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Holographic Imaging: a Versatile Tool for High Angular Resolution Imaging

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Holographic Imaging: a Versatile Tool for High Angular Resolution Imaging Telescopes and Instrumentation Holographic Imaging: A Versatile Tool for High Angular Resolution Imaging Rainer Schödel1 also limited: the change of the incoming measure of the image quality and is Julien H. Girard2 wavefront as a function of the line of defined as the ratio between the peak sight leads to a rapid deterioration in the pixel in the normalised PSF and its theo- image quality at distances from the retical maximum value. It is 100% for 1 Instituto Astrofisica de Andalucia (CSIC), guide star larger than the isoplanatic a perfect image and ~ 1% for a seeing- Granada, Spain angle (nominally around 15 arcseconds limited image. Since turbulence is a 2 ESO at 2.2 μm, the K-band). These anisopla- statistical process, higher Strehl ratios natic effects can be partially compen- can be reached by selecting only the sated for by the use of multi-conjugated frames with the most compact, high Speckle holography can be used to AO (MCAO) systems and the use of multi- signal-to-noise PSFs. In recent years, this re construct high angular resolution ple (laser) guide stars, but at great cost technique, termed lucky imaging, has images from long series of short expo­ in instrumental as well as operational become popular at optical wavelengths, sures if the point spread function (PSF) complexity. In addition to, and independ- where AO is still challenging. Lucky from each frame can be measured reli­ ent of, these effects, various technical imaging suffers, however, from large ably. We show that through use of multi­ limitations make it difficult to calibrate the overheads because typically a large frac- ple reference stars and iterative PSF AO PSF ( Sivaramakrishnan et al., 2003; tion of the data (frequently > 90%) subtraction, we can obtain highly accu­ Lacour et al., 2011). Here, we show that must be discarded in the process. Since rate PSFs. The technique is optimised holography can in many situations offer the number of speckles increases ap­­ for crowded fields and results in images an attractive alternative to AO. It leads to proximately with the square of the tele- with excellent cosmetics and high Strehl high quality images, works with very faint scope aperture, lucky imaging becomes ratio from the optical to the mid­infrared (infrared) reference stars, and can com- extremely inefficient for telescopes with regimes. With examples from NACO, pensate anisoplanatic effects in crowded apertures of more than a few metres. VISIR, and HAWK­I we show that holo­ fields. Details on the experiments de­­ graphy opens up novel and unforeseen scribed here, as well as more analysis possibilities and can be an attractive and discussion can be found in Schödel Holography alternative to adaptive optics. et al. (2012). A more complex, but more efficient, algorithm than SSA is speckle hologra- In the past decade adaptive optics (AO) Speckle imaging phy, which makes use of the informa- assisted observations have become the tion and flux content of the entire speckle standard for obtaining images near the Before the maturity of AO, speckle imag- cloud of each frame, not just of the diffraction limit of large ground-based tel- ing was widely used to obtain diffraction- brightest speckle. This results in higher escopes. At the ESO Very Large Tele- limited images. It played, for example, a Strehl ratios and sensitivity. Efficiency is scope (VLT), the AO-assisted near-infrared key role in determining the proper motions boosted because frame selection be­­ (NIR) camera NAOS/CONICA (NACO) and orbits of stars near the massive black comes (largely) unnecessary. Holography has been in operation since 2002 with hole at the centre of the Milky Way, Sagit- allows one to reconstruct the best esti- spectacular success (see e.g., Lenzen et tarius A* (e.g., Eckart & Genzel, 1996). mate (in the least squares sense) of the al., 2003; Rousset et al., 2003; Girard Speckle imaging is based on recording astronomical object’s Fourier transform: 2 et al., 2010). Its AO capability can im­­ series of hundreds or thousands of O = <ImP*m>/<|Pm| > where O, Im and Pm prove the angular resolution in the NIR images with exposure times around 0.1 are the Fourier transforms of the astro- (viz. 1–5 µm), which is typically limited by seconds. In these frames stars appear as nomical object, of the m-th frame of the atmospheric turbulence, from the seeing, interference patterns or speckle clouds observed image and its instantaneous in the range 0.3–2.0 arcseconds, to (see Figure 1, left). Image reconstruction PSF, respectively (Primot et al., 1990). 0.03–0.15 arcseconds depending on the is performed a posteriori, for example The brackets denote the mean over the wavelength. with the simple shift-and-add (SSA) algo- total number of frames and the asterisk rithm: a different shift is applied to each the complex conjugate. The final recon- Despite its immense advantages, AO is frame so that the brightest speckle of the structed image is obtained after multipli- not a universal solution to the problem reference star always comes to lie at the cation of O with the telescope transfer of diffraction-limited imaging through the reference pixel. Finally, the shifted frames function (TTF), followed by an inverse Earth’s atmosphere. AO systems need are averaged. The PSF of the recon- Fourier transform. The TTF is usually an either a bright natural guide star, which structed image (Figure 1, middle) appears Airy function. The main difficulty in the seriously limits sky coverage, or a laser like a diffraction-limited core superposed application of holography lies in obtaining guide star (LGS), which entails some on a broad seeing halo. reliable estimates of the Pm. In the ideal additional image degradation because of case, the field contains a single, bright, the cone effect (i.e. the finite distance SSA was widely used because it is isolated reference star, whose speckle of the LGS reference from the source) easy to implement, fast and robust. How- cloud can be used to estimate the Pm, and tip-tilt anisoplanatism (elongation of ever, the achieved Strehl ratio is typically similar to the role of the guide star in AO. the PSF when the faint tip-tilt star is off- only around 10% in the K-band with an This situation is, however, very rare axis). The field of view (FoV) with AO is 8-metre telescope. The Strehl (ratio) is a and can be dealt with efficiently by AO. 26 The Messenger 150 – December 2012 Figure 1. Speckle imaging of the Galactic Centre with NACO. Left: Individual short exposure. Middle: Sim- ple shift and add (SSA) ǥ ǥ ǥ reconstruction. Right: Holographic reconstruc- #DB #DB #DB tion. The 11 reference l l l stars have 7 ≤ Ks ≤ 10 mag and are marked by l l l circles in the left panel. l l l l l l 1 ǥ 1 ǥ 1 ǥ Therefore holography has rarely been DIMM seeing ~ 0.5 arcseconds, coher- Sensitivity is, however, one aspect where used in practice. ence time τ0 = 2–3 ms). Figure 1 shows a AO clearly wins out over holography, speckle frame as well as an SSA and a where it is fundamentally limited by the Here we present a novel, game-changing holographic image reconstruction. While readout noise of the detector electronics. approach that allows us to use hologra- the Strehl of the SSA image is only ~ 9%, The point source detection limit is about phy even with faint guide stars in ex­­ the holographic image has a Strehl of 1.5 magnitudes deeper in the AO image tremely crowded fields. It is based on: ~ 82% and also excellent PSF cosmetics. (Ks ~ 20.5) than in the holography image (a) iterative improvement of the PSF; and (Ks ~ 19). This cannot be seen in Figure 2 (b) the (optional) use of multiple reference because the region shown is completely stars. Relative fluxes and positions of High quality images dominated by crowding. However, due to stars in the observed field can initially be the high PSF quality, holography can de­­ obtained from an SSA image (or from a A comparison between AO and holo- liver smaller astrometric and photometric previous holographic reconstruction). graphic imaging of a small region around uncertainties on bright sources than AO. Subsequently, preliminary PSF estimates Sagittarius A* is shown in Figure 2. Ide- can be obtained for each frame from the ally, the comparison has to be done Although holography is closely related to median superposition of multiple refer- between contemporary data taken under deconvolution techniques like Wiener ence stars, whose relative positions are similar conditions. In the absence of such filtering or Lucy–Richardson deconvolu- now known with sub-pixel precision. data, we try to stay on the conservative tion, it does not suffer the typical prob- Then, the preliminary PSFs can be used side and use one of the highest quality lems of those methods, like ringing, pho- to subtract all secondary sources near NACO GC datasets ever taken (31 March tometric biases, difficulties in dealing the reference stars that were detected in 2009, DIMM seeing ≤ 0.5 arcseconds, with ex­­tended emission, or creation of the SSA image. Finally, high accuracy τ0 ≈ 47 ms). The comparison underlines spurious sources. Holography is an en­­ values of Pm are obtained from a median the extraordinary image quality obtained tirely linear process, leads to well-behaved superposition of the reference sources with the holography technique. In addi- noise properties in the reconstructed from the cleaned frames. tion, also in Figure 2, we show a holo- images, and provides reliable photometry. graphic image reconstruction that has We use speckle data of the Galactic been obtained by using only the faintest Centre (GC) obtained with NACO’s cube stars (Ks ~ 13) as reference stars.
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