Recommendations for crafting a NIRISS aperture masking interferometry mode (AMI) observing program are presented. This mode offers high spatial resolution imaging at 3.8, 4.3 and 4.8 μm for bright objects with ≈10^-4 binary contrast at separations of ~70–400 mas.

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The aperture masking interferometry (AMI) mode of NIRISS enables high-contrast imaging by turning the extremely redundant full aperture of JWST into a simpler and more calibratable interferometric array. Light admitted by 7 apertures in an otherwise opaque pupil mask interfere to produce an interferogram on the detector. AMI allows planetary or stellar companions that are up to ~9 magnitudes fainter than their host star and separated by 70–400 mas to be detected and characterized. AMI can also be used to reconstruct high resolution maps of extended sources, such as active galactic nuclei.

The AMI mode is enabled by a non-redundant mask (NRM) in the pupil wheel (PW), which is used in conjunction with one of 3 medium-band filters (F380M, F430M, F480M) or a wideband filter (F277W) in the filter wheel (FW).

NIRISS AMI observations can be read out in full frame mode or with the SUB80 subarray.

A target acquisition (TA) is required when using a subarray and strongly recommended for full frame readout to ensure that the target is always placed on the same detector pixel. Note the recommended TA mode for AMI observations as a function of target brightness near the bottom of the target acquisition article.

Details about the limiting contrast accessible by AMI are available on the HCI NIRISS Limiting Contrast observing techniques article. Advice for choosing proposal parameters, optimizing observation set-up, and designing efficient AMI proposals is given below.

Effects of charge migration in near-infrared detectors in the AMI mode

When 2 neighboring pixels accumulate charge at very different rates, the brighter pixel "spills" photoelectrons to its neighboring pixels, but the reverse effect does not occur. This charge migration causes the full width half maximum of the point spread function (PSF) to be larger for bright point sources compared to faint point sources (the so-called "brighter-fatter effect").

Lab testing and data from cryovacuum testing shows that this effect becomes pronounced in the NIRISS detector above 30,000 e^- in the bright pixel. This effect is mitigated in AMI observations by considering 30,000 e^- to be the effective saturation limit, which is lower than the true non-linearity based saturation limit for the NIRISS detector. Thus, the JWST Exposure Time Calculator will give a saturation warning message when this effective saturation limit is exceeded in the brightest pixel of the AMI PSF.

Choosing an optimal calibrator for a PSF reference star

Data analysis with the non-redundant mask (NRM) requires observations of the target and a point spread function (PSF) reference star. The PSF reference star is used to calibrate out instrumental contributions to the interferometric observables of closure phases (CP) and visibility amplitudes. Closure phases are the sum of the fringe phases from 3 holes. A closure phase must theoretically be zero for a point source (see Lawson 2000 and Monnier 2003 to learn more about these observables). The PSF reference star needs to be single, and of roughly the same magnitude (in the NIRISS filters used for the AMI observation) and spectral type as the science target. It is also best if the calibration star is relatively close to the science target on the sky, since changing the spacecraft attitude may change the temperature of the primary mirror segments slightly and thus affect the Fourier phases observed by the NRM.

Checking that the star is single is the most important factor. There are 2 web resources that allow one to check whether a star is single. First there is the list of single stars maintained by the U.S. Naval Observatory that should be checked to see if the proposed calibrator has been observed interferometrically and found to be single. The European equivalent is also useful for this check. If a star has not been checked by ground-based interferometry the next possibility is to see if there are HST observations, which provide the best possible angular resolution to resolve a companion. If the target is not present in these databases, then the remaining way to check for a possible companion is to look at the near-infrared spectral energy distribution to see if there is evidence of an excess that may be due to a fainter and cooler companion. (A hot companion such as a white dwarf star is unlikely to be bright enough compared to the primary star to be of concern at 3 to 5 μm.)

Observing calibrator(s) close in time to the target

Words in bold are GUI menus/
panels or data software packages;
bold italics are buttons in GUI
tools or package parameters.

Ideally, for higher contrast needs, science target and PSF reference star observations should be scheduled close in time, so that the telescope is in a similar state, thermal or otherwise, for all the observations. Also, they should be observed using the same telescope optical configuration, so no wavefront correction should occur between any of the observations.

In the Astronomers Proposal Tool (APT), this link between science target and PSF reference star observations is enforced by clicking on the Special Requirements tab, adding a Timing requirement of Group/Sequence Observations Link, selecting target(s) and calibrator(s) from the Observation list box and choosing the Non-interruptible option.

Target Acquisition

Target acquisition (TA) is required when using a subarray in the AMI mode and strongly recommended when using full frame readout. Two TA modes are offered: AMIBRIGHT, which uses the F480M filter crossed with the NRM in the pupil wheel for decreased throughput to observe bright acquisition stars, and AMIFAINT, which uses the F480M filter crossed with the CLEARP filter in the pupil wheel for increased throughput to observe faint acquisition stars. Users are advised to the the Exposure Time Calculator to determine the exposure parameters for their TA observations.

Although the target will be placed with high precision in the center of a pixel when doing a target acquisition, there will be shift in position in the science exposure due to filter-to-filter offsets. Figure 1 shows the measured PSF offsets by filter from commissioning observations after using the AMIBRIGHT mode. Offsets using the AMIFAINT mode have not been measured.

When using the AMIBRIGHT TA mode, users may wish to add an OFFSET special requirement in APT to place the target in the center of a pixel. The error can be reduced to ∼2 mas, the scatter around filter-specific offsets, if each filter is placed in its own observation, though this incurs additional overheads. This would enable filter-specific offsets to precisely place the target at the center of a pixel at the cost of observing efficiency. For example, to place a target in the pixel center for the F480M filter after using the AMIBRIGHT TA mode, a user can add an OFFSET special requirement of -0.0045 arcsec in X, +0.013 arcsec in Y. Alternately, a single OFFSET of +0.013 arcsec in Y (i.e., +0.2 pixels) applied to an observation using multiple filters would improve target centering overall. Note that here the units for the offsets are in arcsec in the ideal coordinate frame which is different from the science/DMS coordinate frame.

During commissioning, the offset between the peak of the target PSF and pixel center were measured after target acquisition, showing offsets from the pixel center that are filter dependent. To eliminate systematic errors in target placement, users may wish to add an **OFFSET** special requirement in APT to place a source in the pixel center using the plot above as a guide. This comes with additional observatory overheads. Alternatively, a single offset that reduces systematic target placement errors for the filters of interest can be set for all filters in one observation. This incurs no extra overhead. For example, an offset of +0.013 arcsec in Y (i.e., +0.2 pixels) reduces systematic errors for all filters. Note that these measurements only apply to observations where the **AMIBRIGHT** TA mode was used. Offsets with the **AMIFAINT** TA mode have not been measured. Adapted from Figure 5 in Sivaramakrishnan et al. 2022.

Exposure depth estimation for binary point source

The JWST Exposure Time Calculator (ETC) performs signal-to-noise ratio (SNR) calculations for the JWST observing modes. Sources of interest are defined by the user and assigned to scenes which are used by the ETC to run calculations for the requested observing mode.

For the purpose of this calculation, assume that the flux ratio for the target HD 218396 and the planetary companion we wish to detect is ~10^-4. According to Ireland (2013), the number of photons necessary to detect this contrast is:

1.5 x N_hole²/ (contrast ratio)², where N_hole refers to the number of apertures (holes) in a mask.

Since there are 7 apertures in the AMI NRM, this translates to:

73.5 / (contrast ratio)²

Considering the fact that NRM has not been used in space before, use a slightly more conservative value of:

100 / (contrast ratio)²= 100 / (0.0001)² = 10¹⁰

Therefore, the goal of our calculation is to detect 10¹⁰ photons from the target in the ETC simulations.

Estimating number of groups for an exposure

It is recommended to observe the maximum number of groups in an integration prior to the onset of "effective saturation," which is defined as the limit where charge begins accumulating on pixels that neighbor the central pixel when observing a point source (30,000 e^-). Observers should use the JWST Exposure Time Calculator (ETC) to determine this number, which is reported in the ETC Reports pane. The analytical calculations below are useful for estimating this threshold.

For each filter, analytical noiseless NRM PSFs were used in an aperture of side ~1" (79 × 79 pixels) to estimate N_Groups. This PSF can be simulated using the JWST PSF simulation tool WebbPSF (Perrin et al. 2014).

The number of photons per frame in the brightest pixel of the NRM PSF is:

(6)	$\begin{array}{l}\displaystyle cp\_e\_per\_frame = cpf \times count\ rate \times ph_{corr} \times t_{frame} \ ,\end{array}$

where cpf is the central pixel fraction; ph_corr (photometric correction) is the NRM throughput relative to the clear pupil, combined with the aperture correction for the 1" aperture; and t_frame is the frame time, which for the AMI observing mode using the SUB80 subarray is 0.07544 s.

Table 1 gives the values of the central pixel fraction (cpf) for each filter that can be used by the AMI mode, the NRM throughput relative to the clear pupil, and the zero points of the filters. These values can be used to calculate the maximum number of groups prior to effective saturation (N_{Groups sat}). The total number of photoelectrons in the central pixels in the entire exposure is:

(7)	$\begin{array}{l}\displaystyle cp_{tot} = cpf \times tot_p \ ,\end{array}$

where tot_p is the total number of requested photons in the NRM PSF.

Table 1. Parameters for estimating maximum number of groups for an AMI observation

Filter	CPF ^a	Photometric correction ^b (ph_corr)	Filter zero point^c (Vega)
F227W	0.0444	0.151	25.72
F380M	0.0262	0.148	23.43
F430M	0.0218	0.146	23.00
F480M	0.0179	0.145	22.88

^a CPF is the central pixel fraction, corresponding to the fraction of the total PSF flux in the brightest pixel. It is reported here for a 79 x 79 pixel field-of-view which is relevant to the SUB80 subarray used for most AMI observations..

^bNRM throughput relative to the clear pupil/aperture correction for a 79 x 79 pixel aperture.

^cNote that unlike the filter zero points reported in the NIRISS Filters article, these zero points do not include a loss of throughput due to the PAR in the CLEARP filter since these filters are crossed with the NRM for AMI observations. The loss of throughput due to the NRM is incorporated in the photometric correction factor. The filter zero points are in a magnitude system where Vega is the standard, where Vega has a magnitude of 0.0 in all filters.

Depending on the brightness of the source and the number of required photons needed to achieve science goals, there are 2 scenarios that determines N_{Groups sat}:

$\begin{array}{l}cp_{tot} < sat_e\end{array}$
This is usually the case for faint objects in which the required number of total photons is reached before the brightest pixel reaches effective saturation. In this case, N_{Groups sat} is:
(8) $\begin{array}{l}\displaystyle NGroups_{sat} = cp_{tot} / cp\_e\_per\_frame\end{array}$

This value will be the number of groups for the observation as long as it is less than the maximum number of groups allowed by APT (i.e., < 800). In this case, the observations has one integration.

If the number of groups exceeds 800, then more than one integration will be necessary to achieve the exposure time required to detect the necessary number of photons.
$\begin{array}{l}cp_{tot} > sat_e\end{array}$
In this case, saturation in an integration is reached before the requested number of photons are detected; therefore, an exposure with multiple integrations is needed.
The time to reach saturation is:
(9) $\begin{array}{l}\displaystyle T_{sat} = sat_e/(count\ rate \times ph_{corr} \times cpf)\end{array}$
and
(10) $\begin{array}{l}\displaystyle NGroups_{sat} = T_{sat} / t_{frame}\end{array}$

In addition to these 2 scenarios, there are 2 limiting cases:

Very bright sources: Saturation is reached in under one group (e.g., F480M, magnitude 2.41 source). This means the brightness limit for the filter is exceeded and some pixels may saturate.
Very faint sources: Number of integrations exceeds the maximum number of allowed integrations in an exposure (>10,000). Another observation can then be created to garner additional photons.

Analytically estimating number of groups: worked example

As a worked example for estimating the maximum number of counts analytically, the target of the AMI Example Science Program to observe HD 218396 (magnitude M = 5.26, Vega) using NRM and the F480M filter, is used. The goal of this program is to detect 10¹⁰ photons to achieve the desired contrast ratio. Charge migration, where charge accumulates in pixels neighboring the central pixel when observing a point source, occurs at 30,000 e^-, so this value is used as the saturation limit (sat_e).

Using equation (2) and Table 1:

$\begin{align} cp_{tot} = cpf \times tot_p \\ cp_{tot} = 0.0179 \times 10^{10} \\ cp_{tot} = 1.79 \times 10^{8}\ photons \end{align}$

Since cp_tot > sat_e, use equations (4) and (5) and Table 1 to find N_{Groups sat}:

$\begin{align} T_{sat} = sat_e / (count\ rate \times ph_{corr} \times cpf) \\ T_{sat} = 30000e^{-} / (10^{-(5.26 - 22.88)/2.5)}\ photons/s \times 0.145 \times 0.0179) \\ T_{sat} = 1.03\ s \\ NGroups_{sat} = T_{sat} / t_{frame} \\ NGroups_{sat} = 1.03 s / 0.07544 s \\ NGroups_{sat} = 14 \end{align}$

This value of N_{Groups sat} is calculated for a noiseless PSF and should be used only as an initial estimate. The actual value may be slightly lower than this value.

Recommended parameters for strategy choices for Exposure Time Calculator

When determining exposure parameters in the ETC, users can select the aperture radius from which the flux is extracted and the background subtraction method. The NIRISS AMI image has extended wings which can be used in data analysis. This aperture contains most of the AMI PSF flux. For the AMI mode, choosing noiseless skybackground is recommended because the extended PSF makes background subtraction difficult in AMI subarray data. The main noise contributors to AMI are systematics and photon noise. In any case, AMI analysis solves for any pedestal or background in the data.

For the aperture extraction radius, the following filter-dependent values for point sources are recommended:

Table 2. ETC aperture extraction radius for point sources

Filter	Radius (")
F277W	1.6
F380M	2.0
F430M	2.3
F480M	2.5

The ETC aperture radius defaults to the largest of these sizes, 2.5".

When to take a direct image

The photometry from the AMI observations is expected to be of similar accuracy to that achieved in regular imaging; the largest additional uncertainty in the AMI mode compared to normal imaging is the aperture corrections, as the PSF has more extended structure from the NRM than is present in normal imaging. A direct image may be useful as a check on the photometry and to see if there are other stars in the vicinity of the science target to aid in the data analysis. Note, however, that the regular imaging has a more restrictive bright limit than the NRM imaging, and this will be a limitation on the photometry for brighter objects. As a general guideline, any star bright enough to need to use the bright mode in acquisition is likely to also be too bright to be unsaturated in direct images.

ETC calculations for AMI do not include a direct imaging component. To run simulations for direct imaging, use the NIRISS imaging mode in ETC.

References

WebbPSF

Hirata, C. M., Choi, A. 2019, PASP 132, 1007 (ADS)
Brighter-fatter effect in near-infrared detectors – I. Theory of flat auto-correlations

Ireland, M. J. 2013 MNRAS 433, 2
Phase errors in diffraction-limited imaging: contrast limits for sparse aperture masking

Lawson P. R. 2000
Principles of Long Baseline Stellar Interferometry
Course notes from the 1999 Michelson Summer School, held August 15-19, 1999. Edited by Peter R. Lawson. Published by NASA, Jet Propulsion Laboratory, California

Monnier J. D. 2003, Reports on Progress in Physics, 66, 789
Optical interferometry in astronomy

Perrin, M. D., et al. 2014 Proc. SPIE 9143, 91433X
Updated point spread function simulations for JWST with WebbPSF

Sivaramakrishnan, A., Tuthill, P., Lloyd, J. P., et al., arXiv:2210.17434
The Near Infrared Imager and Slitless Spectrograph for the James Webb Space Telescope – IV. Aperture Masking Interferometry.

Latest updates	21 Nov 2022 Updated to add Figure 1 to show the target offset relative to TA location. Other Cycle 2 updates made. 16 Sep 2019 Included discussion of charge migration and recommended background and source aperture extraction sizes for ETC. 30 Apr 2018 Added note that users need to use ETC imaging calculations to derive exposure parameters for AMI direct imaging
Originally published	28 Nov 2017

JWST User Documentation

NIRISS AMI Recommended Strategies