HCI Contrast Considerations
In JWST high-contrast imaging (HCI), the term contrast means the companion-to-host flux ratio.
When developing an HCI investigation, the user's scientific goal is represented by an operating point, (s, Cflux), where
- s is the expected apparent separation between the companion and host, and
- Cflux = fluxcompanion/fluxhost , the flux contrast between the companion and host.
This operating point is estimated to be feasible if Cflux > Climit(s), where Climit(s) is the limiting contrast.
Climit(s) is a function of many interrelated factors, and is, therefore, a challenge to estimate. In particular, Climit(s) depends on the instrumental configuration, the observing strategy, and the post-observation processing calibrations and processes. Climit(s) is especially sensitive to the step where a scaled reference PSF is subtracted from a science image. PSF subtraction is relied upon to extend the grasp of the investigation deep into the systematic noise (see Soummer et al.). In the absence of data, it is hard to say how well PSF subtraction will perform for JWST.
To be valid, the feasibility test Cflux > Climit(s) assumes that the planned observation has the same technical and procedural factors that produced the calibration of Climit(s).
To gain a better understanding of Climit(s), look more closely at the term "contrast" (C). Although C been widely adopted as a metric of HCI performance, its meaning is sometimes ambiguous in the context of where it appears. Therefore, the various possible meanings of "contrast" are disambiguated as follows:
- Cflux is the term for the companion-to-host flux ratio. Cflux is a property of nature, independent of any instrumental or observational details or considerations.
- CPSF(s) is the ratio of the PSF at separation s to its central value: CPSF(s) = PSF(s)/PSF(0). Here are other useful PSF ratios:
- CJWST_PSF(s), the PSF ratio using the telescope PSF.
- Ccentered_PSF(s), the PSF ratio using the instrument PSF. The numerator is the PSF when it is centered on the occulting mask and is evaluated at input values s > IWA.
- Coffset_PSF(s',s), which is the PSF ratio with the numerator equal to the PSF when it is offset from the center of the occulting mask by separation s', and the PSF is evaluated at an input value of s.
- Craw(s) = Coffset_PSF(0)/Ccentered_PSF(s) is the raw contrast, which is an intrinsic property of the instrument, independent of any natural or observational details or considerations, including noise and integration time.
- Climit(s) is limiting contrast, defined as the value of Cflux, for the minimum detectable companion. Climit(s) affirmatively does take into account any and all relevant technical and procedural factors, such as observational strategy, pointing and instrumental errors, detection threshold, and post-observation processing (especially the PSF-subtraction strategy). The detection threshold is related to the false alarm probability under the assumption that the residual errors after PSF subtraction are normally distributed.
- Cideal(s) is a floor for the limiting contrast Climit(s), because it makes certain optimistic, simplifying assumptions. For example, Cideal(s) may assume that pointing errors are zero or that photometric noise is ideal, with photon-counting noise dominating.
- Gcontrast(s) = Cideal(s)/Craw(s) is the contrast gain. Gcontrast(s) is the factor by which the instrument and procedures of HCI must suppress the telescope PSF.
Q(s) = Cflux × Craw(s) is an auxiliary metric sometimes used to gauge the systematic errors in Craw(s) due to aberrations and their speckles. Q(s) is the wing-to-center surface brightness ratio of the host-companion pair of sources, which has been called the instantaneous signal-to-noise ratio. Q depends only on the instrument and on nature, but not on any observational factors, such as exposure time or strategy for PSF subtraction.
At the current time, few treatments of Climit(s) are available for the JWST HCI modes. For now, users must extrapolate Climit(s) from published treatments of Climit(s):
Beichman, C. A., et al. 2010, PASP, 122:162
Imaging Young Giant Planets from Ground and Space
Boccaletti, A., et al. 2015, PASP, 127, 633
The Mid-Infrared Instrument for the James Webb Space Telescope, V: Predicted Performance of the MIRI Coronagraphs
Greenbaum, A.Z., Pueyo, L., Sivaramakrishnan et al. 2015, ApJ, 798, 68
An Image-Plane Algorithm for JWST's Non-Redundant Aperture Mask Data
Soummer, R., Pueyo, L., and Larkin, J., 2012, ApJ 755 , L28
Detection and Characterization of Exoplanets and Disks Using Projections on Karhunen-Loeve Eigenimages