I + A$9 on the sky; hops were made every $$I \approx \sum_{k=1}^K \langle X, Z^{(k)} \rangle Z^{(k)},$$0–$$I \approx \sum_{k=1}^K \langle X, Z^{(k)} \rangle Z^{(k)},$$1 minutes. This star-hopping RDI delivered a contrast improvement at $$I \approx \sum_{k=1}^K \langle X, Z^{(k)} \rangle Z^{(k)},$$2 of up to $$I \approx \sum_{k=1}^K \langle X, Z^{(k)} \rangle Z^{(k)},$$3 magnitudes relative to ADI, and because meridian transit and large sky rotation were not required, the time of observation could be chosen from within a $$I \approx \sum_{k=1}^K \langle X, Z^{(k)} \rangle Z^{(k)},$$4–$$I \approx \sum_{k=1}^K \langle X, Z^{(k)} \rangle Z^{(k)},$$5 times larger window (Wahhaj et al., 2021).

Galicher et al. extended the strategy by coupling RDI to focal-plane wavefront control. With the SPHERE four-quadrant phase-mask coronagraph, dark-hole techniques improved the raw H-band detection limit by a factor of three inside the $$I \approx \sum_{k=1}^K \langle X, Z^{(k)} \rangle Z^{(k)},$$6–$$I \approx \sum_{k=1}^K \langle X, Z^{(k)} \rangle Z^{(k)},$$7 mas controlled region, and applying RDI inside the dark hole improved the residual level by about $$I \approx \sum_{k=1}^K \langle X, Z^{(k)} \rangle Z^{(k)},$$8 magnitude (Galicher et al., 2024). They measured that $$I \approx \sum_{k=1}^K \langle X, Z^{(k)} \rangle Z^{(k)},$$9 to $Z^{(k)}$0 of the residual intensity inside the dark hole was stable between HR 4796 and the reference star during the sequences, which directly enabled target–reference RDI after dark-hole creation (Galicher et al., 2024).

RDI also appears in planet-centered spectroscopy. In the SCALES medium-resolution mode at $Z^{(k)}$1 over $Z^{(k)}$2–$Z^{(k)}$3, the field of view is centered on the planet rather than the star, so classical ADI cannot be applied directly. Under idealized assumptions—reference star identical to the science target, identical observing conditions, and no temporal PSF evolution—direct-subtraction RDI recovered injected spectra comparably to a custom ADI method for $Z^{(k)}$4 and $Z^{(k)}$5 mas separations and for $Z^{(k)}$6 K and $Z^{(k)}$7 K Sonora Bobcat planets (Desai et al., 2023). The authors emphasized that this result is an upper bound set by the deliberately optimistic reference-star assumptions.

A simultaneous form of RDI is Binary Differential Imaging (BDI), in which each component of a wide binary serves as the PSF reference for the other. With MagAO/Clio, BDI was applied to binaries with $Z^{(k)}$8, achieving contrasts from $Z^{(k)}$9 to $K$0 magnitudes over separations from $K$1 to $K$2, corresponding in favorable cases to masses down to $K$3. The method was found to be most effective for approximately equal-brightness binaries in high-Strehl conditions (Pearce et al., 2022).

6. Limitations, reference contamination, and terminological scope

The central limitation of RDI is that reference quality controls subtraction quality. In the SCALES simulations, the RDI reference star was assumed to have the same stellar spectrum, the same brightness, color, and PSF morphology, the same airmass and precipitable water vapor, and a PSF that was not evolving in time; the authors explicitly noted that “in a more realistic scenario, we may obtain different extracted spectra” (Desai et al., 2023). HST/WFC3 RDI of PDS 70 b makes the same point quantitatively: RDI detected the planet at S/N $K$4, compared with S/N $K$5 for ADI on the same dataset, and the lower RDI significance was attributed to the $K$6 times lower peak-to-background ratios of the archival reference PSFs compared to the ADI PSFs (Sanghi et al., 2021).

Reference contamination is a second practical issue. For JWST/NIRCam coronagraphic RDI, simulations of binary reference stars showed that the brightest binary companions analyzed, with a relative brightness of $K$7, produced the worst local sensitivity loss of $K$8 magnitudes, whereas binary companions at $K$9 relative brightness had almost no effect on local sensitivity. Changing position angle altered the local sensitivity loss by $11.1^\circ$0 to $11.1^\circ$1 depending on companion flux, and separation had to be treated on a case-by-case science-goal basis (Stephenson et al., 9 Apr 2025).

A further misconception is that because RDI avoids ADI self-subtraction, it is automatically free of signal loss. Standard RDI can still oversubtract circumstellar light because the optimization that chooses the reference combination is done on the full image $11.1^\circ$2, so the PSF model is pulled toward fitting the disk signal too (Lawson et al., 2022). Constrained RDI, DIKL, and ARDI were developed precisely to suppress that effect in extended sources (Ren, 2023).

Finally, the acronym is not unique across disciplines. In quantitative phase microscopy, “RDI” also denotes reciprocal diffractive imaging, a non-interferometric, reference-free, single-shot method that reconstructs a complex optical field from a single measured intensity image by enforcing support constraints in the Fourier plane (Oh et al., 17 Mar 2025). That usage is distinct from reference-star differential imaging in astronomy, despite the shared abbreviation.