Simulation of aperture synthesis with the Large Binocular Telescope

Simulation of aperture synthesis with the Large Binocular Telescope E.K. Hege, J.R.P. Angel, M. Cheselka & M. Lloyd-Hart Steward Observatory, University of Arizona, Tucson, AZ 85721 ([email protected]) July 9, 1995

ABSTRACT The Large Binocular Telescope (LBT) will have two 8.4 m apertures spaced 14.4 m from center to center. Adaptive optics will be used to recover deep, long exposure diraction-limited images in the infrared. The LBT con guration has a diraction-limited resolution equivalent to a 22.8 m telescope along the center-to-center baseline. Using simulated LBT images and an iterative blind deconvolution algorithm, (IBD { Jeeries & Christou, 1993) a sequence of three exposures, at suciently dierent parallactic angles, allows recovery of imagery nearly equivalent to that of the circumscribing 22.8 m circular aperture. To establish a credibility basis for these simulations we have studied the performance of IBD for image constructions of several examples of atmospherically perturbed and partially corrected stellar and galactic data. IBD is robust against in uences of real, non-ideal data obtained from large astronomical telescopes, including partial anisoplanicity and Poisson noise from object, sky and thermal background. For faint objects, which are sky-background and photon-statistics limited, the use of adaptive optics is presumed in these simulations. IBD removes the dilute aperture point spread function eects in the set of parallactic angle-diverse images linearly combined to produce the circumscribed aperture result. Optimal image combination strategy is considered for multi-aperture imaging array con gurations.

1 Introduction Experiments at the Multiple Mirror Telescope (MMT) have evaluated the performance of sodium laser guide star referenced adaptive optics[1]. Those experiments demonstrated features necessary for correction of a 6.5 m telescope to the diraction limit using a sodium beacon. It is anticipated that such technology will be mature and applicable to large telescopes of the 21st century[2], including the Large Binocular Telescope (LBT)[3]. The LBT will have two 8.4 m apertures spaced 14.4 m center-to-center. This will yield a diraction-limited resolution equivalent to a 22.8 m telescope along the center-to-center baseline. However, along the perpendicular baseline the resolution in a single exposure is limited to the resolution of a single 8.4 m telescope. As the Earth rotates, the LBT pupil will observe an object at dierent parallactic angles, thereby increasing the spatial information available to aperture synthesis type image constructions. A sequence of three exposures at suciently dierent parallactic angles allows synthesis of a quasi MMT optical transfer function (OTF.) Several recent approaches to recovery of diraction-limited imagery from sets of image data with phase-distorted OTF's could have been used for this work. We note, historically, that multiple frame deconvolution was proposed  Data in this paper was acquired with 1) the Kitt Peak National Observatory (KPNO) 4 m Mayall re ector, 2) the Adaptive Optics corrected Star re Optical Range (SOR) 1.5 m telescope, 3) the Multiple Mirror Telescope (MMT) in addition to 4) the Steward Observatory 2.3 m re ector. KPNO is a facility of the National Astronomical Observatories operated under National Science Foundataion contract by Associated Universities for Research in Astronomy. SOR is a facility of the Air Force Phillips Laboratory. MMT is a joint facility of the University of Arizona and the Smithsonian Institution.

by Weigelt[4] in 1983 and called \Roll Deconvolution." Multiframe blind deconvolution of astronomical images was suggested by Schulz[5]. A similar method, also using conjugate gradient minimization, with implementation of additional constraints is given by Thiebaut & Conan[6]. A very powerful method utilizing phase diversity measurements has been demonstrated by Seldin & Paxman[7]. But we have chosen the method of Jeeries & Christou[8] because of the easy access at gemini.noao.edu via ftp anonymous to the code maintained in the directory /pub/stuartj/ by Jeeries. It is available in Fortran versions for workstations and for the Cray supercomputer. IRAF and FITS image input is supported. We have made no attempt in this work to compare the eectiveness of these various approaches, which all have in common the joint estimation of an object function and the set of point spread functions corresponding to the set of observations of the object with dierently perturbed OTF's. IBD is the least constrained of those methods, so the performance obtained thereby should establish a conservative baseline expectation for this type of image construction. In the previous paper[9] Christou has presented the Jeeries & Christou iterative blind deconvolution algorithm (IBD) and shown detailed performance of IBD in speckle deconvolution imaging in infrared wavelengths. Our con dence in this algorithm is bolstered by its ability as a speckle image constructor as shown in Section 2. In Section 3 we present speckle deconvolution cleaning of adaptive optics imagery as another successful application of IBD with real data. This experience with real data, subject as it is to detector artifacts, image anisoplanicity, and other dicult to model imperfections of real data is presented as the basis for the simulation study which follows in Section 4. The performance of the method in the sky-background, Poisson-noise faint object limit is discussed in Section 5, based on a summary of standard SNR analysis. Some possibilities for other beam combining geometries and Fourier spectrum combination strategies are discussed in Section 6. The principal conclusion regarding expected performance of the LBT as an infrared interferometric imager is summarized in Section 7.

2 Speckle Deconvolution Imaging

Figure 1: Speckle Deconvolution Imaging of Capella. The upper row shows three digitized, short exposure, video cassette recorded, intensi ed video specklegrams[12] of Capella, observed at the Kitt Peak National Observatory 4 m Mayall re ector in a 10 nm bandpass at 420 nm. The image scale was  000:018=pixel. The super-resolved image of this 000.052 binary recovered by iterative deconvolution is shown at center with the corresponding reconstructed PSF's in the lower row. The algorithm requires that the bottom row, the PSF estimates, when convolved with the image estimate, shown at the center, approximate the observed data in the top row in a least-squares minimal sense. Data from Hege et al.[12] Speckle deconvolution imaging exploits the advantages of recent technology, particularly improved detectors and advanced computational facilities. IBD is the most eective speckle image constructor evaluated at Steward Ob-

servatory. The results for speckle deconvolution imaging show 1) the merits of imagery with fast, linear, low-noise CCD detectors, 2) the power of solving the complete problem as determined by the physics of imaging and 3) the improvements obtained by working in rst order, linear in image amplitudes, rather than second- or third-order as with Knox-Thompson or image bispectra. We know of no other method capable of producing such high-Strehl images from so few specklegrams. Speckle deconvolution imaging of Capella is shown in Figure 1. This shows IBD to be robust in reconstructing imperfect, real astronomical data with notable non-linearities in the image detection and processing. The images are non-isoplanatic, due to image intensi er \pincushion", and non-linear, because the D.C. zero-point was set too high. Both of these non-linearities are handled credibly in the constructions of the object and corresponding PSF's. The anisoplanicity, which causes the binary separation to appear variable across the eld of view is manifest in the modulation of the Fourier spectrum shown in Figure 2: the fringes are not a uniform cosine modulation. The D.C. clipping is manifest in the tendency for negativity to persist in the PSF solutions shown in Figure 1: zero is at the predominant grey level in the PSF plane. The big surprise in Figure 2, however, is that when the Fourier bandlimit constraint on the object is relaxed the IBD algorithm tends to extrapolate a \super-resolved" solution beyond the aperture cuto frequency, which occurs just beyond the second visibility minimum. The zero-point error also causes uncertainty in the magnitude dierence which is 0.4 in this construction, rather than the expected 0.2. The signi cance of this result is that the construction appears to be limited by the properties of the detector used and not by the algorithm.

Figure 2: The Fourier Spectrum of the Capella image shown in Figure 1. Modulus (left) and phase (right.) Both are plotted linearly, 0 < mod < 1 and , < pha < . The previous paper[9] also showed the excellent performance of IBD under anisoplanatic atmospheric conditions. Those speckle deconvolution imaging results demonstrate the ability of the algorithm to reconstruct PSF's with sucient precision to yield nearly diraction-limited imaging in a 1500 eld of view. Partial atmospheric isoplanicity allows recovery of fully diraction limited imagery, but with reduced SNR per frame, as the anisoplanicity is just another source of noise which suppresses as the square root of the number of images processed, indicating that it arises from random atmospheric processes in that data set. This is not true if systematic eects dominate, as for the Capella data shown in Figure 1.

3 Deconvolution Cleaning of Adaptive Optics Imaging Preliminary results using IBD to process Adaptive Optics were reported by Christou, et al.[11]. Christou et al.[15] have recently demonstration of the use of IBD in post-processing of AO data. We have also shown, Figure 3, that a \super-resolution" follow-on to the IBD reconstruction is produced by a second iterative deconvolution. This is consistent with the experience of Thiebaut & Conan[6]. Figure 3 also illustrates the capability of IBD to calibrate systematic residuals of a partially correcting adaptive optics system. Figure 4 illustrates the performance of IBD in the signal and background limited case as discussed in section 5.

Figure 3: (Left) Shift-and-add of 5 frames of AO Corrected images of  Cass, (Center) IBD construction which removes AO PSF and (Right) \Super-resolved" result from second IBD. The ve magnitudes (100) fainter secondary is at lower left (about 6:30) in all three panels. Data supplied by Christou[15] In Figure 4 the at-line gravitationally lensed Quasar BN1422+231 was observed[16] with the FASTTRAC tip-tilt removal system[17] at the Steward Observatory 2.3 m re ector. This demonstrates sky-background limited performance consistent with the predictions of this study. Although this does not illustrate recovery of the full 2.3m telescope resolution, it does show recovery of spatial and photometric information consistent with the Nyquist sampling limit imposed by the 000:22 camera pixellation of these observations. The gravitational lens system BN1422+231, MH =13.05, is at the bottom, left in these images. The image at right produced by IBD shows pixel-limited resolution of image components to MH =16.5 (the source at the left edge, just below center.) This IBD construction was constrained by an ensemble of sixteen 60 s exposures, shown coadded at left. Eects of noise ampli cation, and of the size of the PSF support used, are observable for this low SNR data. The detector pixellation precludes resolution of the close components of the brightest part of the bright source, however it is clearly resolved as non-pointlike.

Figure 4: FASTTRAC imaging of BN1422+231 in H-band (1.6 m.) Data supplied by Close[16]. These results with IBD, with real astronomical data, provide the credibility basis for using IBD to make predictions about future capability. In particular, we wish to make a strong case for the high angular resolution bene ts to be achieved with the adaptive optics corrected, actively cophased LBT.

4 Photon Statistics Limited Simulations A well-known spiral galaxy image was binned to a course resolution consistant with projecting that galaxy to a distance at which the eld of view subtends 000:64 arcseconds. At that distance, many of the features are not resolved (single pixels) but the spiral structure is still evident. The 64  64 convolution target used for these simulations is shown on left in the bottom row of Figure 7. The panel at right shows the same projected target ltered to the resolution of a 22.8 m circular aperture. This is taken as the noise-free reference.

Figure 5: Simulations of photon statistics limited diraction limited imaging with the LBT for (top row) 105, (middle row) 106 and (bottom row) 107 photons per long exposure image at each of the three parallactic angles, ,45 (left), 0 (middle) and 45 (right.) The PSF of the fully corrected, cophased LBT is assumed for this experiment. This assumption is based on predictions of performance[18, 2] attainable in adaptive optics systems to be used with large astronomical telescopes. Typical simulated images are shown in Figure 5 at each of three dierent parallactic angles diering by 45 . The limits of performance of image recovery algorithms are set by the signal-to-noise ratio at the highest image frequencies as illustrated in Figure 6. IBD recovers the image visibilities as shown in the last column of Figure 6. Given the nature of image visibilities of resolved objects, the lower frequency visibilities are more easily recovered. Image restoration algorithms have the property of amplifying the noise, especially at frequencies where the measurements have low signal-to-noise. The iterative deconvolution algorithm, being unconstrained in the image frequency domain also tends to \super-resolve" the result. The simulation parameters yield 230 photons per 26 ms (8800 s,1 ) through the binocular pupil of the LBT at mK =17. This corresponds to narrow-band imaging in the infrared K-band,  = 2:2 m, bandpass=0.4m. Realistic eciencies for the telescope and optics (40% combined) and the detector (50%) are assumed, corresponding to a detection eciency  = 0:2. Simulations were generated at three exposures 105, 106 and 107 photons per long exposure image. For the numbers chosen a 20 minute integration at m=22 would collect 105 photons from the object (not including background) at 20% eciency. Each panel of Figure 5 thus corresponds to a 20 minute integration time, a reasonable integration for a faint object. The galaxy is shown in three realizations, at dierent parallactic angles, assuming mK =22 (top row), mK =19.5 (middle row) and mK =17 (bottom row.) These simulations assume that high performance adaptive optics[18] is used to recover the deep long exposures. These then correspond to mK  20:5

(top row), mK  19:5 (middle row) and mK  17 (bottom row,) as discussed in Section 5 and summarized in Table 1, when including eects of OH sky and telescope thermal background, equivalent to mK  13 per square arcsecond[19, 20]. IBD relies on observations which have signi cant energy at the image frequencies to be reconstructed. The limits to image recovery via iterative deconvolution are similar to those given by Beletic & Goody[21] for speckle interferometry with the exception that Adaptive Optics now allows long exposures to build good signal-to-noise at image frequencies up to the diraction limit. The simulation[22] was done with independent Poisson noise realizations1 at each of the three parallactic angles, ,45 , 0 and 45 . Those parallactic angle-diverse images shown in Figure 5 are de-rotated and co-added to produce long exposure images. Figure 6 gives the image moduli for those long exposure images.

Figure 6: Fourier moduli showing the SNR problem. The target (upper left) and for observations at three parallactic angles with the LBT. The moduli of the coadded images have 3  107 (upper center), 3  106 (lower left) and 3  105 photons (lower center.) IBD construction at SNR = 5500 and SNR = 1730 corresponding to 3  107 (upper right) and 3  106 (lower right) photons detected. Loge of Fourier moduli are shown. Poisson noise bias p dominates the predicted high frequency responses. The SNR for Poisson statistics limited imaging is SNR = n
N where n is the number of images observed and N is the average number of photons per p image. In Figure 6 image moduli in frequency space are shown, corresponding to n
N = 5500 (upper center), 1730 (lower left) and 550 (lower center.) A SNR > 1000 is required for the IBD reconstructed LBT imagery to be signi cantly sharper than that of a single 8.4m telescope image for this target. The right column of Figure 6 illustrates the performance of the IBD construction. This analysis in the frequency plane illustrates several limiting eects of Poisson noise, especially the noise bias seen at frequencies beyond those transmitted by the LBT's OTF, which also underlies the response at frequencies within the OTF, degrading the SNR at high frequencies. Noise ampli cation is typical of any deconvolution algorithm. A noise ampli cation eect is seen in Figure 6 manifest near the minima of the LBT's OTF in the lower SNR case (lower right.) Image phase recovery proceeds similarly. The moduli are printed as log(moduli) because of the large dynamic range of image moduli. The target image modulus (upper left, Figure 6) had a dynamic range 22000:1 which would have required 1:6 p 108 photons (mK =14) for observation, without sky background with delity comparable to the \noiseless" case ( 3:  1:6e8 = 21908.) The 105 photons per integration case constructed a slight improvement in resolution compared to that of the single 8.4 m apertures. IBD, which routes the noise to the PSF responses, yields a good low-pass ltered construction at the photon statistics limit. Eects of sky background are discussed further in Section 5. 1

The code called Skylight is available from Twinklesoft, 900 E Cornell Rd, Pasadena, CA 91106, (818) 793-1015.

In Figure 7 the results of the three SNR cases, processed using IBD, are compared to the test pattern (lower left) and the corresponding image which would have been recovered with a perfect 22.8m telescope above the atmosphere (lower right.) The three simulated results in Figure 7 (top three rows) are derived from exposures at three parallactic angles { the data in Figure 5 which have been coadded to produce the long exposure images shown on the left. Circular aperture bandlimit ltering, limiting image frequency response to the domain SNR  1 has been imposed on the IBD results. This yields results corresponding to resolution of 10m telescope (upper), 15m telescope (upper middle) and 22.8m telescope (lower middle) shown on the right. The analysis of the sky and thermal emission background in Section 5 allows translation of the faint object observing limits derived from background-free simulations into a prediction for performance in the background limited case. The only signi cant eect of a Poisson noise additive background is to reduce the SNR of the Fourier spectrum. Because the Poisson noise bias exists even in the background-free case, the data presented to IBD is statistically similar for observations with OH sky and telescope thermal background at similar SNR.

Figure 7: Photon (Poisson) noise limited Large Binocular Telescope imagery. Coadded exposures are shown (left column) compared to the corresponding IBD result (right column) for SNR = 550 (top), SNR = 1730 (upper middle) and SNR = 5500 (lower middle.) Bottom row shows the simulation target, un ltered (left) and band-pass limited to a 22.8 m perfect circular aperture (right.) To appreciate these idealized limits the three results simulated in Figure 7 correspond to observations above the atmosphere with a cold mirror at mK = 26 (upper), mK =23.5 (upper middle) and mK =19 (lower middle) assuming 3 hour exposures at 2.2m with 0.4m bandpass and 20% eciency (telescope + optics + detector) or equivalently mK  20:5, 19.5 and 17 respectively when sky background { as described below { is included. The results for SNR  5500, Figure 7 (third row), were recovered from simulations with image moduli having dynamic range one fourth that of the target image modulus, with only 9 Zernicke-modes corrected in each aperture and with the apertures cophased. A result for perfect adaptive correction is shown in Figure 9.

5 Sky Background Limited LBT Imaging The eect of additive noise, primarily from Sky emissions and the emissivity of the telescope optics, is to reduce the SNR of the observations. Figure 8 shows a simulation for mK =21 but infrared background limited. This has similar SNR to the case show as top row of Figure 5. From this it is immediately evident that ultimate limit for this process is about mK =21, in which case the IBD result will be similar to that of Figure 7 (top.) A photon-limited image d(~r) is a composite of individually detected photons which includes both signal i(~r) and noise b(~r). If ~rk is the location of the kth photon event, the ensemble of Nd detected photons, the detected image is d(~r) =

XN (~r , ~rk) = i(~r) + b(~r): d

(1)

k=1

The detected image d(~r) carrys information about both the object being observed as well as random, presumably uniformly distributed, sky background. Detector readout noise is a further complication, but assumed to be small compared to sky background noise for time-integrated exposures. Neglecting the readout noise, the detected photon signal results from a Poisson process with rate proportional to the combined signal + noise intensity.

Figure 8: Additive noise reduces SNR. Simulation for mK =21. Table 1. Background limited integration time for a given dynamic range DR. mK o (s,1 ) 24.52 8.8 22.0 88 20.5 350 19.5 880 18.0 3500 17.0 8800 16.0 22000 14.5 88000

DR =315 400 hr 4.2 20 min 4.2

DR =1000 DR =5000 42 hr 3.2 42 min 6.2 2.1 47 sec 12

81 hr 17 2.6 53 min 20 4.8

The principal eect of the Nb background noise photons is to reduce the SNR of the image modulus by the factor No , with the noise oor increased by pN , compared to a background free observation of N photons from the b o No + Nb source. It is a practical interest to determine the time t to integrate to a given dynamic range in the image modulus, DR = SNR(~ = 0). DR = pNo (2) Nd o t = (3) (o t + b t) 2 t = DR (o2 + b ) (4) o

p

p

0)(o + b FA) (5) = SNR(~ = 2A o where o and b are the source and signal uxes respectively, and o = o A and b = b AFA are the corresponding detected object and background rates observed with aperture area A and eld-of-view FA respectively, and  is the detection eciency. The results computed for the 000:64 square LBT eld of view studied here, assuming an optimistic detection eciency  25% and background of mK  13 per square arcsecond, are summarized in Table 1.

6 Optimal Combination of Exposures: Beam Combination Considerations Simply coadding exposures at various parallactic angles is not analogous to multiple beam correlation in the focal plane. The frequency coverage is that of the set of individual exposure correlations, but cannot include crosscorrelations among the dierent parallactic angles. This post-corrected aperture-syntheses system diers from the performance of a multiple beam interferometric imager in which all of the beams are brought together simultaneously in a common focus, e.g. the MMT, or a con guration such as the proposed Adaptive Steerable Imaging Array[23]. The noise background, as simulated in Figure 6, is too large in this instance by a factor of three because the three de-rotated paralactic angle-diverse images were coadded in the image domain. Since the support of the OTF is known for each of the individual exposures, the Fourier noise can be suppressed in the regions outside that support in the Fourier domain before co-adding the images in the Fourier domain. Each PSF should be reconstructed using only Fourier spectral data relevant to the support of the individual exposure. The coadditions used for these experiments were not that sophisticated. The performance reported here should be conservative in estimating actual performance attainable with an optimized reconstructor. That raises the question of optimal strategy for a multibeam interferometer design in which a large, central collector is surrounded by long baseline outriggers with smaller collectors. If, for example, the area of the central collector equalled the sum of the areas of the smaller collectors, the light from the large collector could be split in equal intensity beams for interfering the outriggers. This method yields the individual cross-correlations among the dierent parallactic angles, but gives only n baselines, one for each outrigger. Each can be added with only its own noise bias without contamination with underlying bias from other baselines. Does this have higher delity than the fully superposed case in which each baseline frequency is observed against the combined bias of all of the baselines? In that case all of the noise from all of the baselines adds at each frequency. There is a second part to that question, as there are also more baselines observed when all beams are simultaneously combined. The following table illustrates these strategies in the case for a central collector of area A and n outriggers of area a = A=n each, collecting a total signal N, proportional to 2A. Table 2. SNR for various beam combination strategies.

1

Case General Individually

2a Allmajor 2b Allminor 3 Allparallactic

Fourier Signal N2 n(a + a)2

Noise Bias N 2a

(A + na)2 (a + a)2 m(A + na)2

2A 2A 2A

SNR

N2 = N N n4a2 = 2A 2a 4A2 = 2A 2A 4a2 = 2A 2A n2 m4A2 = m2A 2A

We study three cases: 1) the light from the central collector, appropriately subdivided optically, is interfered with each of the outrigger beams independently, 2) all of the beams are brought simultaneously to a common focus, and

3) m observations are made at dierent parallactic angles with the beams simultaneously combined by appropriately coadding with noise suppression outside the OTF support. A non-redundant, dilute aperture is assumed. In case 1, the Fourier noise outside the aperture OTF is masked before coaddition in the Fourier plane, so that the noise bias is just 2a at each frequency. In case 2, addition is in the image domain and all of the noise bias underlies all frequencies. In case 2a incoherent addition of data from only the major baselines is considered, whereas case 2b has coherent addition of all baselines simultaneously. Case 3 assumes incoherent addition, in the Fourier plane with noise masks, of data from m dierent (non-reduntant) paralactic angles. The SNR ratio is the same for the n major baselines in cases 1 and 2a, but the simultaneous combination of beams, case 2b, provides the further advantage of more and possibly longer baselines. However, the SNR of the minor baselines is reduced by 1=n2 compared to the major baselines, so they will contribute only in the bright-object limit. Since they come at no cost in performance on the major baselines, the simultaneous combination will have some advantage, but at lower SNR, in the additional coverage of the frequency plane provided thereby. For the particular con gurations considered, which divide the light equally between a primary element of area A and n equal outriggers each of area A=n, the SNR is independent of n. The LBT is the special case for n = 1. The penalty for a large number of small outriggers, in loss of information at the high frequencies represented only in the cross-correlations between the outriggers, is illustrated in case 2b. With noise suppression by coadding independent observations at dierent parallactic angles, using appropriate ~ -plane noise ltering, SNR builds linearly with the number of parallactic angles observed, case 3.

7 Conclusion: LBT Infrared Imaging Performance

Figure 9: LBT Adaptive Optics image simulation result. The eld of view is 000:64 arcsec square in each panel at 000:010 per pixel for 2.2 m (infrared K-band.) The Large Binocular Telescope (LBT) can recover deep long exposure diraction limited images in the infrared. The panels in Figure 9 show simulated images of a galaxy at 2.2 microns wavelength. A single telescope gives the image in the lower left; when both apertures are combined in phase higher resolution interference fringes are superposed (lower right.) If three similar images are obtained during the night with parallactic angles ,45 , 0 and 45 , a high

resolution image can be deconvolved by the blind deconvolution method of Jeeries and Christou[8]. The result (upper right) is very similar to the diraction limited image from perfect a 22.8 m lled circular aperture telescope without atmosphere (upper left.) This performance should be realized with about 8 hours of observing, in the infrared K-band against a 13 mK per square arcsec sky background, for a 18.5 mK galaxy. The galaxy image used in this simulation has point sources whose Fourier signatures are constant amplitude cosine functions. Those extrapolate and interpolate naturally[23]. The resolved structures do not have comparable energy at high frequencies. The high-frequency extrapolations and interpolations dominate the high-frequency response. This is why good delity image construction is obtained for the galaxy target. For targets such as this, imagery with resolution better than that of a 10 m diraction-limited space telescope will be obtainable from the ground by LBT for objects brighter than magnitude 19 in K-band. As further validation of this expectation, we present results of IBD of real data from the MMT[1]. Figure 10 shows K-band imaging of a point source by the MMT with 6-element AO correction (top row) and without correction (bottom row.) For both cases Shift-and-Add (center) and IBD constructed results (right) are shown. The side-lobes of the cophased MMT PSF are only partially removed in the AO corrected result. The data was not adequately centered on the small IR array available for this experiment. The eectiveness of IBD is demonstrated in both cases, and the SNR improvement of the tip-tilt only AO correction, approximately a factor of 3, is preserved in the post-processed results. Unfortunately, only point sources were observed in the MMT laser guide star demonstration.

Figure 10: MMT imagery (unresolved source.) Tip/tilt on (top) and o (bottom.) Long exposure (left) shift-and-add (center) and IBD (right.) Cophased array response is recovered in SAA and IBD. In further work, we wish to study the optimal implementation of the IBD algorithm, and to learn its performance characteristics for objects with various Fourier signatures at the SNR limit. We expect to validate the predictions with further imagery to be obtained from the adaptive optics corrected MMT, and anticipate that PSF signatures can be removed from the AO corrected MMT data as was demonstrated for the Star re data (Figure 4.) We acknowledge the support of E. M. Hege and the University of Arizona Foundation for the preparation of this manuscript. We thank Dr. Peter Strittmatter for discussions regarding optimal beam combiner strategy.

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