Optical design of the Atacama Cosmology Telescope andthe Millimeter Bolometric Array Camera
J. W. Fowler,1,* M. D. Niemack,1 S. R. Dicker,2 A. M. Aboobaker,1,3 P. A. R. Ade,4 E. S. Battistelli,5
M. J. Devlin,2 R. P. Fisher,1 M. Halpern,5 P. C. Hargrave,4 A. D. Hincks,1 M. Kaul,2 J. Klein,2
J. M. Lau,1 M. Limon,2 T. A. Marriage,1,6 P. D. Mauskopf,4 L. Page,1 S. T. Staggs,1
D. S. Swetz,2 E. R. Switzer,1 R. J. Thornton,2 and C. E. Tucker4
1Department of Physics, Princeton University, Jadwin Hall, Washington Road, Princeton, New Jersey 08544, USA2Department of Physics and Astronomy, University of Pennsylvania, David Rittenhouse Laboratory,
209 South 33rd Street, Philadelphia, Pennsylvania 19104, USA3Present address: School of Physics and Astronomy, University of Minnesota, 116 Church Street SE, Minneapolis,
Minnesota 55455, USA4School of Physics and Astronomy, Cardiff University, Queens Buildings, 5 The Parade, Cardiff CF24 3AA, Wales, UK
5Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver,British Columbia V6T 1Z1, Canada
6Present address: Department of Astrophysical Sciences, Princeton University, Peyton Hall, Ivy Lane, Princeton,New Jersey 08544, USA
The Atacama Cosmology Telescope [1] (ACT) will ob-serve the oldest light in the universe, the cosmic mi-crowave background (CMB), mapping it on sales fromarcminutes to degrees. The CMB is relic thermal ra-diation released when the early universe had cooledenough for the primordial plasma to form a neutralgas, allowing light to stream freely ever since. TheCMB’s blackbody spectrum has redshifted with theexpansion of the universe to a present temperature of2.7 K. The temperature is uniform to tens of parts permillion. Recently, the Wilkinson Microwave Anisot-ropy Probe [2] (WMAP) has measured the CMB powerspectrum (the amplitude of temperature fluctuations
in the CMB as a function of angular scale) at resolu-tions as fine as 0.3°. The data from WMAP in conjunc-tion with other experiments [3–7], some at higherresolution, permit estimates of the universe’s globalcurvature and other properties with unprecedentedprecision [8].
Maps of the CMB with high resolution from ACT—combined with optical, UV and x-ray measurements—will further constrain inflationary models of the earlyuniverse, constrain the equation of the state of darkenergy in the universe, probe light neutrino massesdown to mv � 0.1 eV, and map the mass distributionof the universe [9–11]. Such science will require mea-surements of the CMB temperature in multiple fre-quency bands near the null in the Sunyaev–Zel’ovich(SZ) effect [12] spectrum �217 GHz� to a precision of afew microkelvins at resolutions approaching 1 arc min.Arcminute resolution at these frequencies requires
telescopes in the 5 to 10 m range. As a compromisebetween cost and angular resolution, ACT has a 6 m(projected diameter) primary mirror. In this paper weoutline the optical design that we have developed tomeet our science requirements.
At approximately 217 GHz, atmospheric absorp-tion permits observations only at high, dry sites. TheAtacama plateau in northern Chile offers an excel-lent combination of observing conditions, sky cover-age, and accessibility and was selected as the site forACT. The telescope described here has been built,and it has been shipped to Chile from its constructionsite in Port Coquitlam, British Columbia.
2. Telescope and Camera Overview
Meeting the ACT science goals requires extreme sen-sitivity, better than 10 �K rms uncertainty in mappixels of 3 arc min [2]. Even with sensitive modernmillimeter-wave detectors, large focal planes contain-ing many hundreds of detectors, months of integra-tion time, and careful control of systematics are allessential. This section discusses the major require-ments and features of our approach, which are sum-marized in Table 1.
The fundamental requirement of the ACT andMillimeter Bolometric Array Camera (MBAC) opticsdesign is that the telescope and camera must reimagethe sky onto a focal plane filled with detectors�1.0 mm in size and that the image be diffractionlimited. The design is subject to geometric limitationson the size and separation of the mirrors. The controlof stray light is also of particular importance since theACT detectors will be used without feedhorns. Spill-
over radiation from the ground around the telescopemust be prevented from reaching the detectors, andreflections and scattering within the optics must beminimized.
CMB experiments deliberately modulate their sen-sitivity to cosmic signals in order to reduce the impactof drifts in detector response, such as 1�f noise. Typ-ical modulation methods involve using an opticalchopping mirror or scanning the entire telescope inazimuth. In either case, the telescope beam movesrapidly back and forth on time scales faster than the1�f knee of any low-frequency noise. We chose thescanning method because it avoids a chopping flat’smost intractable scan-synchronous variations, in-cluding primary beam shape, ground pickup pattern,and mirror emission. Our normal observing mode willbe to scan the 50 ton telescope in azimuth over a 5°range repeating every 5 to 6 s, while holding theelevation fixed (typically at 48°). This motion placesconsiderable rigidity requirements on the telescopestructure (see Subsection 5.C). Observing at fixed el-evation ensures that the large gradient in atmo-spheric emission enters the camera as a constantaddition, not as an ac term synchronized with thesignal. To maintain a constant speed for as much ofthe scan as possible, we have aimed for brief acceler-ation periods of 300 ms at either end of each scan.
ACT will make simultaneous observations at 145,215, and 280 GHz to distinguish variations in theprimordial CMB from secondary anisotropies such asSZ galaxy clusters and foregrounds such as galacticdust and point sources [13]. ACT’s receiver, MBACwill contain a 32 � 32 array of transition edge sensor(TES) bolometers [14,15] at each of the three frequen-cies. The arrays will be cooled to 0.3 K by a closed-cycle helium-3 refrigeration system [16,17]. Becausethe TES detectors are bolometric, the ACT opticsmust also have optical filters to define the bandpassfor each camera.
The ACT detectors are 1.05 mm square and arespaced on a 1.05 mm (horizontal) by 1.15 mm (verti-cal) grid. Detectors aimed less than half a beam widthapart on the sky fully sample the field of view in asingle pointing. This is advantageous for minimizingdetector and atmospheric noise in mapmaking [18],and ACT detectors reach this ideal at the lower fre-quencies. The effective focal length is 5.2 m for allarrays, giving a detector spacing of 44 arc sec (hori-zontal) and 48 arc sec (vertical) on the sky. This spac-ing is half the expected beam size at 145 GHz. Theuse of a fast final focus at the detectors will allowMBAC to map the sky rapidly without compromisingdiffraction-limited imaging performance.
3. Gregorian Telescope Optics
The two-reflector ACT was optimized to have the bestpossible average performance across a square-degreefield of view by varying the mirror shapes, angles,and separation. This compromise balances the vari-ous classical telescope aberrations for point imagesagainst each other. The design process for ACT usedboth analytic and numerical methods. Numerical
Table 1. Requirements and Features of the Atacama CosmologyTelescope Optics
Warm Telescope Optics
● Clear aperture (off-axis optics) to minimize scattering andblockage.
● 6 m primary mirror and 2 m (maximum) secondary mirrordiameters.
● Very fast primary focus (F � 1) to keep the telescopecompact.
● Large (1.0°) and fast (F � 2.5) diffraction-limited focal plane.● Ground loading (due to spillover) smaller than atmospheric
loading.● Space for structure and cryogenics between primary mirror
and Gregorian focus.● Entire telescope must scan several degrees in azimuth at 10
methods alone might seem sufficient because the endresult of a global optimization is independent of thestarting design. But the telescope parameter space islarge and complicated, and we found it critical toenter the numerical stage with a good analytic de-sign. We used the Code V optical design software [19]to optimize the telescope design and to analyze itsperformance.
Our initial analytic designs met the Dragone con-dition [20,21] to minimize astigmatism, following theimplementation of Brown and Prata [22]. This condi-tion also minimizes geometrical cross polarization[23]. A comparison of Gregorian and Cassegrain so-lutions showed that in otherwise equivalent systems,the Gregorian offered more vertical clearance be-tween the secondary focus and the rays travelingfrom the primary to the secondary mirror. The extraclearance leaves more space for our �1 m3 cryostat,so the Gregorian was chosen for ACT.
A simple Gregorian telescope satisfying the Drag-one condition did not meet the diffraction-limitedfield of view requirement, but it was taken as thestarting point for the numerical stage. The systemwas optimized by minimizing the rms transverse rayaberration at field points across the focal plane. Sixdesign parameters were allowed to vary: the twoconic constants, the relative tilt of the primary andsecondary axes, the secondary radius of curvature,and the location and tilt of the Gregorian focal plane.The primary focal length was fixed at exactly 5 m tokeep the telescope compact. We found that requiringthe primary and secondary mirrors to be coaxial didnot substantially degrade image quality, so we im-posed this constraint to simplify the manufacturingand alignment of the telescope.
Our final design approximates an ideal aplanaticGregorian telescope, a system with no leading-orderspherical aberration or coma in the focal plane [24].Strehl ratios S were estimated by calculating �, therms optical path variation over a large bundle of rays,and taking [25] ln S � ��2���2. Over a 1.0° squarefield at the Gregorian focus, the Strehl ratio every-where exceeds 0.9 at 280 GHz.
The two mirrors are off-axis segments of ellipsoidsin the final ACT design. Figure 1 contains mechanicaldrawings, while Fig. 2 presents a ray trace and showsthe z and y axes. The parameters of each mirror arelisted in Table 2. Both shapes can be described by
z�x, y� � zvert ��x2 � y2��R
1 � �1 � �1 � K��x2 � y2��R2, (1)
where z is along the shared axis of symmetry (see theaxes in Fig. 2), zvert is the vertex position (the primaryvertex defines z � 0), R is the radius of curvature atthe vertex, the conic constant K � �e2, and e is theellipsoid eccentricity. The usable region of eachmirror is bounded by an elliptical perimeter. Whenprojected into the xy plane, these boundaries are cen-tered at �x, y� � �0, y0� and have semimajor andsemiminor axes of a and b in the x and y directions,
respectively. The primary projection is circular, witha � b.
Diffraction at the small aperture stop (in the cryo-genic camera) can lead to systematic errors, particu-larly if it loads the detectors with radiation emittedby ambient-temperature structures near the two mir-rors. To minimize this spillover effect, each mirror issurrounded by a reflective aluminum guard ring. Therings enlarge the mirror area beyond the geometricimage of the aperture stop; they ensure that mostradiation reaching the detectors comes from the coldsky, in spite of diffraction at the cold stop.
The ACT design also ensures that there is at least1 m of clearance between any ray approaching thesecondary and the top of the Gregorian focal planeused by MBAC. The clearance allows room for a re-ceiver cabin that will protect the cryostat and itssupporting electronics from the harsh environment ofthe Atacama desert.
AMEC Dynamic Structures, Port Coquitlam, Can-ada, has designed, modeled, and built the telescope’smechanical structure [26]. KUKA Robotics, ClintonTownship, Michigan, USA, provided motion control[27]. The primary mirror and secondary surfacesconsist of 71 and 11 aluminum panels, respectively.Forcier Machine Design, Petaluma, California, USA[28], produced all of the panels. The panels were sur-veyed one at a time by a coordinate measuring ma-chine and were found to have a typical rms deviationfrom their nominal shapes of only 2–3 �m. We mea-sure the positions of all the panel surfaces relative totelescope fiducial points with a Faro laser trackingsystem [29]. Four manually adjustable screw mountson the back of each panel then permit precise repo-
Fig. 1. The ACT telescope. The mechanical design has a lowprofile; the surrounding ground screen completely shields the tele-scope from ground emission. The screen also acts as a weathershield. An additional ground screen (not shown) mounted on thetelescope hides the secondary and half the primary from the van-tage point of the lower diagram. This inner ground screen is alu-minum painted white to reduce solar heating. The primary mirroris �7 m in diameter including its surrounding guard ring. “BUS”refers to the mirror’s backup structure (Fig. credit: AMEC Dy-namic Structures).
sitioning. To date, we have aligned the secondarypanels to approximately 15 �m rms. A subset of 12primary panels has also been aligned to 30 �m rmsand monitored in detail over two 24 h periods. Thissubset includes a cluster of six contiguous panelsnear the edge of the primary and six others distrib-uted uniformly over the remaining area. We find thatthe primary expands thermally as if it were a singlealuminum structure, except for mirror panels di-rectly illuminated by the sun. We intend to adjust themirror facets annually, if necessary.
Considerable effort has gone into ensuring the bestpossible performance for the azimuthal scanning ofthe telescope, a difficult task given its size and weight��50 tons�. The telescope meets the scanning target
of 2.5° at an angular speed of 2.0°�s with a turn-around time of 300 ms. Encoders mounted on theazimuthal and elevation axes give 27-bit readings ofthe telescope orientation. We have found that thepointing during scans is repeatable to better than4 arc sec. Turnarounds cause vibrations in the struc-ture which induce brief �8 arc sec shuddering move-ments in elevation and an unavoidable �10 arc secbounce in azimuth, due to the finite bandwidth of thedrive servos. The azimuth bearing is driven by a pairof counter-torquing helical gears, eliminating back-lash. The elevation errors occur only during the ac-celerations, while the azimuth bounce damps outexponentially � 200 ms after the acceleration ends.Studying a large number of successive scans hasshown that the rms deviation from the average scanshape is no more than 6.5 arc sec with 400 Hz sam-pling, demonstrating good repeatability of the scanpattern.
ACT’s compact design minimizes the accelerationsof the secondary and especially the cryogenics (whichare near the rotation axis), simplifying mechanicaldesign and helping to maintain refrigerator stability.The fast Gregorian focus �F � 2.5� keeps the vacuumwindow for the detector cryostat from being too large.Figure 2 shows the size and shape of the receivercabin.
Fig. 2. (Color online) Rays traced into the MBAC cryostat (mounted at the far right of the receiver cabin). The stowed position is shown,corresponding to an elevation of 60° (generally, observations will be in the 40°–50° range). The rays are traced from the central, highest,and lowest fields in the 280 GHz camera (higher in the cryostat) and the 215 GHz camera. Both the 215 GHz camera and the 145 GHzcamera (not shown) lie outside the x � 0 midplane, relieving any apparent conflicts between filters and lenses from different cameras. Thefigure also shows the size and shape of the ACT receiver cabin, as well as the coordinate axes of Eq. (1).
Actuators can move the secondary mirror structurein the y and z directions by 1 cm from the nominalposition and can tilt it up to 1° in elevation orazimuth. We anticipate having to refocus in responseto changes in ambient temperature or observing an-gle. We plan to operate the actuators as infrequentlyas possible, consistent with holding the primary–secondary distance to within 100 �m of nominal.
4. Cold Reimaging Optics in MBAC
Many possible architectures for the cold optics werestudied, including all-reflecting designs, all-refractingdesigns, and hybrids of the two. We also compareddesigns of a single camera having dichroic filters tosegregate the frequencies against a three-in-one cam-era design using a separate set of optics for each fre-quency. The final MBAC design uses only refractiveoptics instead of mirrors and employs the three-in-oneapproach.
A. MBAC Architecture
Off-axis reimaging mirrors were studied by combiningthe equivalent paraboloid approximation [30] with theDragone condition [22], then explored through nu-merical optimization. They were rejected becausethe twin demands of image quality and a wide fieldof view led to designs too large to fit in a cubic-metercryostat. For off-axis mirrors, the compromises be-tween image quality and access to a cold image ofthe primary were also unacceptable. On-axis mir-rors violated the requirement of an unobstructedaperture.
We have built dichroic beam-splitting filters aslarge as 15 cm in diameter and metal mesh filters upto 30 cm in diameter [31]. Dichroics reflect one bandand therefore must be flat to ���40 � 25 �m at280 GHz. Our optical designs required dichroicslarger than any so far produced, and we consideredtheir production and mounting too great a risk.
We chose a camera architecture with a separate setof cold lenses for each frequency, eschewing both coldmirrors and dichroic beam splitters. There are sev-eral advantages of this design: antireflection (AR)coatings and capacitive mesh filters generally havehigher transmission, and are easier to optimize, fornarrow bands; the mechanical design is simpler,more compact, and easier to align; and the three cam-eras are modular and can be removed from the cry-ostat separately for easy maintenance or for deployingMBAC in stages. The disadvantage is that each cam-era observes a different area of sky. Maps made withseparated cameras do not completely overlap, thoughACT’s observing plans mitigate the problem. ACT’sscanning motion (Section 2) ensures that the 215 and145 GHz cameras observe most of the same sky re-gion in a single scan, and the rotation of the earthmoves fields on the sky from MBAC’s lower-elevationcameras to the upper one (or vice versa) in less than15 min.
A triangular configuration was chosen for the threecameras (Fig. 3) because it packs the cameras as closeas possible to the field center, where the Gregorian
image quality is best (as measured by Strehl ratio).The close packing also maximizes the overlap of ob-servations. The 280 GHz camera is centered on thetelescope’s plane of symmetry because it has thetightest diffraction requirements. The 215 and 145GHz cameras are placed symmetrically below it, al-lowing us to use a single design for the two lower-frequency lens sets. All the lenses within eachcamera are parallel and share one axis. The focalplanes and the bolometer arrays are tilted by 8° or 5°from the common axis of the lenses in their respectivecameras.
B. Camera Components
Figure 3 shows all three MBAC cameras. Separatevacuum windows are used for each camera. Thewindows are made of ultrahigh molecular weightpolyethylene (UHMWPE) and have AR coatingsappropriate to their respective wavelengths. Lightentering the camera module passes through anambient-temperature infrared blocking thermal fil-ter [32] (mounted just inside the vacuum window)and three capacitive mesh filters cooled to 40 K(marked LP in Fig. 3); two of the three are thermalfilters, and one is a millimeter-wave low-pass filter.Together, these filters reduce blackbody loading onthe colder stages and block out-of-band leaks in thebandpass filter. A plano–convex silicon lens (Lens1) creates an image of the primary mirror near Lens2. An assembly holds Lens 2 and two final low-passfilters at 1 K and contains a cold aperture stop (Lyotstop). The last two plano–convex silicon lenses(Lenses 2 and 3) refocus the sky onto the array. Thebandpass filter stands between these lenses, wherethe beam is slow enough for the filter to be effective.Lens 1 is cooled to 3 K; Lens 2 and the associated
Fig. 3. Cold MBAC reimaging optics. Each frequency has a sim-ilar set of lenses and filters. The 280 GHz silicon lenses are labeledLens 1 to 3 (with Lens 1 closest to the window). IR-blocking andlow-pass capacitive mesh filters are all labeled LP; the bandpassfilter is labeled BP. An IR-blocking filter (not shown) is also inte-grated into the window assembly. The temperatures of the compo-nents decrease away from the window as indicated. The bandpassfilter, Lens 3, and the array are held at 0.3 K.
filters are cooled to 1 K; Lens 3 and the bandpassfilter are cooled to 0.3 K. The unobstructed circularaperture of each element is large enough so that theoutermost ray that can strike any detector passes atleast five wavelengths from the aperture’s edge,with the intentional exception of the Lyot stop. Theentire camera is contained in a light-tight tube withcold black walls to absorb stray light. The walls areblackened with a mixture of carbon lampblack andStycast 2850 FT epoxy [33]. All walls between thebandpass filter and the array are held at the coldestavailable temperature, 0.3 K, because their emissionreaches the detectors without filtering.
Silicon was chosen as the lens material because ofits high thermal conductivity and high refractive in-dex �n � 3.416 at 4 K� [34,35]. Pure, high-resistivitysilicon �� 5000 � cm� is necessary to minimize ab-sorption loss. Silicon of very low electrical conductiv-ity and low millimeter-wave loss must be made by thefloat zone process rather than by the more common(and less expensive) Czochralski process. Float zonesilicon is available [36] in diameters up to 20 cm,restricting our clear aperture size to 19 cm. Alterna-tive materials considered for the ACT lenses includedhigh density polyethylene (HDPE), crystalline quartz,fused quartz, and sapphire. Quartz and sapphire areboth more expensive to buy and more difficult to cutthan silicon. Optical designs were made using HDPEas a backup option. However, the plastic designshave substantially poorer image quality, a result ofmaking large deflections with a less refractive ma-terial. Also, the lower-index HDPE required muchthicker lenses and consequently higher absorptionloss.
When using high refractive index materials, suchas silicon, AR coatings are critical. We have devel-oped a method for AR-coating silicon with quarter-wave layers of Cirlex �n � 1.85� [37]. Test samplesshow reflectivities less than 0.5% and transmissionexceeding 95% per sample. We expect that the threelenses in each camera will absorb a combined 15% ofincident light, predominantly in the Cirlex coating.Because of the corresponding emissivity in the lensesand their coatings, it is necessary to cool the lensescryogenically, reducing the power they emit.
Plano–convex lenses are used so that only one faceof each lens must be machined. The curved figuresare surfaces of revolution of conic sections plus poly-nomial terms in r4, r6, r8, and r10 to give maximaldesign freedom. As the lenses were diamond turnedon a computer-controlled lathe, there was no costpenalty for adding axially symmetric terms to thelens shapes. The curved and flat surfaces of each lenswere oriented so as to minimize reflection-inducedsecondary (ghost) images (see Subsection 5.D).
C. Design Procedure
The Gregorian telescope design was held fixed duringthe cold optics design process, while the lens shapesand positions were varied. The 280 and 215 GHzcameras were optimized separately. Because the 145
and 215 GHz cameras are placed symmetricallyabout the telescope’s symmetry plane—and becausethere is no evidence for appreciable dispersion in sil-icon at millimeter wavelengths—the two design prob-lems are mathematically equivalent; a single cameradesign was used for both.
The optimization method for the camera was sim-ilar to the method used to design the Gregoriantelescope, but with additional constraints. Most im-portantly, we required a faithful image of the pri-mary mirror in each camera at which to place a Lyotstop. This image quality was quantified by tracingrays from all field points through four points on theperimeter of the primary mirror. The rms scatter ofsuch ray positions where they crossed the Lyot stopplane, projected onto the radial direction, was in-cluded in the merit function. Thus an astigmaticimage of the primary elongated tangent to the stopwas not penalized, but a radial blurring was. Thisadditional parameter measures the radial ray ab-erration at the aperture stop.
A second constraint was the effective focal length,fixed at 5.2 m by checking the plate scale for pointsnear the center of each subfield. Finally, we found itnecessary to require that the chief ray from each fieldstrike the focal plane at no greater than an 8° angle,which keeps the tilt of the detector plane small tomaximize absorption in the detectors. This low-tiltrequirement also produces an approximately telecen-tric image, meaning that the exit pupil is large andfar from the detector plane. A telecentric image hasthe advantage that the plate scale does not depend tofirst order on the relative positioning of the detectorarray and the lenses.
The optimizer varied up to 27 parameters in eachdesign: three lens positions along the optic axis, theposition of the Lyot stop and its tilt, the detectorposition and tilt, and the lens shapes (the parametersincluded curvature, conic constant, and four asphericpolynomial terms). We found that tilting the Lyotstop surface did not offer enough advantage to justifythe added mechanical complication and thereafterdid not allow it to tilt, reducing the number of pa-rameters to 25. The center thickness of each lens wasset by requiring the edge to be at least 2 mm thick formechanical strength; the center thickness was notvaried by the optimizer. We did not constrain thedimensions of the elliptical Lyot stop. Striking theright balance in the merit function between optimiz-ing the image of the sky at the detector plane and theimage of the primary at the Lyot stop was challeng-ing. Our most successful approach to meeting bothgoals simultaneously was to make two optimizingpasses. In the first pass, the Lyot stop image wasgiven large weight. In the second, it was given zeroweight, but all parameters that affect the stop imagewere fixed (including the shape and placement of L1and the placement of the stop).
The MBAC cold optics design is somewhat unusualin its use of AR-coated silicon lenses at cryogenictemperatures. For this reason, we have built a pro-totype 145 GHz receiver (CCam, the column camera)
with a cold optics design based on the same principlesas MBAC. We have tested CCam with a 1.5 m tele-scope and used it successfully to observe astronomicalsources [38], giving us confidence in the soundness ofthe general design of MBAC.
5. Design Evaluation
The full optical design was studied using both raytracing and physical optics. Most analyses were firstdeveloped for the Penn Array Receiver at the GreenBank Radio Telescope [39]. We present the studiesmost relevant to deployment, calibration, and dataanalysis for ACT.
A. Image Quality
The median Strehl ratios across the fields in the finaldesign are calculated to be 0.991, 0.980, and 0.983 at145, 215, and 280 GHz, respectively (Fig. 4). The low-est Strehl ratios corresponding to any of the 225 fieldpoints tested in each camera are 0.971 �145 GHz�,0.939 �215 GHz�, and 0.958 �280 GHz�. This perfor-mance is the baseline for comparison in the toleranceanalysis (Subsection 5.C). These Strehl ratios estab-lish that all points in the field of view will be diffrac-tion limited.
A small amount of field distortion results from re-imaging such a large focal plane (Fig. 5). One effectis anamorphic magnification, or horizontal imagestretching: The plate scale in all cameras is 6.8 arcmin per cm for vertical separations, but for horizontalseparations it is only 6.4 arc min per cm in the280 GHz camera and 6.6 arc min per cm in the oth-
ers. The other effect is a shearing of the image in the145 and 215 GHz cameras; lines of constant eleva-tion are twisted by approximately 1.4° with respectto horizontal rows of detectors. There is no appre-ciable rotation of lines of constant azimuth. Thesedistortions will be taken into account in makingCMB maps from the data, but at the predicted lev-els they will not complicate our observations.
B. Stop Size and Spillover
The size of the elliptical Lyot stop was chosen to passlight from only the central 97% of the primary mirrordiameter in the geometric optics limit. Rays weretraced from many field angles through a circularentrance pupil of diameter 291 cm; the pupil wascentered at the primary and perpendicular to itsaxis. The Lyot aperture stop in each camera waschosen to be the largest ellipse that blocks all suchrays. The illumination of the primary from any sin-gle field point does not quite fill 97% of the mirrordiameter. This is because the Lyot stop is not aperfect image of the primary for all field angles; tomake it so would degrade sky imaging performancebecause the two goals of imaging the sky and thestop compete for control over the shape and positionof the first lens.
The Lyot stops are 43, 64, and 91 wavelengths wideat 145, 215, and 280 GHz, respectively. This resultsin a significant amount of diffraction, so geometricanalysis of the Lyot stop does not correctly predict thespillover. Radiation from point sources at the focalplanes was traced backward through the ACT opticsusing diffraction analysis to calculate the complexelectric field at each surface. The intensity at each
Fig. 4. Strehl ratio at points in the three ACT fields, as a functionof field angle on the sky. The rectangular aspect of the focal planearray is primarily responsible for the departure from square fields,but anamorphic field distortion also contributes. The figure alsoindicates the relative spacing and size of the three fields. Themedian Strehl ratios are 0.983, 0.980, and 0.991 for the 280, 215,and 145 GHz cameras.
Fig. 5. Field distortion for the ACT optical design. The dashedsquare boxes depict a notional rectangular grid of field points onthe sky, without distortion; the solid lines indicate the image ofthe same grid after it is refocused at the detectors (assuming thenominal 5.20 m effective focal length).
mirror surface but beyond the mirror’s physical edgeis considered spillover. A result for the primary andsecondary mirrors from a typical field is shown inFig. 6. To redirect spillover onto the sky, each mirroris surrounded by a reflecting planar guard ring, ori-ented parallel to the plane of the mirror’s edge.
The illumination patterns were used to calculatethe percentage of power missing the primary andsecondary mirrors. For typical points in the 145GHz field, 0.2% of power spills over at the primaryand 0.6% at the secondary. The values are muchsmaller for the 215 and 280 GHz cameras. The spill-over would be approximately twice as large withoutthe guard ring. Decreasing the size of the Lyot stop toilluminate only 95%, 90%, and 85% of the main mir-ror diameter would not significantly reduce spilloverbecause the main contribution is from faint diffrac-tion into wide angles at the secondary mirror. Somediffraction from the edge of the Lyot stop misses thesecondary mirror regardless of how much of the pri-mary mirror is illuminated, barring unrealisticallylarge guard rings on the secondary. Therefore there isno great advantage in reducing the primary mirrorillumination. We do not expect the calculated second-ary spillover to be a problem because the majority ofit is reflected directly toward the sky.
C. Tolerance Analysis
Calculations were undertaken to find out how ac-curately optical elements need to be placed. Posi-tion and angular displacements were varied for alloptical elements. Other parameters varied were therefractive indices of lenses, the shapes of surfaces,and the temperature of the telescope. The size of theperturbations was increased until the rms wave-front error of a test field increased by 0.016� (a
reduction in the Strehl ratio of approximately 0.01).The results of these tests were compared to the re-sults of dynamic finite element analysis (FEA) of thetelescope structure produced by AMEC. In the follow-ing, note that a change in the Strehl ratio produces aproportionate change in the instrument’s forwardgain.
The tolerancing tests were performed both withand without allowing refocusing of the telescope us-ing the secondary mirror (see Section 3). All staticmisalignments predicted by FEA were easily com-pensated by refocusing. We anticipate having to re-focus with each change in elevation, according to atable to be built from beam maps made on bright,unresolved sources. Uniform temperature changesbetween �20 °C and 20 °C do not degrade opticalperformance. Temperature gradients cause changesin the Strehl ratio well below the expected level ofvariations in atmospheric transmission (and at slowertime scales), with the possible exception of direct in-solation on the panels in midday. More serious arethe 1% Strehl changes expected when the telescope isaccelerated at either end of each scan. These changeswill be scan-synchronous and might require cuttingsome small fraction of the data.
Refocusing the secondary could correct for uncor-related random positioning errors of every opticalelement in a single camera if the misalignments donot exceed 2 mm rms in displacement or 5° rms tilts.Unfortunately, though, one compromise correctionmust be made for all three cameras. Given this con-straint, we find that the MBAC optical elements needto be placed to within 1.5 mm and 2° of their nominalpositions and orientations. Careful mechanical de-sign will achieve these values. The one dimension ofsubstantially tighter tolerance is the spacing between
Fig. 6. The calculated illumination patterns of the (left) primary and (right) secondary mirrors projected into the �x, y� plane for thecentral 215 GHz detector. The inner dashed circles show the edge of the mirrors, and the outer ones show the guard ring. Fine-scalestructure in the right panel is an artifact of numerical precision and finite sampling, but all other structure is real. (Units are dB belowpeak level.)
the arrays and the coldest lenses (Lens 3). This dis-tance must be accurate to 0.5 mm owing to the fastfocus onto the detectors. Mounting the detectors andLens 3 to a single metal structure will allow us toreach the required accuracy.
D. Ghost Images
Light undergoing an even number of reflections fromthe nominally transparent lens and filter surfaces inMBAC can produce secondary (ghost) images. Pro-vided that the intensity of such images is well belowthat of the diffraction-limited point spread function(PSF), their effect can be ignored. Where this is notthe case, ghost images will act as extra sidelobes tothe main beam. We have estimated the ghosting ef-fects using ray tracing. For each pair of cold surfaces,10,000 rays were traced through the system to thedetector focal plane, and an image was built up byadding the ray intensities incoherently. Each ray wasweighted by the reflectivity of the two surfaces fromwhich it reflected. For simplicity, reflectivity was as-sumed to be independent of incident angle. Conser-vative (i.e., large) estimates were used: 3% reflection
for the window, 4% for each low-pass filter, 2% for thebandpass filter, 10% for the array, and 1% per surfacefor the AR-coated lenses. To account for diffraction,the resulting ghost images were smoothed with thePSF of the main image.
The calculations for all fields in all three camerasgave results qualitatively similar to those shown inFig. 7. The reflections between closely spaced planarelements (such as the first three low-pass filters orthe bandpass filter and the last lens) create a ghostcoincident with the main image, resulting in a peakat approximately �28 dB, centered on the main PSF.This ghost is much less intense than the diffraction-limited main image and is of little consequence. Lightreflected from the bandpass filter and any of severalother lens or filter surfaces creates a much broaderghost image on the opposite side of the array from themain image, with amplitudes as high as �41 dB.Although this is brighter than the diffraction side-lobes of the main PSF at that distance, the diffuseghost image will be below the noise of any antici-pated integration except around the brightest pointsources. With the conservative reflectivity estimatesused in the present analysis, the ghost image’s inte-grated intensity is approximately 2% that of the mainPSF. We expect a ghost image of this magnitude to bedetectable during beam-mapping studies of bright,unresolved sources (e.g., planets), but ghosting willnot be a problem for our planned CMB observations.
6. Conclusions
We have developed a diffraction-limited optical de-sign that can be used to illuminate large arrays ofmillimeter-wave detectors. The design meets the re-quirements described in Table 1, and we have studiedthe system properties using geometric and diffractionanalysis techniques. The Gregorian system describedin this paper has been built in British Columbia (Fig.8). The 6 m telescope was installed in Chile in early2007. The cold optics are being built separately andwill be installed on the telescope subsequently. A
Fig. 7. (Color online) Secondary (ghost) images formed by straylight reflected twice from lens, filter, window, and array surfacesfor a source imaged near the top of the 215 GHz detector array. Theamplitude and shape of the ghost images shown here are typical ofall fields, assuming conservative values for surface reflectivities.The dotted lines cross at the center of the main image (not shown).The solid rectangle 3.4 cm wide by 3.6 cm high shows the extentof the focal plane array. The shading indicates the ghost imageintensity on a linear scale relative to the peak of the main PSF,saturating at 5 � 10�4; the contours show intensities of �47, �44,�41, �38, �35, and �32 dB relative to the main PSF. The ghostintensity peaks very near the main PSF at approximately �28 dB,where it is negligible. The diffuse ghost on the opposite side of thearray reaches only �41 dB and is unlikely to affect CMBobservations.
Fig. 8. The ACT telescope mostly assembled at AMEC in June2006. The inner ground screen is not completed in this photograph.
prototype camera with a cold optics design based onsilicon lenses has been built and has observed astro-nomical sources using a Gregorian reflector muchsmaller than ACT.
ACT is a dynamic collaboration, and we thank allits members for many conversations and friendly de-bates. We thank Bob Margolis for his years as ACTproject manager and thank the employees of AMECDynamic Systems, KUKA Robotics, and Forcier Ma-chine Design for their countless contributions to thisproject. We thank the Princeton Physics MachineShop for their work on the design and construction ofCCam. We thank Mandana Amiri, Bryce Burger, Ro-lando Dunner, Norm Jarosik, Barth Netterfield, andYue Zhao for thoughtful conversations about optics,telescope operation, and related detector matters, aswell as for their collaboration in the laboratory andon-site at AMEC. This work was supported by theU.S. National Science Foundation through awardsAST-0408698 for the ACT project and PHY-0355328.Princeton University and the University of Pennsyl-vania also provided financial support. M. D. Niemackacknowledges support from 2004–2006 SPIE Educa-tional Scholarships in Optical Science and Engineer-ing; A. D. Hincks acknowledges a NSERC PGS-Dscholarship; M. D. Niemack and T. A. Marriage ac-knowledge Princeton University Centennial andHarold Dodds Fellowships; and T. A. Marriage ac-knowledges a NSF Graduate Fellowship.
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