High-contrast, High-angular-resolution Optical Speckle Imaging: Uncovering Hidden Stellar Companions

Speckle interferometry as a technique for high-resolution optical imaging began in 1970 with the initial work of Labeyrie (1970). Using a coherent light source to analyze short exposure photographic images of the "speckle" patterns produced by starlight passing through the Earth's atmosphere, Labeyrie was able to show that such observations could remove the effects of seeing induced fluctuations due to distortions in the wave front and reach the diffraction limit of the telescope. This early work is highlighted in Gezari et al. (1972) and Labeyrie et al. (1974) who present observational results obtained at Mt. Palomar revealing resolved stellar disks and close binaries.

Numerous speckle interferometric studies have been performed since the early 1970's, using the better detectors of the day such as photomultiplier tubes, video tubes, and reticons (e.g., Bonneau & Foy 1980; Weigelt & Baier 1985; McAlister et al. 1987; Horch et al. 1992; Balega et al. 1993). Obtaining higher signal-to-noise ratio (S/N) digital values for the images, compared with photographic results, allowed for successful speckle image reconstructions using Fourier analysis and interferometric image reconstruction techniques. Bright binary stars have long been the primary speckle research activity over the years, with repeated imagery producing precise stellar orbits (e.g., McAlister et al. 1989). Many dozens of papers using speckle interferometry were written in the 1980's and 1990's and produced image reconstructions based on the original, decades old interferometric Fourier-type solutions originally suggested by Labeyrie (1970). Fourier-based image reconstructions are often enhanced today with the bispectrum technique developed by Weigelt (1977) and Lohmann et al. (1983).

Significant advances in astronomical detectors, in particular the higher quantum efficient charge-coupled devices (CCDs), provided a leap forward in this field, allowing for photon intensification, digital outputs, and higher S/N observations to be obtained (e.g., McAlister et al. 1989; Mason et al. 1997; Hartkopf et al. 2000; Horch et al. 2000). In recent years, the introduction of the electron multiplier CCD (EMCCD) as a detector (Tokovinin & Cantarutti 2008; Horch et al. 2011b) has been a game changer. With their ability for ultrafast readout, having essentially zero read noise, near perfect high quantum effeciency, optical flatness, and ease of use, EMCCDs have revolutionized speckle imaging. Fainter astronomical targets can now be observed (Howell et al. 2021a), the overall data quality and S/N of the observations are greater, and the final reconstructed images have more fidelity (e.g., Howell & Furlan 2022).

This renaissance in speckle imaging has led to the development of new dedicated speckle instruments (e.g., Pedichini et al. 2016; Clark et al. 2020; Howell et al. 2021b), a broadening of the observational science goals, and the placement of such instruments on the worlds largest telescopes (Horch et al. 2012; Wooden et al. 2018; Howell et al. 2021a; Scott et al. 2021). Speckle work is no longer limited to just bright star astrometry but has expanded into many areas of point source and nonpoint source imagery providing astrophysical information (e.g., Salinas et al. 2020; Scott et al. 2021; Shara et al. 2022). IR/adaptive optics (AO) systems typically reach ∼007 resolution at the K band and often use some type of occulting disk or coronagraph to block out bright starlight in order to achieve high contrasts and search for close, faint companions. Speckle imaging does not need any starlight suppression and routinely reaches an inner working angle near the diffraction limit of the telescope (e.g., 002 at 600 nm for an 8 m; Lester et al. 2021).

A second major advance of the past few years is the development of new software techniques for speckle image reconstruction. The analysis of a series of images with distorted wavefronts (i.e., speckle images) can be approached as a deconvolution problem. Jefferies & Hart (2011) and Hope et al. (2022) have pioneered wave front deconvolution techniques to better estimate the atmospheric distortions and produce high-quality image reconstructions. Multiframe blind deconvolution (MFBD) is a postprocessing technique using software algorithms to approximate what deformable mirrors and feedback loops do in IR/AO systems, however it is far less costly to implement. MFBD is especially useful in the optical bandpass where observations will yield higher angular resolutions.

This paper examines current speckle imaging using EMCCD detectors on 8 m class telescopes, the analysis of these data using our implementation of Fourier interferometric techniques (Howell et al. 2011; Horch et al. 2015), and the MFBD algorithms for image reconstruction. We will show that by using MFBD techniques, robust milestones in achieved contrast levels and the accuracy of the flux ratios are reached using current instrumentation on the Gemini 8 m telescope. Contrasts of ≥10⁻³ (8 mag) at the diffraction limit are achieved, flux ratio accuracy of ±0.03 mag are obtained, and truly diffraction limited images can be produced. All the Gemini 8 m 'Alopeke speckle data used in this paper is publicly available at the NASA Exoplanet Archive. ⁵

Speckle imaging performed in the optical bandpass (0.35–1.0 μm) provides the highest angular resolution available today on any single telescope, delivering 2–4 times better angular resolution than IR/AO observations at the K band. Speckle imaging with large (4–8 m) ground-based telescopes routinely observe stars from very bright to as faint as R = 16+ and obtain contrasts near 5 mag at 02 and ∼8 mag near 10 (Howell et al. 2016, 2021c). Today, for observations performed on 8 m class telescopes under superb observing conditions we find that the angular resolution meets or can exceed the diffraction limit (Horch et al. 2012) and achieved contrasts can be large (Hope et al. 2019; Howell & Furlan 2022).

Speckle imaging of a target requires many thousands of short exposures (10–60 ms, depending on the wavelength-dependent atmospheric coherence time; that is, the observing night conditions) to be obtained and processed. A large number of images are required in order to build up sufficient S/N especially at contrasts greater than 10⁻³ at very close angular separations. While this number of images seems daunting in terms of observing time, at tens of milliseconds per image, typical speckle observations last only a few to a few tens of minutes per target (Hope et al. 2019; Howell et al. 2021c). A recent summary of speckle imagers in astronomy was presented in Scott et al. (2021).

2.1. Speckle Data Reduction and Image Reconstruction

Nearly all currently used speckle image reconstruction software packages are based on Fourier speckle interferometric (SI) methods (see Labeyrie 1970; Lohmann et al. 1983; Horch et al. 2015). The Fourier results presented in this paper are based on our implementation of Fourier methods as described in Howell et al. (2011) and Horch et al. (2012). Fourier speckle deconvolution techniques are computationally efficient but with the downside that they need additional observations or information about the point-spread function of the telescope convolved with the instrument in order to "calibrate" the restored object's spectral amplitudes. That is, for point source observations, an additional single ("PSF standard") star is often observed near in position and time to the target star. Sometimes this reference point source does not provide a very good match to the target point-spread function due to changing atmospheric conditions, color differences between the two stars, or the reference star is itself an unknown close binary.

Due to the nature of Fourier interferometric analysis the reconstruction, the background contrast limits achieved tend to be shallow close to the star, only reaching their full contrast depth near separations of ∼05 and beyond (see Howell & Furlan 2022, and Figure 1). It is also axiomatic that speckle interferometric Fourier reconstructions contain a 180° ambiguity (a ghost) for detected close companions. However, differentiating the correct companion star from its ghost is often solvable, with good data, using phase information and bispectrum analysis (Lohmann et al. 1983; see Figure 2).

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Of interest in this paper are the current highest resolution, deepest contrast speckle instruments available ('Alopeke and Zorro) on the Gemini 8 m telescopes in Hawaii and Chile (Scott et al. 2021; Howell & Furlan 2022). 'Alopeke and Zorro are identical dual-channel speckle instruments using EMCCD detectors which have very low noise, plate scales of 001 pixel⁻¹, and are capable of fast imaging. Speckle imaging using these instruments has been shown to produce an inner working angle at the diffraction limit (∼20 mas; Horch et al. 2012; Lester et al. 2021) and even some subdiffraction limit measurements have occurred under conditions of excellent seeing (Howell et al. 2021a). While the necessity of high S/N and good native seeing is crucial for such (sub)diffraction limited inner working angles, modern telescopes such as Gemini are at very good sites and routinely deliver native seeing under 05; a Fried atmospheric coherence length of r₀ ≃ 20 cm at 500 nm (Fried 1966).

A modern approach to speckle imaging image reconstruction is provided by MFBD (Jefferies & Christou 1993; Schulz 1993). The MFBD algorithm is an inverse problem assuming the convolution of the form i = O*PSF, where i equals the observed image, O is the true object, and PSF is the point-spread function. MFBD estimates both the object and the point-spread function (PSF) directly from the observations using computational reconstruction of the wave front. The use of MFBD provides greater S/N results than typical Fourier speckle reconstruction techniques, but its use for processing speckle data has not yet gained much traction in the astronomy community. The reason for this is mainly due to the high computational cost of the MFBD algorithm. A recent development to help speed up the process and yield even better image reconstructions is to provide high-quality initial wave front estimates to the MFBD algorithm in terms of the PSF shape and x,y location by using a "compact" version of the MFBD algorithm (i.e., CMFBD; Hope & Jefferies 2011; Hope et al. 2019, 2022). Figure 2 presents a comparison of the reconstructed images produced using the standard SI and the MFBD algorithms.

3.1. The Algorithm

The MFBD (see e.g., Jefferies & Christou 1993; Schulz 1993) process proceeds as follows. For each speckle data frame, we compute the signal-to-noise of each Fourier component ($\tfrac{| {G}_{k}({\boldsymbol{u}})| }{{\sigma }_{N}}$); where ∣G_k ( u )∣ is the Fourier amplitude at spatial frequency u and the noise estimate σ_N is estimated from the data at spatial frequencies beyond the diffraction-cutoff frequency. At each spatial frequency, the maximum value of the S/N is determined and used to build a map of the maximum Fourier S/N obtained in each frame. The speckle images are then ranked by their Fourier S/N, where the "best" frames are the frames with the highest Fourier S/N. The advantage of our frame selection algorithm is that it finds the set of data frames that provide the highest S/N at all the sampled Fourier frequencies inside the cutoff frequency. This outcome is not guaranteed using an algorithm based purely on image sharpness such as that proposed by McCarthy & Cobb (1986).

To remove background light, such as the night sky or scattered from a nearby bright star, we take the pixels in the outer three columns and rows in each frame, ⁶ find the median value, and subtract this background value from each frame. We then take the best few tens to hundreds of frames, perform a shift and add, to yield good approximations of the bright target star x,y position. It is well known that the brightest speckle is not always at the center of the target PSF, thus we use an intensity weighted centroid technique when performing a shift and add on speckle images. We use the shift-and-add technique not as a method to find any close companions or provide any accurate representation of the object scene, it simply is an easy way to get starting priors on the approximate location and rough object shape for the bright target. In general, this operation will not reveal any faint companions, only an estimate of the bright star location and extent.

The reconstruction then follows a three-step process. In the first step, CMFBD is run on a set of the best frames which we call control frames (e.g., first 15 out of all 500 frames; see top left image in Figure 3) and initialized using the shift-and-add results. Only the pupil tips and tilts are sought, while the amplitudes are kept constant and assumed to be unity. The resulting PSFs are used as initialization for the rest of the frames in the data set (see top middle image in Figure 3). In the second step we perform a joint estimation of the object and all the PSFs on all the frames using full MFBD. The flux ratios for the companion(s) will not be completely accurate at this stage. In this step we only solve for the pupil phase component of the PSF (see top right image in Figure 3; Hope & Jefferies 2011). In the third step, we additionally solve for the pupil amplitudes, further improving the PSF model. The object estimate at the end of this procedure may contain "ring-like" or other low-level blobby structures close to the stars due to static aberrations in the instrument (see bottom image in Figures 3 and 2).

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Depending on the total number of frames being used, this full MFBD operation can take many hours up to a few days of computation time (using a modern Intel i9-10700 processor). The computation time can easily be reduced with current technology and in our future implementation, we plan to rewrite various algorithms to increase computational performance, make use of modern day software practices, examine trades such as compute every frame wave front versus average frames together and only compute every N wavefronts and interpolate, make use of higher speed CPUs, and invoke GPU processors. Such implementations would provide a factor of 50–100 times in speed up (e.g., see Nelson et al. 2020), bringing the MFBD analysis time per target into line with that of the current Fourier analysis

In general, any of the "ring-like" or blobby structures are not real features, but light from the stellar source that has not fully been integrated into the final PSF, that is, not perfectly modeled. An additional deconvolution can be run using the above PSF model to further refine the modeling and place the light from the erroneous structures back into the stellar PSFs. We note that with MFBD, any static component of the PSF (e.g., due to aberrations in the optical system) will be modeled as part of the object estimate. In the imperfect optical system case, an unresolved source which should reconstruct as a δ-function, will be blurred by a PSF whose morphology depends on the aberrations from the instrument's optics, and time-dependent parameters such as seeing, mechanical changes, and defocus. This additional "blurring" is clearly seen in Figure 2.

Figure 4 shows the object estimates after the removal of an instrumental PSF, including imperfections, for each observation. ⁷ Note that the 60 ms images shown in Figure 2 look "fuzzy" as they are the convolution of the pure diffraction limited point source images plus any atmospheric seeing changes, telescope motions (focus, wind, vibration, guiding) as well as the static optical abberations from "Alopeke itself. This "second deconvolution," shown in Figure 4, now yields near perfect diffraction limited images.

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3.2. Application of MFBD to Stellar Sources

One primary goal of high-resolution, high-contrast imaging techniques is to detect faint, angularly close companions to a primary target star. Using the new MFBD image reconstruction processing discussed above, the sensitivity and contrast of speckle imaging has been greatly improved. Contrasts of ≈10⁻²–10⁻³ ≈ 5–7 mag are routinely obtained beyond 035 using our standard Fourier reconstruction techniques with data collected on the 8 m Gemini telescopes. For a typical G0V star, this enables the detection of stellar companions down through the middle of the M-dwarf sequence (see Figure 5). The achieved contrasts are independent of the primary star spectral type (assuming the integration time has been adjusted for the apparent brightness of the target); if the primary star is of a later spectral type (e.g., K dwarf or M dwarf), the spectral interferometry contrast can reach further into later spectral types and even into the brown-dwarf regime (e.g., Howell et al. 2016). However, the typical Fourier achieved contrast is strongly dependent upon the separation from the primary star, decreasing to only ∼6 × 10⁻² ≈ 3 mag at 01—nearly 4 times the diffraction limit of the 8 m Gemini telescope.

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The new data reduction and image reconstruction technique described above achieves contrasts of 5 × 10⁻³ (8 mag) starting at essentially the diffraction limit of the telescope (see Figure 5). This improvement in angular resolution and contrast sensitivity over the Fourier techniques enables the detection of nearly 90% of the entire main sequence below a G0V primary star (Figure 5). Using a sufficient number of frames (i.e., long enough total integration time), the sensitivities could reach contrasts of ∼10⁻⁴ (9–10 mag), at separations of 004 or larger. The limiting inner working angle, shown as vertical line in Figure 5, represent the Rayleigh diffraction limit (1.22λ/D) at 825 nm for an 8 m telescope.

The traditional Fourier technique reaches a "flat" sensitivity level near separations of 04–05—separations where other measurement techniques, such as Gaia, can also play a role in companion detection. MFBD reaches near-full sensitivity almost immediately—near the wavelength defined full diffraction limit of the telescope. An example of the enhanced improvement is the faint companion detected for TOI-884, a stellar companion at 004—barely detected in original SI data reduction and easily detected with the MFBD reduction (Figures 2 and 5). The nearly constant sensitivity, starting near the physical diffraction limit of the telescope, enables a substantial increase in the detectable fraction of possible stellar companions.

A Monte Carlo simulation of the total fraction of binary companions expected from a Raghavan et al. (2010) companion distribution was performed to investigate the improvement that the new MFBD technique could yield. The Monte Carlo simulation takes into account the semimajor axis distribution and mass-ratio distribution expected for the local neighborhood population and compares that to the contrast curves from both SI and MFBD (Figure 5; Lund & Ciardi 2020). Because of the near-diffraction limited imaging and near-constant sensitivity, MFBD increases the companion detection rate by 30%–40% depending on the distance of the star from Earth—yielding a ≈90% detection rate of stellar companions to G-stars (Figure 6). The detection fraction is even higher as the primary star become lower in mass (K and M dwarfs).

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Optical speckle imaging has the advantage of darker skies (than the IR), no need for guide stars (natural or laser), far less expensive and complex instrumentation than IR/AO systems, and is easier setup and use. Speckle observations can be made from 400 to 1000 nm using CCD detectors, yielding a spectral energy distribution for any detected companion across the optical bandpass. Additionally, speckle imaging does not care if the target star is single or multiple, the observations and data reduction processes proceed in the same way. This is not an ability shared by coronagraphic instruments.

We have shown above that speckle imaging in the optical bandpass using currently available instruments on the Gemini 8 m telescopes, when reduced with our CMFBD/MFBD algorithms, can achieve contrast levels of 10⁻³ to ∼10⁻⁴ from near the diffraction limit out to 10 or more. MFBD provides the knowledge of the PSF from the data itself, ending the SI required need for additional observations of point source standards, thus increasing overall observing efficiency. Also the MFBD reconstructed images provide better flux ratios and astrometric information, allowing more precise astrophysical results. We have shown that optical speckle imaging can provide astronomers with a nearly complete census of solar-type main sequence binaries. Such an instrument would provide the highest angular resolution and deepest contrast levels available today in the optical bandpass and would open a new window in astronomical imaging.

The observations in this paper made use of the High-Resolution Imaging instrument 'Alopeke and were obtained under Gemini LLP Proposal Number: GN/S-2021A-LP-105. 'Alopeke was funded by the NASA Exoplanet Exploration Program and built at the NASA Ames Research Center by Steve B. Howell, Nic Scott, Elliott P. Horch, and Emmett Quigley. Alopeke was mounted on the Gemini North 8 m telescope of the international Gemini Observatory, a program of NSF's OIR Lab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. on behalf of the Gemini partnership: the National Science Foundation (United States), National Research Council (Canada), Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea). This research has made use of the NASA Exoplanet Archive and ExoFOP, which are operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. Additional information was obtained from the SIMBAD database, operated at CDS, Strasbourg, France. We acknowledge support from AFOSR awards FA9550-14-1-0178 (DAH and SMJ) and FA9550-21-1-0384 (SMJ).

Facility: - Gemini:Gillett, Gemini:South