DISCO: a Spatio-Spectral Recombiner for Pupil Remapping Interferometry
Florentin Millour, Romain Petrov, Stéphane Lagarde, Philippe Berio, Yves Bresson, Lyu Abe
aa r X i v : . [ a s t r o - ph . I M ] M a r Improving the performances of current optical interferometers & future designsProceedings of Haute Provence Observatory Colloquium (23-27 September 2013)Edited by L. Arnold, H. Le Coroller & J. Surdej
DISCO: a Spatio-Spectral Recombiner for PupilRemapping Interferometry
F. Millour , R. Petrov , S. Lagarde , P. Berio , Y. Bresson ,L. Abe Laboratoire Lagrange, UMR7293, Universit´e de NiceSophia-Antipolis, CNRS, Observatoire de la Cˆote dAzur, Bd. del’Observatoire, 06304 Nice, France
Abstract.
Pupil-remapping is a new high-dynamic range imag-ing technique that has recently demonstrated feasibility on sky.The current prototypes present however deceiving limiting magni-tude, restricting the current use to the brightest stars in the sky.We propose to combine pupil-remapping with spatio-spectral en-coding, a technique first applied to the VEGA/CHARA interferom-eter. The result is an instrument proposal, called ”Dividing Inter-ferometer for Stars Characterizations and Observations” (DISCO).The idea is to take profit of wavelength multiplexing when usinga spectrograph in order to pack as much as possible the availableinformation, yet providing a potential boost of 1.5 magnitude ifused in existing prototypes. We detail in this paper the potentialof such a concept.
1. Introduction
The need for a better dynamic range in direct imaging techniques istoday identified as a top priority for the detection and characterizationof extrasolar planets. As an illustration, several high-dynamic rangeimaging instruments are currently being developed (notably: SPHERE,HICIAO or GPI / Beuzit et al., 2006; Tamura & Abe, 2006; Macin-tosh et al., 2006). These instruments make use of so-called ”Extreme-Adaptive Optics” (XAO) in order to make coherent (i.e. interfering)the highest number of photons in the resulting image.An other way existed before the advent of adaptive optics to get co-herent photons: speckle imaging (Labeyrie, 1970; Lohmann & Weigelt,1978) makes use of short-integration times to freeze the Earth’s atmo-sphere disturbance and take over its resolution-washing effect. However,1
F. Millour et al.the speckle technique and all of its derivatives (speckle masking, seg-ment tilting, lucky imaging, etc.) are bound to waste photons in a wayor in another. This is why pupil remapping was proposed by Perrinet al. (2006), to take profit of both fully coherent photons and full-pupilflux collection.Since the original idea was proposed, pupil remapping has evolvedfrom a pure concept up to a readily demonstrated instrument on-sky(Huby et al., 2012, 2013). The built prototypes have shown the greatpotential of this technique and also some limitations.Here, we propose an improvement over the pupil remapping con-cept as presented in Huby et al. (2012), in order to collect more photonsper pixel for a given setup. While this might sound useless for someapplications where pixels are ”cheap” (like in visible applications), IRwavelength detectors still have limitations on their detector readoutnoise, making each pixel valuable. A sketch of such an instrument ispresented in Fig. 1, which is similar to the proposal of Perrin et al.(2006). It differs mainly in the addition of short-stroke delay lines tocontrol the optical path difference (hereafter OPD) and in the outputpupil configuration, which is described in the next section.We will therefore briefly describe how do we plan to save on pixels,and present optimized OPD configurations to use in such an instrument.
2. A recall of the technique and proposal of a new scheme
In an all-in-one multi axial interferometer, several beams are combinedaltogether, coding the fringes by their frequencies. One baseline corre-sponds then to one spatial frequency (a ”fringe peak”) in the FourierTransform (FT) of the fringe pattern.It has long been theorized that only a fully non-redundant config-uration would allow one to extract the interferometric signal. Hence,several instrument were built on such a beam configuration: the AM-BER (Petrov et al., 2007), or MIRC (Monnier et al., 2004) combinerare a few examples.However, it was proposed in the first times of optical long-baselineinterferometry (Vakili & Koechlin, 1989), any more recently demon-strated on a wider scale with the VEGA instrument (Mourard et al.,2011), that a fully redundant configuration could also be used giventhat the fringes could be spectrally dispersed with a sufficient spectralresolution. In such a case, the fringe peaks of several baselines are atthe same spatial frequency, noted V pi in order to take the same nota-tion as in Mourard et al. (2011), making them totally cluttered in usualanalysis algorithms. However, they can be disentangled by inputting adifferent fixed OPD, which in turn allows one to change the peaks posi- patio-spectral recombination A possible setup for DISCO. Please note the similaritieswith the sketch in Perrin et al. (2006). The differing parts are theshort-stroke delay lines and the arrangement of fibers in the V groove,described in the current paper.
F. Millour et al.tions in the wavelength frequency domain, noted U pi in Mourard et al.(2011). A different approach for data analysis has to be used, withthe use of 2D FTs instead of 1D FTs, which is extensively describedin Mourard et al. (2011). An additional way of uncluttering the fringepeaks is to input an OPD modulation on groups of sub-apertures andto make use of 3-dimensional Fourier Transforms (the third dimensionbeing along time), as was proposed by Vakili & Koechlin (1989).We reproduce in Fig. 2 the 9 sub-apertures non-redundant outputpupil used in the FIRST instrument (Huby et al., 2012), and side toside, the output pupil of a fully redundant configuration. o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o oo o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o oo o o o o o o o oo o o o o o o o o Figure 2.:
On top is the output pupil of a fully redundant configuration.On the bottom is the non-redundant configuration used in the prototypeFIRST instrument.
Such a configuration saves a great deal of pixels compared to non-redundant configuration, with a given number of sub-apertures andspectral resolution. In the case of 9 sub-apertures, one can save a factor5, i.e. a direct ≈ .
3. Optimizing a spatio-spectral interferometer
Minimal condition
We recall the minimal condition on the number of spectral channels touse, given in Mourard et al. (2011, equation 13): N ch ≥ N tel (1) patio-spectral recombination R ≥ N tel λ ∆ λ (2)with λ the central wavelength of the observations, and ∆ λ theobservation bandwidth. For a 9 sub-apertures instrument, working inthe K band ( λ = 2 . µ m, ∆ λ = 0 . µ m), this imposes a minimumspectral resolution of ≈ N tel − N tel − N tel − ≈ Atmosphere and/or adaptive optics jitter
Another criterion to consider is the wobbling of the fringe peaks bynatural-atmospheric or adaptive optics-induced OPD. The peaks sepa-ration in the U direction must be greater than twice the atmosphericwobbling. If we consider the atmospheric OPD over Paranal which hasa peak overrun OPD max of typically 25 µ m (Tatulli et al., 2007), thismeans that two adjacent fringe peaks must be separated typically by50 µ m.This imposes conditions on the coherence length L c , that mustfollow the condition: L c ≥ × OPD max (3)or R ≥ × OPD max λ (4)So, still for the 9-telescope configuration example given above, theminimum spectral resolution to use would be ≈ F. Millour et al.use of adaptive optics prior to the input pupil (by reducing the OPDwandering from 25 µ m to less than 1 µ m), or the use of OPD modulationproposed in Vakili & Koechlin (1989) could strongly relax this constrain. Fringe peaks overlap
As was highlighted by J. Monnier during the conference, an overlap ofthe fringe peaks could occur due to the spectrum shape of the target.Two ways of overcoming this effect were presented in Mourard et al.(2011) by using differential measurements combined with either settinga minimal width of the work channel, or by solving a set of equationdescribing the peaks overlap.It is worth to mention that partial peaks overlap could also occur innon-redundant configurations, as happens in the AMBER instrument(Millour et al., 2004; Tatulli et al., 2007). The use of an image-basedalgorithm (the P2VM) solves this issue, and one could consider alsousing a 2D-image-based model-fitting algorithm, similar to the P2VM,to avoid the peaks contamination in our case.3.2 OPD offsets optimizationIn the literature, a few papers consider the problem of optimizing fre-quencies in an array. We can cite for example Moffet (1968); Vertats-chitsch & Haykin (1986); Ribak et al. (1988); Pearson et al. (1990)for aligned sub-apertures with or without some redundancy, and Golay(1971) for 2D optimization. However, we found no trace of spatio-spectral optimization, except in the two papers Vakili & Koechlin(1989); Mourard et al. (2011) where setups for specific configurationswere provided.In Mourard et al. (2011) are addressed the cases of 3 and 4 tele-scopes for the spatio-spectral instrument VEGA. In Vakili & Koechlin(1989) is presented an example with 12 telescopes. Since we discuss thepossibility to combine tens of sub-apertures for a potential full-pupil in-strument, we investigated the optimization of the spatio-spectral schemefor up to 64 sub-apertures, though we present here only a subset, up to30 sub-apertures.We considered for this optimization the minimization of the CDR,in order to separate the peaks at maximum. We define this new criterioninstead of using moment of inertia or other criteria defined in Golay(1971) because though we end up with 2D fringe peaks patterns, weaim at only optimizing one dimension (the OPD dimension).We made use of a Monte-Carlo approach similar as in Ribak et al.(1988), using a simulated annealing algorithm. Indeed, the number offringe peaks for a given configuration scales as N , so the number ofdistances between fringe peaks to optimize scales as N . Therefore patio-spectral recombination N tel − µ mfor an instrument working in the K-band ( λ = 2 . µ m, ∆ λ = 0 . µ m).We see that a even a moderate spectral resolution of ≈
160 can be usedto combine 9 telescopes.Table 1.: µ m) Beam N tel CDR R min Figure 3 illustrates the appearance of the 2D Fourier transform bymaterializing the positions of the fringe peaks for 3 to 9 sub-apertures.We also note that these given offset can be set as fixed OPDs, butcan also be set as fringe drift speeds, if one considers a fully redundantinterferometer with OPD modulation. In such case, instead of inputtingfixed OPDs and analyzing the data as a function of wavelength, onecan input OPD drifts with drifting speed proportional to the values inTable 1, and analyze the data as a function of time. The great advantageof this alternate solution is to allow for a broadband instrument to besetup. A detailed analysis of such a concept is out of the scope of thecurrent paper.3.3 avoiding zero OPDWe see in Fig. 3 that up to 6 fringe peaks can be exactly at OPD 0 (forthe 8 telescope configuration), which in some cases can be annoyingdue to the diffraction spike of the zero-frequency photometric peak. A
F. Millour et al. i V i Figure 3.:
The UV fringe peaks relative positions of the most compactoptimized OPDs of Table 1. way of overcoming such an issue is to input additional OPD offsetsto the ones provided here, which are proportional to the sub-aperturenumber. Such additional OPD offsets ”skew” the peaks position sketchshown in Fig 3 and move all the central fringe peaks away from thezero OPD. Such an additional offset degrades slightly the CDR of theconfiguration. For example, for sub-aperture, one would need to add tothe values of Table 1, OPD offsets of 4, 8, 12, 16, 20, 24, 28, 32 and 36 µ m on each sub-aperture, making none of the fringe peaks at the zeroOPD. The final CDR is 7.5 instead of 7.
4. Conclusions
We discussed the requirements and limitations of a spatio-spectral re-combiner, for a large number of sub-apertures.We found that 7 configurations exist with the most densely packedfringe peaks, allowing for relatively low spectral resolutions to be used.These revised configuration provide more densely packed fringepeaks than before, allowing for a gain in spectral resolution and there-fore in sensitivity of such an instrument concept.
Acknowledgements.