An Introduction to High Contrast Differential Imaging of Exoplanets and Disks

The High-Contrast Imaging (HCI) technique is a relative newcomer in the world of exoplanet detection techniques, with the first discoveries in 2004 and 2008 (Chauvin et al. 2004; Kalas et al. 2008; Marois et al. 2008). Although the number of planet detections is currently lower for high-contrast imaging ¹ than for indirect (radial velocity, transit, and microlensing) techniques, directly imaged companions are arguably the best characterized exoplanets. HCI also provides the best prospects for current and future characterization of exoplanet atmospheres, particularly temperate ones conducive to life as we know it. The commitment of the community to HCI is evident in the first theme of Pathways to Discovery in Astronomy and Astrophysics for the 2020s (also known as the Astro2020 Decadal Survey)—"Pathways to Habitable Worlds." It calls for a "step-by-step program to identify and characterize Earth-like extrasolar planets, with the ultimate goal of obtaining imaging and spectroscopy of potentially habitable worlds" (pg. 2, National Academy of Sciences Engineering & Medicine 2021, emphasis mine). The gap between the modern directly imaged planet population and Earth-analogs is large in both mass and semimajor axis space (see Figure 1). However, while indirect planet detection methods are currently more sensitive to terrestrial planets, the decadal survey goal of imaging and spectroscopy of exo-Earths cannot be achieved without direct detection.

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Although the current state of the art in HCI is imaging of >1M_J planets at ∼tens of au separations, the future of the technique is bright (pun intended!), and vigorous ongoing technology development will push its sensitivities to lower mass and more tightly separated planets.

In the context of HCI, the term "contrast" refers to the brightness ratio between an astronomical source (planet, disk) and the star it orbits. "High" contrast images are those where the ratio $\tfrac{{F}_{\mathrm{source}}}{{F}_{\mathrm{star}}}$ is small, meaning the source is much fainter than the star—these detections are difficult. "Low" contrast images are therefore ones where the source-to-star ratio is larger, meaning the source is brighter relative to the star—these detections are less challenging.

Unlike stars, where absolute brightness is almost entirely a function of mass, for planets, brightness is a function of both mass and age. Planets begin their lives hot and bright and, lacking an internal source of energy sufficient to maintain that temperature, cool with time.

As they evolve, planetary spectra, and therefore contrast, change drastically. Figure 2 shows contrast at a range of wavelengths for the same planet (Jupiter) when "young" (20Myr) and "old" (4.5 Gyr, the age of our solar system). It highlights the extreme variation in contrast as a function of wavelength as planets age.

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In thinking about contrast for point sources, it is useful to keep several benchmark quantities in mind, namely:

• 1.  
  In the near-infrared (1–3 μm), young (∼few to few tens of Myr) giant planets generally have contrasts in the range ∼10⁻⁵–10⁻⁶ relative to their host stars. They radiate away much of their initial thermal energy over the course of the first tens of millions of years after formation, thus higher contrasts are required to detect them as they get older.
• 2.  
  At 3–5 μm, the same young (∼few Myr) planets, have more moderate contrasts of ∼10⁻³–10⁻⁴. With temperatures of ∼500–1500 K, this is because their thermal emission peaks in this wavelength regime, and the brightness gap relative to the much brighter and hotter (peak emission bluer) star is narrowed. This remains the region of most favorable contrast even as planets age.
• 3.  
  In the optical, planets have undetectably low levels of direct thermal emission, and are seen instead in reflected light (stellar photons redirected/scattered by their atmospheres toward Earth). For mature planets (≳100 Myr), this wavelength regime provides more moderate contrasts than the NIR. For example, at 4.5 Gyr, Jupiter and Earth have contrasts of ∼10⁻⁹ and 10⁻¹⁰, respectively at 0.5 μm. Combined with resolution advantages inherent in shorter wavelength imaging (See Section 2 for details) optical wavelengths provide the best prospects for future detection of solar system analog planets.

A simple analogy will help drive home the near (but not wholly) intractable nature of the contrast problem. As shown in Figure 3, for thermal emission from hot young exojupiters, the contrasts outlined above are comparable to the ratio of light emitted by a firefly relative to a lighthouse. For true (4.5 Gyr) Jupiter analogs in optical reflected light, a more apt comparison is a single bioluminescent alga relative to a lighthouse. This highlights the tremendous technological barriers that the field must overcome in order to achieve direct characterization of mature, potentially habitable exoplanets.

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Precisely how hot a planet is at formation (and therefore how bright it appears) depends on how it was formed, and a range of formation modes are likely to overlap within the exoplanet population. In other words, planets (and brown dwarfs) of the same mass may have formed via different mechanisms, and their brightnesses therefore yield clues to their formation pathway.

Planets like those in our solar system most likely formed via a "cold start" mechanism involving the gradual assembly of solid material within a circumstellar disk. Their "cold" starts are only cold in comparison to so-called "hot start" planets, which also form in a circumstellar disk, but rapidly as a result of gravitational collapse. The high masses and wide separations of most directly imaged planets make them good candidates for hot start formation, but current and next-generation instruments are detecting lower mass, closer-in planets for which formation mechanism is more ambiguous. The range of formation models and their predictions and assumptions is well-described in Spiegel & Burrows (2012). For our purposes, the most important takeaways are that directly imaged exoplanet brightnesses can only be translated to mass estimates under assumptions of: (a) stellar age, and (b) planetary formation pathway/initial entropy of the planet (unless a direct measure of the planet's mass is available from another method, such as astrometry or radial velocity).

1.2.1. What do We Learn from HCI Planet Detections?

1.2.2. What do We Learn from HCI Disk Detections?

Adaptive optics is perhaps the most critical HCI enabling technology for ground-based imaging campaigns. Without it, image resolutions are limited by astronomical seeing, or the size of coherent patches in the earth's atmosphere (approximated by the "Fried parameter" r₀, which has a λ^6/5 dependence). With adaptive optics, modern HCI instruments can approach the diffraction limit,

$$\begin{eqnarray*}&&\theta =1.22\displaystyle \frac{\lambda }{D}\end{eqnarray*}$$

where λ is the wavelength and D the diameter of the telescope. Table 1 gives the diffraction-limited resolution of an 8 m telescope at 0.55 μm (V band), 1.6 μm (H band) and 3.5 μm (L band) in physical units as compared to the seeing limit at an exceptional telescope site under good weather conditions (0 25 at 0.55 μm) at each wavelength.

The diffraction-limited Point-Spread Function (PSF) ⁵ of a circular telescope aperture is the so-called "Airy pattern." In practical terms, this PSF places the majority of the incoming starlight into a "diffraction-limited core," with a radius of 1.22λ/D and a Full Width at Half Maximum (FWHM) of 1.03λ/D. Extending from this central core are a characteristic set of "Airy" diffraction rings that decrease in amplitude outward and are spaced by roughly 1λ/D from one another with the first minimum at 1.22λ/D. In a perfect diffraction-limited system, the central "Airy disk" contains 84% of the total light in the PSF, with the remainder of the light in the Airy rings.

In the case of a telescope with a circular aperture and a central obscuration (e.g., by a telescope secondary mirror) the Airy pattern has a functional form of:

$$\begin{eqnarray*}&&{\text{}}I({\text{}}u)=\displaystyle \frac{1}{{\left(1-{\epsilon }^{2}\right)}^{2}}{\left[\displaystyle \frac{2{J}_{1}(u)}{u}-{\epsilon }^{2}\displaystyle \frac{2{J}_{1}(\epsilon u)}{\epsilon u}\right]}^{2}\end{eqnarray*}$$

where u is a dimensionless radial focal plane coordinate defined as:

$$\begin{eqnarray*}&&u=\displaystyle \frac{\pi }{\lambda }D\theta \end{eqnarray*}$$

and θ is the angle between the optical axis and the point of observation. The center of the PSF is at θ = 0 and therefore u = 0, and I(u) is the PSF intensity at location u. The quantity is a measure of the amount of central obscuration expressed as a fraction of the total aperture (which acts to decrease the effective aperture and thus the predicted peak intensity), and J₁ is the first order Bessel function of the first kind.

In practice, HCI PSFs tend to be dominated by Airy or Airy-like diffraction patterns with a few key deviations. First, no modern AO systems achieve perfectly diffraction-limited performance. The PSF of a modern adaptive optics PSF is often characterized by its so-called "Strehl Ratio" (SR), which is the ratio of a star's observed peak intensity relative to that of its theoretical diffraction-limited peak intensity. ⁶ Modern Extreme Adaptive Optics (ExAO) systems routinely achieve SRs of 80%–95% in the Near Infrared, but only 10%–30% in the optical at present.

A proper treatment of the effect of the atmosphere on incoming starlight requires detailed atmospheric turbulence modeling (e.g., a Kolmogorov model). However, a decent first-order approximation of the effect of the Earth's atmosphere on incoming starlight, depicted in Figure 4, is to imagine a plane-parallel electromagnetic wave ⁷ with some constant phase and amplitude encountering a layer in the Earth's atmosphere composed of coherent patches of size r₀ (atmospheric "cells"). Inside these cells, the wave front phase is aberrated such that it remains locally flat, however phase offsets occur between neighboring cells. Phase aberrations can take many forms and are often represented as an orthogonal basis set of polynomials with both radial and azimuthal dependencies (e.g., the Zernike polynomials). Low order aberrations have familiar names, and ones that you are likely to encounter in your annual eye exam, such as "astigmatism" and "coma." Higher order aberrations take more complex forms in phase space, but all are essentially disruptions in the intrinsic shape of the incoming PSF. For illustrative purposes, let us imagine only the simplest two low-order modes, the so-called "tip" and "tilt" modes, which preserve the shape of the PSF but modify the direction of the incoming wave front relative to the original travel direction.

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The effect of tip/tilt aberrations is that a wave front exiting a layer of atmospheric cells is no longer plane-parallel. Instead, it is corrugated (the angle of arrival varies across the telescope aperture, see Figure 4's "distorted incoming wave front") with some wavelength-dependent characteristic length scale (The Fried coherence length, r₀ ∼ λ^6/5). For an atmospheric layer at a certain height, this characteristic length scale can also be represented as an angular scale called the "isoplanatic angle," θ₀. Note again that this is just a first-order approximation, albeit a useful one for building intuition, and that, in reality, there are a number of aberrating layers in the atmosphere with their own characteristic coherence lengths, heights, and wind speeds. The practical consequence when integrated over the telescope aperture is that the light of each coherent patch manifests as its own diffraction limited PSF at a different location in the image plane centered around the optical axis of the telescope. The instantaneous result is a number of superposed independent images of the star equal to the number of coherent atmospheric patches that the wave front incident on the telescope passed through—i.e., the image is blurry.

Locally coherent patches at a given layer in the atmosphere only remain so on timescales of hundredths- to thousandths- of a second (due to wind, temperature/pressure variation, etc.) which means Adaptive Optics systems must operate on these timescales in order to detect and correct wave front aberrations with Wave front Sensors (WFS). Extending our toy example of an incoming plane-parallel wave front that experiences pure tip/tilt aberrations at a single layer in the atmosphere, imagine a series of corrugated wavefronts exiting this layer and being collected continuously by an astronomical detector over a realistic exposure time of several to several tens of seconds. The result will be a superposition of many hundreds or thousands of diffraction-limited PSFs (so-called "speckles") at various locations relative to the central optical axis. The result is a seeing-limited PSF, whose size/FWHM will vary according to various properties of the atmosphere, but will always be much larger than the diffraction limit. Modern AO systems are able to operate at 1–2 kHz frequencies, however they are not able to perfectly sense the wave front, nor to perfectly or completely correct it on the relevant timescales. Many advancements are being made in both the hardware and software of wave front control, including the advent of algorithms that attempt to account for the time delay between sensing and applying a wave front correction by predicting the state of the wave front into the future (so-called "predictive control" algorithms, e.g., Poyneer et al. 2007; Guyon & Males 2017).

The consequence of a perfect AO system that could fully detect for and correct wave front aberration would be a perfect SR = 100% diffraction-limited PSF. The reality is, of course, not perfect. A partially or imperfectly corrected wave front results in the alignment of many but not all of these instantaneous PSFs. Some uncorrected, residual seeing-limited "halo" with a width of approximately $\tfrac{\lambda }{{r}_{0}}$ is expected, and its amplitude should decrease as the performance of the AO system (Strehl Ratio) improves. Imperfect wave front correction can also lead to certain persistent speckles, so-called "quasi-static speckles," that are stable on timescales of minutes to hours. These are particularly worrisome because they can mimic planets, but they have the advantage of being static in their location in the instrument frame. They also exhibit spectra that are identical to that of the central star. These properties make them amenable to removal by angular and spectral differential imaging (ADI/SDI, see Section 4).

NIR HCIs can have a dozen or more clear, detectable Airy rings in their unocculted AO PSFs. These Airy rings present a fundamental barrier to achieving high contrast in the environs of the central star, and additional optics are often employed to mitigate them. Because Airy rings are a consequence of diffraction at the edges of the entrance pupil, mitigating optics are generally pupil plane ⁸ optics that block light near its edges. One example is the "Lyot stop."

The Airy PSF is also predicated on the assumption of a circular entrance aperture, which no realistic telescope entrance pupil is able to achieve. The presence of various optics, especially the secondary mirror and its supports, induce deviations from a perfect Airy PSF. To simulate an HCI PSF, therefore, requires a model of the telescope entrance aperture and any additional optics in the telescope beam. An example PSF for the Gemini Planet Imager is provided in Figure 5.

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In addition to deformable mirrors (DMs), adaptive optics systems require instrumentation that can sense atmospheric aberrations and convert them to DM control signals on kHz frequencies. From an observer's perspective, the most important features of this "Wave front Sensor" (WFS) and its accompanying control algorithm are its: wavelength, limiting magnitude, stability, gain, and cadence, each of which is described below.

WFS wavelength—WFS operate most often at optical wavelengths. Since most HCI is done in the NIR, such systems implement a dichroic that sends all optical light to the wave front sensor and all NIR light to the science camera. Although this results in no loss of light at the science wavelength, it does introduce a difference in the scale of the wave front aberrations that are sensed versus detected (namely, ${\left({\lambda }_{\mathrm{sensed}}/{\lambda }_{\mathrm{detected}}\right)}^{6/5}$). NIR wave front sensing is an active area of development in HCI instrumentation for this reason. For a visible light HCI instrument, wave front sensing in the optical generally requires a beamsplitter, resulting in a substantial loss of signal to the science camera (50% or more) as light at the science wavelength is diverted to the WFS.

WFS limiting magnitude—is a measure of the faintest targets for which the wave front can be effectively sensed, and is determined at the most basic level by the architecture of the WFS. Though there are many types of WFS, the most common are the Shack–Hartmann and Pyramid WFS. Tradeoffs in WFS qualities, such as sensitivity to wave front errors of various scales and linearity between WFS measurements and DM commands, determine the choice of WFS architecture (for a full discussion, see Guyon 2018). From the perspective of the observer, one practical consequence of WFS architecture is the range of magnitudes for which AO correction can be accomplished. A Shack–Hartmann WFS (SHWFS, see Figure 4 for a simple depiction) relies on a grid of lenslets placed in the pupil plane, each of which creates a spot on the WFS camera. The location of the spot created by each lenslet is controlled by the direction of the incoming wave front, and this shape can then be applied to the DM to correct aberrations. The limiting magnitude of a SHWFS is a fixed quantity determined by the required brightness for an individual lenslet spot to be sensed. Because the lenslets are physical optics, this cannot be modified without swapping out the grid of lenslets. A pyramid WFS, on the other hand, modulates the incoming light beam around the tip of a four-faced glass pyramid, each facet of which creates an image of the telescope pupil on a WFS camera. These four pupil images can be analyzed to reconstruct the incoming wave front. A pyramid WFS camera's pixels can also be binned to achieve correction on fainter guide stars. Although wave front information is lost in the binning process and the quality of the AO correction is therefore necessarily compromised, this does preserve the ability to apply (more modest) AO correction when imaging fainter stars.

WFS stability—is effectively a measure of how long and under what conditions a WFS can provide continuous adaptive optics correction. When AO systems are operating in "closed loop" mode, meaning corrections are being applied in real time, the loop will "open" in order to protect the DM if the sensed wave front deformations require corrections whose amplitudes are too great for the control range of the DM. This is called a "breaking" of the AO control loop. One of the more critical aspects of a wave front control algorithm is the "gain" applied to each sensed aberration.

WFS control gain— can be thought of as a multiplicative factor applied to the sensed wave front so that all of the sensed aberration is not corrected for at once, but instead some proportion of it. This is to avoid overcorrecting an aberration and driving the mirror into an oscillation, and also to allow unsensed or incorrectly sensed aberrations to pass without breaking the loop. Different sensed wave front aberrations (e.g., "low order" and "high order" modes) can have different gains, and this is one of the principal quantities that can be adjusted in real time during AO observations. Gain, wave front stability, WFS signal strength, and the nature of the control algorithm all conspire to determine the stability of the AO loop—basically its ability to remain closed during an observing sequence.

WFS cadence—is the timescale on which the wave front is sensed, and is the final factor controlling the quality and stability of AO correction. In this case, the wavelength of observation and nature of the telescope site (seeing, wind speed, etc.) sets the timescale on which the incoming wavefronts change, and the AO system must run faster than this timescale in order to apply high-quality correction. Many current AO systems operate at 1–2 kHz frequencies, with faster speeds being required at shorter wavelengths.

Another enabling HCI technology is coronagraphy, which utilizes one or more physical optics inside the instrument to suppress both direct and diffracted starlight before it reaches the detector. This allows for deeper imaging of planetary systems, as longer integration times can be used before saturation of the primary star. Coronagraphy is distinct from external occulters ("starshades") and software algorithms ("wave front control") that are designed to do similar things i.e. suppress and control light from the central star so that faint objects in its environs can be sensed. Available coronagraphic architectures have been rapidly expanding in recent years, and I will not provide a comprehensive review here, but will instead focus on the practical effects of a coronagraph for image processing.

The purpose of a coronagraph is to redirect starlight away from the image plane by blocking or modulating it with optical components, thus reducing the amount of light that must later be removed in post-processing in order to image faint companions.

Coronagraph optical components can modulate wave front amplitude or phase or, in many cases, both. The most basic coronagraphic architecture is an opaque or reflecting image plane spot in the center of the field, which prevents on-axis starlight from reaching the detector. Other coronagraphic architectures utilize interferometric techniques (e.g., the "vortex" coronagraph) to accomplish the same goal. Additional optics are often placed in the pupil plane to mitigate diffraction around coronagraph edges and around the edges of the entrance aperture more generally, which effectively decreases the amplitude of the Airy rings and allows for higher contrast imaging and detection of fainter circumstellar signals.

Polarized Differential Imaging is the most common and successful technique for imaging circumstellar disk material in scattered light, and is shown schematically in Figure 6. PDI relies on the fact that light emitted directly from the central star is (generally) unpolarized. Dust grains in the circumstellar environment, on the other hand, preferentially scatter starlight with a particular polarization geometry. Scattering is most efficient for light with an electric field vector aligned orthogonal to both: (a) the line of sight from the scattering location on the disk surface to earth and (b) the vector connecting the scattering location and the central star. In principle, this means that disk scattered light signals should dominate PDI images, and (unpolarized) stellar emission should be absent.

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PDI imaging separates incoming starlight according to the orientation of its electric field vector (i.e., it is linear polarization). An optic called a Wollaston prism accomplishes this by passing incoming light through a material that has different indices of refraction for different linear polarization states. If a single Wollaston is used, the light is split into two beams with orthogonal polarizations (often called the "ordinary" and "extraordinary" beams), while a double Wollaston will yield four beams, adding redundancy that helps in removal of detector location-specific artifacts. The precise orientation of the orthogonal ordinary and extraordinary polarization vectors relative to the sky is manipulated to fully sample the polarized emission from the source by rotating an optic called a half- or quarter-wave plate, which modulates the orientation of the linear polarization state of incoming light for the two channels. This modulation (generally sequences of 4 angles—0°, 225, 45°, 675) allows the images to be combined to yield the Stokes polarization vectors I, Q, and U. ⁹ Addition of images with orthogonal polarization captures the unpolarized intensity of the star, while subtraction yields either "Q" or "U" images, depending on the orientation of the wave plate. Q and U images are combined to isolate polarized light from the source via the equation ${PI}=\sqrt{{Q}^{2}+{U}^{2}}$. Each sequence of wave plate angles thus produces four images—I, Q, U, and PI.

The angle of the polarization vector can also be extracted from these quantities via the equation

$$\begin{eqnarray*}&&{\theta }_{P}=0.5\arctan \left(\displaystyle \frac{U}{Q}\right)\end{eqnarray*}$$

The θ p vectors, when overplotted on images of a scattered light disk, demonstrate a characteristic centrosymmetric pattern. This is because of the preferred geometry of the scattering process; the most efficient scattering occurs when a photon's electric field orientation (θ_p ) is orthogonal to both the line of sight and the vector connecting the scattering dust grain and star.

Extraction of polarized signals is complicated somewhat by multiple scattering and the internal optics of the instrument. Internal reflections result in depolarization effects that vary with wavelength, incident angle, and the thickness and index of refraction of the optical components. This induces so-called "instrumental polarization," which is typically estimated from observations of both unpolarized, disk-free stars and polarization standard stars. The simple picture of polarization presented above also assumes that each photon received was scattered by only a single small dust grain in the disk on its journey from star to disk to Earth. This is a reasonable assumption in many cases, but multiple scattering does occur, resulting in deviations in the centrosymmetry of polarization vectors and, in the characteristic pattern of positive and negative signal in Q and U images (often called a "butterfly" pattern because the symmetric positive/negative lobes look a bit like butterfly wings). The inclination of the disk (i.e., whether emission is "forward" or "back" scattered) also impacts the efficiency of scattering, as do grain properties such as size, composition, and porosity.

The most common variation on the process described above is to compute the so-called "azimuthal" or "local" Stokes Q and U vectors, often denoted Q_ϕ and U_ϕ (e.g., Monnier et al. 2019; de Boer et al. 2020) and defined as:

$$\begin{eqnarray*}&&{Q}_{\phi }=-\,Q\cos (2\phi )-U\sin (2\phi )\end{eqnarray*}$$

$$\begin{eqnarray*}&&{U}_{\phi }=+\,Q\sin (2\phi )-U\cos (2\phi )\end{eqnarray*}$$

where ϕ is the azimuthal angle. This formulation has the advantage of concentrating signal with the expected polarization vector orientation into the Q_ϕ image, while the U_ϕ image becomes an estimate of the noise induced by multiple scattering and instrumental polarization.

The Reference Differential Imaging (RDI) technique utilizes images of stars other than the science target to subtract starlight from a target image and is shown schematically in Figure 7. It is an ideal approach when either (a) the PSF of a system is exceptionally stable, often the case for space-based observatories such as HST, or (b) the source being targeted has extended, symmetric features (e.g., a circumstellar disk) that might be subtracted by more aggressive algorithms that rely only on images of the target star for reference (see next several sections). Reference PSF libraries for RDI generally consist of images of many other stars taken at the target wavelength and in the same observing mode (e.g., same coronagraph) with the same instrument. In the case where a large library of reference images is available (e.g., a large HCI campaign, a well-established space telescope instrument), just a subset of the most highly correlated images may be chosen to construct a PSF.

Some HCI observers, particularly of disks, regularly conduct PSF reference star observations as part of their efforts to observe a science target. PSF references are often chosen to be similar in location on the sky (so they can be observed interspersed with or immediately before or after the science target, at similar airmass), of similar apparent brightness at the wavelength of the WFS (so that the AO system performs similarly ¹⁰ ), and of similar color (so that the science image(s) have similar properties). ¹¹ Some modern HCI systems (SPHERE, MagAO-X) are equipped with "star-hopping" modes that allow the AO loop to be paused on one target (e.g., the science target) and then re-closed once the telescope is pointed at another nearby target (e.g., the PSF reference star). This ensures maximal similarity in their PSFs.

The Angular Differential Imaging (ADI) technique builds on the legacy of "roll-subtraction" pioneered with the Hubble Space Telescope (HST, e.g., Schneider et al. 2014). It leverages angular diversity to separate stable and quasi-stable PSF artifacts from true on-sky emission. ADI is predicated on the assumption that the instrumental PSF remains (relatively) stable in the frame of reference of the instrument throughout the image sequence, while true on-sky signal rotates with the sky. This allows the time series of images to be leveraged for pattern matching or statistical combination to estimate the stellar PSF and remove it. In practical terms, the quality of any ADI-based subtraction is a strong function of the amount of on-sky rotation of the source. For this reason, most direct imaging target observations are roughly centered around the time of that object's transit across the meridian, as this maximizes the amount of rotation achieved for a given amount of observing time. Rotation is essential to reduce a phenomenon called "self-subtraction," in which the signal of a source (disk or planet) is present in a different but nearby location in the PSF image being subtracted, resulting in characteristic negative lobes on either side of the source where it has been subtracted from itself (hence the name).

The simplest form of ADI, so-called "classical" ADI (cADI), constructs a single PSF for subtraction from the median combination of all images in a time series, subtracts this median PSF from each image and then rotates these subtracted images to a common on-sky orientation. These PSF subtracted and re-oriented images are then combined, further suppressing the residual speckle field, which varies from image to image.

HCI observing programs often aim not just to detect exoplanets and circumstellar disks, but also to characterize them, for which multiwavelength information is invaluable. Due to the many challenges of absolute photometric calibration in HCI (see Section 7), characterization is best facilitated by obtaining simultaneous imagery at multiple wavelengths. Thus, many modern HCI instruments are so-called "Integral Field Spectrographs" (IFSes). IFS instruments are used throughout Astronomy with a range of architectures, but in the case of HCI, they are generally of a similar lenslet-based design. In lenslet-based IFSes, a grid of lenslets is placed in the focal/image plane of the optical system (not unlike the grid of lenslets placed in the puil plane of a SHWFS, see Section 2.2), and the lenslet spots are dispersed to produce a spectrum for each lenslet. Each "spectral pixel," or "spaxel" (also referred to as a "microspectrum"), contains spectral information at a particular location in the image plane. Microspectra are wavelength calibrated using observations of internal arc lamps, generally taken close in time to the science observations because the wavelength solutions are strongly dependent on instrument flexure. Raw IFS images are converted to multiwavelength image cubes by extracting photometry from the microspectra at specific wavelengths (using knowledge of the instrumental PSF). Photometric values for each extracted wavelength of the microspectrum are assigned to appropriate spatial locations relative to those from neighboring microspectra in synthetic images. A raw IFS HCI of the planet-host Beta Pictoris is shown in Figure 9.

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Spectral Differential Imaging (SDI) takes advantage of differences in the spectral properties of planet and star. In particular, it leverages images at wavelengths where planets are dim (e.g., for methane dominated planetary atmospheres, at 1.5 and 1.7 μm) to construct a PSF model that is largely uncontaminated by planet light, limiting self-subtraction. Because images are collected at multiple wavelengths contemporaneously, this circumvents some of the effects of a temporally varying PSF. As a result, the library of reference images is often better matched to the target PSF.

Most high-contrast SDI imaging to date has been done with an Integral Field Spectrograph such as GPI or SPHERE. SDI can also 'be implemented without an IFS by simply splitting incoming light into two beams with a 50/50 beamsplitter, dichroic, or Wollaston prism, ¹² and passing each beam through a different narrowband filter. This is sometimes called Simultaneous Differential Imaging (still SDI). The filter pairs lie on- and off- of a spectral line of interest, and the most common lines used in today's high-contrast imaging campaigns are on- and off-methane in the NIR and on- and off- Hα in the optical. In the case of young moving group stars (ages 10–300 Myr), it is expected that planets with methane-dominated atmospheres will be faint or undetectable in the methane band and brighter outside of it (see Figure 10). Hα differential imaging, on the other hand, leverages the fact that many younger (<10 Myr) systems show evidence of ongoing accretion onto their central stars. The accreting material originates from and is processed through the circumstellar disk, meaning that any planets embedded in that disk are also likely to be actively accreting. One principal escape route for the energy of infalling material is radiation in hydrogen emission lines, particularly Hα, and we expect accreting protoplanets to be bright at this wavelength and faint or undetectable in the nearby continuum.

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In terms of its utility as a tool to separate star and planet light, in its most generic form (what we might term "classical" SDI imaging, shown schematically in Figure 10) simply leverages the fact that the physical size of a stellar PSF on a detector is a function of wavelength. For simultaneously acquired imagery at multiple wavelengths (i.e., A 3D cube of images with 2 spatial coordinates and 1 wavelength coordinate), this manifests as a magnifying effect as wavelength increases, and means that PSF features shift radially outward in detector coordinates, while true on-sky objects remain at the same position regardless of wavelength. Much like ADI angular rotation, the size of this effect is well-known (having a λ/D dependence), therefore it can be compensated for in post-processing. By expanding shorter wavelength images or compressing longer wavelength ones so that all simultaneously-obtained images share a common PSF scale, wavelength-independent features of the PSF can be estimated. This rescaling alters the position of real objects in the images so that they are no longer in precisely the same location at all wavelengths, thus the rescaled images can be combined (e.g., via median or weighted-mean combination) to construct a relatively ¹³ planet-free PSF reference. This reference can be subtracted from rescaled images and the rescaling reversed to restore true on-sky coordinates, effectively realigning planetary signals across wavelengths. Multiwavelength image cubes can be collapsed in wavelength space to provide a robust planetary detection, enabling astrometric characterization. More commonly, however, wavelengths are kept separate and combined across a sequence of multiple IFS images. This enables extraction of planet photometry at each wavelength to create a coarse spectrum, with a spectral resolution controlled by how many spectral channels can be extracted from the microspectra, generally a few dozen over a ⪅0.5 μm wavelength range, for resolutions on the order of ∼25–100.

SDI processing is rarely used in isolation or executed in the simple "classical" sense described above. Instead, it almost invariably applies more sophisticated PSF estimation techniques to create custom PSFs for each image within a sequence and each wavelength within the image cube (i.e., using KLIP or another algorithm). Combination of SDI and ADI processing allows the user to leverage both angular and spectral diversity to identify reference images where sources have moved enough to prevent their surviving into any combination (either through angular rotation or image rescaling).

In addition to taking advantage of the physical rescaling of the instrumental PSF, SDI processing also often involves the application of one or more planetary spectral templates to expand the reference library. For example, for a planet with a methane-dominated atmosphere, such as the planet 51 Eridani b, there are certain H-band wavelengths where methane absorption makes planetary signal undetectable. Regardless of their separation from the wavelength being subtracted, these "planet-free" wavelengths can be leveraged to construct the PSF model.

The size of a stellar PSF is a function of wavelength; it increases as the wavelength does. Raw SDI image cubes are therefore not initially good references for one another. Their spatial scales must first be adjusted to a common magnification in order to construct a PSF library. While this makes the instrumental PSFs of the multiwavelength images match, a side effect of rescaling is that the true on-sky spatial scale varies across the wavelength dimension of the reference images. This often creates radial self-subtraction of the planetary PSF when planet light at another (rescaled) wavelength makes it into the library of reference images.

A distinct advantage of SDI is the acquisition of spectral information, which allows for atmospheric characterization of directly imaged companions and composition analyses of circumstellar disks. Although the mechanics of the technique are somewhat different and outside of the scope of this tutorial (relying on the placement of optical fibers on and off of the known location of a directly imaged companion), it is worth noting that medium- and high-resolution spectroscopy is increasingly used to finely characterize the atmospheres of directly imaged companions.

A common form of preprocessing for high contrast images is the application of so-called "high-" or "low-pass" filters to the data. This terminology refers to the spatial frequencies ¹⁴ that are least suppressed by the filtering algorithm—they "pass through" the process relatively unscathed, while other spatial frequencies are suppressed. A highpass filter "passes" high spatial frequency signals such as narrow disk features and planets. A low-pass filter suppresses these signals while preserving extended structures such as the stellar halo or broad disk features.

Highpass filters can be applied to high-contrast imaging data before or after PSF subtraction. A simple example of a highpass filter is the so-called "unsharp masking" technique, wherein an image is convolved with a simple kernel (often a Gaussian), and then this smoothed image is subtracted from the original. High spatial frequency structures are drastically altered (spread across many more pixels than their original extent) by this convolution, while low spatial frequency structures remain largely unaltered. Thus, subtraction of the smoothed image suppresses these low-frequency signals while preserving high-frequency structure. There are a range of additional algorithms used to achieve highpass filtering, many of which are applied to the Fourier transform of an image in the frequency domain all designed to serve the same purpose.

A number of post-processing algorithms extend the concept of "classical" differential imaging to construct custom PSF models for every image in a time series individually, rather than adopting a single representative PSF for the entire image sequence. Two of the most commonly used algorithms are outlined below. Like ADI, RDI, and SDI, both of these algorithms rely on assembly of a library of reference images (often other images of the target itself taken in the same imaging sequence), and reference images are used to construct the PSF model(s) for the target image. The quality of PSF models relies on the strength of correlations between the target image and the other images in the reference library, with the algorithms weighting most heavily reference images that are most closely correlated with the target image. ¹⁵ In this way, these algorithms are able to capture the time varying nature of the PSF and quasi-static speckles rather than relying on a single PSF for the entire image sequence. PSFs can be constructed for an entire image, or for azimuthally and/or radially divided subsections of the image, and these algorithms can be applied for ADI, SDI, RDI, and occasionally even PDI image processing.

For these more advanced PSF-subtraction algorithms, restrictions are placed on which reference images are used to estimate the PSF for a given target image. The specific images in the sequence that are excluded and included in the reference library will change for each target image. Exclusion of images taken near in time or wavelength limits the amount of planet light that survives into the PSF model. The consequence of planet signal appearing in the PSF models is azimuthal (ADI) and/or radial (SDI) self-subtraction, as illustrated in Figure 11.

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5.2.1. KLIP

Karhunen Loeve Image Processing, or KLIP, is a statistical image processing technique in which images are converted to 1D vectors and cross correlated with all other images in a time sequence. This application of Principal Component Analysis (PCA) allows for identification of common patterns ("principal components") in the image cube.

PCA is used in a range of contexts inside and outside astronomy to reduce the dimensionality of data. A simple example of how it works is to imagine a 3D scatterplot with evident correlations among the x, y, and z-axis quantities (as shown in Figure 12). The x, y, and z coordinates are, in such a case, not particularly good descriptors of the overall data, in that it is only in combination that they can describe its variation. If we were to instead define a first "principal component" axis along the line of best fit, this single variable would capture the most distinct first order pattern in the data (it is the best single descriptor of the data's variance). If we were to add a second, perpendicular axis (in PCA each principal component is required to be orthogonal to all others), it would point in the direction of maximum scatter off the line of best fit, a good second order descriptor of the variance in the data.

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It's difficult to extend this toy example conceptually into high numbers of dimensions, but the principal is the same—each additional orthogonal vector must be orthogonal to all others and is chosen to describe the maximum amount of additional variance in the data. Conceptually, in the case of PCA for HCI applications, this corresponds to patterns across many pixels that are present in the target image and some number of reference images. The first few principal components generally contain large scale PSF structures like core and halo, and the highest order principal components look like different realizations of the speckle pattern. Adding components to the model therefore increases its "aggressiveness." This makes the likelihood of a well-matched PSF model higher, but also increases the likelihood that planet light will be oversubtracted or self-subtracted.

"KL modes" are the principal components of a library of reference images that have been transformed into 1D arrays (albeit with some complexities that I will not cover in detail here). Once they are computed, an individual image is "projected" onto these KL modes, which in practice looks like a weighted linear combination of the principal components. KLIP algorithms lend themselves easily to returning models of varying complexity (different numbers of KL modes) simultaneously, so PSF subtractions can readily be generated with a range of aggressiveness and compared. Low numbers of KL modes correspond to more conservative reductions, in that they (a) contain only the most widely varying PSF structures, and (b) have relatively lower probability of any true circumstellar signals (disk, planet) being mistaken for PSF features. The probability of circumstellar sources being picked up in the KL modes is much higher for spatially extended disks than for planetary point sources, so KLIP-ed disk images often use a low number of KL modes (e.g., <10), while point-source reductions use dozens to hundreds. A schematic illustration of the KLIP process is shown in Figure 13.

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5.2.2. LOCI

When reporting a high-contrast imaging detection, contrast is an important metric; however, it is also important in quantifying instrument performance in the case of a non-detection. Modern high-contrast imaging campaigns have surveyed a large number of young nearby stars with relatively few detections of exoplanets (e.g., ${9}_{-4}^{+5}$ planets for 5–13M_Jup planets at separations of 10–100 au, Nielsen et al. 2019), though they have been more successful at detecting circumstellar disks (detection rates of ∼30%–100%, depending on selection criteria, Esposito et al. 2020). One of the main currencies of HCI surveys is therefore quantification of the instrumental performance, or limiting contrast, at a range of separations from each targeted star. This limiting contrast is a steep function of separation from the star, with lower contrasts achieved close to the star and higher contrasts at greater distances (see Figure 15). This means that a source at a given contrast is detectable in high-contrast images at a range of separations, with bright sources being detectable at all but the tightest separations and the faint sources only detectable far from the star.

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"Contrast curves" therefore denote the detection threshold at each separation, with a few caveats and considerations. First and most importantly, many high-contrast imaging post-processing techniques (discussed in detail in Section 5) do not conserve the flux of astronomical sources. This means that the "raw" contrast, which is generally computed as 5 times the standard deviation of the noise at a given separation in the post-processed images, is not a true measure of the achieved sensitivity.

In order to make a more accurate calculation, the algorithmic "throughput" must be computed by injecting sources into the image at a range of separations and quantifying their recovered brightnesses. Throughput is defined as the ratio of an object's injected to recovered brightness (generally computed via the brightness of the peak pixel at the location of the source before and after PSF subtraction). Like contrast itself, it is a strong function of separation from the star. Throughput for most high-contrast imaging algorithms is low close to the star, meaning that source brightness is heavily suppressed by PSF subtraction, and approaches 1 at greater distances (meaning the planetary signal is relatively unaltered by PSF subtraction). The best estimate of recoverable planet brightness is therefore the 5σ noise level of the image divided by the instrument throughput at each separation from the star. This is sometimes called the "throughput–corrected" contrast, but is most often just referred to as "the contrast."

When computing throughput, an important consideration is minimization of overlap/crosstalk between injected sources. As sources can overlap both azimuthally and radially, the general approach for quantifying detection limits has been to inject false planets in an outwardly spiraling pattern with appropriate separations radially and azimuthally. This requires a choice of injected contrast for each false source. Generally, a low to moderate contrast is chosen and set uniformly throughout the injected planet spiral so that recovery is assured, however it is likely that injected object throughput is, at least to some extent, a function of brightness.

Contrast curves have several limitations. First, they are sensitive to post-processing choices (e.g., KLIP parameters), therefore optimization can be computationally intensive. Second, they generally assume azimuthal symmetry in the sensitivity of post-processed images though, in reality, stellar PSFs often have azimuthally dependent structure. One common example of this is the so-called "wind butterfly" effect in AO-corrected images wherein lobes of higher noise/lower contrast are apparent on either side of a star in the direction of the wind. This means that neither noise nor algorithmic throughput is truly azimuthally symmetric. One way to mitigate this is to inject false planetary signals at various locations azimuthally and average their throughputs. For example, one might inject three spirals of false point sources with the spiral clocked by 120^◦ each time in order to sample azimuthal variation in throughput.

A further complication is in the definition of the "noise" in post-processed images. The most typical noise estimate is the standard deviation of the residuals in the post-PSF subtracted image computed in small concentric annuli extending outward from the star. The convention in high-contrast imaging is to consider sources whose peak recovered brightness is at least 5 times above the noise level to be robust detections, and objects in the 3–5σ range to be marginal. Many contrast curves reported in the literature are so-called "5σ" contrast curves, but 3 or even 1σ curves are also sometimes reported. One must be careful to understand and correct for any differences when comparing contrasts among surveys.

One final consideration in computing and interpreting noise in a post-processed image is that the dominant noise source close to the star is stellar speckles. In this speckle-dominated regime, there is a strong correlation between flux in adjacent pixels, since the stellar PSF has a width of several to many pixels. This has led to a best practice of implementing t-distribution rather than Gaussian noise statistics at tight separations, accounting for the small number of independent samples close to the star. In practice, this means dividing the computed standard deviation at a given separation by the factor $\sqrt{1+1/{n}_{2}}$ (Mawet et al. 2014), where n₂ is the number of independent noise realizations at that separation (∼2π r/FWHM).

In summary, there are several important questions to ask oneself when studying a contrast curve.

• 1.  
  Is it throughput corrected? If not, remember that the true limit is likely at lower contrast (a higher curve).
• 2.  
  By what factor has the noise level been multiplied (1, 3, 5)? If less than five, recall that objects near the curve might be considered marginal or non-detections.
• 3.  
  Has the noise level been corrected to reflect appropriate noise statistics near the star? If not, the true limit may be a steeper function of separation from the star than depicted.
• 4.  
  How azimuthally symmetric is the post-processed image? If azimuthal structure is apparent, the curve should be interpreted as an average. In some parts of the image, objects below the curve may be detectable; in others, objects above the curve may be undetectable.

To put it plainly, the caveats described above mean that all contrast curves should be interpreted as relatively rough and fuzzy boundaries between detectable and undetectable planets. Furthermore, one must keep in mind when comparing contrast curves between studies and instruments that these choices may not be uniform among them and the curves may not be directly comparable. It is important when planning observations and interpreting detections (or non-detections) relative to contrast performance, to carefully read contrast curve descriptions and discern these important details. You may practice contrast curve comparison and parsing of these details by perusing Figure 16, which compares demonstrated and expected contrast for a range of current and future HCI instruments in several wavelength regimes.

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7.2.1. Aside: Contrast Curves for Disk Detections

Signal-to-noise maps are standard in all fields of astronomy. In the case of direct imaging of point sources, there are several subtelties in computing them. First, the post-processed planetary PSF has characteristic "self-subtraction lobes" on either side of the planetary core. These are caused by the presence of the planet at different azimuthal angles in the reference library. The region containing the planetary core and self-subtraction lobes must be excluded in order to robustly estimate noise. This is typically done by masking this region and computing the standard deviation of the remaining pixels at a given radial separation. The nature of the speckle-dominated region of the PSF means that independent samples of the noise at a given radial separation are defined by the size of a speckle (the PSF FWHM), leaving relatively few independent noise samples at tight radial separations and requiring t-distribution noise statistics (Mawet et al. 2014).

PSF-subtraction techniques, while powerful for isolating faint signals, complicate the extraction of accurate astrometry, photometry, and spectra from a detected object because the process of PSF subtraction does not conserve planet signal. A number of strategies are used to mitigate these complications and extract robust estimates of planetary photometric, astrometric, and spectral signals in HCI.

False Planet Injection—Injection and recovery of false planet signals in the image helps quantify the amount of planetary signal lost during image processing (as described in Section 7.1). This is used, in turn, to correct photometry and estimate the true intensity of planet light at a given wavelength. Similarly, false planets can be used to quantify astrometric and photometric uncertainties, often by injecting them into raw images and utilizing the statistics of their recovered versus injected locations and fluxes to quantify uncertainty on astrometry and photometry of the companion.

Forward Modeling—Injection of a model companion or disk into raw images and examination of its morphology, astrometry, and photometry in post-processed images, is known as "forward modeling." The properties of these false planets (brightness, location, fwhm) or disks (extent, inclination, radial brightness distribution) are iterated upon and forward models compared to data. This process is essential in interpreting post-processed images, which suffer from both self-subtraction (see "Signal-to-Noise Calculation" above) and so-called "over-subtraction," in which some of the planet or disk signal is flagged as noise and subtracted. Forward models are tuned by minimizing residuals in the difference of the PSF subtracted and forward modeled images. In many cases, models are injected not into the target image sequence, but into a reference image sequence or at a wavelength in the target sequence at which the target signal is absent or minimized. Post-processed signals are dependent on their azimuthal and radial location, and on the precise PSF, which is wavelength dependent, so neither of these techniques provides a perfect match. However, Pueyo (2016) showed that a post-processed PSF can also be modeled for a particular location mathematically, without altering the original images, by propagating a perturbation to the covariance matrix forward through the algorithm (KLIP or LOCI). This removes the problem of mismatch by constructing a forward model at the same location and wavelength, and the authors demonstrated its ability to boost the accuracy of spectral extraction. Inferences made via forward-modeling are, however, limited by our ability to accurately model the true planet or disk signal, which is particularly difficult for complex off-axis or time-varying PSFs and non-axisymmetric disk structures. Nevertheless, post-processed PSFs, by virtue of our precise knowledge of their constructed photometry and astrometry, are powerful probes of the effects of PSF subtraction on the properties of real signals.

Negative Planets—Another technique for determining planetary flux and location is to inject negative false planets into the raw image sequence at the location of the planet candidate, effectively canceling its signal. Post-processed residuals are then minimized to determine a best fit. Although this results in robust photometry and astrometry estimates, arguably better than using forward modeling, it is computationally intensive, and uncertainties on this technique are harder to estimate. Often, observers assign error bars "by eye" to capture the range of values that result in good subtractions. For example, an appropriate flux scaling should result in near-zero residuals and not clear over- or under-subtractions (i.e., clear residual planetary excess or a clear residual negative signal at the planet location).

One astrophysical false positive that can mimic a directly imaged companion signal is the coincidental alignment of a distant background source with a young star. This scenario is a possibility any time a faint point source is detected near a young star, thus it is among the first forms of vetting that all candidate planets are subjected to. For an initial single epoch detection, there are two important pieces of information used to assess the probability of a candidate being a background source—(1) the proximity of the target star to the galactic plane and (2) its spectrum. Coincidental alignments are much more common in the galactic plane, so the probability of false positives is higher in this case. As the most common background objects masquerading as planet candidates are distant red giants, spectral information—either true spectra or NIR colors—is also crucial in assessing the probability that a faint apparent companion is a young planet or brown dwarf.

With a few notable exceptions (e.g., 51 Eri, Macintosh et al. 2015, an object whose methane-dominated spectum made its planetary nature clear from the outset), planet candidates are rarely announced until they have undergone an additional form of vetting—that of common proper motion with their host stars. Because the targets of direct imaging campaigns are close (generally <50 pc), a necessity in order to achieve the requisite contrasts at planetary separations, their proper motions are invariably higher than those of distant background objects. Thus, most planet candidates are confirmed after obtaining a second epoch observation months or years after the initial detection to confirm that the candidate and host star exhibit the same proper motions over that time period, as shown schematically in Figure 17. Candidates are ruled out as planets if they exhibit little to no proper motion between epochs.

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In principle, establishment of common proper motion could be complicated by the additional motion of a true bound companion as it orbits its host star. In practice, however, most planet candidates are separated from their hosts by large enough physical separations that orbital motion is negligible compared to proper motion.

The most insidious form of false positive in establishing common proper motion is the coincidental alignment with the target star of an unbound foreground or background object with non-negligible proper motion. If the proper motion vectors of the two objects are in rough alignment and of similar magnitude, the time baseline needed to distinguish a comoving object is longer, as was the case with the apparent planetary companion HD 131399Ab (Nielsen et al. 2017).

Another form of astrophysical false positive results from the prevalence of circumstellar material around young stars targeted for direct imaging. Upon PSF subtraction, disk features can masquerade as planets, especially in cases where they are narrow (surviving highpass filtering) and non-axisymmetric. This is especially problematic for younger systems (<10 Myr), where such features are ubiquitous (e.g., Benisty et al. 2023).

In the case of older (>10 Myr) objects, for which the initial protoplanetary disk has usually either been incorporated into companions or dissipated, we see primarily second generation dust generated by the grinding of asteroids and/or comets in belts akin to our own asteroid and Kupier belts. These belts tend to be fairly symmetric and have limited spatial extent, making them much less likely to be confused for planet candidates. In known disk-bearing systems, candidate planets are vetted in several ways.

Comparison with known disk features—in both millimeter thermal emission and NIR scattered light (especially PDI-resolved features) informs the probability of confusion occurring at the location of a planet candidate. In cases where a candidate is well inside of a cleared cavity (e.g., PDS 70b, Keppler et al. 2018), the odds of confusion are minimal.

Colors or spectra—of companion candidate(s) can be compared to those of the star. In a case where the star and candidate spectra closely match, odds are good that the candidate is a scattered light feature. This could mean an envelope or disk around a planet, or a clump of disk material that has not yet formed a planet. In cases where a planet candidate exhibits a substantially different spectrum from that of the star, it is considered strong evidence for a planetary nature.

Multiepoch information—can distinguish static disk features from orbiting companions. Signals that show orbital motion are likely to be planetary, and those that are static are more likely disk features. This is complicated in the case of planet-induced spiral arms, which likely rotate with a pattern speed equal to the orbital speed of the companion inciting them. An important test is, therefore, whether apparent point sources that lie along spiral arms orbit with the speed of a companion at the point source's orbital separation. If they orbit faster (or slower), this is consistent with incitement by a different planet on a closer (or more distant) orbit.

The robustness of the signal among post-processing techniques—particularly those that vary somewhat in "aggressiveness" is also an important part of vetting a planet candidate. In the most insidious cases, the presence of an extended but narrow disk feature at different azimuths in the PSF reference library can lead it to appear point-like in post-processed images. Persistence of the feature across PSF subtraction algorithmic properties, and in particular its persistence across various HCI techniques, helps to distinguish this scenario from a true point-like source. In cases where the disk structures are well constrained (e.g., from PDI imaging), forward modeling can be used to understand the likely appearance of disk structures following PSF subtraction and compared against the images. RDI and cADI are considered the most conservative processing techniques, while LOCI-ADI and KLIP-ADI are more "aggressive" in that they tend to model smaller spatial scale PSF features, and model mismatch can therefore result in smaller spatial scale substructures mimicing planetary signals. Tunable parameters in the algortihms, such as the degree of rotational masking, the size of the regions for which PSFs are constructed separately, and the complexity/number of modes applied to construct the model, can also be altered to be more or less aggressive. For example, including images in the reference library that are close in rotational space (a small rotational mask), constructing custom PSFs for very small regions of images, and increasing the number of modes in the PSF model all represent more "aggressive" reductions that will effectively remove stellar signal, but will also increase the probability of false positives. These parameters should be iterated over to probe the robustness of apparent planetary signals.

Various optical artifacts, quasi-static speckles, cosmic rays, and speckle noise can also masquerade as planets in post-processed images. In general, the properties of such artifacts should not closely mimic those of true astrophysical sources (e.g., by demonstrating self-subtraction). Nevertheless, careful analysis of false alarm probabilities is important in conducting HCI, particularly for low SNR recoveries. The gold standard in candidate vetting remains multiepoch, multi-wavelength, multi-instrument observations of candidates demonstrating common proper motion with the host star and evidence of a non-stellar spectrum.