31 January 2019 Comparing nonredundant masking and filled-aperture kernel phase for exoplanet detection and characterization
Author Affiliations +
Abstract
The limitations of adaptive optics and coronagraph performance make exoplanet detection close to λ  /  <i>D</i> extremely difficult with conventional imaging methods. The technique of nonredundant masking (NRM), which turns a filled aperture into an interferometric array, has pushed the planet detection parameter space to within λ  /  <i>D</i>. For high Strehl, the related filled-aperture kernel phase technique can achieve resolution comparable to NRM, without the associated dramatic decrease in throughput. We present NRM and kernel phase contrast curves generated for ground- and space-based instruments. We use both real and simulated observations to assess the performance of each technique, and discuss their capabilities for different exoplanet science goals such as broadband detection and spectral characterization.

1.

Introduction

Direct imaging has recently emerged as a viable planet detection and characterization method. Near- to midinfrared observations are particularly useful for discovering giant planets, since they have relatively low contrast at these wavelengths.1 Several molecules that are expected to be in giant planet atmospheres have significant opacity in this wavelength range,2 making infrared spectroscopy useful for constraining atmospheric composition. Furthermore, infrared imaging of young planets can constrain evolutionary scenarios such as hot- versus cold-start models and can distinguish between planetary atmosphere and circumplanetary accretion disk emission.23.4

Typical direct imaging planet searches are limited to angular separations of a few λ/D. Point-spread function (PSF) deconvolution algorithms are less effective within these separations due to the small number of resolution elements available.5 Phase leakage in even the highest performance coronagraphic observations prevents high-contrast detections within 12λ/D.6 These limitations make semi-major axes less than 10AU accessible for only the most nearby stars.7 Expanding this detection parameter space to smaller semimajor axes and/or to more distant stars (including nearby star-forming regions8) requires imaging techniques such as interferometry.

1.1.

Nonredundant Masking

Nonredundant masking9 is well suited for detecting young, giant planets around more distant stars than those targeted by typical direct imaging surveys. NRM uses a pupil-plane mask to turn a conventional telescope into an interferometric array. The images are the interference fringes formed by the mask, which we Fourier transform to calculate complex visibilities. Since the mask is nonredundant, no two baselines have the same orientation and separation; information from each baseline is encoded in a unique location in Fourier space.

Nonredundancy means that the instrumental component of each Fourier phase can be written as a linear combination of two pupil phases. Calculating closure phases,10 sums of phases around baselines forming a triangle, eliminates these instrumental phases to first order, leaving behind sums of phases intrinsic to the target. (We note that if the instrumental pupil-plane phases for each subaperture are treated as static pistons, then closure phases cancel instrumental phase exactly. However, spatial and temporal pupil-plane phase variations, as well as amplitude variations such as scintillation, lead to higher order closure phase errors that require calibration.11) Closure phases are particularly powerful for close-in companion detection because they are sensitive to asymmetries. Since closure phases are correlated, we project them into linearly independent combinations called kernel phases.1112.13 We also calculate squared visibilities, the powers on each mask baseline.

Despite the low throughput (10%), NRM’s superior PSF characterization probes angular separations at and even within the diffraction limit. This angular resolution means that spatial scales of 10  AU can be resolved for stars 150  pc away. NRM has led to detections of both stellar14 and substellar companions,15,16 as well as circumstellar disks13,17,18 at these small angular separations. It led to the discovery of a promising system for planet formation studies, the protoplanetary candidates in LkCa 15.14 Dual-aperture LBTI masking observations recently resolved a solar-system-sized disk around the star MWC 349A,18 at a distance of 1.2  kpc from Earth. With a maximum baseline of 23 m, this is a preview of NRM’s potential on 30-m class telescopes. NRM on current telescopes and on future facilities will expand the exoplanet detection parameter space.

1.2.

Filled-Aperture Kernel Phase

Extreme adaptive optics systems have made filled-aperture kernel phase12 an interesting alternative to NRM. Kernel phase involves treating a conventional telescope as if it were a redundant array. Redundancy prevents Fourier phases from being written as a linear combination of pupil-plane phases in general. However, in the high Strehl regime (where instrumental pupil-plane phases are small), one can justify Taylor expanding the instrumental wavefront. This means that the redundant instrumental Fourier phases can be approximated as a linear operator on the pupil-plane phases. Finding the nullspace of this linear operator yields kernel phases, linearly independent combinations of Fourier phases that are robust to instrumental phase errors to first order. Like closure phase (and kernel phase) in NRM, filled-aperture kernel phase is sensitive to asymmetries and is thus powerful for close-in companion detection.

Kernel phase has been demonstrated on archival Hubble Space Telescope observations of ultracool dwarfs.19 In addition to confirming several known companions to these L dwarfs, it led to the detection of five binary systems at angular separations of 40 to 80 mas at 1.1 to 1.7  μm. Kernel phase has also been applied to ground-based data from Keck20 and Palomar,21 where it led to the detection of stellar and substellar companions at (1 to 2λ/D). The Keck observations were taken at Ms band, where the high sky background reduces the SNR of masking observations. These kernel phase datasets provided comparable resolution to that expected for NRM, with a shorter integration time.

1.3.

Outline of this Paper

Here we compare NRM and filled-aperture kernel phase in a controlled way, with a specific focus on exoplanet science. We generate simulated datasets for three imagers: NIRC2 on Keck, and NIRCam and NIRISS on James Webb Space Telescope (JWST). We also generate observations for two integral field spectrographs (IFSs): OSIRIS on Keck, and NIRSpec on JWST. Integral field spectroscopy is a particularly interesting kernel phase application, since dispersing the light and applying a pupil-plane mask would require long integration times for high signal-to-noise. Furthermore, when broadband kernel phase observations of bright stars may be unfeasible due to detector saturation, IFS kernel phase observations may not saturate.

We describe the simulated datasets in Sec. 2. We use the simulated observations to generate contrast curves for both filled-aperture kernel phase and NRM, and to place detection limits on planetary atmosphere and circumplanetary accretion disk models. We present these results in Sec. 3. In Secs. 4 and 5, we discuss the potential of each technique as a method for exoplanet detection and characterization.

2.

Simulated Observations

We simulate nonredundant masking and filled-aperture kernel phase observations for three imagers—Keck NIRC2, JWST NIRCam, and JWST NIRISS—and kernel phase observations for two integral field spectrographs—Keck OSIRIS, and JWST NIRSpec. For the IFS simulations, we use the central wavelength bin to estimate the average performance for each instrument and mode. For all instruments, we compare the two techniques by setting the total amount of observing time, including overheads, to be the same (6h). To ensure a systematic comparison, we use simulated observations so that we can control the various noise sources. When possible, we anchor these simulations using real datasets. We include random noise sources from the star, sky background, and detector. We also simulate changing optical path difference (OPD) maps for each instrument to account for quasi-static (“speckle”) noise that can lead to kernel phase calibration errors. To simulate these calibration errors, we divide the total observing time for all instruments into observations of a science target and of a PSF calibrator with the same brightness as the science target, but with different quasi-static errors. We break the observations up into “visits.” each of which is a single datacube containing a number of frames on a single target (science or PSF calibrator).

We calculate kernel phases using an updated version of the data reduction pipeline presented in Sallum and Eisner.22 For both Keck and JWST filled-aperture observations, we assume one subaperture per mirror segment. This is an arbitrary choice, and while it prevents phase noise due to jumps between mirror segments, denser pupil-plane sampling may lead to improved results. We use the “Martinache” kernel phase projection,12 which makes orthonormal combinations of Fourier phases (see Sec. 6). We note that other phase combinations can provide higher contrast away from the PSF core; one example is the “Ireland” projection,11 which makes statistically independent combinations of Fourier phases using the kernel phase covariance matrix. This has been shown to boost contrast away from the PSF core in the photon noise limit.11 Since some of our simulated observations are in the calibration error limit, where the advantages of the “Ireland” projection do not apply,11 we use the “Martinache” projection. The contrast curves shown in Sec. 3 could be improved by using different projections for probing different angular separations or for different noise regimes.

For both techniques, we apply a super-Gaussian window to create interpixel correlations in the Fourier plane before calculating kernel phases. These interpixel correlations are helpful for reducing the random kernel phase scatter induced by noise sources such as sky background and detector noise. For NRM datasets, we tune the super-Gaussian so that it has a value of 0.9 at the null in the PSF of an individual hole (λ/dh). For filled-aperture kernel phase, the super-Gaussian has a value of 0.9 at 3λ/D. To minimize the impact of sky background and detector noise beyond these regions—where the PSFs have low signal—we use an eighth-order super-Gaussian. Alternative techniques such as the “Monnier” method, which involves averaging the bispectra for many pixel triangles when calculating each closure phase,23 as well as image-plane fringe fitting24 can reduce random phase scatter without windowing. These have been demonstrated for NRM observations, and similar techniques could be applied to filled-aperture kernel phase.

For all instruments and bandpasses, we simulate a grid of stellar apparent magnitudes between 6 and 13. This corresponds to absolute magnitudes between 0 and 7, at the distance of Taurus (140  pc8). While this does not cover the bright end of expected young stars’ absolute magnitudes,25 for filled-aperture kernel phase observations, the apparent magnitude 6 stars are close to or beyond the saturation limit for NIRC2 and NIRCam. We thus focus on this range of stellar brightnesses to compare the two techniques on these instruments. We generate contrast curves for each simulated dataset by comparing the χ2 of the null model (χnull2; a single point source) to a grid of single companion models with different separations, contrasts, and position angles. For each single companion separation, we calculate the average χ2 value for all sampled position angles (χsep2) and take the 5σ contrast to be the contrast at which χsep2χnull2=25. The details of the individual simulations can be found in the following subsections and in Sec. 7.

2.1.

Keck NIRC2

We simulate kernel phases for filled-aperture and masked Keck NIRC2 observations at Ks=2.15  μm, L=3.78  μm, and Ms=4.67  μm. The filled-aperture and NRM modes yield 45 and 28 kernel phases, respectively. For each target observation, we simulate a cube of nframes frames, each of which is the sum of ncoadd coadds (see Tables 7Table 8Table 9Table 10Table 1112). We add sky background, dark current, and readout noise to the images according to the number of coadds and exposure times; Table 1 lists the relevant noise parameters and other detector information for each bandpass. For all observations, we background subtract each frame and apply any window functions. We then calculate complex quantities for each kernel phase that are analogous to bispectra for closure phases (see Sec. 7). Like averaging bispectra for calculating mean closure phases, we average these complex quantities over the cube of images before taking the phase as the mean kernel phase for a single visit.

Table 1

NIRC2 noise and detector parameters.

Bandλca (μm)λ/Db (pix)Sc (mag/arc sec2)ZPd (mag)DCe (e−/pix/s)RNf (e−/pix)WDg (DN)gh (e−/DN)
Ks2.1464.4512.6624.840.11518,0004
L3.7767.833.0123.60.11518,0004
Ms4.6709.690.2321.420.11518,0004

a

Central wavelength in microns.

b

Detector PSF sampling in pixels.

c

Sky background in magnitudes per square arc second.

d

Zero point in magnitudes for Strehl = 1.0.

e

Dark current in electrons per pixel per second.

f

Read noise in electrons per pixel.

g

Well depth in counts at 5% linearity.

h

Gain in electrons per count.

We simulate OPD maps to account for quasistatic PSF aberrations. Keck AO is known to be affected by low-order residual wavefront errors; modeling these as segment piston errors has been shown to produce realistic PSFs.26 To simulate PSFs, we create OPD maps that are a combination of low- and high-order residual wavefront errors. We generate low-order errors over the entire Keck pupil and on each individual mirror segment. For the entire pupil, we make combinations of the first 20 Zernike modes (Zn; excluding tip and tilt), drawing each coefficient from a uniform distribution with a width [2f(n)] that depends on the Zernike order (n):

(1)

OPDlow=n=020Unif[f(n),f(n)]Zn=n=020ClowZn.
The function f(n) has the form nα, and we tune α to match real observations (see below). For the individual mirror segments, we add tip, tilt, and piston errors, drawing each coefficient from a uniform distribution with a fixed width:

(2)

OPDseg=n=02Unif(g,g)Zn=n=02CsegZn.

When we apply this prescription, we use arbitrary normalizations for f(n) and g, and then rescale the final OPD maps to have an RMS tuned to match real observations. We also tune the dependence of the low-order Zernike coefficients on Zernike order (α). The best OPD parameters are listed in Table 2. These lead to uncalibrated kernel phase scatters of 1.2  deg for L NRM observations (compared to 1.0  deg to 1.5 deg for real observations), and Strehl values of 0.55, 0.85, and 0.9 at Ks, L, and Ms (consistent with typical Strehls observed using NIRC2), respectively. They also match observed PSF radial profiles to within 4% fractional error. Figures 1 and 2 show example images and power spectra, respectively, for NRM and kernel phase for each bandpass.

Fig. 1

Simulated individual (a) Ks, (b) L, and (c) Ms images for the observing parameters listed in Table 1. The top row shows filled-aperture data, and the bottom row nonredundant masking data. The images are displayed on a square root scale to highlight structure in the wings of the PSF. The fields of view are different for the two techniques: the kernel phase images are 45 mas on a side, and the NRM images are 100 mas on a side.

JATIS_5_1_018001_f001.png

Fig. 2

Simulated (a) Ks, (b) L, and (c) Ms power spectra for a single frame using the observing parameters listed in Table 1. The top row shows filled-aperture kernel phase data, and the bottom row nonredundant masking data. Random noise from the large sky background is apparent in the L and Ms power spectra; building signal-to-noise in the long baselines requires combining more frames. The scattered points show the sampling locations for calculating kernel phases; they are shown in two colors since the Fourier transform is symmetric.

JATIS_5_1_018001_f002.png

Keck’s low-order errors are quasistatic27 and contribute to calibration errors in the final kernel phases. We thus generate calibrator observations after evolving the low-order and segment OPD Zernike coefficients by a factor drawn from a one-mean uniform distribution with width 2h. Equations (3) and (4) describe this procedure:

(3)

Cn,low,cal=Unif(1h,1+h)Cn,low,targ,

(4)

Cn,seg,cal=Unif(1h,1+h)Cn,seg,targ.
We use the original and evolved OPD maps to generate PSFs for each target and calibrator observation, respectively. To calibrate, we subtract the calibrator kernel phases from the target kernel phases. We tune the evolution parameter (h) so that the calibration decreases the kernel phase scatter by the same amount as it does in typical NIRC2 NRM observations (h=0.3). This results in calibrated NRM kernel phase scatters of 0.2  deg to 0.3 deg for observations of a L=5.8  star, consistent with the observed scatter in PSF calibrator observations from Keck at L. Figure 3 shows an example of OPD evolution for both techniques; the residual OPD map has 60-nm rms. We note that this prescription does not include residual AO errors such as fitting error, bandwidth error, or aliasing, which would change on timescales comparable to the AO frame rate (much shorter than the integrations presented here). Adding these effects would make the OPD simulations more realistic, but since they would average over many AO loops and since the simplified prescription can match real observations, we do not include them.

Fig. 3

Example OPD evolution for (a) NIRC2 filled-aperture kernel phase and (b) nonredundant masking. The left shows an initial OPD made up of both low- and high-order wavefront errors, and the center panel shows the result of evolving the OPD map. The right side shows the difference between the two; it has an rms OPD of 60 nm.

JATIS_5_1_018001_f003.png

We design a half night of observations for each target star magnitude and bandpass, accounting for overheads. We split the half night into a number of visits to target and PSF calibrator stars. The length of each visit depends on the number of photons collected from the star and sky; for a small number of source photons, kernel phase errors may be dominated by random noise. As the number of source photons increases, the random kernel phase scatter decreases, and the visit approaches the contrast limit—where quasi-static errors dominate over random errors. Longer integrations in this limit do not decrease the kernel phase scatter significantly. Thus, we design our visits to be either long enough to reach the contrast limit, or to take 3 h (half the observing time), since the observing is split evenly between target and PSF calibrator observations. Datasets on brighter stars will contain more visits than datasets on fainter stars. When multiple visits can fit into a half night, we treat them as snapshots at different parallactic angles that change in 5-deg increments and have independent calibration errors.

To account for NIRC2 overheads, we treat each visit as a collection of frames and each frame as the sum of a number of coadds. We design each coadd to be long enough to reach 5000 to 10,000 maximum counts—this is to minimize overheads but remain in a linear regime on the detector. We assume a 512×512  pixel subframe, which results in a single coadd overhead of 0.05 s. We enforce a minimum frame time of 20 s, which adds an additional overhead of 2.18 s every 20 s. We assume that the observations are dithered every 200 s to enable sky subtraction, which adds an overhead of 6 s for each dither. Lastly, we assume target acquisition overheads of 90 s per pointing.28 Tables 7Table 8Table 9Table 10Table 1112 in Sec. 7 provide frame, coadd, and dither details for each target star brightness. Figures 24 and 25 show histograms of the raw (uncalibrated) and calibrated kernel phases for each technique and bandpass for two different target star brightnesses.

2.2.

JWST NIRCam and NIRISS

We use the Pandeia engine29 and WebbPSF software30 to simulate NIRCam kernel phase and NIRISS aperture masking (AMI) observations to compare the two techniques. NIRCam imaging and NIRISS AMI yield 21 and 15 kernel phases, respectively. Since exoplanets are relatively bright in the near- to midinfrared, we simulate data for filters centered on wavelengths 4  μm that can be used with NIRISS AMI and NIRCam imaging (F430M and F480M). Since slew and telescope roll overheads are large for JWST, we do not allow the number of visits for the different target stars to vary like we do for NIRC2. We rather assume that the observations are made up of two pairs of target—PSF calibrator visits taken at different telescope roll angles 45 deg apart. We assume that the length of each visit is 1.5 h, for a total observation time of 6 h, excluding slew and roll angle overheads. When designing the observations, we account for detector overheads within each 1.5-h visit.

JWST visits are split into sets of integrations, each of which is composed of a number of groups. To calculate overheads, for each target magnitude, we first find the maximum number of groups (ng) that can be used in a single integration before saturation. For NIRCam imaging, this means choosing the readout mode that provides the maximum integration time, but for NIRISS AMI only one readout mode is available. We then assume that each visit is composed of the maximum number of ng-group integrations that can be acquired in 1.5 h (ni), given that each integration comes with a readout overhead (0.0494 s for NIRCam in a sub64P subarray, and 0.0745 s for NIRISS in a sub80 subarray). When the remaining time after ni integrations allows for more than a single group, we add an additional integration containing (ng,rem) groups. Tables 13Table 14Table 1516 in Sec. 6 list ng, ni, and ng,rem for each instrument.

We use Pandeia’s “detector” output for the observational parameters in Tables 13Table 14Table 1516. This generates a long-exposure image for the entire visit that contains the Poisson noise from the target and JWST’s “medium” thermal background, and read noise. We note that the data product for each real JWST exposure will be a cube of integrations, allowing for coadding of smaller pieces of each exposure, or for averaging kernel phases over all short integrations. We do not explore different options for coadding or averaging of short-exposure kernel phases using Pandeia. However, we do test the effects of using a single summed image versus averaging many short-exposure images using our Keck simulations. Contrast curves generated from these two extreme options are nearly identical in the bright limit, where OPD errors dominate. In the limit where random noise dominates, averaging short exposures performed better by 0.5  mag; averaging kernel phases generated from short exposures would thus improve the achievable contrast for the faintest simulated targets (11th mag). For real JWST observations, averaging the kernel phases for many short exposures will be more practical, since effects such as pointing jitter and noise sources such as cosmic rays will degrade long-exposure datasets. Tables 3 and 4 list the relevant noise and detector parameters for these observations.

Table 2

NIRC2 OPD parameters.

Low-order RMS160 nm
Low-order order dependence (α)0.2
Low-order evolution parameter (h)0.3
Segment RMS280 nm
Segment evolution parameter (h)0.3

Table 3

NIRCam noise and detector parameters.

λcaμm4.3, 4.8
λ/Db (pix)2.10, 2.34
DCc (e/pix/s)0.027
RNd (e)13.5
WDe (DN)83,300
gf (e/DN)1.82

a

Central wavelength in microns.

b

Detector PSF sampling in pixels.

c

Dark current in electrons per pixel per second.

d

Read noise in electrons per pixel.

e

Well depth in counts.

f

Gain in electrons per count.

For each pointing, we generate science target and calibrator frames using different OPD maps to simulate PSF evolution. We begin by randomly choosing one of the 10 OPD maps included in WebbPSF. We then fit a hexike basis31 to each mirror segment, including up to 100 coefficients. We evolve each of the hexike coefficients (Cn) by a factor drawn from a one-mean uniform distribution with a width (2h) tuned to result in an rms residual WFEs of 10  nm [see Eq. (5)]. This is consistent with the thermal evolution expected for JWST over approximate hour long timescales.32

(5)

Cn,seg,cal=Unif(1h,1+h)Cn,seg,targ.
For both NIRCam and NIRISS, this corresponds to h=0.2. Figure 4 shows an example initial, final, and residual OPD map for a single simulation for both instruments, and Fig. 5 shows example images and power spectra. Figures 26 and 27 show histograms of the raw and calibrated NIRCam filled-aperture kernel phases and NIRISS NRM kernel phases for target stars with apparent Ms band magnitudes of 6.3, and 11.3, respectively.

Fig. 4

Example JWST OPD evolution. The left panels show one of the 10 predicted (a) NIRCam and (b) NIRISS OPD files from WebbPSF. The center panels show the resulting OPDs after fitting hexikes to each JWST mirror segment and evolving their coefficients by a small fraction in random directions. The right panels show the difference between the first two OPD maps and have RMS residual OPDs of 10  nm.

JATIS_5_1_018001_f004.png

Fig. 5

Simulated (a) NIRCam and NIRISS integrations and (b) power spectra. This dataset uses the F430M filters and residual OPD files comparable to those in Fig. 4. The scattered points show the sampling locations for calculating kernel phase; they are shown in two colors since the Fourier transform is symmetric.

JATIS_5_1_018001_f005.png

2.3.

Keck OSIRIS

OSIRIS is a K band integral field spectrograph on Keck. We simulate OSIRIS kernel phase observations in the Kn3 bandpass, since it covers the accretion-tracing emission line Br-γ, which would be of interest for observing protoplanet candidates. This mode contains 433 0.25 nm wide wavelength bins between 2.121 and 2.229  μm. With one subaperture per mirror segment, it yields 45 kernel phases. We assume 6 h of available observing time and account for readout, dither, and slew overheads. We optimize our observing strategy in an identical manner to NIRC2, designing visits that either reach the contrast limit or a length of 3 h including overheads. We keep the peak counts per frame under 30,000 (the OSIRIS saturation limit) and use a readout time of 0.829 s per frame, a dither overhead of 6 s, and a target acquisition overhead of 90 s. We use an OPD evolution prescription identical to NIRC2, and account for detector, sky, and Poisson noise in the same way as for NIRC2. Table 5 lists the relevant detector and noise parameters for OSIRIS, and Table 17 lists the number of frames and integration times for each target brightness. Figure 6 shows an example image and power spectrum, and Fig. 28 shows kernel phase histograms for targets with Ks band brightnesses of 6 and 11 magnitudes.

Table 4

NIRISS noise and detector parameters.

λcaμm4.3, 4.8
λ/Db (pix)2.10, 2.34
DCc (e/pix/s)0.0125
RNd (e)18.32
WDe (DN)100,000
gf (e/DN)1.61

a

Central wavelength in microns.

b

Detector PSF sampling in pixels.

c

Dark current in electrons per pixel per second.

d

Read noise in electrons per pixel.

e

Well depth in counts fGain in electrons per count.

Fig. 6

Example-simulated (a) OSIRIS image and (b) power spectrum.

JATIS_5_1_018001_f006.png

2.4.

JWST NIRSpec

We use the Pandeia engine and WebbPSF software to generate simulated data for NIRSpec IFU observations. We simulate observations for stars with target magnitudes between 6 and 13. We use the G395H grating and the F290LP filter, which yield 4000 wavelength bins from 2.87 to 5.27  μm. We follow the same methods for OPD evolution and calibration as for NIRCam / NIRISS, evolving the hexike coefficients to achieve 10 nm rms residual OPD [h=0.11 in Eq. (5)]. We use the NRSRAPID readout mode. Table 18 lists the observation parameters for each target brightness.

Since the NIRSpec spaxels are 0.1 arc sec across, they do not Nyquist sample the PSF. We thus generate a nine-point small grid dither for each target observation, with the goal of reconstructing a Nyquist sampled image. To ensure adequate signal to noise for each dither position, we allocate 3 h for each target and calibrator observation and assume a single observing roll angle. As we did for NIRCam and NIRISS, we find the maximum number of groups (ng) that can be included in an integration before saturation. We then split the observations up into nine sets (one for each dither) of nint integrations, each of which has an associated frame-time overhead. Table 6 lists the relevant detector and noise parameters, and 18 lists the observing parameters for each target star magnitude.

Table 5

OSIRIS noise and detector parameters.

λcaμm2.175
λ/Db (pix)2.24
Sc (mag/arcsec2)11.2
ZPd (mag)25.1
DCe (e/pix/s)0.035
RNf (e)11.0
WDg (DN)33,000
gh (e/DN/DN)4.35

a

Central wavelength in microns.

b

Detector PSF sampling in pixels.

c

Sky background in magnitudes per square arc second.

d

Zero point in magnitudes for Strehl = 1.0.

e

Dark current in electrons per pixel per second.

f

Read noise in electrons per pixel.

g

Well depth in counts.

h

Gain in electrons per count.

Table 6

NIRSpec noise and detector parameters.

λcaμm4.07
λ/Db (pix)1.29
DCc (e/pix/s)0.0092
RNd (e)6
WDe (DN)60,000
gf (e/DN)1

a

Central wavelength in microns.

b

Detector PSF sampling in pixels.

c

Dark current in electrons per pixel per second.

d

Read noise in electrons per pixel.

e

Well depth in counts.

f

Gain in electrons per count.

We use the first nine available pointings in the NIRSpec SMALL CYCLING pattern to create a simulated small grid dither. We assign the flux at each pixel in each undersampled image to the angular coordinates located at the center of that pixel. We then use a linear interpolation to assign fluxes to the angular coordinates at the centers of the pixels in the Nyquist sampled image (which have sizes of 0.03). Figure 7 shows example undersampled and interpolated images, compared to a simulated Nyquist sampled PSF. This interpolation does not account for the spatial extent of each pixel; using a more sophisticated interpolation scheme may improve the results. We also note that up to 60 pointings can be used in the CYCLING pattern, and having more pointings may improve the reconstructed PSF quality. Since the PSF reconstruction is imperfect and some signal is lost on the highest spatial frequencies, we do not include the longest baselines in the kernel phase projection model. This makes the number of observable kernel phases 18. This modified projection degrades the kernel phase effective resolution, but decreases the noise significantly (see Fig. 8). Figure 29 shows kernel phase histograms for targets with L band brightnesses of 6 and 11 magnitudes.

Fig. 7

(a) Undersampled and interpolated simulated NIRSpec images, with (b) a simulated Nyquist sampled PSF for comparison. The bottom right panel shows the radial profiles for the Nyquist sampled (black, thin line), and the interpolated (purple, thick line) PSF. While similar large-scale changes are seen in both, the interpolated image does not have the same small-scale variations as the Nyquist sampled PSF.

JATIS_5_1_018001_f007.png

Fig. 8

(a) Simulated NIRSpec power spectrum of an interpolated Nyquist sampled image, displayed on a log scale to highlight the features at high spatial frequencies. The hollow circles show the (u,v) sampling points we use to calculate kernel phases. Their histogram is shown in purple in (b). The red x’s show the (u,v) points that would have been used for a perfect Nyquist sampled observation, but that we omit from the kernel phase model to reduce the observed scatter. The black histogram shows the kernel phases calculated for a point source when these (u,v) points are included in the kernel phase model. The standard deviations of the purple and black histograms are 1.1 deg and 5.2 deg, respectively.

JATIS_5_1_018001_f008.png

3.

Results: Contrast Curves and Planet Detection Limits

3.1.

NIRC2

As a check, we compare the contrast curves for real Keck NRM observations of PSF calibrators to those for simulated observations with the same target star brightness and exposure parameters. The L target star magnitude is 5.8, and the observation consists of a single cube of twenty 20-s images. The results are shown in Fig. 9; the contrast curves are nearly identical.

Fig. 9

Contrast curves for a single target observation made from (a) real L NIRC2 NRM observations and (b) simulated observations. The contrast curves are nearly identical, with 5σ contrast of >5.5 magnitudes.

JATIS_5_1_018001_f009.png

Figure 10 compares the simulated NIRC2 contrast curves for NRM and kernel phase at two representative target brightnesses: apparent magnitudes of 6 and 11. The sixth magnitude case represents the contrast-limited regime for Ks and L; comparing the NRM and kernel phase contrast curves here shows that kernel phase performance degrades at low Strehl. Kernel phase can achieve comparable contrast to NRM in the bright limit at high (0.85) Strehl. This is evident in the observed kernel phase scatter (see Fig. 24)—the calibrated scatter is much lower for NRM observations at Ks band, but they are comparable at L. When NRM and kernel phase are both in the contrast limit, NRM provides slightly higher contrast very close to the core of the PSF (i.e., within 80 mas or λ/D for the L M*=6.0 contrast curves).

Fig. 10

Kernel phase (thick lines) and NRM (thin lines) for (a) Ks, (b) L, and (c) Ms bands. Solid purple lines show observations of 6th apparent magnitude stars, while black dashed lines show 11th apparent magnitude stars.

JATIS_5_1_018001_f010.png

The L contrast curves for the M*=11 star, and all of the Ms contrast curves demonstrate kernel phase and NRM’s different behaviors with the same sky brightness. The NRM PSF is spread over more pixels than the filled-aperture PSF. Thus, contrast degrades more quickly with an increasing sky brightness for NRM observations. This is also apparent in the kernel phase histograms (see Fig. 25); the raw scatter in the L and Ms observations is larger for NRM than for kernel phase. Furthermore, calibration decreases the L kernel phase scatter more significantly for filled aperture observations than for NRM observations. This shows that random noise dominates the NRM observations at lower sky background levels compared to filled-aperture observations.

The contrast as a function of stellar apparent magnitude supports these points. Figure 11 shows this: at Ks, the achievable contrast is constant with stellar brightness, and higher for NRM than for kernel phase. At L, the kernel phase observations stay close to the contrast limit until an apparent magnitude of L9, while NRM degrades more quickly. Both techniques degrade quickly at Ms, although kernel phase provides higher achievable contrast.

Fig. 11

The colorscale shows the 5σ single companion contrast for NRM (top) and filled-aperture kernel phase observations (bottom), as a function of target star apparent magnitude and angular separation. Ks, L, and Ms bands, respectively. Gray-shaded regions are regions of the parameter space where no companion model was significant at the 5σ level, compared to the null (single point source) model. The gray-dotted lines show 1 magnitude increments in companion contrast.

JATIS_5_1_018001_f011.png

We convert our 5σ contrast curves to hot-start planet mass limits using DUSTY models,33 and to planet mass times accretion rate limits using circumplanetary accretion disk models.3,4 For the DUSTY models, we assume an age of 1  Myr, since the apparent magnitude range we explore corresponds to the absolute magnitudes of 2  Myr old stars with masses ≲  5M25 at the distance of Taurus (140  pc8). For the circumplanetary accretion disk models, we assume full disks with an inner disk radius of 2 Jupiter radii.3 Figures 12 and 13 show the planet and accretion disk limits, respectively, for a range of separations and stellar absolute magnitudes assuming a distance of 140 pc. Depending on the stellar magnitude, both NRM and kernel phase at Ks and L can reach planet masses of a few to a few tens of Jupiter masses, or planet masses times accretion rates of a few times 106 to 105  MJ2yr1.

Fig. 12

Five σ planet mass limits using 1 Myr DUSTY models (solid lines) for all NIRC2 bandpasses and both techniques. The color scale shows the 5σ absolute companion magnitude, calculated using the contrasts shown in Fig. 11 and by translating the stellar apparent magnitudes to absolute magnitudes at 140 pc. Gray-shaded regions are regions of the parameter space where no companion model was significant at the 5σ level, compared to the null (single point source) model. The gray-dotted lines show 1 magnitude increments in absolute companion magnitude. The changing noise regimes (OPD error dominated to random error dominated) in the L and Ms NRM simulations cause the achievable contrast to fall off nonuniformly as the target brightness changes (see Fig. 11, upper center and upper right panels). This causes local regions in the L and Ms stellar magnitude—separation parameter space to be better suited for detecting lower planet masses (see upper center and upper right panels here, colorscale and contours).

JATIS_5_1_018001_f012.png

Fig. 13

Five σ circumplanetary accretion disk (planet mass times accretion rate) limits (solid lines) for all NIRC2 bandpasses and both techniques. The color scale shows the 5σ absolute companion magnitude, calculated using the contrasts shown in Fig. 11 and by translating the stellar apparent magnitudes to absolute magnitudes at 140 pc. Gray-shaded regions are regions of the parameter space where no companion model was significant at the 5σ level, compared to the null (single point source) model. The gray-dotted lines show 1 magnitude increments in absolute companion magnitude. The changing noise regimes (OPD error dominated to random error dominated) in the L and Ms NRM simulations cause the achievable contrast to fall off nonuniformly as the target brightness changes (see Fig. 11, upper center and upper right panels). This causes local regions in the L and Ms stellar magnitude—separation parameter space to be better suited for detecting lower planet masses times accretion rates (see upper center and upper right panels here, colorscale and contours).

JATIS_5_1_018001_f013.png

In the bright limit, L NRM and L kernel phase are both sensitive to lower planet masses and accretion rates than Ks NRM. For fainter stars (tenth apparent magnitude or fifth absolute magnitude), Ks NRM outperforms L NRM due to the higher sky background at L. However, for these stellar brightnesses, L kernel phase performs best. Despite brighter expected fluxes for hot-start planets at Ms, the high sky background prevents the detection of planets less massive than 10  MJ. We note that these mass limits look worse for older planets, and for models other than hot-start models. For example, the “warm-start” absolute magnitudes predicted by Spiegel and Burrows34 are not detectable even for 1 Myr old 10  MJ planets with either technique and at any bandpass.

3.2.

JWST: NIRCam Kernel Phase and NIRISS Aperture Masking Interferometry

Figure 14 shows representative contrast curves for M*=6.3 and M*=11.3 apparent magnitude stars for NIRCam and NIRISS. Again, in the bright limit (M*=6.3), NRM outperforms kernel phase within λ/D (150 mas), by 0.5 to 1.0 magnitudes. At larger separations, kernel phase provides comparable contrast. The faint M*=11.3 mag contrast curves show that at lower signal-to-noise, NIRCam kernel phase can provide higher contrast than NRM on NIRISS. Figures 26 and 27 support this. The raw and calibrated kernel phase scatters for NIRCam and NIRISS are comparable in the bright case, but in the faint case, the NIRCam kernel phases calibrate to a lower noise level than the NIRISS kernel phases. This is apparent in Fig. 15, which shows that NIRISS’s contrast falls off as the stellar apparent magnitude becomes >9, but NIRCam’s contrast does not. We also note that for apparent magnitudes <6 to 6.5, NIRCam is at its saturation limit and thus kernel phase cannot be used.

Fig. 14

NIRCam kernel phase (thick lines) and NIRISS NRM (thin lines) for (a) F430M and (b) F480M bands. Solid purple lines show observations of 6.3 apparent magnitude stars, while black dashed lines show 11.3 apparent magnitude stars.

JATIS_5_1_018001_f014.png

Fig. 15

The colorscale shows the 5σ single companion contrast for (a) NIRISS NRM and (b) NIRCam filled-aperture kernel phase observations, as a function of target star apparent magnitude and angular separation. The gray-dotted lines show 1 magnitude increments in companion contrast. The top and bottom panels show F430M and F480M bands, respectively. Gray-shaded regions are regions of the parameter space where either no companion model was significant at the 5σ level, compared to the null (single point source) model, or regions where the target magnitude was below the bright limit.

JATIS_5_1_018001_f015.png

Figures 16 and 17 show the 5σ planet and circumplanetary accretion disk limits for a range of stellar absolute magnitudes and angular separations. The absolute magnitudes were calculated assuming a distance of 140 pc. The greater stability of JWST leads to higher contrast than that achieved with NIRC2, making lower mass planets and lower accretion rates more accessible for brighter stars. Planet masses of 1  MJ are detectable for more than half the stellar absolute magnitudes in the hot-start case, and for the high stellar absolute magnitudes in the warm-start case for NIRCam. The range of detectable planet masses times accretion rates reaches below 107  MJ2yr1. Comparing the top and bottom panels of Figs. 16 and 17 shows that, with NIRISS NRM in the bright limit (Mabs≲ 2 to 3), slightly lower mass (accretion rate) planets can be detected at smaller angular separations. The maximum detectable absolute planet magnitude is higher for NIRCam, as a result of the improved contrast for fainter stars; this is particularly useful for detecting planets that have formed via nonhot-start scenarios.

Fig. 16

Five σ planet mass limits using 1 Myr DUSTY models (solid lines) and 1 Myr warm-start Spiegel and Burrows (2012) models (dashed lines) for the F430M and F480M bandpasses and both techniques/instruments. The color scale shows the 5σ absolute companion magnitude, calculated using the contrasts shown in Fig. 15 and by translating the stellar apparent magnitudes to absolute magnitudes at 140 pc. The gray-dotted lines show 1 magnitude increments in absolute companion magnitude. For clarity, since the 1 Myr warm-start models are tightly clustered in absolute magnitude, we only contour the 1  MJ model. Warm-start planets with masses <10  MJ are only detectable in the NIRCam observations for high stellar absolute magnitudes. Gray-shaded regions are regions of the parameter space where either no companion model was significant at the 5σ level, compared to the null (single point source) model, or regions where the target magnitude was below the bright limit.

JATIS_5_1_018001_f016.png

Fig. 17

Five σ circumplanetary accretion disk (planet mass times accretion rate) limits (solid lines) for all NIRC2 bandpasses and both techniques. The color scale shows the 5σ absolute companion magnitude, calculated using the contrasts shown in Fig. 15 and by translating the stellar apparent magnitudes to absolute magnitudes at 140 pc. The gray-dotted lines show 1 magnitude increments in absolute companion magnitude. Gray-shaded regions are regions of the parameter space where either no companion model was significant at the 5σ level, compared to the null (single point source) model, or regions where the target magnitude was below the bright limit.

JATIS_5_1_018001_f017.png

3.3.

Keck OSIRIS

Figure 18 shows the achievable kernel phase contrast for OSIRIS as a function of Ks stellar apparent magnitude for the central wavelength bin in the Kn3 bandpass (λ=2.175  μm). Contrasts of 5 magnitudes are detectable at the 5σ level. This is lower than the achievable contrast for NIRC2 at broadband Ks, and the calibrated kernel phase scatter is also higher for OSIRIS (see Fig. 28) for target stars with the same brightness. This may be due to the fact that a single OSIRIS wavelength bin has 1700 times lower throughput than NIRC2: random noise sources from the sky and detector may be a more significant noise source for OSIRIS, degrading contrast.

Fig. 18

The colorscale shows the 5σ single companion contrast for OSIRIS kernel phase observations as a function of target star apparent magnitude and angular separation. The gray-dotted lines show 1 magnitude increments in companion contrast.

JATIS_5_1_018001_f018.png

Figures 19 and 20 translate these contrast limits to planet mass limits as a function of stellar absolute magnitude. We again assume a distance of 140 pc. With OSIRIS, planet masses of 5 to 20  MJ are detectable for stellar absolute magnitudes >2. Warm start models with masses <10  MJ are not detectable. Planet masses times accretion rates of 105  MJ2yr1 are detectable for the fainter stars (Ks10; MKs5). We note that these detection limits would be worse for the shortest wavelength bin (λ=2.121  μm) and better for the longest wavelength bin (λ=2.229  μm) due to the wavelength dependence of the Strehl ratio.

Fig. 19

Five σ planet mass limits using 1 Myr DUSTY models (solid lines) for OSIRIS kernel phase. The color scale shows the 5σ absolute companion magnitude, calculated using the contrasts shown in Fig. 18 and by translating the stellar apparent magnitudes to absolute magnitudes at 140 pc. The gray-dotted lines show 1 magnitude increments in absolute companion magnitude.

JATIS_5_1_018001_f019.png

Fig. 20

Five σ circumplanetary accretion disk (planet mass times accretion rate) limits (solid lines) for OSIRIS. The color scale shows the 5σ absolute companion magnitude, calculated using the contrasts shown in Fig. 18 and by translating the stellar apparent magnitudes to absolute magnitudes at 140 pc. The gray-dotted lines show 1 magnitude increments in absolute companion magnitude.

JATIS_5_1_018001_f020.png

3.4.

JWST NIRSpec

Figure 21 shows the achievable kernel phase contrast for JWST NIRSpec as a function of L stellar apparent magnitude for the central wavelength bin (λ=4.07  μm), and Fig. 29 shows example histograms of the raw and calibrated kernel phases. Contrasts of 5 magnitudes are detectable at the 5σ level for all target star magnitudes. Figures 22 and 23 translate these contrast limits to planet mass limits as a function of stellar absolute magnitude, assuming a distance of 140 pc. With NIRSpec, planet masses of a few MJ are detectable for stellar absolute magnitudes >4 to 5. Warm start models with masses <10  MJ are not detectable. Planet masses times accretion rates of 105  MJ2yr1 are detectable for all target star absolute magnitudes, and lower accretion rates a few times 107  MJ2  yr1 to 106  MJ2yr1 are detectable for stars with absolute magnitudes >5. We note that these detection limits would be worse for the shortest wavelength bin (λ=2.87  μm), partly due to lower Strehl, and partly due to the fact that the PSF is more poorly sampled in this wavelength bin. They would be better for the longest wavelength bin (λ=5.27  μm) where the Strehl is higher and the PSF is larger.

Fig. 21

The colorscale shows the 5σ single companion contrast for NIRSpec kernel phase observations as a function of target star apparent magnitude and angular separation. The gray-dotted lines show 1 magnitude increments in companion contrast.

JATIS_5_1_018001_f021.png

Fig. 22

Five σ planet mass limits using 1 Myr DUSTY models (solid lines) for NIRSpec kernel phase. The color scale shows the 5σ absolute companion magnitude, calculated using the contrasts shown in Fig. 21 and by translating the stellar apparent magnitudes to absolute magnitudes at 140 pc. The gray-dotted lines show 1 magnitude increments in absolute companion magnitude.

JATIS_5_1_018001_f022.png

Fig. 23

Five σ circumplanetary accretion disk (planet mass times accretion rate) limits (solid lines) for NIRSpec kernel phase. The color scale shows the 5σ absolute companion magnitude, calculated using the contrasts shown in Fig. 21 and by translating the stellar apparent magnitudes to absolute magnitudes at 140 pc. The gray-dotted lines show 1 magnitude increments in absolute companion magnitude.

JATIS_5_1_018001_f023.png

4.

Discussion

The contrast curves and derived planet mass/accretion rate limits for NIRC2, NIRCam, and NIRISS show that filled-aperture kernel phase is a viable alternative to nonredundant masking for high Strehl (0.8 to 9) observations. This corresponds to wavelengths redder than 3.8  μm for ground-based observations. At these wavelengths, the sky brightness is a lesser problem for kernel phase observations, since the NRM PSF is spread out over more pixels than the filled-aperture PSF. Space-based observations with a thermal background would also benefit from kernel phase for the same reason. The simulations demonstrated this: filled-aperture kernel phase provided lower noise levels and thus better planet mass/accretion rate limits for faint stars (apparent magnitude 8 mag for NIRC2 L, and apparent magnitude 9 to 10 for JWST NIRCam and NIRISS). For both Keck and JWST in the bright limit (apparent magnitude 6), kernel phase can achieve comparable contrast to NRM at separations outside λ/D. However, at angular separations within λ/D, nonredundant masking provided slightly higher contrast (0.5 to 1 mag) than filled-aperture kernel phase.

While NRM can provide slightly higher contrast close-in, the required integration times are much longer—a factor of 10 to achieve similar signal-to-noise as kernel phase. With limited observing resources, using kernel phase for stars that are faint compared to the thermal background would save time. This would be useful in the context of a large survey for young planets, since the two techniques can place similar constraints on (accreting) planet populations in the contrast limit, with kernel phase outperforming NRM when the sky background becomes significant. NRM’s better performance close to the PSF core in the contrast limit suggests that an intermediate case such as a redundant mask may be the ideal observing setup for carrying out faster observations without a loss in contrast in the bright limit.

The OSIRIS and NIRSpec simulations show that kernel phase on an IFS can reach contrasts of 5 to 6 magnitudes. This is an exciting mode for characterizing young planets at smaller angular separation than that typically achieved with an IFS. For fully formed planets, this will lead to better atmospheric constraints than possible with narrowband imaging.1 For accreting planets, it will help to distinguish between different formation scenarios: e.g., hot-start versus circumplanetary disk accretion.3,4,16 The single-bin contrast curves show that kernel phase on an integral field spectrograph is capable of simultaneous detection and characterization; individual wavelength bins can be treated independently.

The broadband simulations showed an improvement in both achievable contrast and planet mass/accretion rate limits at L compared to Ks. This suggests that a midinfrared integral field spectrograph would be particularly useful for planet characterization with these techniques. Arizona Lenslets for Exoplanet Spectroscopy (ALES)35 on the Large Binocular Telescope is a 3 to 5  μm integral field spectrograph with a nonredundant masking mode. ALES provides a spectral resolution of R20, and the nonredundant mask has six holes with a maximum baseline of 8 m in single-aperture mode, and 12 holes with a maximum baseline of 23 m in dual-aperture mode. ALES’ redder wavelength range should lead to higher contrast (and lower planet mass/accretion rate limits) compared to other ground-based integral field spectrographs. ALES has not yet been characterized for nonredundant masking or filled-aperture kernel phase observations; this will be the subject of future work.

Current ground-based observations can only reach planet masses of several Jupiter masses, and planet masses times accretion rates of a few times 106 to 105  MJ2yr1. Furthermore, the resolution limit of 8 to 10 m class telescopes means that they can only probe spatial separations of 10  AU in the near- to midinfrared. Both of these limits will improve as the next generation of extremely large telescopes comes online; building signal-to-noise on faint stars will take less time, and the factor of 3 boost in resolution will probe spatial scales of a few AU. The 23-m baseline dual-aperture Large Binocular Telescope can achieve similar resolution now and has an NRM mode, which has been demonstrated to work even without operational cophasing.18 NRM and kernel phase on LBT could produce ELT-like planet detections before the ELTs are operational and allow us to develop these tools for use on the next generation of telescopes.

Both NRM and filled-aperture kernel phase, applied on James Webb have the potential to expand the planet detection parameter space beyond that of ground-based observations. While JWST will not have higher resolution than current ground-based facilities, its greater stability will lead to lower kernel phase scatter and provide higher contrast. Furthermore, it will not have the same limitations on target star brightness as an AO-corrected telescope. These factors combined mean that JWST will detect and characterize lower mass/accretion rate planets than we can observe from the ground.

5.

Conclusions

We presented contrast curves for nonredundant masking and filled-aperture kernel phase on several broadband imagers and integral field spectrographs. The observations were simulated to carefully control noise sources, and when possible we used real observations to anchor our OPD prescription. The simulated contrast curves show that for high Strehl, kernel phase can perform comparably to or better than NRM outside of λ/D. The compactness of the kernel phase PSF makes it particularly well suited for low SNR observations where random noise sources dominate. In the contrast-limited regime, masking outperforms filled-aperture kernel phase by 0.5 to 1 magnitudes within the diffraction limit. This slightly lower contrast suggests that, in the bright limit, redundant masks may be a good compromise to reach high contrast with shorter exposure times than NRM.

Both NRM and kernel phase are capable of detecting giant, recently formed planets and accretion signatures from forming planets. Filled-aperture kernel phase applied on an integral field spectrograph will be capable of simultaneous detection and characterization, and will reach smaller separations than traditional IFS high-contrast imaging. Both techniques, applied on the next generation of adaptive optics systems and space- and ground-based observing facilities, will expand the planet detection parameter space in volume, semimajor axis, and contrast. This will greatly inform our understanding of planet formation and evolution.

6.

Kernel Phase Projection and Weighting

6.1.

Projection

We use the “Martinache” projection12 to calculate kernel phases; this forms orthonormal combinations of Fourier phases that eliminate instrumental phase. The projection is based on representing Fourier phases as linear combinations of pupil-plane phases:

(6)

ϕ=R1·A·ϕ+ϕ0,
where ϕ represents a vector of Fourier phases with length M, R is a diagonal matrix containing the redundancy of each kernel phase, A is a matrix that describes how pupil-plane phases (ϕ) are combined to create Fourier phases, and ϕ0 is a vector of Fourier phases that are intrinsic to the source. The kernel of R1·A, K,36 found using singular value decomposition, projects Fourier phases into kernel phases and eliminates the instrumental phase term, ϕ. We note that the kernel of A can also be used as a projection after multiplying Eq. (6) by R. We apply the kernel of R1·A, which has been used in previous studies.36 The matrix K is analogous to the closure phase projection in interferometric observations, but is not restricted to values of only 0, 1, and 1.

6.2.

Weighted Averaging

In interferometric observations, closure phases are calculated from bispectra, the product of three complex visibilities on baselines forming a triangle.10 When closure phases are calculated for a cube of images, the bispectra are averaged over the cube, and the phase of the average bispectrum is taken as the average closure phase.37 Averaging bispectra rather than phases has been demonstrated to perform better in noisy conditions.38 We thus generalize this form of vector averaging, which upweights higher signal-to-noise observations by including amplitude information in the average, from closure phase to kernel phase.

For each frame, for the i’th kernel phase, we calculate a complex quantity by taking a weighted product of complex visibilities:

(7)

j=1MVjKi,j,
where Ki,j is value in the i’th row and j’th column of the kernel phase projection matrix, j is the index that describes the M Fourier phases, and Vj is the j’th complex visibility, which has both amplitude and phase. The average kernel phase over a cube of nim images is then:

(8)

Arg(1nimk=1nimj=1MVjKi,j).
This ensures that the Fourier phases are combined using the weights contained in the matrix K, but that amplitude information is used to weight the kernel phases by signal-to-noise when averaging them over multiple frames. We checked that this weighting scheme performs similarly or better than averaging kernel phases themselves for individual frames, depending on the noise regime.

7.

Simulated Observation Planning

Tables 718 list the details of the simulated datasets for each instrument, bandpass, and observing mode.

Table 7

NIRC2 Ks NRM observation details.

Ks (mag)ancoaddsbnframescnditdtcoaddetexpfttotgnvisheffi
5.73877920.0453175491220.36
5.836621020.0502184491220.37
5.934871020.0553193491220.39
6.033291020.0603201491220.41
6.130331120.0703213491220.43
6.229121120.0753219491220.45
6.327831220.0803224491220.46
6.425841220.0904234491220.48
6.523991220.1012243491220.49
6.622471320.1105248491220.51
6.721151320.1205255491220.52
6.819981320.1305261491220.53
6.918331420.1455267491220.54
7.017431420.1556271491220.55
7.116241420.1707277491220.56
7.214801520.1907282491220.57
7.313931520.2057287491220.58
7.412921520.2257292491220.59
7.511841520.2509297491220.61
7.611101520.2709301491220.61
7.710081620.3012304491220.62
7.89411620.3262307491220.63
7.98611620.3612311491220.63
8.07931620.3964314491220.64
8.17351620.4317317491220.65
8.26721620.4768320491220.65
8.36151620.5257323491220.66
8.45661720.5716324491220.66
8.55191720.6279326491220.66
8.64771720.6876328491220.67
8.74381720.7533330491220.67
8.84031720.8231332491220.68
8.93691720.9035333491220.68
9.03371720.9941335491220.68
9.13091721.0887336491220.69
9.22831721.1933338491220.69
9.32581721.3138339491220.69
9.42371721.4346340491220.69
9.52171721.5714341491220.69
9.61981721.727342491220.7
9.71801721.9047343491220.7
9.81641722.0954344491220.7
9.91501722.2957344491220.7
10.01371722.5182345491220.7
10.11251722.7648346491220.7
10.21151822.9906344491220.7
10.31051823.2802344491220.7
10.4961823.5924345491220.7
10.5871823.9692345491220.7
10.6801824.3209346491220.7
10.7731824.74346491220.7
10.8661825.248346491220.71
10.9611825.6823347491220.71
11.0551826.3076347491220.71
11.1501826.9434347491220.71
11.2461827.5515347491220.71
11.3421828.2755348491220.71
11.4381829.1518348491220.71
11.5351829.9405348491220.71
11.61717220.647351491220.71
11.71717220.647351491220.71
11.81717220.647351491220.71
11.91717220.647351491220.71
12.01717220.647351491220.71
12.11717220.647351491220.71
12.21717220.647351491220.71
12.31717220.647351491220.71
12.41717220.647351491220.71
12.51717220.647351491220.71
12.61717220.647351491220.71
12.71717220.647351491220.71

a

Target apparent magnitude.

b

Total number of coadds per visit.

c

Total number of frames per visit.

d

Total number of dithers per visit.

e

Integration time per coadd.

f

Exposure time per visit.

g

Total observing time (including overheads) per visit.

h

Number of science target visits in one half night.

i

Observing efficiency (exposure time divided by total observing time).

Table 8

NIRC2 Ks KP observation details.

Ks (mag)ancoaddsbnframescnditdtcoaddetexpfttotgnvisheffi
5.76975220.005136491220.07
5.86975220.005136491220.07
5.96975220.005136491220.07
6.06321420.010164491220.13
6.16321420.010164491220.13
6.26321420.010164491220.13
6.36321420.010164491220.13
6.46321420.010164491220.13
6.56321420.010164491220.13
6.65801520.015288491220.18
6.75801520.015288491220.18
6.85801520.015288491220.18
6.95801520.015288491220.18
7.05356620.0202108491220.22
7.15356620.0202108491220.22
7.24969720.0252125491220.26
7.34969720.0252125491220.26
7.44969720.0252125491220.26
7.54659720.0302141491220.29
7.64359820.0352154491220.31
7.74359820.0352154491220.31
7.84093920.0402165491220.34
7.93877920.0453175491220.36
8.036621020.0502184491220.37
8.136621020.0502184491220.37
8.234871020.0553193491220.39
8.331651120.0653207491220.42
8.430331120.0703213491220.43
8.529121120.0753219491220.45
8.626801220.0854229491220.47
8.725841220.0904234491220.48
8.823991220.1012243491220.49
8.922471320.1105248491220.51
9.021151320.1205255491220.52
9.119981320.1305261491220.53
9.218331420.1455267491220.54
9.317021420.1606273491220.56
9.415881420.1757279491220.57
9.514801520.1907282491220.57
9.613661520.2108288491220.59
9.712681520.2309293491220.6
9.811841520.2509297491220.61
9.910901520.2768302491220.61
10.010081620.3012304491220.62
10.19291620.3311308491220.63
10.28611620.3612311491220.63
10.37931620.3964314491220.64
10.47281620.4363318491220.65
10.56721620.4768320491220.65
10.66151620.5257323491220.66
10.75661720.5716324491220.66
10.85191720.6279326491220.66
10.94771720.6876328491220.67
11.04351720.7588330491220.67
11.14011720.8274332491220.68
11.23671720.9087333491220.68
11.33351721.0003335491220.68
11.43071721.0961336491220.69
11.52811721.2021338491220.69
11.62581721.3138339491220.69
11.72361721.4409340491220.69
11.82151721.5865341491220.69
11.91971721.736342491220.7
12.01791721.9156343491220.7
12.11641822.0821341491220.7
12.21501822.2811342491220.7
12.31371822.5023343491220.7
12.41251822.7474343491220.7
12.51141823.0173344491220.7
12.61041823.3122344491220.7
12.7951823.6307345491220.7

a

Target apparent magnitude.

b

Total number of coadds per visit.

c

Total number of frames per visit.

d

Total number of dithers per visit.

e

Integration time per coadd.

f

Exposure time per visit.

g

Total observing time (including overheads) per visit.

h

Number of science target visits in one half night.

i

Observing efficiency (exposure time divided by total observing time).

Table 9

NIRC2 L′ NRM observation details.

L′ (mag)ancoaddsbnframescnditdtcoaddetexpfttotgnvisheffi
5.717021420.1606273491220.56
5.816621420.1656275491210.56
5.915881420.1757279491220.57
6.015131420.1869283491220.58
6.114801520.1907282491220.57
6.214211520.2007285491220.58
6.313931520.2057287491220.58
6.413401520.2158289491220.59
6.513151520.2209290491220.59
6.612681520.2309293491220.6
6.712461520.2359294491220.6
6.812251520.2408295491220.6
6.911841520.2509297491220.61
7.011641520.256298491220.61
7.111461520.2608299491220.61
7.211271520.2661300491220.61
7.311101520.2709301491220.61
7.410711620.2806300491220.61
7.510711620.2806300491220.61
7.610541620.2859301491220.61
7.710381620.2911302491220.62
7.810231620.2961303491220.62
7.910081620.3012304491220.62
8.011531820.3205370568190.65
8.113862230.3245450675160.67
8.216392630.3202525771140.68
8.319703140.3147620900120.69
8.423303740.337691080100.71
8.528014550.3541992135080.73
8.633155460.34191133154370.73
8.739846470.33371329180060.74
8.847167780.34321618216050.75
8.9566993100.36412064270040.76
9.06815111120.4192855360030.79
9.18068134140.33842730360030.76
9.29699161170.45084372540020.81
9.311,660193200.3594186540020.78
9.413,808232240.6786937010,80010.87
9.516,600279280.5484910410,80010.84
9.619,956335340.4399877810,80010.81
9.723,991402410.3496838810,80010.78
9.824,711414490.335827810,80010.77
9.924,623413550.335824910,80010.76
10.024,302414550.34826210,80010.77
10.124,302414550.34826210,80010.77
10.224,302414550.34826210,80010.77
10.324,302414550.34826210,80010.77
10.424,302414550.34826210,80010.77
10.524,302414550.34826210,80010.77
10.624,302414550.34826210,80010.77
10.724,302414550.34826210,80010.77
10.824,302414550.34826210,80010.77
10.924,302414550.34826210,80010.77
11.024,004415540.345828110,80010.77
11.124,004415540.345828110,80010.77
11.224,004415540.345828110,80010.77
11.324,004415540.345828110,80010.77
11.424,004415540.345828110,80010.77
11.524,004415540.345828110,80010.77
11.624,004415540.345828110,80010.77
11.724,004415540.345828110,80010.77
11.824,004415540.345828110,80010.77
11.924,004415540.345828110,80010.77
12.024,004415540.345828110,80010.77
12.124,004415540.345828110,80010.77
12.224,004415540.345828110,80010.77
12.324,004415540.345828110,80010.77
12.424,004415540.345828110,80010.77
12.524,004415540.345828110,80010.77
12.624,004415540.345828110,80010.77
12.724,004415540.345828110,80010.77

a

Target apparent magnitude.

b

Total number of coadds per visit.

c

Total number of frames per visit.

d

Total number of dithers per visit.

e

Integration time per coadd.

f

Exposure time per visit.

g

Total observing time (including overheads) per visit.

h

Number of science target visits in one half night.

i

Observing efficiency (exposure time divided by total observing time).

Table 10

NIRC2 L′ KP observation details.

L′ (mag)ancoaddsbnframescnditdtcoaddetexpfttotgnvisheffi
5.74659720.0302141491220.29
5.84359820.0352154491220.31
5.94093920.0402165491220.34
6.04093920.0402165491220.34
6.13877920.0453175491220.36
6.236621020.0502184491220.37
6.336621020.0502184491220.37
6.434871020.0553193491220.39
6.533291020.0603201491220.41
6.631651120.0653207491220.42
6.730331120.0703213491220.43
6.829121120.0753219491220.45
6.927831220.0803224491220.46
7.025841220.0904234491220.48
7.124951220.0954238491220.48
7.223991220.1012243491220.49
7.323201320.1054245491210.5
7.421791320.1155252491220.51
7.521151320.1205255491220.52
7.619981320.1305261491220.53
7.719321420.1355262491220.53
7.818331420.1455267491220.54
7.917871420.1506269491220.55
8.017021420.1606273491220.56
8.116621420.1656275491210.56
8.215881420.1757279491220.57
8.315131420.1869283491220.58
8.414801520.1907282491220.57
8.514211520.2007285491220.58
8.613931520.2057287491220.58
8.713401520.2158289491220.59
8.813151520.2209290491220.59
8.912681520.2309293491220.6
9.012461520.2359294491220.6
9.112041520.2459296491220.6
9.211841520.2509297491220.61
9.311641520.256298491220.61
9.411461520.2608299491220.61
9.511271520.2661300491220.61
9.610901520.2768302491220.61
9.710711620.2806300491220.61
9.810541620.2859301491220.61
9.910541620.2859301491220.61
10.010381620.2911302491220.62
10.110231620.2961303491220.62
10.210891720.3182346540200.64
10.312882020.3302425635170.67
10.415482430.3116482720150.67
10.518302930.3104568831120.68
10.621993540.35467801080100.72
10.726024150.3307861120090.72
10.831275050.37021158154370.75
10.937006060.36711358180060.75
11.044477280.36941643216050.76
11.152648690.39992105270040.78
11.26327103110.45882903360030.81
11.37606124130.36572781360030.77
11.49004149150.49374445540020.82
11.510,824179180.39454271540020.79
11.613,012215220.7269945910,80010.88
11.715,409259260.5983921910,80010.85
11.818,523311320.4812891410,80010.83
11.922,268373380.3842855510,80010.79
12.024,768415450.335829710,80010.77
12.124,639413540.335825410,80010.76
12.224,623413550.335824910,80010.76
12.324,302414550.34826210,80010.77
12.424,302414550.34826210,80010.77
12.524,302414550.34826210,80010.77
12.624,302414550.34826210,80010.77
12.724,302414550.34826210,80010.77

a

Target apparent magnitude.

b

Total number of coadds per visit.

c

Total number of frames per visit.

d

Total number of dithers per visit.

e

Integration time per coadd.

f

Exposure time per visit.

g

Total observing time (including overheads) per visit.

h

Number of science target visits in one half night.

i

Observing efficiency (exposure time divided by total observing time).

Table 11

NIRC2 Ms NRM observation details.

Ms (mag)ancoaddsbnframescnditdtcoaddetexpfttotgnvisheffi
5.753304850.19731052154370.68
5.864075860.19151227180060.68
5.977027070.19351490216050.69
6.092608490.20631910270040.71
6.111,131101110.23962667360030.74
6.213,382121130.18682499360030.69
6.316,087145150.25484100540020.76
6.419,340175180.19933854540020.71
6.522,622210210.3976899510,80010.83
6.627,196252260.3179864510,80010.8
6.732,695303310.2517822910,80010.76
6.839,306364370.1966772910,80010.72
6.940,936379440.185757310,80010.7
7.040,725377530.185753410,80010.7
7.140,699377540.185752910,80010.7
7.240,699377540.185752910,80010.7
7.340,699377540.185752910,80010.7
7.440,699377540.185752910,80010.7
7.540,699377540.185752910,80010.7
7.640,699377540.185752910,80010.7
7.740,699377540.185752910,80010.7
7.840,699377540.185752910,80010.7
7.940,699377540.185752910,80010.7
8.040,699377540.185752910,80010.7
8.140,699377540.185752910,80010.7
8.240,699377540.185752910,80010.7
8.340,699377540.185752910,80010.7
8.440,699377540.185752910,80010.7
8.540,699377540.185752910,80010.7
8.640,699377540.185752910,80010.7
8.740,699377540.185752910,80010.7
8.840,699377540.185752910,80010.7
8.940,699377540.185752910,80010.7
9.040,699377540.185752910,80010.7
9.140,699377540.185752910,80010.7
9.240,699377540.185752910,80010.7
9.340,699377540.185752910,80010.7
9.440,699377540.185752910,80010.7
9.539,833379540.19756810,80010.7
9.639,833379540.19756810,80010.7
9.739,833379540.19756810,80010.7
9.839,833379540.19756810,80010.7
9.939,833379540.19756810,80010.7
10.039,833379540.19756810,80010.7
10.139,833379540.19756810,80010.7
10.239,833379540.19756810,80010.7
10.339,833379540.19756810,80010.7
10.439,833379540.19756810,80010.7
10.539,833379540.19756810,80010.7
10.639,833379540.19756810,80010.7
10.739,833379540.19756810,80010.7
10.839,833379540.19756810,80010.7
10.939,833379540.19756810,80010.7
11.039,833379540.19756810,80010.7
11.139,833379540.19756810,80010.7
11.239,833379540.19756810,80010.7
11.339,833379540.19756810,80010.7
11.439,833379540.19756810,80010.7
11.539,833379540.19756810,80010.7
11.639,833379540.19756810,80010.7
11.739,833379540.19756810,80010.7
11.839,833379540.19756810,80010.7
11.939,833379540.19756810,80010.7
12.039,833379540.19756810,80010.7
12.139,833379540.19756810,80010.7
12.239,833379540.19756810,80010.7
12.339,833379540.19756810,80010.7
12.439,833379540.19756810,80010.7
12.539,833379540.19756810,80010.7
12.639,833379540.19756810,80010.7
12.739,833379540.19756810,80010.7

a

Target apparent magnitude.

b

Total number of coadds per visit.

c

Total number of frames per visit.

d

Total number of dithers per visit.

e

Integration time per coadd.

f

Exposure time per visit.

g

Total observing time (including overheads) per visit.

h

Number of science target visits in one half night.

i

Observing efficiency (exposure time divided by total observing time).

Table 12

NIRC2 Ms KP observation details.

Ms (mag)ancoaddsbnframescnditdtcoaddetexpfttotgnvisheffi
5.720551320.1255258491220.53
5.819981320.1305261491220.53
5.919321420.1355262491220.53
6.018811420.1405264491220.54
6.118811420.1405264491220.54
6.218331420.1455267491220.54
6.318331420.1455267491220.54
6.417871420.1506269491220.55
6.517431420.1556271491220.55
6.617431420.1556271491220.55
6.717021420.1606273491220.56
6.817021420.1606273491220.56
6.917021420.1606273491220.56
7.016621420.1656275491220.56
7.119401720.1713332568190.58
7.222642020.1838416675150.62
7.327202430.1747475771140.62
7.432702830.1735567900120.63
7.539303440.17696951080100.64
7.645894150.1986911135080.67
7.755164950.18861040154370.67
7.866305960.18311214180060.67
7.979707070.18531477216050.68
8.093148490.20481907270040.71
8.111,197101110.23792664360030.74
8.213,460122130.18522493360030.69
8.316,180146150.25294093540020.76
8.419,450176180.19773846540020.71
8.523,382211220.3827894910,80010.83
8.628,109253260.3058859710,80010.8
8.733,791305310.2418817010,80010.76
8.839,525366370.1952771410,80010.71
8.940,936379440.185757310,80010.7
9.040,725377530.185753410,80010.7
9.140,699377540.185752910,80010.7
9.240,699377540.185752910,80010.7
9.340,699377540.185752910,80010.7
9.440,699377540.185752910,80010.7
9.540,699377540.185752910,80010.7
9.640,699377540.185752910,80010.7
9.740,699377540.185752910,80010.7
9.840,699377540.185752910,80010.7
9.940,699377540.185752910,80010.7
10.040,699377540.185752910,80010.7
10.140,699377540.185752910,80010.7
10.240,699377540.185752910,80010.7
10.340,699377540.185752910,80010.7
10.440,699377540.185752910,80010.7
10.540,699377540.185752910,80010.7
10.640,699377540.185752910,80010.7
10.740,699377540.185752910,80010.7
10.840,699377540.185752910,80010.7
10.940,699377540.185752910,80010.7
11.040,699377540.185752910,80010.7
11.140,699377540.185752910,80010.7
11.240,699377540.185752910,80010.7
11.340,699377540.185752910,80010.7
11.440,699377540.185752910,80010.7
11.540,699377540.185752910,80010.7
11.640,673377550.185752410,80010.7
11.740,673377550.185752410,80010.7
11.839,833379540.19756810,80010.7
11.939,833379540.19756810,80010.7
12.039,833379540.19756810,80010.7
12.139,833379540.19756810,80010.7
12.239,833379540.19756810,80010.7
12.339,833379540.19756810,80010.7
12.439,833379540.19756810,80010.7
12.539,833379540.19756810,80010.7
12.639,833379540.19756810,80010.7
12.739,833379540.19756810,80010.7

a

Target apparent magnitude.

b

Total number of coadds per visit.

c

Total number of frames per visit.

d

Total number of dithers per visit.

e

Integration time per coadd.

f

Exposure time per visit.

g

Total observing time (including overheads) per visit.

h

Number of science target visits in one half night.

i

Observing efficiency (exposure time divided by total observing time).

Table 13

NIRCam F430M observation details.

Ms (mag)aMODEbngcnintdng,remettot (S)feffg
6.3rapid254,65527000.5
6.4rapid254,65527000.5
6.5rapid254,65527000.5
6.6rapid254,65527000.5
6.7rapid336,43636000.67
6.8rapid336,43636000.67
6.9rapid336,43636000.67
7.0rapid427,32740500.75
7.1rapid427,32740500.75
7.2rapid427,32740500.75
7.3rapid521,86243200.8
7.4rapid521,86243200.8
7.5rapid618,21845000.83
7.6rapid715,615446280.86
7.7rapid715,615446280.86
7.8rapid813,663547250.87
7.9rapid912,145448000.89
8.0rapid1010,93148600.9
8.1rapid1010,93148600.9
8.2bright26993749090.91
8.3bright26993749090.91
8.4bright278408249840.92
8.5bright287287250400.93
8.6bright287287250400.93
8.7bright29643050820.94
8.8bright210575351160.95
8.9bright210575351160.95
9.0shallow45520551430.95
9.1shallow45520551430.95
9.2shallow46420451920.96
9.3shallow47352652260.97
9.4shallow47352652260.97
9.5shallow483036252500.97
9.6shallow49266652680.98
9.7shallow4102376252820.98
9.8shallow4102376252820.98
9.9medium86214352940.98
10.0medium86214352940.98
10.1medium871791553110.98
10.2medium881539453240.99
10.3medium881539453240.99
10.4medium891349453330.99
10.5medium810120153400.99
10.6deep86108253460.99
10.7deep86108253460.99
10.8deep87903253550.99
10.9deep8877553610.99
11.0deep8877553610.99
11.1deep89678753660.99
11.2deep810603853700.99
11.3deep811543853731.0
11.4deep812494653751.0
11.5deep813453653771.0
11.6deep8144181053791.0
11.7deep816363253821.0
11.8deep817340853831.0
11.9deep8193021453851.0
12.0deep8202861753861.0
12.1deep8202861753861.0
12.2deep8202861753861.0
12.3deep8202861753861.0
12.4deep8202861753861.0
12.5deep8202861753861.0
12.6deep8202861753861.0
12.7deep8202861753861.0

a

Target apparent magnitude.

b

Readout mode.

c

Total number of groups per integration.

d

Total number of ng length integrations in 90 min.

e

Additional groups (in one final shorter integration to finish a 90-min observing block).

f

Total integration time in 90 min.

g

Observing efficiency (rounded to 0.01).

Table 14

NIRCam F480M observation details.

Ms (mag)aMODEbngcnintdng,remettot (S)feffg
6.0rapid254,65527000.5
6.1rapid254,65527000.5
6.2rapid254,65527000.5
6.3rapid254,65527000.5
6.4rapid336,43636000.67
6.5rapid336,43636000.67
6.6rapid336,43636000.67
6.7rapid427,32740500.75
6.8rapid427,32740500.75
6.9rapid427,32740500.75
7.0rapid521,86243200.8
7.1rapid521,86243200.8
7.2rapid618,21845000.83
7.3rapid715,615446280.86
7.4rapid715,615446280.86
7.5rapid813,663547250.87
7.6rapid912,145448000.89
7.7rapid1010,93148600.9
7.8rapid1010,93148600.9
7.9bright26993749090.91
8.0bright26993749090.91
8.1bright278408249840.92
8.2bright287287250400.93
8.3bright287287250400.93
8.4bright29643050820.94
8.5bright210575351160.95
8.6bright210575351160.95
8.7shallow45520551430.95
8.8shallow45520551430.95
8.9shallow46420451920.96
9.0shallow47352652260.97
9.1shallow47352652260.97
9.2shallow483036252500.97
9.3shallow49266652680.98
9.4shallow4102376252820.98
9.5shallow4102376252820.98
9.6medium86214352940.98
9.7medium86214352940.98
9.8medium871791553110.98
9.9medium881539453240.99
10.0medium881539453240.99
10.1medium891349453330.99
10.2medium810120153400.99
10.3deep86108253460.99
10.4deep86108253460.99
10.5deep87903253550.99
10.6deep8877553610.99
10.7deep8877553610.99
10.8deep89678753660.99
10.9deep810603853700.99
11.0deep811543853731.0
11.1deep812494653751.0
11.2deep813453653771.0
11.3deep8144181053791.0
11.4deep816363253821.0
11.5deep817340853831.0
11.6deep8193021453851.0
11.7deep8202861753861.0
11.8deep8202861753861.0
11.9deep8202861753861.0
12.0deep8202861753861.0
12.1deep8202861753861.0
12.2deep8202861753861.0
12.3deep8202861753861.0
12.4deep8202861753861.0
12.5deep8202861753861.0
12.6deep8202861753861.0
12.7deep8202861753861.0

a

Target apparent magnitude.

b

Readout mode.

c

Total number of groups per integration.

d

Total number of ng length integrations in 90 min.

e

Additional groups (in one final shorter integration to finish a 90-min observing block).

f

Total integration time in 90 min.

g

Observing efficiency (rounded to 0.01).

Table 15

NIRISS F430M observation details.

Ms (mag)angbnintcng,remdttot (S)eefff
5.73520703152460.97
5.83819071552580.97
5.94217253152710.98
6.04615753152820.98
6.15014493152920.98
6.25513174653020.98
6.36111881353110.98
6.46710815453190.99
6.5739926553260.99
6.68090653320.99
6.7888235753390.99
6.89675553440.99
6.91066838353490.99
7.01166249753530.99
7.11275709153570.99
7.214051710153610.99
7.315347311253650.99
7.41684317353680.99
7.518439316953710.99
7.620235816553731.0
7.722132721453751.0
7.82432986753781.0
7.926627212953801.0
8.02922486553811.0
8.132022616153831.0
8.235120617553841.0
8.338518810153861.0
8.442217131953871.0
8.546315625353881.0
8.650814234553891.0
8.75571307153901.0
8.861111838353911.0
8.967010812153921.0
9.07359845153931.0
9.17999057153931.0
9.27999057153931.0
9.37999057153931.0
9.47999057153931.0
9.57999057153931.0
9.67999057153931.0
9.77999057153931.0
9.87999057153931.0
9.97999057153931.0
10.07999057153931.0
10.17999057153931.0
10.27999057153931.0
10.37999057153931.0
10.47999057153931.0
10.57999057153931.0
10.67999057153931.0
10.77999057153931.0
10.87999057153931.0
10.97999057153931.0
11.07999057153931.0
11.17999057153931.0
11.27999057153931.0
11.37999057153931.0
11.47999057153931.0
11.57999057153931.0
11.67999057153931.0
11.77999057153931.0
11.87999057153931.0
11.97999057153931.0
12.07999057153931.0
12.17999057153931.0
12.27999057153931.0
12.37999057153931.0
12.47999057153931.0
12.57999057153931.0
12.67999057153931.0
12.77999057153931.0

a

Target apparent magnitude.

b

Total number of groups per integration.

c

Total number of ng length integrations in 90 min.

d

Additional groups (in one final shorter integration to finish a 90-min observing block).

e

Total integration time in 90 min.

f

Observing efficiency (rounded to 0.01).

Table 16

NIRISS F480M observation details.

Ms (mag)angbnintcng,remdttot (S)eefff
5.73918581952610.97
5.84217253152710.98
5.94615753152820.98
6.05114211052940.98
6.15612941753030.98
6.26111881353110.98
6.36710815453190.99
6.4749793553270.99
6.5818946753330.99
6.6898143553390.99
6.7987395953450.99
6.81076774253490.99
6.91176195853540.99
7.012956111253580.99
7.1141514753620.99
7.21554679653650.99
7.31704266153680.99
7.418638912753710.99
7.520535311653741.0
7.622432312953761.0
7.724629415753781.0
7.827026812153801.0
7.929624425753821.0
8.032422322953831.0
8.135620321353851.0
8.239018533153861.0
8.342816914953871.0
8.446915425553881.0
8.5514141753891.0
8.656412828953901.0
8.761811717553911.0
8.867810661353921.0
8.97439741053931.0
9.08009048153931.0
9.18009048153931.0
9.28009048153931.0
9.38009048153931.0
9.48009048153931.0
9.58009048153931.0
9.68009048153931.0
9.78009048153931.0
9.88009048153931.0
9.98009048153931.0
10.08009048153931.0
10.18009048153931.0
10.28009048153931.0
10.38009048153931.0
10.48009048153931.0
10.58009048153931.0
10.68009048153931.0
10.78009048153931.0
10.88009048153931.0
10.98009048153931.0
11.08009048153931.0
11.18009048153931.0
11.28009048153931.0
11.38009048153931.0
11.48009048153931.0
11.58009048153931.0
11.68009048153931.0
11.78009048153931.0
11.88009048153931.0
11.98009048153931.0
12.08009048153931.0
12.18009048153931.0
12.28009048153931.0
12.38009048153931.0
12.48009048153931.0
12.58009048153931.0
12.68009048153931.0
12.78009048153931.0

a

Target apparent magnitude.

b

Total number of groups per integration.

c

Total number of ng length integrations in 90 min.

d

Additional groups (in one final shorter integration to finish a 90-min observing block).

e

Total integration time in 90 min.

f

Observing efficiency (rounded to 0.01).

Table 17

OSIRIS Kn3 KP observation details.

Ks (mag)anframesbnditctframedtexpettotfnvisgeffh
5.75725.99342491220.7
5.85326.51345491220.7
5.94827.27349491220.71
6.04428.01352491220.72
6.14128.66355491220.72
6.23829.41357491220.73
6.334210.61361491220.73
6.432211.32362491220.74
6.529212.58365491220.74
6.626214.13367491220.75
6.724215.38369491220.75
6.822216.85371491220.76
6.920218.62372491220.76
7.019219.64373491220.76
7.117222.05375491220.76
7.215225.1376491220.77
7.314226.95377491220.77
7.413229.09378491220.77
7.512231.58379491220.77
7.611234.53380491220.77
7.710238.06381491220.78
7.89242.38381491220.78
7.98247.78382491220.78
8.07254.73383491220.78
8.17254.73383491220.78
8.26263.99384491220.78
8.35276.95385491220.78
8.45276.95385491220.78
8.54296.4386491220.79
8.64296.4386491220.79
8.74296.4386491220.79
8.832128.81386491220.79
8.932128.81386491220.79
9.032128.81386491220.79
9.122193.63387491220.79
9.222193.63387491220.79
9.322193.63387491220.79
9.422193.63387491220.79
9.522205.31411514210.8
9.622218.17436540200.81
9.722248.17496600180.83
9.822265.82532635170.84
9.922285.67571675160.85
10.022333.89668771140.87
10.122363.56727831120.88
10.222398.17796900120.88
10.322439.08878982110.89
10.422488.179761080100.9
10.522548.171096120090.91
10.622548.171096120090.91
10.722623.171246135080.92
10.822719.61439154370.93
10.922719.61439154370.93
11.022848.171696180060.94
11.1221028.172056216050.95
11.2221028.172056216050.95
11.3221028.172056216050.95
11.4221298.172596270040.96
11.5221298.172596270040.96
11.6221748.173496360030.97
11.7221748.173496360030.97
11.8221748.173496360030.97
11.9222648.175296540010.98
12.0222648.175296540010.98
12.1222648.175296540020.98
12.2222648.175296540020.98
12.3222648.175296540020.98
12.4225348.1710,69610,80010.99
12.5225348.1710,69610,80010.99
12.6333563.1710,69010,80000.99
12.7333563.1710,69010,80010.99

a

Target apparent magnitude.

b

Total number of frames per visit.

c

Total number of dithers per visit.

d

Integration time per frame.

e

Exposure time per visit.

f

Total observing time (including overheads) per visit.

g

Number of science target visits in one half night.

h

Observing efficiency (exposure time divided by total observing time).

Table 18

NIRSpec observation details.

L′ (mag)angbnintcng,remdttot (S)eefff
6.62555910.5
6.72555910.5
6.82555910.5
6.92555910.5
7.02555910.5
7.13377840.66
7.23377840.66
7.33377840.66
7.442738910.74
7.542738910.74
7.65229450.79
7.75229450.79
7.861839880.82
7.961839880.82
8.0715610200.85
8.1813710410.87
8.2813710410.87
8.3912310520.88
8.4101110630.89
8.5111010740.9
8.6129310840.9
8.71471311060.92
8.8157611060.92
8.9176911170.93
9.0186311170.93
9.12051111270.94
9.222511270.95
9.32441511380.95
9.4274311380.95
9.52932411490.96
9.63231511490.96
9.7353611490.96
9.83923311600.96
9.94222711600.96
10.04721711600.96
10.1512911600.96
10.25615511700.97
10.36115011700.97
10.46714411700.97
10.57413711700.97
10.68113011700.97
10.78912211700.97
10.89811311700.97
10.91071411700.97
11.0111111810.98
11.1111111810.98
11.2111111810.98
11.3111111810.98
11.4111111810.98
11.5111111810.98
11.6111111810.98
11.7111111810.98
11.8111111810.98
11.9111111810.98
12.0111111810.98
12.1111111810.98
12.2111111810.98
12.3111111810.98
12.4111111810.98
12.5111111810.98
12.6111111810.98
12.7111111810.98

a

Target apparent magnitude.

b

Total number of groups per integration.

c

Total number of ng length integrations per small grid dither position.

d

Additional groups (in one final shorter integration to finish one observing block in a single small grid dither position).

e

Total integration time per dither position per target.

f

Observing efficiency (rounded to 0.01).

8.

Kernel Phase Histograms

Figures 2429 show example raw and calibrated kernel phase histograms for each instrument, bandpass, and observing mode.

Fig. 24

Histograms of raw (top) and calibrated (bottom) kernel phases for (a) Ks, (b) L, and (c) Ms band NIRC2 observations for a bright (sixth apparent magnitude) target star. Thick purple lines show filled-aperture kernel phases, while thin black lines show NRM kernel phases.

JATIS_5_1_018001_f024.png

Fig. 25

Histograms of raw (top) and calibrated (bottom) kernel phases for (a) Ks, (b) L, and (c) Ms band (center) NIRC2 observations for a faint (11th apparent magnitude) target star. Thick purple lines show filled-aperture kernel phases, while thin black lines show NRM kernel phases.

JATIS_5_1_018001_f025.png

Fig. 26

Histograms of raw (top) and calibrated (bottom) kernel phases for (a) F430M and (b) F480M band observations for a bright (sixth apparent magnitude) target star. Thick purple lines show NIRCam filled-aperture kernel phases, while thin black lines show NIRISS NRM kernel phases.

JATIS_5_1_018001_f026.png

Fig. 27

Histograms of raw (top) and calibrated (bottom) kernel phases for (a) F430M and (b) F480M band observations for a faint (11th apparent magnitude) target star. Thick purple lines show NIRCam filled-aperture kernel phases, while thin black lines show NIRISS NRM kernel phases.

JATIS_5_1_018001_f027.png

Fig. 28

Histograms of (a) raw and (b) calibrated kernel phases for simulated OSIRIS observations for bright (sixth apparent magnitude; top), and faint (11th apparent magnitude; bottom) target stars.

JATIS_5_1_018001_f028.png

Fig. 29

Histograms of (a) raw and (b) calibrated kernel phases for simulated NIRSpec observations for bright (sixth apparent magnitude; top), and faint (11th apparent magnitude; bottom) target stars.

JATIS_5_1_018001_f029.png

9.

Scaling Contrast Curves for Other Target Stars and Observing Parameters

Since we provided contrasts for a small range of target star brightnesses, here we discuss how to adapt them to other target stars and observing scenarios. If the amount of observing time per visit and number of visits is kept fixed, and the target star magnitude is decreased below an absolute magnitude of 6, for all observing modes presented here one would expect a similar contrast to the M*=6 case. This is because the M*=6 observations represent the contrast limit, where OPD and calibration errors dominate. However, for all target star brightnesses, increasing the number of (assumed independent) visits would increase the achievable contrast in the bright limit by a factor of Nvisits,new/Nvisits,old.

For the stars that are not contrast limited, e.g., for observing stars that are fainter than M*=11 to 12—if the observing time and number of visits were kept fixed, the contrast would decrease as the target star magnitude increased. Since the kernel phase signal-to-noise is proportional to Nphotons,target, the contrast would scale as fluxtarget,new/fluxtarget,old. However, the kernel phase scatter is also proportional to the square root of the number of sky background photons Nphotons,sky; for high enough target star magnitudes, eventually the background noise would dominate the kernel phases completely. This is already apparent in the upper regions of the Ms NRM and kernel phase panels in Fig. 11. If one were to scale the observing time per visit for stars not in the contrast limit, the contrast would increase as tvisit,new/tvisit,old, until the contrast limit is reached.

Acknowledgments

Steph Sallum is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under Award No. AST-1701489. The authors would like to acknowledge Zack Briesemeister and Jordan Stone for thoughtful conversations. An earlier version of this paper has been submitted as a SPIE conference proceeding for Astronomical Telescopes and Instrumentation: Optical and Infrared Interferometry and Imaging VI. The authors have no relevant financial interests in the paper and no other potential conflicts of interest to disclose.

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Biographies of the authors are not available.

© The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.
Steph Sallum and Andy Skemer "Comparing nonredundant masking and filled-aperture kernel phase for exoplanet detection and characterization," Journal of Astronomical Telescopes, Instruments, and Systems 5(1), 018001 (31 January 2019). https://doi.org/10.1117/1.JATIS.5.1.018001
Received: 2 July 2018; Accepted: 26 December 2018; Published: 31 January 2019
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