Characterizing aperture masking interferometry in the near-infrared as an effective technique for astronomical imaging
CCharacterizing Aperture Masking Interferometryin the Near-Infrared as an Effective Technique forAstronomical Imaging
Kyle J. Morgenstein ∗ April 23, 2020
Abstract
Radio interferometry is the current method of choice for deep spaceastronomy, but in the past few decades optical techniques have become in-creasingly common. This research seeks to characterize the performanceof aperture masking interferometry in the near-infrared at small scales.A mask containing six pairs of apertures at varying diameters and sep-arations was constructed for use with a 24 inch telescope at the MITWallace Astrophysical Observatory. Test images of Spica and Jupiterwere captured for 28 different telescope configurations, varying apertureseparation, aperture diameter, collection wavelength, and exposure time.Lucky imaging was used to account for atmospheric perturbations. Eachimage was reduced via bias and dark frames to account for sensor noise,and then the full width at half maximum for each image was computedand used as a proxy for maximum angular resolution. The data implythat at small scales aperture size primarily controls the observed maxi-mum angular resolution, but further data are required to substantiate theclaim. ∗ Undergraduate, Department of Aeronautics and Astronautics, Department of Earth, At-mospheric, and Planetary Science. a r X i v : . [ a s t r o - ph . I M ] A p r omenclature Ω = angular resolution λ = wavelength D = primary mirror diameter s = subaperture separation d = subaperture diameter Interferometric techniques have become increasingly common in the astrophysicsand planetary science communities primarily due to their ability to resolve deep-space objects with higher angular resolutions at lower cost than traditional op-tical methods. This growing popularity is due to the effective angular resolutionΩ eff of interferometric systems, which is proportional to the diameter betweenreceptors. As a result, receptors spaced far apart and interfered can achieveresolutions far higher than traditional methods could feasibly produce. Evenshort baseline systems experience a resolution gain greater than the angularresolution possible with an equally-sized traditional system, making them moreefficent at performing the same tasks.Because of the resolution gains possible using large systems and the easeof interfering long wavelengths to produce high fidelity results, most researchregarding stellar interferometry has focused on very large radio telescope arrays,such as the Very Large Array (VLA). As a result, very little work has been doneregarding the dymanics of small-scale stellar interferometers. In the past twentyyears optical stellar interfeometers have become more common in large part dueto the work of Dr. Peter Tuthill [7], but infrared applications at small scaleshave remained less well understood.Beyond deep space astronomical imaging, stellar interferometry at smallscales has potential to be effectively applied to a variety of other applications aswell. Amateur astronomers may find stellar interferomerty to be significantlymore cost effective, as the price for larger equiptment grows exponentially. Smallsubsystems acting as an interferometer may be able to achive similar results tolarger systems at a fraction of the cost. Similarly, the proliferation of smallsatellites has produced growing interest in portable, inexpensive passive track-ing systems for both military and commercial applications. Small-scale stellarinterferometry may be effective in both cases, but the optics and the relation-ship between frequency and performance are not well documented in literature,limiting the development of such systems.2his research proposes to tackle both problems: characterizing the dynamicsof small-scale stellar interferometry and understanding the spectral dependanceof their performance. To that end, a variable sweep will be performed in simu-lation to derive a reasonable test matrix of telescope configurations to test. Inorder to ensure ample light is available to construct high resolution images evenat short exposure times, this work will use Spica and Jupiter as the primarytargets. To unravel what parameters affect telescope and interferometer per-formance, it is important to first understand the underlying optical propertiesthat lay the groundwork from which this research will build. Earth-based systems have always suffered from distortions due to atmosphericeffects. While these aberrations can never be completely accounted for, a varietyof techniques have been derived to deal with this unwanted source of noise. Onesuch technique, speckle interferometry, “freezes” atmospheric effects using short-exposure bursts and then accounts for these distortions to yield high resolutionimages. The distortion caused by atmospheric perturbations is known as aspeckle pattern. Increased understanding of the effects of this speckle patternhave allowed both traditional and interferometric techniques to greatly improvein the last few decades [7].As an upper bound, the theoretical maximum angular resolution with atelescope with no physical or atmospheric distortions is given by the RaleighCriterion [1] by Ω = 1 . λD (1)This angular resolution is purely theoretical, however, and breaks down due toatmospheric effects rapidly, bounding the maximum spatial resolution to 0.5 to1 minute of arc, independent of primary mirror diameter. This atmospheric res-olution limit is commonly referred to as “the seeing.” The wavefront distortionsthat cause this limit are statistically modeled by two parameters. Fried’s pa-rameter, r , is the characteristic length over which the root-mean-square (rms)wavefront aberration is one radian. The Greenwood time constant, t , is theatmospheric coherence time and estimates the evolutionary timescale of thewavefront distortions [7]. Typical values of r range from 10 to 20 cm, and ¡10msec for t in the near-infrared. 3 .2 Diffraction and Interference The diffraction pattern of a single circular objective in the infrared is character-ized by a single peak with fringes decaying from the image center. The RaleighCriterion 1 provides the maximum angular resolution over which two objectscan be distinguished. In the case of observing a single object through a singleaperture, the diffraction pattern is identical, albeit with lower resolution and in-tensity. When two equally bright objects are observed through one aperture theresult is a simple interference pattern with uniformly oscillating fringes causedby the location of the maximum and minimum fringes from each object [3].When a second aperture is introduced, the interference pattern from eachis superimposed to form a combined image whose structure is a function ofthe spacing of the apertures. As the apertures are moved apart the fringepatterns also separate until the fringe patterns interfere destructively, with onlythe central peak remaining. This interference pattern happens when the twoindividual patterns are separated by an angle Ω i given byΩ i = λ s (2)where s is the separation between the apertures. This resolution representsthe system’s maximum angular resolution when configured as an interferometer[3]. A majority of the literature has focused on the photon-starved regime tostudy the limitations of image-reconstruction by pushing the system to resolvedimmer and dimmer objects [7]. For bright objects in the infrared, the primarysource of noise is atmospheric effects and so the imaging of bright objects suchas Spica and Jupiter fall outside the scope of those studies. The most effectiveway to reduce noise and amplify the intensity pattern is to limit the influx oflight incident on the telescope. While it may seem counter intuitive to block outincoming light to increase the resolution of the resulting image, the theoreticaljustifications are well known [5]. The resolution gain induced by this effect canbe calculated by ΩΩ i = 2 . sD (3)Taking the limit as s = D , we find that by masking the main telescope objec-tive with a plate containing an array of subapertures (hence, aperture maskinginterferometry), angular resolutions almost 2.5 times higher than the tradition-ally configured telescope can be obtained [3]. This result is surprising, andmakes aperture masking interferometry a powerful tool for deep space imaging.Aperture masking interferometry can offer significant advantages in the infraredincluding reduced atmospheric noise, improved resistance to variations in thetheoretical limit of resolution, and greater flexibility in minimum detector per-formance. This resolution gain can be seen in Figure 1. The top two plots depict4he increased peak in the irradiance distribution spreading out symmetricallyfrom the center of the screen. This gain is in terms of the measured inten-sity with respect to the non-masked intensity. Note the bands in the maskedaperture case due to destructive interference in the fringes on the bottom righthand plot. Using an interferometric system yields higher resolution images withgreater intensities but as a result the captured images contains fringes.Figure 1: Irradiance distribution of a traditional telescope (Left) Distributionfor an aperture masked system (Right). Aperture masking allows for bothheightened intensities as well as a larger coverage area compared to traditionaltelescopes. This resolution gain is at the cost of fringes caused by destructiveinterference. Under ideal conditions, the fringes of a well resolved interference pattern willvanish as the fringe maxima from one aperture will cancel with the fringe minimafrom the opposing aperture. Of course, this is rarely the case, and so the fringevisibility over a baseline b is given by | V b | = i max − i min i max + i min (4)where i min and i max are the intensities in the fringe pattern. Visibility is animportant measure because it is directly proportional to the Fourier transformof the object flux distribution. Fourier amplitude data alone is not sufficient toreconstruct an unambiguous image, as the phase is required to locate compo-5ents in Fourier space [7]. Phase information is particularly sensitive to randomatmospheric fluctuations and so must be accounted for.One technique in radio astronomy that has also found success in opticaland near-infrared interferometry is the notion of closure phase . This methodrequires at minimum three apertures, however, and so cannot be used in thistwo-aperture set-up. Phase aberrations due to atmospheric effects and differingpath lengths from the source to the aperture have the effect of skewing thedestructive interference of the fringes, causing the intensity pattern to blur. Toreduce this effect, the path difference between the source and each aperturemust not be greater than the coherence length , given by l = λ ∆ λ (5)For wavelengths in the near-infrared ( λ = 750 nm — 1000 nm) and bandwidthsof ∆ λ <
150 nm, the path difference for an interferometer with apertures sep-arated by up to 24 inches is well below the coherence length, allowing for goodtheoretical interference patterns. The second requirement for high resolutionimaging is robustness in path length to atmospheric perturbations such thatthe path differences vary by only a fraction of the observation wavelength [2].This requirement is much more difficult to satisfy in optical and infrared sys-tems than it is in more common radio wave observations due to the scale of thewavelengths involved. The most effective method to mitigate these atmosphericeffects is to overlay a series of short exposure images.The primary goal, then, is to reconstruct the intensity of an object, O ( (cid:126)x ),given its measured value, I ( (cid:126)x ), and a point-spread function of atmospheric andtelescopic distortions, τ ( (cid:126)x ). This relationship can be represented as I ( (cid:126)x ) = O ( (cid:126)x ) (cid:126) τ ( (cid:126)x ) (6)where (cid:126) is the convolution operator. Taking the Fourier transform yields I ( (cid:126)f ) = O ( (cid:126)f ) τ ( (cid:126)f ) (7)where f is the reciprocal Fourier coordinate to the angular sky coordinate, x [7]. The angular diameter of an object is given by 2 .
44 Ω i [3]. If the angulardiameter of the object, Ω t , is already known or can be estimated accurately,then this relation can be used to determine the aperture separation for perfectphase matching. This condition was described earlier in equation (2), in whichthe fringe patterns from each aperture perfectly cancel yielding only the centralpeak in intensity. This ideal aperture separation, D i is given by D i = 2 . λ t (8)6his distance will be used to determine aperture geometries to test experimen-tally. See Methods for calculations. All data was collected at the MIT Wallace Astrophysical Observatory in West-ford, Massachusetts. The basis of the interferometer was the 24 inch PlaneWaveInstruments CDK24 telescope. See Appendices A.2 and A.3 for schematics andCAD drawings. Data was collected by a ZWO174 Complementary metal–oxide–semiconductor(CMOS) Imager at the rear of the telescope, cooled to 20 ◦ C below ambient .See A.4 for schematics. A single mask made of an aluminum sheet containingeach pair of apertures, depicted in A.1. Six geometries were tested: two aper-tures at 20.4 inches separation for maximum resolution, two apertures at 3.3inches separation and two apertures at 3.7 inches separation for the zero-fringecondition, as given by D i at 750 nm and 850 nm, respectively. The same setis produced for both 1 inch and 2 inch diameter apertures yielding six uniquemasks, each containing a pair of apertures. Only one pair of apertures are openat a time, with the other five pairs blocked. A cross-section of the apparatuscan be seen in Figure 2. Data was also be taken with all apertures covered forthe generation of dark and bias frames. See 3.3 for further discussion on darkand bias frames.Figure 2: Cross-section of stellar interferometer configuration.7he optimal aperture diameter, d , was found by running over 10,000 simu-lations sweeping over the variables of collection wavelength, aperture spacing,and aperture diameter. The simulation provided an ideal aperture width of 1mm. This is to be expected, as the peak of the intensity pattern grows inverselywith aperture width for small apertures. To ensure sufficient light is collectedto resolve Jupiter and Spica, the minimum aperture diameter is set larger thanthe optimal value. Beyond 25 mm the intensity peak falls off quickly, but 80%to 90% of the intensity in the diffraction patterns for the 1 mm configurationcan be preserved with aperture widths up to that width.For this simulation, the diffraction pattern of the interferometer was ap-proximated as a double slit with Fraunhofer diffraction. Fraunhofer diffractionassumes parallel wavefronts in the far-field and is valid for F <<
1, where F isthe Fresnel Number. This number is a measure of length-scale and determineswhat approximations are appropriate for different distances between the doubleslit and observation point. For this configuration, the Fresnel Number is ˜12.5,meaning that the distance between the mask and the CMOS is not sufficientlyfar for the assumptions of Fraunhofer Diffraction to hold. Instead, this regimeis dictated by Fresnel Diffraction which is characterized by parabolic wavefrontsin the near-field. However, because we only care about the relative intensity ofthe diffraction pattern at the midway point between the two apertures, whichis the same whether in the parallel or parabolic wavefront regimes, we can con-sider this approximation good enough for first pass analysis to determine maskgeometries. Data collection occured during April of 2019. Spica and Jupiter were chosenas the primary targets. Spica is a bright binary star which can be viewed as apoint source, while Jupiter is the second brightest object in the night sky afterthe moon. Each mask was bolted to the telescope and the telescope was setto track the target object. With each mask a series of images were taken attwo different exposure times for each aperture with each corresponding filter.In total 30,000 images were taken representing 28 different configurations ofaperture diameter, aperture separation, wavelength filtering, and exposure timefor each target. The full test matrix is listed in Table 2.
The main goal of post-processing is to reduce blur and atmospheric effects fromthe data, as well as any other perturbations causing the signal to lose fidelity.It is important to keep in mind physical limitations that cannot be overcome.There are broadly two sources of distortion: atmospheric and telescopic. The8perture Diameter Aperture Separation Filter Exposure Time1 in 20.4 in Clear 100 ms1 in 20.4 in Clear 5s1 in 20.4 in i’ 750 nm 500 ms1 in 20.4 in i’ 750 nm 5s1 in 20.4 in z’ 850 nm 1250 ms1 in 20.4 in z’ 850 nm 5s1 in 3.7 in Clear 100 ms1 in 3.7 in Clear 5s1 in 3.7 in i’ 750 nm 500 ms1 in 3.7 in i’ 750 nm 5s1 in 3.3 in Clear 100 ms1 in 3.3 in Clear 5s1 in 3.3 in z’ 850 nm 1250 ms1 in 3.3 in z’ 850 nm 5s2 in 20.4 in Clear 25 ms2 in 20.4 in Clear 1250 ms2 in 20.4 in i’ 750 nm 125 ms2 in 20.4 in i’ 750 nm 1250 ms2 in 20.4 in z’ 850 nm 312 ms2 in 20.4 in z’ 850 nm 1250 ms2 in 3.7 in Clear 25 ms2 in 3.7 in Clear 1250 ms2 in 3.7 in i’ 750 nm 125 ms2 in 3.7 in i’ 750 nm 1250 ms2 in 3.3 in Clear 25 ms2 in 3.3 in Clear 1250 ms2 in 3.3 in z’ 850 nm 312 ms2 in 3.3 in z’ 850 nm 1250 msTable 2: Full test matrixatmosphere is a strong absorber in certain bands of the infrared, but thereexist “windows” in which transmission is high. The 600 nm to 800 nm bandis a prime example of one such window [6]. Taking short exposure imagesmitigates variable path length and resulting phase shifts due to atmosphericdistortions. An additional method of dealing with atmospheric aberrations isknows as chopping . Chopping is the process by which consecutive images aretaken of the area of the sky of interest and an immediately adjacent area andthen the second image is subtracted from the first [6]. This method only worksover very short time and spatial scales, however, as atmospheric cells cannotbe assumed to be congruent at distances greater than 300 mm. Factors thatinfluence the noise from the telescope itself include the telescope’s black-bodyradiating temperature and the transmissivity of the CMOS. The transmissivitycurve for the filters used on the ZWO174 CMOS can be seen in Figure 3. The9’ and z’ filters will be used for this experiment. The two filters are centeredon 750 nm and 850 nm, respectively, which is the wavelength used for the finalsimulations. Each filter approximately covers a 100 nm band.Figure 3: Transmissivity of the ZWO174 CMOS Imager. The bottom axis iswavelength in nm and the right axis is percent transmission. Transmission staysabove 98% for the i’ and z’ filters, which lie in the near-infrared.A photometric pipeline is required to reduce raw photo data into a usableimage. First, dark, bias, and flat frames must be acquired. A bias frame isthe result of taking the fastest possible image with the shutter closed/telescopecovered. Doing so eliminates any integration time and measures intrinsic CMOSnoise. A dark frame is similar but requires integration times on par with thoseused to capture the data. Because the CMOS is cooled and the exposure time soshort, the dark frame and bias frame can be expected to be very similar for thisexperiment. In order to construct a master dark and master bias frame, a fewhundred of each bias frames and dark frames will be captured, and their valuesaveraged pixel-by-pixel to produce a master bias and master dark frame for thatobservation session. The flat frame is acquired by imaging a source of uniformillumination to estimate the pixel efficiency of the CMOS. The photometricpipeline is then as follows, as sourced from [4]:1. The bias frame is subtracted off from the object raw frame.2. The bias frame is then subtracted from the flat frame, and then thatquantity is normalized to its mean value.10. The first result is then divided by the second to produce a reduced imagefrom the raw photo data.which can be summarized mathematically as:Reduced Pixel = raw − bias ( flat − bias ) µ (9)For this experiment, flat frames were not used and a uniform matrix of 12-bitpixels was used instead. Flat frames primarily correct for variations in the chip,but because the chip is small, has a fairly consistent response, and the anglesubtended was small, it was determined that flat frames would not enhance thereduced image quality significantly. Beyond noise from the CMOS, cosmic raysalso cause distortions in the form of “hot pixels,” or pixel values erroneouslyhigh when compared to its surrounding neighbors. These pixels can be averagedwith their neighboring pixels to mitigate this effect. This process can be donewith a simple filter. The result from this entire process is a reduced image thatcan be used to make measurements about the relative angular size of targets.An example of a raw image and a reduced image can be found in A.5 and A.6,respectively.The final step in the data post-processing pipeline is downsampling. Due torapidly changing atmospheric conditions, “Lucky Imaging” was used wherebymany hundreds of images are taken for a given configuration, and then down-sampled for each configuration such that only a small percent of the imagesare selected for the final dataset. The remaining images represent the best at-mospheric conditions for a given night, which mitigates a large proportion ofatmospheric noise. The images were selected via a two-step process. First, themaximum valued pixel for each reduced image was found. If that pixel valuewas greater than 80% of the maximum possible intensity (2 = 4096 for a 12bit sensor), then the image was discarded, as pixel values nearing the satura-tion point of the sensor cause distortions in image quality. Second, the FullWidth at Half Maximum (FWHM) is calculated for each of the remaining im-ages. FWHM is twice the distance between the maximum value point and thenearest half maximum point for a data series, and is a measure of how wellresolved the data are. Smaller FWHM scores correlate with higher maximumangular resolutions. Because many of the images of Jupiter were overexposedand because Jupiter was too large to constitute a point source, the decision wasmade to at this time only consider data points collected of Spica. An exampleof one of the overexposed images of Jupiter can be found in A.7.11 Results
In order to measure the performance of the interferometer, baseline measure-ments are first required. Taking the 2D Fourier Transform of a given maskconfiguration yields a point spread function (PSF), which is a reconstruction ofthe image that would be generated by that mask, as shown in Figure 4. Theykey difference between a single aperture configuration versus the two-apertureconfiguration shown is the existance of vertical fringes. See section 2.2 for anexplanation of fringes. Taking the FWHM of the PSF gives the maximum an-gular resolution of that mask configurtion, assuming no atmospheric effects. Todemonstrate the resolution gain described in equation 3, the theoretical mini-mum FWHM for various telescope configurations is provided in Table 3. Fromthe table it is clear to see the resolution gained by the interferometer over thesingle aperture configuration. Lower values are better because they imply thatthe system could detect a fainter object.Figure 4: Point spread function (Right) generated from an example mask con-figuration (Left). 12perture Diameter Configuration FWHM1 in Single Aperture 0.002 rad2 in Single Aperture 0.0005 rad20.4 in Single Aperture 0.0005 rad24 in Single Aperture 0.000003 rad1 in 20.4 in Separation 0.00009 rad1 in 3.7 in Separation 0.0005 rad1 in 3.3 in Separation 0.0005 rad2 in 20.4 in Separation 0.00004 rad2 in 3.7 in Separation 0.0002 rad2 in 3.3 in Separation 0.0003 radTable 3: Theoretical minimum full width at half maximum
To determine the effect of the tested parameters on the angular FWHM, eachpair of variables was separated and plotted against the demonstrated FWHM.While four variables were varied throughout the experiment, they are not allindependant. The aperture separation determines the collection wavelength bysetting the zero-fringe condition. The aperture diameter sets the exposure timeto prevent oversaturation at larger diameters. Thus, by varying the aperturediameter and separation – the two physical qualities set by the mask – withrespect to the achieved FWHM, the full variable space is accounted for. Figure5 and figure 6 show these isolated variables. While aperture separation did notappear to be significantly correlated with the demonstrated full width at halfmaximum, aperture diameter shows strong negative correlation.
The argument best supported by the data is that variation in full width at halfmaximum is primarily controlled by the diameter of the aperture. This is in-tuitive – a larger aperture allows more light to be captured and so allows forthe system to more percisely discriminate between targets. However, this resultalso stands in contrast to the primary justification for using stellar interferome-try. Stellar interfeometry dominates earth-based deep space imaging primarilybecause its performance is characterized by the separation of the apertures, notthe size of the aperture. The data imply that at small scales, aperture size is ofgreater importance to the system’s resolving power than the separation of theapertures. Therefore, the data suggest that there is a fundimental tradeoff be-tween resolving power and scalability for stellar interferometers. At sufficentlylarge scales, the separation between the apertures dominates the observed res-olution, while at small scales this relationship reverses.13his conclusion has three primary implications. First, there is a hard cutoffto the achivable resolving power of optical stellar interferometers for amateurastronomical use. Given the wavelengths involved, the complexity of interferingoptical wavefronts grows expoentially with the baseline, and for the amateurastronomer this growth in complexity will not be worth the marginal gain inresolution, assuming the maximum aperture size is fixed by price limitations.Second, military applications are still viable but remain impractical until agreater understanding of the tradeoff suggested is achieved. Third, commercialapplications also remain viable but will be driven primarily by the ability ofcompanies to find profitable uses of the data. The technology alone is notsufficent to commercial adoption.There exist two primary areas of future work. First, more data are needed toconclusively argue that aperture size controls the observed variation in FWHM.Because so many different configurations were tested, there are not sufficentdata points to confirm this trend, especially given its departure from theory.Additionally, more data are required to conclude that aperture separation isas uninfluential in the observed variation in FWHM as the current data sug-gest. The second area of future work relates to the reversal in trends that thedata suggest. If it is the case that at small scales aperture size determines theobserved angular resolution, then finding the crossover point, both in terms ofminimum aperture size and minimum aperture separation, will be integral tothe future design of stellar interferometric systems.14igure 5: Variation in aperture separation is poorly correlated with full widthat half maximum 15igure 6: Variation in aperture diameter is negatively correlated with minimiz-ing full width at half maximum 16 cknowledgments
I would like to first and foremost extend a huge thank you to Professor Lozano,Professor Hall and Jennifer Craig for all their help throughout the year. Iwould like to thank Professor Cahoy, Dr. Ewan Douglas, and Greg Allen for alltheir support and for helping me through my ideation. I would like to thankDr. Michael Person and Tim Brothers of the Wallace Observatory for allowingme to use the observatory as well as meeting with me to discuss my projectand teaching me how to use all the equipment. My project would be literallyimpossible without telescope access, so to them I am incredibly grateful. Iwould additionally like to thank Todd Billings and David Robertson for theirhelp in designing and fabricating the physical mask that allowed this research tohappen. I could not have completed this project without the enormous amountof support I recieved, and so for that I am very thankful.
References [1] Born, M., and Wolf, E., “Chapter 7: Theory of Interference and Inter-ferometers,” Principles of Optics: Electromagnetic Theory of Propa-gation Interference and Diffraction of Light, London: Pergamon Press,1959.[2] Hariharan, P., ”Chapter 14: Stellar Interferometry”, Optical Interfer-ometry, Second Edition, San Diego: Academic Press, 2003[3] Kitchin, C R, ”Chapter 2: Imaging”, Astrophysical Techniques, FourthEdition, Bristol: Institute of Physics Publishing, 2003[4] Poggiani, R., ”Chapter 6: Optical Photometry”, Optical, Infrared, andRadio Astronomy, From Techniques to Observation Cham: Springer,2017[5] Readhead, A., Nakajima, T., Pearson, T., Astronomical Journal, 1988[6] Sterken, C. and Manfroid, J., ”Chapter 12: Infrared Photometry”,”Chapter 13: Charge-Coupled Devices”, Astronomical Photometry. AGuide, Dordrecht: Kluwer Academic Publishers, 1992[7] Tuthill, P., ”Imaging Stars Through the Atmosphere.”,
British LibraryEThOS , Cambridge, England, 1994,17 ppendix
Figure A.1: Finished mask bolted to the 24in telescope at the MIT WallaceObservatory. The mask is larger than the 24 inch telescope diameter in order tobolt the mask to the outside casing, as shown in A.3. The mask contains 6 pairsof subapertures. There are four centered axial pairs (1L, 1S750, 1S850, 2L) andtwo off-axial pairs (2S750, 2S850). At the time of imaging the pair of interest isuncovered, while the remaining subaperture array remains covered.18igure A.2: PlaneWave CDK24 Telescope CAD Model (cid:2)(cid:3)(cid:4)(cid:5)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12)(cid:8)(cid:13)(cid:14)(cid:10)(cid:2)(cid:15)(cid:3)(cid:16)(cid:2)(cid:16)(cid:10) (cid:10)(cid:16)(cid:2)(cid:3)(cid:17)(cid:18)(cid:5)(cid:10)(cid:10)(cid:16)(cid:15)(cid:3)(cid:19)(cid:5)(cid:15)(cid:10) (cid:8)(cid:3)(cid:12)(cid:3)(cid:20)(cid:3)(cid:10)(cid:8)(cid:21)(cid:9)(cid:17)(cid:22)(cid:10)(cid:23)(cid:24)(cid:25)(cid:26)(cid:10)(cid:24)(cid:27)(cid:11)(cid:19)(cid:5)(cid:10)(cid:11)(cid:12)(cid:8)(cid:13)(cid:14)(cid:28)(cid:27) (cid:2)(cid:3)(cid:29)(cid:16)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12)(cid:8)(cid:13)(cid:14)(cid:10)(cid:17)(cid:16)(cid:3)(cid:4)(cid:16)(cid:17)(cid:10)(cid:10)(cid:16)(cid:2)(cid:3)(cid:19)(cid:2)(cid:5)(cid:10)(cid:10)(cid:16)(cid:15)(cid:3)(cid:19)(cid:5)(cid:15)(cid:10) (cid:8)(cid:3)(cid:12)(cid:3)(cid:20)(cid:3)(cid:10)(cid:8)(cid:21)(cid:9)(cid:17)(cid:22)(cid:10)(cid:23)(cid:24)(cid:25)(cid:26)(cid:26)(cid:28)(cid:21)(cid:27)(cid:24)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12)(cid:8)(cid:13)(cid:14)(cid:28)(cid:27) (cid:10)(cid:4)(cid:2)(cid:3)(cid:5)(cid:16)(cid:2)(cid:10) (cid:10)(cid:4)(cid:16)(cid:3)(cid:19)(cid:18)(cid:5)(cid:10) (cid:21)(cid:8)(cid:6)(cid:7)(cid:7)(cid:6)(cid:8)(cid:21) (cid:16)(cid:17)(cid:4)(cid:22)(cid:2)(cid:15)(cid:18)(cid:29)(cid:29) (cid:18) (cid:15) (cid:2) (cid:22) (cid:4) (cid:17) (cid:16)(cid:28)(cid:11) (cid:28)(cid:11) (cid:14)(cid:8)(cid:7)(cid:30)(cid:28)(cid:31)(cid:16)(cid:31)(cid:16)(cid:17) (cid:14)(cid:24) (cid:28) (cid:21)(cid:23)(cid:20)(cid:3)(cid:10)(cid:10)!(cid:12)(cid:3) (cid:2) (cid:27)(cid:28)"(cid:3) !(cid:7) (cid:14)(cid:26)(cid:28)(cid:28)(cid:25)(cid:10)(cid:16)(cid:10)(cid:12)(cid:11)(cid:10)(cid:16) (cid:8)(cid:7)(cid:21)(cid:11)(cid:24)(cid:30)(cid:28) (cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12)(cid:13)(cid:3)(cid:7)(cid:10)(cid:8)(cid:6)(cid:14)(cid:10)(cid:8)(cid:3)(cid:13)(cid:7)(cid:8)(cid:5)(cid:2)(cid:6)(cid:7)(cid:8)(cid:6)(cid:3)(cid:4)(cid:7)(cid:15)(cid:6)(cid:2)(cid:11)(cid:13)(cid:16)(cid:7)(cid:8)(cid:17)(cid:7)(cid:15)(cid:6)(cid:3)(cid:4)(cid:5)(cid:6)(cid:15)(cid:10)(cid:18)(cid:5)(cid:6)(cid:19)(cid:11)(cid:10)(cid:19)(cid:5)(cid:11)(cid:3)(cid:20)(cid:6)(cid:10)(cid:9)(cid:6)(cid:19)(cid:18)(cid:13)(cid:8)(cid:5)(cid:16)(cid:13)(cid:21)(cid:5)(cid:6)(cid:7)(cid:8)(cid:15)(cid:3)(cid:11)(cid:22)(cid:12)(cid:5)(cid:8)(cid:3)(cid:15)(cid:23)(cid:13)(cid:8)(cid:20)(cid:6)(cid:11)(cid:5)(cid:19)(cid:11)(cid:10)(cid:2)(cid:22)(cid:14)(cid:3)(cid:7)(cid:10)(cid:8)(cid:6)(cid:7)(cid:8)(cid:6)(cid:19)(cid:13)(cid:11)(cid:3)(cid:6)(cid:10)(cid:11)(cid:6)(cid:13)(cid:15)(cid:6)(cid:13)(cid:6)(cid:16)(cid:4)(cid:10)(cid:18)(cid:5)(cid:16)(cid:7)(cid:3)(cid:4)(cid:10)(cid:22)(cid:3)(cid:6)(cid:3)(cid:4)(cid:5)(cid:6)(cid:16)(cid:11)(cid:7)(cid:3)(cid:3)(cid:5)(cid:8)(cid:6)(cid:19)(cid:5)(cid:11)(cid:12)(cid:7)(cid:15)(cid:15)(cid:7)(cid:10)(cid:8)(cid:6)(cid:10)(cid:9)(cid:6)(cid:19)(cid:18)(cid:13)(cid:8)(cid:5)(cid:16)(cid:13)(cid:21)(cid:5)(cid:7)(cid:8)(cid:15)(cid:3)(cid:11)(cid:22)(cid:12)(cid:5)(cid:8)(cid:3)(cid:15)(cid:6)(cid:7)(cid:15)(cid:6)(cid:19)(cid:11)(cid:10)(cid:4)(cid:7)(cid:24)(cid:7)(cid:3)(cid:5)(cid:2)(cid:23) (cid:19)(cid:11)(cid:10)(cid:19)(cid:11)(cid:7)(cid:5)(cid:3)(cid:13)(cid:11)(cid:20)(cid:6)(cid:13)(cid:8)(cid:2)(cid:6)(cid:14)(cid:10)(cid:8)(cid:9)(cid:7)(cid:2)(cid:5)(cid:8)(cid:3)(cid:7)(cid:13)(cid:18) (cid:13)!(cid:30)(cid:28)(cid:14)(cid:14)(cid:10)(cid:12)(cid:25)(cid:26)(cid:28)(cid:27)(cid:23)(cid:24)(cid:14)(cid:28)(cid:10)(cid:14)$(cid:28)(cid:8)(cid:24)(cid:11)(cid:24)(cid:28)(cid:21)(cid:25)(cid:12)(cid:30)(cid:28)(cid:27)(cid:7)!(cid:8)(cid:28)(cid:14) (cid:3)%%%%(cid:3)(cid:5)(cid:5)(cid:5)(cid:2)(cid:3)%%%(cid:3)(cid:5)(cid:5)(cid:2)(cid:3)%%(cid:3)(cid:5)(cid:17) (cid:7)!(cid:20)(cid:13)(cid:30)(cid:7)(cid:27)(cid:10)(cid:21)(cid:24) (cid:17)(cid:22)(cid:5)(cid:16)(cid:5)(cid:16)(cid:6) (cid:6) (cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:3)(cid:8)(cid:9)(cid:10) (cid:5)(cid:6)(cid:11)(cid:12)(cid:11)(cid:12) (cid:29)((cid:16)(cid:18)((cid:17)(cid:5)(cid:16)(cid:17)(cid:9)(cid:7)(cid:24) (cid:13)(cid:14)(cid:15)(cid:7)(cid:16)(cid:15)(cid:10)(cid:13) (cid:9)(cid:8)(cid:10)(cid:2)(cid:17) (cid:25)(cid:24)(cid:25)(cid:30)(cid:28) (cid:8)(cid:26)(cid:28)(cid:8)(cid:9)(cid:28)(cid:21) (cid:51)(cid:79)(cid:68)(cid:81)(cid:72)(cid:58)(cid:68)(cid:89)(cid:72) (cid:3) (cid:8)(cid:18)(cid:19)(cid:20)(cid:21)(cid:22)(cid:23)(cid:24)(cid:18)(cid:20)(cid:19)(cid:8)(cid:18)(cid:19)(cid:20)(cid:21)(cid:22)(cid:23)(cid:24)(cid:18)(cid:20)(cid:19)