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Large chopping secondary mirror for the 15-m submillimeter James Clerk Maxwell telescope Herman van de Stadt and Jaap Verkerk A 75-cm diam chopping secondary mirror has been developed for the 15-m diam James Clerk Maxwell telescope. The large focal ratio (DIF = 1:0.36) requires a highly convex secondary mirror, which was manufactured out of a solid slab of high-grade aluminum, consisting of a 3-mm thick shell with a support ring alongthe edge. The mirror surface approaches a predescribed hyperboloid with a rms precision better than 9 ,um, which is adequate for use in the submillimeter wavelength region. The design aspects, the performance of a two-axis chopping mechanism, and the construction of the mirror are described. I. Introduction The James Clerk Maxwell telescope is being built as a collaborative project between the United Kingdom and The Netherlands at the Mauna Kea Observatory on the island of Hawaii. It will be used for astronomi- cal observations in the submillimeter region of the spectrum. The parabolic main mirror has a diameter of 15 m and a focal length of 5.4 m; the focal ratio is 1:0.36. The secondary mirror is used in a classical Cassegrain configuration; thus it has a hyperbolic sur- face. With its diameter of 0.75 m it produces an effec- tive magnification of 33.3 with a focal length of 0.275 m. To detect weak astronomical sources in the pres- ence of strong and fluctuating background radiation, it is customary", 2 to use a chopping motion of the second- ary mirror. The larger such a mirror is, the more difficult it becomes to keep the moment of inertia small enough and to achieve a reasonably small switch- ing time. In Table I we summarize some physical properties of the chopping secondary mirror, as de- scribed in this paper. In Sec. II we discuss various design aspects; in Sec. III we describe the production process of the mirror and in Sec. IV we discuss the results of test measurements on the mirror produced. 11. Design Aspects A. Chopper Response Time In nearly all practical situations a chopping second- ary mirror is moved in a square-wave fashion so that the mirror stays for equal times in on-source and off- source positions. This simplifies the process of back- ground subtraction. The efficiency of this method of observation depends on the switching time of the mir- ror. To follow the square-wave function, a servo with an optimum control strategy is demanded: maximum acceleration of the mirror is needed from one position until midway in the other position, followed by maxi- mum deceleration to a full stop at the end position. In such situations the total travel time t is t = 2 JXM/F, (1) where F is the applied force, M is the effective mirror mass at the point of application of the force, and X is the total travel distance of the mirror in a direction normal to the axis of rotation of the mirror. If I is the moment of inertia and L is the distance between axis of rotation and point of application of the force, we may write I = ML 2 . If we take the usual definition of response time as the time to travel from 10%to 90% of the distance between starting position and end posi- tion, we find that tr = 0.553t = L 7T Herman van de Stadt is with Sonnenborgh Astronomical Observa- tory, Zonnenburg 2, 3512 NL Utrecht, The Netherlands, and J. Verkerk is with State University, Subcentral Physical Workshop, Sorbonnelaan 4, 3584 CA Utrecht, The Netherlands. Received 20 February 1987. 0003-6935/87/163446-09$02.00/0. ©1987 Optical Society of America. In practice it will be difficult to achieve an optimum control strategy, so we have set a design goal to achieve a response time not longer than 1.5 times the theoreti- cal value of Eq. (2). The other important quantity for the chopper is its natural frequency, which is determined by the values 3446 APPLIED OPTICS / Vol. 26, No. 16 / 15 August 1987 (2)
Transcript
Page 1: Large chopping secondary mirror for the 15-m submillimeter James Clerk Maxwell telescope

Large chopping secondary mirror for the 15-m submillimeterJames Clerk Maxwell telescope

Herman van de Stadt and Jaap Verkerk

A 75-cm diam chopping secondary mirror has been developed for the 15-m diam James Clerk Maxwelltelescope. The large focal ratio (DIF = 1:0.36) requires a highly convex secondary mirror, which wasmanufactured out of a solid slab of high-grade aluminum, consisting of a 3-mm thick shell with a support ringalong the edge. The mirror surface approaches a predescribed hyperboloid with a rms precision better than 9,um, which is adequate for use in the submillimeter wavelength region. The design aspects, the performanceof a two-axis chopping mechanism, and the construction of the mirror are described.

I. Introduction

The James Clerk Maxwell telescope is being built asa collaborative project between the United Kingdomand The Netherlands at the Mauna Kea Observatoryon the island of Hawaii. It will be used for astronomi-cal observations in the submillimeter region of thespectrum. The parabolic main mirror has a diameterof 15 m and a focal length of 5.4 m; the focal ratio is1:0.36. The secondary mirror is used in a classicalCassegrain configuration; thus it has a hyperbolic sur-face. With its diameter of 0.75 m it produces an effec-tive magnification of 33.3 with a focal length of 0.275m. To detect weak astronomical sources in the pres-ence of strong and fluctuating background radiation, itis customary",2to use a chopping motion of the second-ary mirror. The larger such a mirror is, the moredifficult it becomes to keep the moment of inertiasmall enough and to achieve a reasonably small switch-ing time. In Table I we summarize some physicalproperties of the chopping secondary mirror, as de-scribed in this paper. In Sec. II we discuss variousdesign aspects; in Sec. III we describe the productionprocess of the mirror and in Sec. IV we discuss theresults of test measurements on the mirror produced.

11. Design Aspects

A. Chopper Response Time

In nearly all practical situations a chopping second-ary mirror is moved in a square-wave fashion so thatthe mirror stays for equal times in on-source and off-source positions. This simplifies the process of back-ground subtraction. The efficiency of this method ofobservation depends on the switching time of the mir-ror. To follow the square-wave function, a servo withan optimum control strategy is demanded: maximumacceleration of the mirror is needed from one positionuntil midway in the other position, followed by maxi-mum deceleration to a full stop at the end position. Insuch situations the total travel time t is

t = 2 JXM/F, (1)

where F is the applied force, M is the effective mirrormass at the point of application of the force, and X isthe total travel distance of the mirror in a directionnormal to the axis of rotation of the mirror. If I is themoment of inertia and L is the distance between axis ofrotation and point of application of the force, we maywrite I = ML2. If we take the usual definition ofresponse time as the time to travel from 10% to 90% ofthe distance between starting position and end posi-tion, we find that

tr = 0.553t = L 7T

Herman van de Stadt is with Sonnenborgh Astronomical Observa-tory, Zonnenburg 2, 3512 NL Utrecht, The Netherlands, and J.Verkerk is with State University, Subcentral Physical Workshop,Sorbonnelaan 4, 3584 CA Utrecht, The Netherlands.

Received 20 February 1987.0003-6935/87/163446-09$02.00/0.© 1987 Optical Society of America.

In practice it will be difficult to achieve an optimumcontrol strategy, so we have set a design goal to achievea response time not longer than 1.5 times the theoreti-cal value of Eq. (2).

The other important quantity for the chopper is itsnatural frequency, which is determined by the values

3446 APPLIED OPTICS / Vol. 26, No. 16 / 15 August 1987

(2)

Page 2: Large chopping secondary mirror for the 15-m submillimeter James Clerk Maxwell telescope

for L, I, and the spring constant C of the driving me(anism. We use electromagnetic vibrators as the dring mechanism of the chopper. If C is the spriconstant of a pair of vibrators we find a natural fquency fo:

L/

The design aim is to make fo as high as possible andas small as possible for a certain stroke X. This meathat L must be as large as possible, i.e., the vibralmust be placed as close as possible to the mirror edFurthermore, the moment of inertia I must be kesmall and the force F should be as large as possible.

For the driving power we chose electromagneticbrators in which a coil is mounted between springsthe narrow air gap of a permanent magnet. Becauthe coil is the only moving part, the inertia of tvibrator is low. We selected the strongest availalvibrators with acceptable size, weight, and stroke awith forced air cooling: a pair of model 403 Livibrators delivering a force of 400 N. If we require of the order of 20 ins, we have an acceptable efficienof 80% for a frequency of 5 Hz. For X = 10mm andL285 mm this requires a mirror with a total momentinertia of -1.0 kg M2

.

We will show how a relatively small moment of in(tia for a 75-cm diam mirror can be achieved withaluminum mirror structure consisting of a thin sh(-3 mm thick) and a sturdy ring (30 X 20 mm2 ) alothe outer edge. The stiffness is investigated in S(II.D.

B. Optical Design Aspects

1. Chopper Axis PositionThe position of the chopper axis with respect to t

vertex of the mirror is important because it influencthe image quality of the telescope If the secondaryrotated around its vertex, an intolerably high amouof coma is created; but if the chopper axis coincidwith the focal point of the hyperboloid, coma is elinnated and only a small amount of astigmatism remaifor the largest chop angles.4

Thus the optimum position of the chopper axis isthe focal point of the hyperboloid, at a distance of 2mm from the mirror vertex. However this causesproblem: the ratio between the rotation angle of tmirror 0 and the effective angular movement in tfocal plane y is increased from 12.0 when the choppaxis is located in the vertex to 19.2 in the optimuposition. Thus, for a certain required y we would hato rotate the mirror over a larger angle. An additionproblem is a considerable increase of the required staic balancing mass (see next paragraph) and an asso(ated increase of the moment of inertia.

As a mechanically convenient intermediate solutiwe have placed the chopper axis at a distance of 85 min front of the optimum position. In this case thereno appreciable increase in the spot radius of the imafor wavelengths longer than 0.8 mm, if the mirror chc

ch- Table 1. Properties of the Chopping Secondary Mirroriv- 'Diameter: 750 mmng Focal length: 275 mmre- Axial thickness of structure: 126 mm

Eccentricity: 1.065Surface shape accuracy: <9-jum rmsMaximum chop angle 0 at mirror: 2.140 or 128 min of arc

(3) Maximum chop angle -y in focal plane: 8 min of arcResponse time at maximum chop angle: <37 ms

[tr Frequency range: 1-15 Hz

N

Ei

S

Fig. 1. Top view of the chopping mechanism with the gimbalmounting in the center and four vibrators labeled with a V.

angle is not more than 3 min of arc from the telescopeoptical axis. It can be shown that the ratio between and y is now 16.0, so a total angular rotation of thesecondary mirror of 128 min of arc results in an effec-tive change in the pointing of the telescope of 8 min ofarc, i.e., +4 and -4 min of arc with respect to theoptical axis. Such large chopping angles cause somedegradation of the beam quality.

2. Projected Sky MovementA further consideration for the chopper design is the

adjustability of the direction of the chopping move-ment as projected on the sky. Since the Maxwelltelescope has an altazimuth mounting, a nonadjust-able chopper orientation would mean a continuouschange of the chopper direction with respect to anequatorial coordinate system in the sky. Thus, someadjustment mechanism is required to be able toachieve integrations of the difference signal between-fixed source and reference positions for observingtimes longer than 1 h. In principle one could use arotating mechanism as illustrated, for example, byLow and Rieke' to achieve such an adjustment, but itwould require a lot of space. We have opted insteadfor a more compact solution with a two-axis gimbalmounting, using four vibrators (two per axis) as illus-trated in Fig. 1.

3. Gimbal MountingA chopping secondary mirror with a gimbal mount-

ing is a unique construction as far as we know. Itallows easy and fast control of the chopping directionin a continuous way by varying the currents through

15 August 1987 / Vol. 26, No. 16 / APPLIED OPTICS 3447

Page 3: Large chopping secondary mirror for the 15-m submillimeter James Clerk Maxwell telescope

Table II. Calculated Values of Mass and Moment of Inertia for a 3-mmThick Mirror Shell and Support Structure

Mass in kg Inertia in kg M2

Shell 4.7 0.26Ring 2.8 0.24Spokes 4.3 0.13Central bushing 1.4 0.04Counterweight (steel) 13.9 0.19

Total 27.1 0.86

Fig. 2. Side view of the chopping mechanism: V, vibrator; C,counterweight; W, west; E, east.

the two sets of vibrators, denoted in Fig. 1 as N-S andE-Wafter the four compass directions. Apart from itscompactness it also has other advantages: it opens thepossibility of using 2-D chopping patterns and point-by-point image scans. The image size can be as largeas 8 X 8 min of arc. For a wavelength of 0.8 mm and acorresponding diffraction-limited spot size of 13.4 secof arc this means a total number of 1280 pixels.

4. Shadowing of the ChopperAs a final remark we note that the dimensions of the

chopper mechanism are such that it is kept within theshadow of the secondary mirror (see Fig. 2), so that nofalse signals or standing waves caused by reflections oflocal oscillator signals on parts of the chopper mecha-nism can occur. For a similar reason the mirror sur-face has a 50-mm diam hole in its center, while thecenter part of the chopper table and its support mecha-nism are also free of any mechanical obstructions.

C. Mechanical Design Aspects

1. Static BalanceSince the chopper axis lies 85 mm in front of the focal

point (or 190 mm behind the vertex) nearly all the massof the mirror and its support structure lies in front ofthe chopper axis. Without further precautions, themoving mass would not be in static balance, which isundesirable for two reasons. First, a static compensa-tion force must be supplied by the electromagneticvibrators, leaving less power available for choppingmovements, depending on the telescope pointing.Second, an unbalanced moving mass would exert aconsiderable reaction force on that part of the tele-scope construction that supports the secondary mir-ror, the so-called tetrapod (see below). Therefore wehave mounted a counterweight on the opposite side ofthe chopper axis (see Fig. 2). In a statically balancedconstruction an uncompensated reaction torque re-mains, but this can be tolerated if the tetrapod is stiffenough. The counterweight has been made of steel tobe dimensionally as small as possible. The counter-weight raises the moment of inertia with <30%, seeTable II. The mirror and its spokes are made of alumi-num.

-- ----___L - T. '----

1,.

I . . -

.4 _ _

-- - 1 -

Fig. 3. Principle of the connection between vibrator and mirror.

2. Dynamic BalanceDuring the design phase we also considered using

dynamic balancing. This is a construction where abalance mass with the same moment of inertia as themirror moves in the opposite direction. Thus, all reac-tion forces and torques would be compensated. Thisis especially important for space applications, where ithas been used with success for small mirrors.5 In ourcase of a fairly large mirror and a two-axis gimbalmounting, a dynamic balancing mechanism would be-come a complicated structure, adding more mass andconsuming more power than the compensation of allreaction forces and torques is worth. We thereforedecided not to use a dynamic balancing mechanism.

3. Connection Between Vibrator and MirrorThe coupling mechanism between the chopping mir-

ror and the vibrators must allow for linear movementsat both ends combined with small angular rotations onthe mirror end, as illustrated in Fig. 3 in an exaggeratedway. At a chopper frequency of 5 Hz, the mechanismperforms nearly a million switching operations perday. So the mechanism must be simple, reliable, andnot prone to wear. We selected pieces of 2.5-mm thickspring steel wire to provide a large axial stiffness butlow stiffness in the transverse directions: a bent bar,also called a sting, exerts only a small transverse forceon the vibrator coil which moves linearly in the rathernarrow air gap of a magnet. The sting must be strongenough to withstand a certain amount of bending with-out buckling. The gripping pieces at both ends of thesting have been designed to eliminate the chance ofcreep of the sting as a result of the regular switching ofthe loading conditions.

3448 APPLIED OPTICS / Vol. 26, No. 16 / 15 August 1987

- - -152L17'

i

Page 4: Large chopping secondary mirror for the 15-m submillimeter James Clerk Maxwell telescope

Fig. 4. Actual construction of the sting mechanism that connectsthe vibrator to the mirror.

The design of the chopper was such that each chop-per axis intersects two stings halfway, because thisminimizes the amount of bending of each sting. Thestings were shotblasted to improve the resistance ofthe surface to small fatigue fractures. The grip at thetop-end and bottom-end of each sting forms a slightlyconical hole in which the sting is clamped. The conicalshape provides a smoothly decreasing strain distribu-tion in the stings. Beyond these grips the stings arefixed in position with a pin that fits in a hole throughthe sting and prevents creep, see Fig. 4. Several proto-types have been made along these general design prin-ciples. The final design was tested in real operatingconditions before the actual items were manufactured.

4. Connection Between Mirror Structure andTelescope Structure

The tetrapod which supports the secondary mirrorhas to meet a number of conflicting requirements. Onthe one hand it must support a relatively large mass(-400 kg for the chopping mirror and an associatedthree-axial Cartesian position mechanism) with thesmallest possible gravitational and thermal deflec-tions. On the other hand it should block as little aspossible of the detected wavefront. In addition theload itself is active and imposes a complex spectrum oftorques. The traditional design of a four-legged tetra-pod proved to be far from satisfactory, whereupon weinvestigated the use of an eight-legged structure of theSerrurier type, often used in modern optical tele-scopes, see Fig. 5. Although it contains eight legs, ithas only four feet and thus can still be called a tetra-pod. It can be shown that such a tetrapod has excel-

Fig. 5. Sketch of the eight-legged tetrapod that supports the chop-ping secondary mirror unit in the Maxwell telescope.

lent rotational and lateral stiffness, mainly because itis basically a set of simple triangles. The only condi-tion for stiffness is the provision of a rigid square at thetop, and this can be met easily. To minimize thermalexpansion effects the legs are made of carbon fibertubing, 5.5 m long and 5 cm in diameter. Such rela-tively thin tubes cause a blocking of the wavefront ofthe order of 7%, as calculated by Lamb and Olver.6This was considered to be small enough to use thiseight-legged tetrapod concept. It is not a new featurein radio telescopes,7 but it has not been used recently insubmillimeter radio telescopes other than in the Max-well telescope.

D. Mirror Construction Aspects

The mirror construction consists of four parts, allmade of aluminum: shell, ring, four spokes, and cen-tral cylinder. The outer surface of the shell is theactual mirror surface; it has a hyperbolic shape and thering forms a support along the outer edge of the shell.The four spokes form radial connections between thering and a central cylindrical bushing that connects tothe gimbal mounting. Actually the shell and ring aremanufactured as one piece, while the four radialspokes are manufactured as two spokes over the fulldiameter of the mirror. The main features are illus-trated in Fig. 2.

1. Moment of InertiaThe expected values for mass and moment of inertia

of the mirror structure were calculated to see if wecould meet the values of Sec. II.A. The results aregiven in Table II, where we assumed a spherical mirrorof radius 0.548 m and a thickness of 3 mm. Althoughwe will show below that a 2-mm thick mirror shellwould still have been strong enough, we did not want totake the risk involved in fabricating such a thin shell.Moreover, the moment inertia is 0.86 kg M2

, which isstill smaller than the aimed value of 1.0 kg 2 men-tioned in Sec. II.A.

2. Mirror StiffnessThe stiffness of the mirror was investigated by

Rigters8 for four different loading situations: twostatic cases caused by gravity (a and b) and two dynam-ic cases caused by vibrator forces (c and d). In Fig. 6we illustrate the loading situations. In each case it issufficient to calculate the deflections in one quadrantonly, because of symmetry. Cases a and b represent

15 August 1987 / Vol. 26, No. 16 / APPLIED OPTICS 3449

Page 5: Large chopping secondary mirror for the 15-m submillimeter James Clerk Maxwell telescope

f(

o)g

I9

05F 05F

I

.1F ! OJF

I I

Iol

2.32 2.97390

3.66 3,78 4.31

3.744, 3.76 3.77 3,90

3.69 *3.75 2.96

A 3.73 3,77 3.66 2.32

C

f.s

0 0070, 0.0904 0.07 .07

04 0.05 0.13 0,04

0 * 0.08 0.02

0.01 0.10 0.17 0

OI

B0.04 0.25 0,33 0

0.41 0520.72

0.72 0,79 .98

0.83 0.84 0,90 0.95

0,921 *0.86 0910 0 - 0

D 0.79 0.88 097 0.87

Deformnation In micrometers

Fig. 8. Calculated deformations in the micrometer of the mirrorsurface in the four loading situations of Fig. 6.

Fig. 6. Loading situations of the secondary mirror and signs of theexpected deflections.

0--

Fig. 7. Network used in the finite element computer program.

the gravitational loading situations where the tele-scope is looking at zenith and horizon, respectively. Incase c the mirror structure is loaded with the maximumforce of two vibrators; this is a dynamic loading thatoccurs only when the mirror switches from one positionto another (angular) position. Case d represents asituation where a static load might occur due to un-equal vibrator forces: individual vibrators may gener-ate different forces per ampere of current and, sincethey are used in parallel, an asymmetric force may be

Table . Calculated Deformation of the Mirror Surface (Az) and ItsRotation (AO) for Two Different Mirror Structures8

Structure I Structure II

Az in m A 2.0 1.6B 1.8 1.3C 0.2 0.6D 0.6 0.5

Af in rad A 0 0B 3.5 X 10-6 1.3 X 10-5C -4.3 X 10-5 -7.5 X 10-5D 0 0

f in Hz 274 232fsain Hz 317 337faa in Hz 127 109

a I: mirror thickness 2 mm; cross sections of ring and spokes, 625and 1400 mm2 ; II: mirror thickness 3 mm; cross sections of ring andspokes, 1200 and 1800 mm2. The resonant frequencies are f&, fsa,

and faa for double symmetric, symmetric-antisymmetric, and dou-ble antisymmetric modes, respectively.

present of up to 20% of the maximum force of onevibrator.

For the four situations a, b, c, and d the deflectionsof the mirror structure were calculated by Rigters8

with a finite element computer program. The ele-ments used in the program are illustrated in Fig. 7:the shell is divided into twenty-one elements per quad-rant. A further subdivision into fifty-four elementsgave <1% change in the calculated deflections. In Fig.8 we show the deflections of the mirror surface in thedirection of the z axis, which is the optical axis. Thedifference Az between maximum and minimum de-flection is given in Table III, where we also list theaverage angular rotation A/0 of the mirror surface overthe y axis; Fig. 8 corresponds to structure I from TableIII.

The main difference between structures I and II isthat the former is lighter. An important detail is thatthe spokes in structure I have a cross section like acapital I, while structure II contains simple rectangu-

3450 APPLIED OPTICS / Vol. 26, No. 16 / 15 August 1987

f5,

Page 6: Large chopping secondary mirror for the 15-m submillimeter James Clerk Maxwell telescope

1/i C) p

I C3 P

~~4 / /)

lar bars as spokes. The significant consequences forthe calculated deformations of structure I are thesmaller values for Az in case C and the smaller valuesfor 1X. Thus we chose an I-profile for the spokes, asindicated in Fig. 2.

Also given in Table III are the resonant frequenciesof the shell in three modes: fss, fsa, and faa. Thefrequency f8, refers to symmetric deflections with re-spect to the x and y axes (as in cases A and D); frequen-cyfsa refers to an asymmetric deflection over the y axis(cases B and C); frequency faa refers to a double asym-metric mode (alternating positive and negative deflec-tions for all neighboring quadrants) but this mode willhardly be excited, because the ring around the mirroredge restricts the amplitude of this mode to a second-order quantity. The manufacturing process will yielda rms surface error of 9 ,m so it can be concluded thatthe deformations due to mechanical loading of themirror are negligible.

111. Mirror Fabrication

The mirror and its support ring have been manufac-tured as one piece out of a solid slab of high-gradealuminum with a mass of 200 kg. The final producthad a mass of only 7.5 kg. The bulk material wasselected for excellent homogeneity and lack of stressand is known under the trade name Constructal, acopper containing alloy AlZnMgCu 0.5; the Brinellhardness is 100, ultimate stress and strain is 410 NImm2 , 3% a(0.2 = 330 N/mm 2 .

Fig. 9. Various phases in the fabrication processof the mirror.

The manufacturing process is illustrated in Fig. 9,steps (a)-(f). In step (a) enough material was removedon a CNC milling machine so that the final mirrorshape (as indicated by the dashed line) was, for safetyconsiderations, not approached closer than 10 mm. Insteps (b) and (c), the rough steps on the outer and innersides were removed by CNC turning. Finally, in steps(d), (e), and (f), the mirror shell was cut to a thicknessof -4 mm. Important was the use of a plate (p), asupport ring (r), and leaf springs S. The plate provid-ed a well-defined reference plane, and the ring and leafsprings provided a means for support and stress-freemounting of the mirror. Between the various steps (b)and (f) the mirror was not only turned upside downeach time, but also a new reference plane or a new outeredge for correct centering was cut, because flatness andconcentricity of the rim were of utmost importanceand could change after each step due to relief of residu-al material stress and strain.

After step (f) (Fig. 9), the mirror was in good shape,but the outer mirror surface was not yet smoothenough. It was subsequently sent to the Philips Phys-ical Laboratory in Eindhoven, The Netherlands, forprecision cutting of the outer surface on a very highprecision hydraulic lathe.9 The final hyperbolic sur-face of optical quality was fabricated by letting a dia-mond cutting tool copy a template that served as a 2-Dreference gauge.

We mention two of the technical problems encoun-tered during the cutting process. First, the normal

15 August 1987 / Vol. 26, No. 16 / APPLIED OPTICS 3451

i

I

I

I .\\\QU

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Fig.11. Photograph of the mirror. The surface reflects ceiling andwindows.

Fig. 10. Contour plot of the mirror surface deviations from an idealhyperboloid. The figures indicate number of micrometers.

cutting force cannot be too high because it may depressthe shell locally and introduce a shape error. To keepthe deformations <1 jim, it was calculated that thenormal cutting force had to be <25 and 1.1 N for shellthicknesses of 10 and 2 mm, respectively. These wereacceptable values. A second problem is caused bygeneration of heat. The diamond tool cuts with apitch of 23 jim. With 2.5 revolutions of the mirror persecond, this results in a cutting time of one and a halfhours. The cutting was done from the outer edgeinward, and there was a slight increase of temperaturetoward the middle of the mirror. This caused a moreconvex surface so that too much material was removedand after cooling to room temperature the mirror wasless convex than intended. So it was essential to re-move heat by conduction via a central aluminum sup-port bar and by air cooling around the cutting tool,especially when the shell became thinner.

The periodic pattern in the mirror surface has anegligible depth: the radius of the diamond was 2.5mm so that a notch pattern exists with a period of 23jim and a depth of only 0.026 Am. Thus the surface hasa near-optical quality on a small scale, while the overallsurface quality is determined by the accuracy of thetemplate and the stability of the copying process. Theoverall surface quality is discussed in Sec. IV.

IV. Results

The shape of the mirror was measured at the Philipsfactories with a 3-D Zeiss measuring machine UMC-850 with a precision of d2 Aim in all three axes. Beforethe actual surface was measured, the mirror was care-fully centered by measuring the surface at an innerring with R = 30 mm, i.e., 5 mm from the inner edge(with 25-mm radius) and at an outer ring with R = 360mm, i.e., 15 mm from the outer edge. The number ofdata points at the inner and outer rings was twenty-

four per ring and the standard deviations were 3.1 and4.2 Am, respectively.

The surface measurements were performed in eightradial directions. In four perpendicular directionssamples were taken at intervals of 10 mm and in fourintermediate directions (under 45°) samples were tak-en at intervals of 20 mm. Interpretation of the mea-suring data takes into account the size of the measur-ing sphere that touched the surface. Comparison withthe predescribed hyperbolic surface yields a rms sur-face error of 8.9 Am over 215 data points. This is thedifference between the actual and the predescribedsurface in directions normal to the surface. In Fig. 10we show a contour plot of the errors, calculated bylinear interpolation between the 215 points. Figure 11shows the actual mirror.

Finally, in Table IV we compare the calculated andthe measured response times of the chopping mirror.To calculate t with Eq. (2), we need to know the actualmoment of inertia . This was deduced from the mea-sured resonant frequencies and Eq. (3). We measured8.50 and 7.37 Hz and this means I = 0.84 and 1.14 kg m2

for the N-S and E-W axes, if we use L = 0.285 m and C= 22.2 X 103 N/m for a pair of vibrators. The N-Svalue agrees with the predicted value of 0.86 kg m2 inTable II, which means that the mechanical construc-tion is stiff and adds little to the spring constant of thevibrators. In the E-Wdirection, however, we measuretoo low a frequency, which means a relatively high I ora low C. Since the mirror structure is very symmetri-cal and well balanced, it must be concluded that the

Table IV. Calculated and Measured Response Times; X, e, and -y Referto Peak-to-Peak Values

Calculated t Measured trX 0 (Mirror) y (Focus) in ms, Eq. (2) in ms

(mm) (min of arc) (min of arc) N-S E-W N-S E-W

0.74 9.0 0.56 4.8 5.6 6 72.12 25.6 1.60 8.3 9.7 10 103.74 45 2.82 10.8 12.6 12 135.3 63 3.96 12.8 14.9 15 166.7 81 5.08 14.6 17.0 16 17.58.3 99 6.22 16.2 18.9 18 189.8 118 7.36 17.6 20.5 20 21

11.3 136 8.48 18.9 22.0 22 23

3452 APPLIED OPTICS / Vol. 26, No. 16 / 15 August 1987

Page 8: Large chopping secondary mirror for the 15-m submillimeter James Clerk Maxwell telescope

Fig. 12. Photograph of the chop-ping mechanism. The mirror

surface reflects the ceiling.

extra inertia of the octagonal ring of the gimbal mount-ing can add only very little to the value.of I. Thismeans that the lower resonant frequency of the E-Waxis is not due to a higher value of I, but due to a lack ofstiffness of the gimbal mounting, i.e., more flexure anda lower spring constant C for the E-W axis. Figure 12is a photograph of the chopper construction.

Using the mentioned values of I we have calculatedthe values for tr with Eq. (2) for various values of X, thedisplacement of the vibrator coils. In Table IV we alsogive the angular rotation of the mirror 0, as well as theeffective angular rotation y in the telescopes focalplane. The values for X, 0, and y refer to peak-to-peakvalues of a square-wave chopper motion.

The electronic servo loop used for the chopper isbased on a design for the chopping secondary mirror ofthe Canadian French Hawaiian telescope. The samedesign principle has also been used for the choppingmirror on UKIRT. Both telescopes are located onMauna Kea, Hawaii. The servo loop can be used in theoptimum mode, which uses a signed squared velocity(V V) feedback, but it also has a linear mode, whichmeans a simple velocity feedback. In both modes aposition feedback is also used. The response times inthe linear mode are much smaller than in the optimummode, but the larger amplitudes show a very largeovershoot. Thus the linear mode cannot be used foramplitudes larger than 2 min of arc in ry. For suchamplitudes the optimum mode is adjusted so that itshows virtually no overshoot for symmetric choppingpatterns. But for strongly asymmetric patterns anappreciable (10%) overshoot occurs in one directionbecause of energy release of the vibrator springs.

From Table IV it can be concluded that we succeed-ed in reaching the design goal of response times smallerthan 1.5 times the predicted values.

V. Conclusion

The construction of a 75-cm diam chopping second-ary mirror incorporates some new design and construc-tion aspects: the chopping mechanism contains a two-axis gimbal mounting and the mirror consists of a 3-mm thin aluminum shell. From test measurements itcan be concluded that the mirror surface approachesan ideal hyperboloid with a rms precision of 8.9 gm,which is a hundredth of the short wavelength limit ofthe telescope ( = 0.8 mm) and a thirtieth part of theshortest radio wavelength transmitted through the at-mosphere (0.3 mm). The moment of inertia is keptsmall enough so that response times of the order of 20ms are attained for the largest amplitudes.

We wish to thank E. J. Mulder for his design effortsin the early stage of this project and A. M. J. Rigters forhis expert computational support on stiffness aspects.R. C. Sidey of Imperial College London advised inmany aspects of the chopping mechanism. The staffof the Philips Physical Laboratory in Eindhoven wasresponsible for the excellent job of fine cutting themirror surface.

This project was financially supported by the U.K.Science & Engineering Research Council and by theOrganization for the Advancement of Pure Research ofThe Netherlands.

15 August 1987 / Vol. 26, No. 16 / APPLIED OPTICS 3453

Page 9: Large chopping secondary mirror for the 15-m submillimeter James Clerk Maxwell telescope

References1. F. J. Low and G. H. Rieke, "Instrumentation and Techniques for

Infrared Photometry," Methods Exp. Phys. 12, 446 (1974).2. J. M. Payne, "Switching Subreflector for Millimeter Wave Radio

Astronomy," Rev. Sci. Instrum. 47, 222 (1976).3. H. van de Stadt, "Optimum Location of the Wobble Axes of

Secondary Mirrors in Cassegrain-Type Telescopes," IEEETrans. Antennas Propag. AP-32, 1128 (1984).

4. A. B. Meinel and M. P. Meinel, "Aberrations of an IR ChoppingSecondary," Appl. Opt. 23, 2675 (1984).

5. A. Krabbe, D. Lemke, and K. Proetel, "Chopping SecondaryMirror for a Cooled Infrared Telescope," Appl. Opt. 25, 523(1986).

6. J. W. Lamb and A. D. Olver, "Blockage Due to SubreflectorSupports in Large Radiotelescope Antennas," IEE Proc.-H, Mi-crowave Antennas Propag. 133, 43 (1986).

7. J. R. Cogdell et al., "High Resolution Millimeter Reflector Anten-nas," IEEE Trans. Antennas Propag. AP-18, 515 (1970); the JPL18-ft Table Mountain telescope, Fig. 18.

8. A. M. J. Rigters, "Response of a Secondary Mirror on Static andDynamic Loads," M.S. Report 797, Laboratory for TechnicalMechanics, Technical U., Delft (Feb. 1985).

9. J. J. M. Braat, T. Gijsberts, J. Haisma, W. Mesman, J. M. Oomen,and J. C. Wijn, "Optomechanics, an Ultra-High-Precision Ma-chining Technique," Philips Tech. Rev. 41, 10 (1983/84).

Penn State/McDonald ObservatoryInnovative Telescope

An innovative new telescope capable of probing deeper into the universe at a moreeconomical price than any instrument now available has been undertaken as a joint project byastronomers at Pennsylvania State University and the University of Texas. Designed at PennState, the proposed $5 million telescope will be located at the University of Texas McDonaldObservatory in Ft. Davis, TX. The telescope's designers are Penn State's Daniel W. Weed-man, professor of astronomy, and Lawrence W. Ramsey, associate professor of astronomy.Their Texas collaborators include Harlan Smith, director of the McDonald Observatory; ChrisSneden, associate professor of astronomy; and Frank Ray, research associate. This newSpectroscopic Survey Telescope will be larger than any now in existence, but its size is itsleast important feature. More important is the fact that the new instrument will producespectra more rapidly than any existing telescope and in a cost-effective way. It will also beable to survey larger numbers of faint objects than ever before and to see deeper into theuniverse on a routine basis. Ramsey has pointed out that the SST will be able to observe brightstars and faint galaxies simultaneously.

The astronomers have begun prototype development with support from the NationalScience Foundation and the two universities. The team could complete the telescope by1992, depending on the progress of fund raising. According to the Penn State astronomers, $5million is a fraction of the usual $25 to $100 million price for a traditional telescope of similarsize. The savings result from the SST's innovative design which takes advantage of the factthat optical telescopes are used 70% of the time with spectrometers. Modern astronomersrarely sit at the eyepieces of telescopes describing or photographing what they see. Rather,the light captured and focused by the telescope is analyzed and measured by spectrographs.The resulting data yield Information about the types and intensity of the light given off by the starand can be Interpreted to reveal the star's distance, composition, density and temperature. Inthe design proposed by Weedman and Ramsey, the telescope is entirely devoted to spectros-copy and therefore does not need or have an eyepiece or photographic capability.

The telescope's mirror, which collects the light, is composed of seventy-three segmentsarranged In a dish-shape 8 m across which rests on a turntable. The dish revolves to accessthe sky and need not be tilted from side to side-again a cost saving. The seventy-three mirrorsegments are identical, and are easy and economical to make from commercially availablesheets of glass.

Light collected by the mirror dish is focused onto a small receiver, called the acquisitionmodule, which tracks a star or galaxy by moving on circular scaffolding high above the mirror.The acquisition module sends the light to the spectrograph via fiber-optic cables, anotherinnovation. The entire assembly will be housed inside a modified grain storage bin to avoid thecost of a custom-designed dome.

The astronomers noted that in West Texas the weather is clear most of the year and the areahas very low background light to interfere with observations.

3454 APPLIED OPTICS / Vol. 26, No. 16 / 15 August 1987


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