Interferometric imaging tests for the Large Binocular Telescope

Astronomy and Astrophysics Supplement Series, Jul 2018

We present an experiment of interferometric imaging for the Large Binocular Telescope (LBT), conducted at the 1.5 m TIRGO infrared telescope. The raw data were produced by simulating the LBT pupil with a mask on the secondary mirror. Two different conditions of , where is the single aperture diameter and the Fried parameter, were simulated by the choice of ; field rotation was simulated by rotating the mask. The data set collected consists of several sequences of short exposure interferograms of one point-like and one binary star in the J-band, for two different conditions. We show preliminary results, in particular concerning the fringe contrast loss with integration time. The ability of a Lucy-Richardson-based deconvolution algorithm to reconstruct an object from a set of LBT-like interferometric real data was demonstrated on the binary star  Leo. The retrieved binary parameter values are compared to catalog values, and a good astrometric agreement is found. Photometric and resolution limitations are also discussed. In a first part, the reconstruction method and preliminary numerical simulations of LBT image restoration using this method are presented.

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Interferometric imaging tests for the Large Binocular Telescope

Astron. Astrophys. Suppl. Ser. Interferometric imaging tests for the Large Binocular Telescope? S. Correia 0 1 A. Richichi 0 1 0 Send o print requests to: S. Correia 1 Osservatorio Astro sico di Arcetri , Largo E. Fermi 5, I-50125 Firenze , Italy We present an experiment of interferometric imaging for the Large Binocular Telescope (LBT), conducted at the 1.5 m TIRGO infrared telescope. The raw data were produced by simulating the LBT pupil with a mask on the secondary mirror. Two di erent conditions of D=r0, where D is the single aperture diameter and r0 the Fried parameter, were simulated by the choice of D; eld rotation was simulated by rotating the mask. The data set collected consists of several sequences of short exposure interferograms of one pointlike and one binary star in the J -band, for two di erent D=r0 conditions. We show preliminary results, in particular concerning the fringe contrast loss with integration time. The ability of a Lucy-Richardson-based deconvolution algorithm to reconstruct an object from a set of LBT-like interferometric real data was demonstrated on the binary star γ Leo. The retrieved binary parameter values are compared to catalog values, and a good astrometric agreement is found. Photometric and resolution limitations are also discussed. In a rst part, the reconstruction method and preliminary numerical simulations of LBT image restoration using this method are presented. instrumentation; methods; data analysis | processing | techniques; telescopes | stars; imaging 1. Introduction The Large Binocular Telescope (LBT) will consist of two 8.4 m mirrors on a common mount. When the two mirrors are coherently cophased, this will work as a total baseline of 22.8 m. In several respects, observations with the LBT in this con guration will di er from those with more \conventional" interferometers. For example, LBT will o er a large eld of view, and will permit true imaging by simultaneously measuring all the Fourier components (Angel et al. 1998) . At the same time, the peculiar point spread function (PSF) and its rotation in the sky due to the alt-azimuthal mount, will require speci c data acquisition algorithms, and specialized treatment in the data reduction process. With these points in mind, we started a project to perform tests and develop relevant software. The aim was to investigate the process of image formation and reconstruction at the LBT, taking into account the characteristics of the atmosphere, the telescope performance and adding realistic estimates for the detector read-out noise (RON). Previously, at least two others groups of authors have already discussed LBT image reconstruction. However, only numerical simulations, based on di erent reconstruction techniques, have been carried out up to date. Reinheimer et al. (1997) have applied the so-called iterative building block method (bispectral analysis) to some point-like and extended objects. They presented a reconstruction method to apply to a speckle utilisation of LBT, with the known limitation in sensitivity of this observation mode. They complemented their simulations with a laboratory experiment. However, this latter was carried out under very favorable turbulence conditions (r0 = 2 m) and unspeci ed brightness of the source. Prior to this Hege et al. (1995) had explored the use of iterative blind deconvolution (IBD algorithm of Je eries & Christou 1993) , on simulated LBT images of an extended object. On the contrary, our work is based on real LBT-like data. In Sect. 2 we present the algorithm of reconstruction that we have used and modi ed. It is based on the Lucy-Richardson deconvolution algorithm (Richardson 1972; Lucy 1974) , widely used in standard image restoration methods. Section 3 shows the potential of this reconstruction technique on some preliminary tests performed on simulated point-like and extended objects. In Sect. 4 we present the experiment realized at the TIRGO observatory. The measurements allowed us to study some quantitative aspects concerning the process of image formation under low-order atmospheric degradation conditions (see Sect. 4.1). Section 4.2 shows the result of the application of the reconstruction method on LBTlike data from the TIRGO experiment. 2. The reconstruction method In this work, we used a Lucy-Richardson (LR) iterative algorithm adapted for multiple deconvolution, i.e. an algorithm based on the LR method that allows to retrieve full angular resolution images from LBT interferograms. This adaptation was rst developed and tested at the University of Genova (Bertero & Boccacci, in preparation) on simulated data made of one frame per orientation angle. From this code, we have implemented the possibility to add the information of more than one frame per orientation angle, i.e. to do a simultaneous deconvolution of a set of frames per orientation angle. This approach is useful when dealing with noisy and atmospheric-degraded data, in the case of the LBT-like data we have collected. The method yields the common maximum-likelihood estimate object from the full data set. Details of this algorithm are outlined hereafter. Let's denote f (x; y) the brightness distribution of the object, and hi(x; y) the PSF corresponding to the ith baseline position angle of the LBT interferometer. For each position angle, we observe the interferogram intensity gi(x; y) de ned by the object image convolution relationship: gi(x; y) = hi(x; y) f (x; y) + n(x; y) where n(x; y) refers to a spatially variant noise process. The original LR algorithm is a non-linear algorithm derived from Bayesian considerations, and based on the knowledge of the PSF. The principle consist in multiplying the result of each iteration by a correction factor Ck(x; y), with k denoting the iteration number, that relates to the remaining tting error. In standard LR image restoration, i.e. for i = 1, the iterative relation is the following: (1) (2) (3) to successive estimates f k(x; y) which are implicitly positive. Since di erent values of this constant do not lead to signi cant consequences in term of convergence rate, f 0(x; y) was xed to unity. Another interesting characteristic of this algorithm is the conservation of the total energy. It is also demonstrated (Shepp & Vardi 1982) that this relation leads to the maximum-likelihood object estimate, under the assumption of a Poisson process in image formation. In the multiple deconvolution case, i.e. for i > 1, we simply sum the contribution of each position angle at each iteration. The iterative scheme is identical to Eq. (2) only the correction factor is changed into: Ck(x; y) = Because of the normalization of each hi(x; y) to unity, H = N . The same approach is used when a set of frames per orientation angle gi;j (x; y) exists, with j denoting the position of the frame in the set. Adaptation of the algorithm to this leaves unchanged Eq. (2) and only modi es the correction factor as following: Ck(x; y)= H i=1 j=1 1 XN XM hi (−x; −y) gi;j (x; y) hi(x; y) f k(x; y) (6) where M is the number of frames per angle in the set. Note that the PSF may also be di erent, and therefore written as hi;j (x; y). But, concerning our data, we were not able to obtain a good knowledge of the corresponding PSF for each frame and therefore preferred a common PSF estimate. 3. Image simulation and reconstruction test In this section, we present the application of the reconstruction method of Sect. 2 to numerical simulations of LBT imaging, taking into account the telescope performance and adding realistic estimates for the detector. In a rst step, the construction of simulated interferometric observations was carried out using an ideally AO corrected PSF within the whole eld of view. In addition we considered perfect optics and co-phasing of the two pupils. The PSF's were therefore modeled as cosine-modulated Airy functions. In the near future we plan to obtain a more realistic PSF modeling by taking into account the attainable level of AO correction. The simulated interferometric observations, performed in R-band, were obtained as the convolution of the target with the f k+1(x; y) = f k(x; y) Ck(x; y) with Ck(x; y) = h (−x; −y) g(x; y) h(x; y) f k(x; y) where h (−x; −y) is the conjugate of h(−x; −y). With a positive constant estimate f 0(x; y), this algorithm leads Fig. 2. Same as Fig. 1 for a binary star with main component magnitude mR = 27:5 and mR = 2:5 PSF corresponding to each parallactic angle, adding sky-background emission. Independent Poisson noise realizations were then computed, and realistic detector RON added for each parallactic angle. In all simulations presented below, we assumed 1000 s integration time per parallactic angle, 30% e ciency (mirrors + optics + detector), a sky brightness of 20:80 mag=arcsec2 and a RON equivalent magnitude of 35:8 mag=pix. Since the large extension ( 3000 in R-band) of the foreseen AO corrected LBT eld, it will be theoretically possible to obtain a su ciently bright reference star in the eld for PSF calibration. Indeed the average density of stars with mv 21 is about 0.9 per sq arcmin at 90 galactic latitude, and almost ten times greater at lower galactic latitudes. Therefore the PSF's used in these restorations were assumed without noise-contamination. A few applications carried out on both point-like (binary star) and extended objects are presented hereafter. 3.1. Reconstructed images of binary star objects We have applied the reconstruction method to binary stars of di erent relative magnitude, and outlined effects of the SNR on both astrometric and photometric precision of the reconstruction. In the two examples presented here, we have chosen extreme magnitudes and magnitude di erences. Note that we have considered 4 equidistant parallactic angles (0 , 45 , 90 and 135 ), and each star was located on a pixel of the 64 64 pixels array, which leads, with the sampling of 4 pixels per fringe adopted, to a 0 0:010 eld of view. The separation of the binaries were xed to a value of 14.1 pixels, corresponding to 22.6 mas i.e. about 3 times the di raction angular resolution limit, and the orientation angle to 45 . The relative photometry was computed by measuring the peak pixel values of the reconstructed sources since the sources were initially located at integer pixel locations. In the rst case, mR = 1 and mR = 29 for the main component. This leads to an average peak SNR of only 5.5 for the simulated interferograms. If we do not consider fringe pattern overlapping between main star and companion, the peak SNR for this latter is only 2.2 (see Fig. 1). Concerning the reconstructed object, the binary location is fully retrieved, while we will comment separately on the photometric accuracy. In the second case, mR = 2:5 and mR = 27:5 for the main component. This leads to an average peak SNR of 11.3 for the simulated interferograms, and 1.1 for the companion. As in the rst case, the reconstruction leads to a fully retrieved \astrometric" position of the original object. The relative magnitude, after 1000 iterations, of the reconstructed object is 3.1, a good result when the di culty of detecting this faint companion in the noise level is considered (see Fig. 2). In both cases, we measured a magnitude di erence larger than the true magnitude di erence. We noticed however that this discrepancy was signi cantly reduced in tests with higher SNR. In Fig. 3, we show the variation of the photometric accuracy with iteration number. The residuals of the magnitude di erence appear to remain stable after several hundred of iterations in both cases. Note also that, even though the algorithm convergence takes place essentially in < 102 iterations (Fig. 4), the photometric accuracy seems to continue to improve, but this fact is only a consequence of performing photometry on the peak pixel. For the purpose of the present work, we were satis ed to verify this stability, and did not concern ourselves with a criterion to stop the iterations. In practical applications, the algorithm will be stopped according to the usual considerations on noise. 3.2. Reconstructed image of an extended object We also tested the ability of the algorithm to reconstruct images of extended objects from LBT interferograms. The target used here is an image of the spiral galaxy NGC 1288 rebinned in a 128 128 pixels array that, with the sampling adopted, corresponds to a eld of view of 00:020 in R-band. The image was apodized in order to avoid the e ect of edge discontinuities in the restoration. In this example, the reconstruction was based on simulated observations at 6 equidistant parallactic angles (0 , 30 , 60 , 90 , 120 and 150 ). With the 1000 s integration time assumed per parallactic angle, the total integration time is about 1.7 hours. The magnitude of the galaxy was set to mR = 19, which leads to approximately 2 107 photons per iterations 100 1000 Fig. 4. Variation of the error metric with iterations number for the mR = 29 − 30 binary (solid line) and the mR = 27:5 − 30 binary (dashed). Error metric is de ned as the sum, for all parallactic angles, of the Euclidian distance between the simulated interferogram and the convolution of the result with the PSF 0″.1 Fig. 5. Numerical simulation of interferometric imaging of an extended object with LBT. Top left: one of the observed interferograms of the 0 0:014 eld of view of a mR = 19 galaxy (parallactic angle = 30 ), obtained after an integration time of 1000 s. Bottom row shows the simulated target, un ltered (left) and band-pass limited to a 22.65 m perfect circular aperture (right). Top right: result of the algorithm for 6 interferograms of 1000 s integration time each after 150 iterations d long exposure image and a peak SNR of 80. One can notice the sharper aspect of the reconstructed galaxy shown in Fig. 5 with respect to the theoretical di raction-limited image. This is due to the behaviour of the algorithm in cases of high SNR. Also, a closer inspection shows that the nucleus does not appear as smooth as in the original picture. This is a consequence of the phenomenon of \noise ampli cation", which basically arises for such a maximumlikelihood deconvolution algorithm from the di erence of converging rate between extended objects and point-like features (White 1994) . For our aim, we did not concern ourselves with this problem, but di erent approaches concerning the solution of this drawback of the LR algorithm can be found in the literature (Lucy 1994; White 1994; Waniak 1997) . 4. Experiment at the TIRGO telescope In early 1998, we started an experiment at the 1.5 m TIRGO infrared telescope, with a mask simulating the pupil of the LBT telescope. The main idea was to record realistic LBT-like data by simulating the level of adaptive optics (AO) correction expected for LBT by the choice of the ratio D=r0 (where D is the diameter of one of the mask apertures projected on the primary and r0 the Fried parameter), in order to investigate the properties of the atmospheric parameters and study the process of image formation and reconstruction (Fig. 6). 4.2. Application of the reconstruction technique to real data: γ Leo An observing run, on the nights of 21 and 22 March 1998, permitted to collect a serie of measurements of one point-like and one binary star under two di erent values of the ratio D=r0 (Table 1). Actually, it can be noticed that the reduction in D=r0 obtained with the use of a mask (i.e., by making D smaller) is not equivalent to that expected from the use of adaptive optics on the real LBT (i.e., by making r0 larger). In fact, in our case the mask holes produce a rescaling of the frequencies in the turbulence power spectrum. The e ect of correction by adaptive optics, on the other hand, is not equal at all frequencies. But, for the aim of this experiment, these two corrections present enough similarities to be considered equal in rst approximation. In order to simulate the rotation of the LBT-like pupil function, i.e. the aperture synthesis by earth rotation, we recorded object interferograms at four nearly equidistant mask orientation angles by rotating the secondary mirror. The data were recorded in a broad band J lter at the 1.5 m TIRGO infrared telescope using the ARNICA camera (Lisi et al. 1996) which is equipped with a 256 256 pixels NICMOS 3 detector and presents a pixel size of 0 0:098. During the run, we made use of the fast read-out mode of a 32 32 pixels sub-array, developed for lunar occultations, which allows typical integration times of around 20 ms. A brief description of this mode can be found in Richichi et al. (1996) . We present below a summary of some of the data reduction results. The aperture size of the mask and the seeing conditions led, for this observation, to D=r0 = 0:84. In the following, we used mainly a data set of 100 ms integration time exposures. This data set is composed of a total of 1200 interferograms of the binary γ Leo (Algieba), a sequence of 300 interferograms for each of the four di erent mask orientation angles (0 , ' 46 , ' 86 , ' 126 ). The object is a binary star (ADS 7724) composed of a K1III main component and a G7III companion. According to the Hipparcos catalogue (ESA 1997) and to calibrated V − J colors, the main component magnitude and the magnitude di erence are respectively mJ = 0:21 and mJ = 1:39. The angular separation is 4 0:058, almost two times the di raction limit of the simulated interferometer. In addition, 300 interferograms of an unresolved bright star (BS 5589, a M4.5III star with mJ ' 0) were recorded for the rst mask orientation. These reference data are used for the system response (optics + atmosphere), the so-called PSF, in the deconvolution process. In this run, the total collecting aera was limited by the xed pixel size of the camera. For this reason, only 0:26% of the mirror area was used, leading for this integration time to a relatively poor signal-to-noise (S/N) ratio on the frames. Assuming frozen turbulence driven by the wind velocity v, the characteristic evolution time is of the order of B=v, where B is the projection of b on the primary i.e. here B = 9:5 cm. Taking v = 10 m/s 4.1. Measurement of atmospheric parameters leads to a typical evolution time of the order of 10 ms. Consequently, the level of atmospheric degradation conditions (which is evaluated from the D=r0 ratio to a 46% Strehl ratio) allowed us to assume that the blurring arising A least-square PSF tting program was developed and ap- from high order atmospheric turbulence of evolution time plied to our data in order to extract some atmospheric pa- scale inferior to 100 ms remains important. Note that, in rameters of interest. It allowed us to retrieve the evolution order to minimise variations in seeing conditions during with time of the fringe contrast, and of the random average data acquisition, all frames of both binary and point-like optical path di erence between the two apertures (that is stars have been recorded during consecutive periods of the the di erential piston). This was done for the two values night. of the ratio D=r0, on a 30 s period, and for an unique base- In the reconstruction, we used 200 interferograms of line orientation (Fig. 7), and we found consistent results the binary star per orientation angle. A total of 800 interin terms of average contrast and piston root-mean-square ferogram patterns were pre-processed before applying the (rms) values. Indeed the case of major atmospheric degra- reconstruction method. Pre-processing consisted in subdation leads to a smaller average contrast: for D=r0 = 0:84 tracting the average sky background, a bilinear upsamand D=r0 = 0:57 we found respectively an average con- pling from 30 30 pixels to 90 90 pixels and then the trast of 0.26 and 0.60. Accordingly, we found a piston rms extraction of a 64 64 pixels frame centered on the photovalue of respectively 0.11 and 0.06 in unit wavelength. center fringe pattern (see Fig. 9). This oversampling tech In addition, combining several consecutive short expo- nique allowed a sub-pixel centering of each original 30 sure PSF interferograms, we studied the variation of con- 30 pixels interferogram, i.e. to remove the atmospherically trast with integration time under the same two conditions induced image motion. of turbulence degradation (Fig. 8) and de ned a coherence Moreover, in order to obtain an accurate PSF estimate time tc as the integration time which corresponds to a loss needed for the LR algorithm, a Shift-and-Add (SAA) proof a certain percentage of fringe contrast. We deduced the cess was computed over the whole PSF data set. Then we value of tc with 10% loss for our experiment and attempted used the same pre-processing of the object interferograms to extrapolate the result to the LBT case (Correia 1998) . to obtain the PSF estimate (see Fig. 9). Unfortunately, D/r0 = 0.84 ilsp tihnu 0.0 ia ng t le re av- 0.2 n e e w iff in(- 0.4 D - 0.6 0 100 t s a 80 r t n o c e 60 v i t a l e r 40 % 20 0 D/r0 = 0.57 time (s) D/r0 = 0.57 20 30 the PSF was only recorded for the rst orientation angle. The PSF corresponding to other orientation angles were obtained by computer rotation using a bilinear interpolation. Note that this rotation was performed on the oversampled frames, allowing to conserve more information in the PSF shape. However, it is unlikely that the responses of the system for each orientation angle are identical to the rotated responses. Therefore the rotated PSF's obtained in this way are only an approximation. The companion is clearly visible in the reconstructed image of Fig. 10, in spite of numerous limitations in this data set. Indeed, in addition to the low S/N ratio, and the approximation of the rotated PSF, the original data were also slightly under sampled ( 1:8 pixels per fringe FWHM ). We further analysed the e ect of the number of frames on the reduced data. Figures 11 and 12 show the evolution with this parameter of, respectively, the reconstructed object, and the pro le of the reconstructed s l e x i p E Fig. 11. Reconstruction of the binary γ Leo according to the number of data frames per orientation angle processed, using the adapted LR algorithm (1000 iterations). The pixel size is 0 0:098=3 0 0:033. Contour levels are from 5% to 100% in steps of 5% 1.0 ity 0.8 s n e itn 0.6 d e lis 0.4 a m r oN 0.2 0.0 0 5 10 50 200 5 10 arcseconds 15 20 binary along the direction of separation. It can be seen that the gain obtained in the resulting reconstruction using multiframes deconvolution is important for a small number of data frames, and tends to converge rapidly. The variation of the FWHM of the main component is consistent with the fact that deconvolving more frames simultaneously improves the quality of the reconstructed object, i.e. the sharpness of the reconstruction. In fact, for a number of 5, 10, 50 and 200 frames per angle used, the FWHM of the main component obtained is respectively 2 0:047, 2 0:034, 2 0:031 and 2 0:021. It is interesting to note that we approached the theoretical di raction limit for our mask of 1 0:073, but we were unable to reach it because of the limitations previously mentioned. It is however important to stress that this 2 0:011 interferometric resolution does allow us to resolve γ Leo, whereas the 5 0:083 resolution of only one aperture would not permit it. We noticed moreover that this simultaneous multiframes deconvolution leads to a better result than deconvolving simultaneously the sum of the frames for all baseline orientation. A data set composed of 50 ms integration time frames was reduced in the same way and the result obtained is presented in Fig. 13. This shorter integration time \freezes" better the atmospheric distorted fringe pattern and the result is a more detached binary image. Note that the spurious signal present on the main component sides probably came from a non perfect centering of each fringe patterns due to the poor S/N ratio. We tested the validity of these reconstructed images by performing the comparison of the retrieved binary parameter values with those of the Hipparcos catalogue (included in the CHARA catalogue, Hartkopf et al. 1998) . Centroid calculations performed on 5 5 pixel boxes centered on each maximum intensity pixel of the two star brightness distributions led to the relative location of the binary. Two methods were used in order to measure the magnitude di erence mJ . Firstly, relative aperture photometry was performed with aperture radii from 3 pixels to 7 pixels, and we deduced therefore a range of retrieved mJ . Secondly, we obtained photometry by PSF- tting of the non-deconvolved frames, using the location retrieved by means of deconvolution as an input xed parameter. This PSF- tting is based on a least-square tting routine identical to that used in Sect. 4.1 and was applied to a same number of coadded frames for each orientation angle. Results reported in Table 2 are an average over the four orientation angles, weighting with the 2 in order to take into account the error tting of the other free parameters. From the values reported in Table 2, one can see that we are able to retrieve both the position angle and the angular separation of γ Leo, with a better accuracy in the 100 ms case. Concerning the relative magnitude retrieved by aperture photometry, mJ is larger than the catalogue value by an amount of 0.77 to 0.58 mag for respectively 3 to 7 pixels aperture radius and 100 ms integration time. This discrepancy is probably due to the poor S/N ratio present in the recorded frames, and seems to be a common characteristic of most of the non-linear image restoration techniques when applied to strongly noise-contaminated data (Lindler et al. 1994; Christou et al. 1998) . On the other hand, this interpretation is con rmed by the simulations performed in Sect. 3. Photometry measurements obtained by means of PSF- tting lead to more accurate mJ values and have the advantage to give error estimates. 5. Conclusion We have presented a method for interferometric imaging with the Large Binocular Telescope. We have illustrated the capability of a Lucy-Richardson based deconvolution algorithm to reconstruct the object image from a set of LBT-like interferometric data. We outlined potential performances on simulated LBT data and robustness of the algorithm has been tested on real LBT-like data. It is of great importance, in order to achieve the reconstruction, to be able to obtain, from a reference star, a su ciently good estimate of the PSF for each baseline position. The use of a Lucy-Richardson deconvolution algorithm is limited by the quality of the PSF calibration. The most favorable case would be to be able to record simultaneously object image and PSF. The LBT will provide a wide coherent eld of view for interferometric imaging, thanks to innovative technological solutions (Salinari 1996) . Therefore simultaneous measurements of both target and a bright reference star will be possible and, from this point of view, the algorithm presented here is of particular interest. The quality of the PSF calibration will be then limited by the di erence of wavefront compensation achieved for these two objects. The future implementation of a AO correction in the simulation code will allow us to quantify this limitation. Acknowledgements. We are indebted to F. Lisi and G. Marcucci for their help with the experimental set-up. We thank the director of the TIRGO observatory, Prof. G. Tofani, for the allocation of observing time. We are grateful to M. Bertero and P. Boccacci (University of Genova) for providing the initial version of the reconstruction algorithm, developed under contract number 16/97 funded by the Italian Consorzio Nazionale per l'Astronomia e l'Astro sica. We wish also to thank P. Salinari, M. Carbillet and J.C. Christou for useful discussions, and A. Marconi and G.P. Tozzi for assistance during the observations. Angel J.R.P. , Hill J.M. , Strittmatter P.A. , Salinari P. , Weigelt G. , 1998 , in: Astronomical Interferometry, Proc. SPIE 3352 , Reasenberg R .D. 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S. Correia, A. Richichi. Interferometric imaging tests for the Large Binocular Telescope, Astronomy and Astrophysics Supplement Series, 301-311, DOI: 10.1051/aas:2000122