Simulating the performance of aperture mask designs for SCALES

The technique of high-contrast direct imaging enables the study and characterization of proto-planetary disks [1, 2] and relatively young, hot planets that are at large angular separations from their stars. It can provide spectroscopic data on systems that are inaccessible to study via the transit or radial velocity methods, i.e. systems that do not transit or that have very wide angular separations [3]. A number of new exoplanets have been discovered and studied with this method [4, 5], and it has also allowed inferences to be made about the overall exoplanet population [6]. The next generation of direct imaging instrumentation is expected to push detection limits and study a wider and more diverse population of planets, and will expand spectroscopic characterization capabilities.

SCALES, which stands for Slicer Combined with an Array of Lenslets for Exoplanet Spectroscopy, is an upcoming integral field spectrograph (IFS) that will operate from 2.0$\mu$m to 5.2$\mu$m and is expected to see first light at the W. M. Keck Observatory in 2025 [7] (also see Ref. 8 in these Proceedings). As the first facility-class IFS that will operate at wavelengths longer than 2.5$\mu$m, SCALES will expand the currently accessible population of directly imaged planets to cooler and lower-mass planets. The high contrast between planet and host star is a major challenge for direct imaging; SCALES reduces this issue somewhat by operating in the thermal infrared, a wavelength regime where planet-star contrast is less extreme and where planets and disks are relatively bright. SCALES improves upon the design of the Arizona Lenslets for Exoplanet Spectroscopy (ALES) instrument, which is housed at the Large Binocular Telescope Interferometer (LBTI), and which provided the first spatially resolved spectra of substellar companions in the thermal infrared [9].

Non-redundant aperture masking (NRM) is a technique that is relatively cheap and simple to implement and that can significantly increase spatial resolution at moderate contrast (5-8 magnitudes at $\lambda/D$, depending on the image quality of the individual setup), surpassing the diffraction limit [10, 11, 12, 13]. It consists of converting a telescope aperture into an interferometer by covering the aperture by an opaque mask with holes cut out. Typically this masking is done with a small mask in the instrumental pupil plane, often in a filter wheel. In a non-redundant mask, each pair of holes contributes uniquely to the Fourier transform of the fringes produced in the image plane, with no two baselines having the same length and angular position. In this work, we assess the performance of three different non-redundant aperture masks on SCALES. We utilize the Python-based scalessim software package¹¹1The scalessim package may be found at: https://github.com/scalessim/scalessim to simulate SCALES observations using each mask. We then produce closure phases and squared visibilities and use the SAMpy package [14] ²²2SAMpy can be downloaded at: https://github.com/JWST-ERS1386-AMI/SAMpy to generate contrast curves.

The design of sparse aperture masks that are fully non-redundant is challenging. Masks with large numbers of holes are difficult to produce, as are masks with large holes. This is due to the finite size of holes; a baseline between two holes can be chosen in more ways when the hole diameter is larger. Non-redundant masks with fewer or smaller holes are easier to design, although throughput is reduced. For these reasons, mask designs are frequently generated using computational methods [15, 10, 13].

Three mask designs were used in this study, with 9, 7, and 6 holes. These masks, as projected onto the Keck primary mirror, are shown in Fig. 1. To develop SCALES NRM simulation tools and as a first exploration of mask designs, the three masks were either chosen or modified from designs currently in use. The 9-hole mask design is currently in use in Keck/NIRC2. The 7- and 6-hole designs were modified from VLT SPHERE and LBT designs, respectively. The modifications were required in order to ensure that the holes do not overlap any mirror segment edges or spiders. Furthermore, several holes were adjusted in both in order to add longer baselines to the configuration and to ensure non-redundancy.

SCALES observations with each mask were simulated using the scalessim software. An observing scene was produced with a 10000K point source centered in the frame. A cube of PSFs was generated for each mask at oversampled spatial and spectral resolutions with respect to the SCALES low-resolution mode and was then convolved with the observing scene. The resulting cube was downsampled to coarser wavelength bins to match the SCALES low-spectral-resolution mode ($\lambda_{min}=2.0\mu$m, $\lambda_{max}=5.2\mu$m, $R<300$). A cube of raw images was then generated with an FOV of $2.2"$ x $2.2"$, spaxel plate scale of $0.02"$/pixel, and integration times of 1s and 3600s to simulate cases of short and long exposures. Ten frames were generated at each wavelength with random Poisson noise added. Further details about the scalessim data reduction pipeline are given in Ref. 16.

The Python-based SAMpy package was used to generate closure phases and squared visibilities. Closure phases for each mask, wavelength bin, and integration time simulated in this study are shown plotted versus average baseline length in Fig. 3. A supergaussian filter was applied to the SCALES frames to remove edge effects before these were calculated. The closure phases and squared visibilities were then calibrated as discussed in Section 3.1 and were used to generate contrast curves.

Fig. 3 shows the calibrated absolute closure phases, for each mask and wavelength bin, for each closure triangle as a function of average baseline length for that triangle. Integration times of 1s and 3600s are shown. The contrast curves generated using these closure phases are shown in Fig. 4 for a $5-\sigma$ confidence interval. These are calculated by comparing $\chi^{2}$ values between single companion models to the null model for each dataset. Mask performance in a given band can be assessed by the depth of their contrast curves. In the K and L bands, a modest improvement in contrast can be observed between the 6- and 9-hole masks. The 3600s integration time does not achieve significantly better contrast than 1s in these bands due to the noise being dominated by OPD evolution as opposed to the sky, although there is some visible improvement with longer integration in the L-band. The M-band shows significant sky noise that is considerably mitigated with a longer integration. This can also be seen in the reduced closure phase scatter of Fig. 3. The 6-hole mask appears to offer improved contrast over the 7- and 9-hole masks in the background limit; this could be due to the simpler 6-hole pattern producing overall larger fringes that stand out better from the sky background.

Designing fully non-redundant aperture masks that are optimized for direct imaging studies is a challenging process. In future work, we will systematically generate a larger, more diverse sample of masks to test with the SCALES mask simulation pipeline presented here. Varying parameters such as number and size of holes, geometry, and degree of redundancy will be explored. Attempts will be made to achieve uniform u-v snapshot coverage that may be optimized for different targets. For example, masks with a wide range of baseline lengths, including several long baselines, could perform better when imaging extended targets with complex spatial features than masks lacking long baselines. Additional methods of assessing mask performance will also be implemented, including by injecting and attempting to recover a variety of science targets (e.g., companions, disks, or both). This work will be continued with the eventual goal of designing and testing a non-redundant aperture mask that is suitable for integration with SCALES.