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ADAPTIVE RADIO TELESCOPE DESIGN USING A DEFORMABLE SECONDARY MIRROR
		     

                   G. S. Tsarevsky

       Australia Telescope National Facility, Sydney 
                          and 
              Astro Space Centre, Moscow 

S u m m a r y
An adaptive wave front correction of the existing antennae 
by a deformable secondary mirror (DSM) is considered. The wave front
distortions of the primary mirror (PM) surface are mainly caused by the
 (i)  existing deviations from the best-fit paraboloid; 
 (ii) elevation dependent non uniform gravity distortions; 
(iii) season, weather and day-to-night variable thermal distortions. 
These essentially asymmetric and slow variable wavefront errors can
be effectively removed (in the on-line or off-line mode) by the DSM 
designed using the existing active structures. 
A feedback in this AT/DSM system would be performed by the
 - independent high precision distance measurements or/and
 - optimization of the reference signal level. 
Modern technology makes it possible to exploit an active surface ("rubber
mirror") and a laser theodolite to develop an effective wave front correction 
device with a precision well above the level needed for the mm-wave radio 
telescope. 
It is concluded that such a relatively short-term and low cost D&D would
result in a considerable improvement of the mm wavelength efficiency of 
the existing cm wave range antennae, particularly ATCA. 
Also, a highly profitable product could be developed based on the AT/DSM 
device consisting of the active SM, high precision distance measurement 
unit and other relevant hardware/software.
  ____________________________________________________________
  C o n t e n t s:                     Abbreviations:
  ----------------                     -----------------------
  1. Introduction                      AT - adaptive telescope
   2. W h y ?                          ATCA - everybody knows
    3. What has been done?             DSM - deformable SM
     4. What has to be done?           LTS - laser theodolite system
      5. H o w ?                       PM - primary mirror
        6. C o n c l u s i o n         RR - retroreflector
           R e f e r e n c e s         SM - secondary mirror
           A1. H o w  l o n g ?        AT/DSM = AT by DSM
           A2. H o w  m u c h ?

1. I n t r o d u c t i o n                  

The deformable subreflector is a device to be engineered to compensate
for gravity and temperature dependent distortions in the main reflector of
a radio telescope. We would like to describe here briefly what is to be
made in order to acquire this effective facility which should be performed
mainly on the modern technology basement. 

A tendency to explore in the shorter wavelength range is the most
prominent sign of the modern astrophysics. In the radio astronomy, it
means a millimetre wave range utilization which gives better angular
resolution, study of new cosmic species mostly connected with a star
formation process and deeper embedding into the still enigmatic quasar and
active galactic nuclei interiors. 

To assimilate mm wavelength we should begin from the scratch, that
means a design and construction of the telescope with a rms surface error
below 0.1 mm. Moreover, this antenna surface should be kept steady under
the very variable gravity, temperature, wind, humidity, dust and other
natural and human environment conditions. 

Sooner or later, almost all modern radio telescopes are subjected to
the upgrade stage which means a short wavelength conquest as a rule.
Usually, a first step of the upgrade is an antenna front-end improvement
by the surface adjusting which consists of the dish back-up structure,
panel surface and panels setting-alignment improvement. But the large
length scale errors due to mechanical and thermal variable effects still 
remain. 

We consider here some modern way for the stable high precision incoming
wave front correction suitable for the existing and working radio
telescopes, that is wavefront correction by the deformable secondary
mirror. This way might be considered as a classical adaptive telescope
concept in its quite popular so called "convergent beam" version. 

The method considered here was developed and successfully used at the
Haystack, Green Bank and Jodrell Bank radio observatories. 


 2.  W h y ?            

A scientific goal of the mm wavelength astronomy is briefly outlined
above, and it seems not a worth considering it in details here. We just
would refer to the reviews by Sargent and Welch 1994, and Burton 1996; see 
also a comprehensive report by te Lintel-Hekkert 1996. 

Considering the technical aspects of the surface upgrade problem we
would like to try answer here a much more specific question: "Why
adaptive telescope in a converge beam namely with the correctable
secondary mirror?" So there are at least three whys to be answered: 
Q1: - Why should we apply for the adaptive telescope method? 
Q2: - Why to conduct an adaptive process specifically in the convergent
not parallel beam? 
Q3: - Why is it preferable to correct wave front at the ray half path, that
is with active secondary mirror and not in the output pupil beam? 

A1. Adaptive telescope (AT) gives wave front correction provided by the
conventional closure servo control "PM Measure- Feedback- SM Active Surface" 
system (Tyson 1991). Such a system ensures a considerable improvement of 
the antenna efficiency and seems to be the only way to design a very large
diameter short wave wavelength telescope, particularly an optical
telescope and a large space antenna (Buyakas et al. 1979; NRAO GBT 
Techn. Report 1994; O'Birne et al. 1995). 

A2. Correction of the wave front can be conventionally performed not only
in a parallel beam, that is by the primary mirror surface adjusting, but
also in the convergent beam even in the output pupil. This design seems 
to be much more accessible, compact and convenient and therefore more
profitable than the direct primary mirror adaptive adjustment. 

A3. Wave front correction in the output pupil requires pre focal semi
transparent or focal array devices to be used which still is a problem not
solved in practice properly (Napier and Cornwell 1995). We propose
adaptive wave front correction by the deformable secondary mirror as a
reliable practically approved method. It seems especially useful for the
existing and working telescope upgrade purpose as it could be done in a
short replacement time at a reasonable cost. 

  3. What has been done?                    

As we know the first mm wavelength antenna with adaptive on-line SM
wavefront error correction was developed by Aizenberg (1976). He used a
reference radio signal from each of discrete parts of the PM illuminating
a corresponding part of the sectioned DSM. A peak of the integrated signal 
was taken as a feedback signal of the AT system. 

Again, also about twenty years ago, the correctable subreflector device
was engineered for position dependent distortion in the primary reflector
of the NRAO 43-m telescope (Lacasse 1978). 

The recent design of the AT/DSM system with a Haystack 37-m radio
telescope is described in detail by Ingalls et al. (1994). Installation of
the DSM at the 76-m Lowell telescope, Jodrell Bank, is also reported
(Davis 1996). 

Table 1 well illustrates an unique power of the AT/DSM method. Rms
surface error of the Haystack antenna became 3-4 times better after DSM
installation (Ingalls et al. 1994). 

Table 1. Surface rms errors (in mm) due to gravity deformations 
of the Haystack 37-m radio telescope primary mirror 

  ________________________________________________________      
                                Telescope elevation, deg.
   C o n d i t i o n      --------------------------------
                                    15               70
  --------------------------------------------------------
  Before DSM corrections           0.49             0.41
  After  DSM corrections           0.15             0.10                        
 ---------------------------------------------------------


  4.  What has to be done?                  

As an initial (and really desirable for the upgrade purpose) case let us
consider one of the ATCA Cassegrain type 22-m antennas (Cooper et al.
1992) having 96 solid panels (four rings of the inner 15-m) and 64
perforated panels (outer two rings), see Figures 1 and 2. A typical 3 cm
efficiency is about 0.5 (full diameter surface) and predicted (quite far
extrapolated) 7 mm efficiency is about 0.4 for the inner 15-m. The
efficiency at 3 mm should be near 0.15. Most of the CA antennas has not
been measured holographically at the high frequency yet. 12 GHz holography
of the Mopra dish shows at least 1 mm amplitude astigmatism (trough type) 
error and clear evidence of the certain panel sag. So it is not excluded
that above prediction might be rather optimistic in realty.

We propose here a relevant and relatively cheap way to double (or even
triple) the mm-wave full 22-m diameter efficiency of the already existing
and working CA radio telescopes using a correctable subreflector system.

Two cases should be considered, off-line (more cheap) system and on-line
relatively expensive one. They both must be extensively assisted by the
introductory and, also, current high precision holographic measurements
(Kesteven 1994). It should be stressed that these two systems essentially
do not contradict each other and, instead, could be considered as a chain
of the ATCA upgrade actually. Corrsponding investment and possible D&D
schedule is considered in the Appendices 1 & 2. 

  5.  H o w ?                        

Such development should be considered as an adaptive DSM system design
which properly corrects the PM deformations caused by the variable non
uniform gravity, mechanics and thermal antenna distortions (that is the
large length scale, D/20, and long time scale, 10-30 min, antenna surface
errors, see Fig. 3). 

It is well known that the two-mirror system can turn any wanted aperture
illumination of any given feed pattern suggested by the proper design of
two reflecting surfaces (Galindo 1964). 

However, we would like to consider a different case when the primary
antenna mirror (PM) is already given and we want to correct system
wavefront errors by the proper correction of the SM surface. Such approach
was studied in detail by von Hoerner (1976). He proved that any given
shape of a primary mirror corresponds to the certain shape of a secondary
yielding zero path length errors for all paraxial rays, see Fig. 4. The
only condition to be fulfilled is (for the Cassegrain type telescope) that
incoming rays, after reflection at the primary, do not cross each other in
the convergent beam. In our case, it means that a proper initial telescope
system alignment should be done before the corrective facility would be
put into operation. Accurate measurement of the antenna surface is
required to achieve this demand, and the only relevant radio holography
facility should be used for this purpose (Kesteven 1994). 

The improvement of an existing telescope by this method would consist of 
the following steps:
(i) Measure the PM surface with adequate accuracy and find the remaining 
deviations Sigma-Zp from the best-fit paraboloid.
(ii) Derive the necessary derivations Sigma-Zs of the SM from a hyperboloid, 
such as all path lengths are equal.
(iii) Acquire a SM of the shape required. 

This sole SM correction method was recently successfully used to improve
300 GHz capacity of the Texas 5-m (Mayer et al.1991) and NRAO 12-m (Mayer
et al. 1993) radio astronomical antennae. 

But now we would like to consider an essentially improved stage of this
fruitful approach, that is adaptive (on-line or off-line) correction of
the distorted wave front by the deformable SM.

The wave front distortions of the PM surface are mainly caused by
(i) the existing deviations from the best-fit paraboloid; 
(ii) the elevation dependent non uniform gravity distortions in the 
antenna structure (mostly the astigmatism and panel sag errors); 
(iii) the season, weather and day-to-night variable thermal distortions. 

These distortions are essentially stable and slow variable. We do not
include in this consideration distortions caused by the wind gusts and
atmospheric (troposphere and ionosphere) turbulence. A low elevation water
vapour content influence can be taken into account by the relevant phase
correction system (see Hall 1995). 

A deformable mirror can be designed from the existing active structures
(Fanson et al. 1990; Ealey 1990; Marlow 1994), which combine a flexible
smooth surface ("rubber mirror") with high precision piezoelectric
actuators. 

In the case of an on-line system, a feedback signal should be performed
by the independent high precision distance measurements and/or
optimization of the reference signal level. 

A new 2.75-m DSM of the CA 22-telescope should be made as a substantially
rigid, strong, light and not distorted by the gravity and thermal heating-
cooling effects construction. A composite carbon-epoxy material having a
nearly zero thermal expansion coefficient should be used for this purpose.
A possible design of the DSM unit is shown at the Fig. 5 taken from
Ingalls et al. 1994. 

A 350 mm diameter blind spot at the centre of DSM should be used to
place a laser theodolite system, LTS (Docchio et al. 1994). The LTS
measures the distances from SM to each of the 160 reference points with
rms error 0.1 mm. Each reference point is provided by the retroreflector,
RR, corner like reflector, or kataphothe, which reflects strongly in the
direction opposite to the incident beam. The RR is fixed to the left 
outer corner of each panel (Fig. 2). 


  6. Conclusion        

This first draft proposal contains the concept and plan of design &
development of an adaptive wavefront correcting system based on the
deformable secondary mirror. The aim of this proposal is to consider a very
fruitful way to upgrade the ATCA telescopes, that is at least to double
their millimetre-wave efficiency. The structure of the AT/DSM based on the
well known idea is proposed. 

Modern technology makes it possible to use the laser theodolite and active
surface ("rubber mirror") in order to perform an wave front correction
device at a reasonable cost with a precision well above the level needed
for the mm-wave radio telescope. 

As a result the unique Southern millimetre-wave array would be made up. 
Its capacity should be quite competitive with the BIMA, Caltech, IRAM and
NRO millimetre-wave arrays. 

In conclusion, it should be stressed that a highly profitable product 
could be developed based on the AT/DSM device consisting of the active SM, 
high precision distance measurement unit and other relevant hardware and
software. We could expect a considerable demand of such effective and 
relatively low cost mm-wave upgrade of the space network, military and 
civilian radar and communication antennae and, first of all, many radio 
telescopes around the world. Some of them could be found between Seduna 
and Narrabri... 

I acknowledge B. MacA Thomas, M. Kesteven, K. Wellington, V. Buyakas,
M. Rupen, R. Lacasse, A.E.E. Rogers, R.J. Davis, R. Ekers, M. Bolotin, 
N. Golub, P. Hall, J. Brooks and P. te Lintel-Hekkert for the interests, 
constructive remarks and useful information. 

R e f e r e n c e s

Aizenberg A.: 1965, USSR Patent No. 170566 
Backers, J.M.: 1994, Annual Rev. Astr. Astroph. 31, 13
Burton, M.: 1996, Proc. ASA (in press)
Buyakas, V., Kardashev, N., Tsarevsky, G. et al.: 1979, Acta Astronautica 6, 175
Cooper, D.N., James, G.L., Parsons, B.F. and Yabsley, D.E.: 1992, JEEEA 12, 121
Davis R.J.: 1996, "Upgrading the Lowell 76-m Telescope" , In: Proc. of the HSRA
International Conference, Jodrell Bank (in press) 
Docchio, F., Perini, U. and Tiziani, H.: 1994, Meas. Sci. Technol. 5, 807
Ealey, M.A.: 1990, Optical Engeneering 29, 1319
Fanson, J.L., Anderson, E.H. and Rapp, D.: 1990, Optical Engineering, 29, 1320
Galindo, V.: 1964, IEE Trans. AP 12, 403
Hall, P.: 1995, AT/31.6.7/018
Hoerner von, S.: 1976, IEEE Trans. AP 24, 336
Ingalls, R.P., Antebi, J., Ball, J.A. et al.: 1994, Proc. IEEE 82, 742
IRAM Newletter No. 24/25, p. 5, 1996
Kesteven, M.J.: 1994, JEEEA 14, 85
Lacasse, R.J.: 1978, "Correctable Subreflector Controller", NRAO Electronic 
 Division Int. Rep. No. 193 
Lintel-Hekkert te, P.: 1996, MNRF Science Workshop report, ATNF 
 (also: 1996, Proc. ASA, in preperation)
Marlow, W.C.: 1994, Optical Engineering 33, 1016
Mayer, C.E., Davis, J.H. and Foltz, H.D.: 1991, IEEE Trans. AP 39, 309
Mayer, C.E., Emerson, D.T. and Davis, J.H.: 1994, Proc. IEEE 82, 756 
Napier, P.J. and Cornwell, T.J.: 1995, In 'Multi-feed Systems for 
 Radio Telescopes', eds. D. Emerson and J. Payne, ASP Conference Ser. 75, p. 48
NRAO REV 2.0 "GBT: Active Surface Requirements Document", 1994 
 O'Birne, J.W., Bryant, J.J., Minard, R.A., Fakete, P.W. and Cram, L.E.: 
 1995, Publ. ASA 12, 106
Rupen, M.: 1996 (Private communication)
Sargent, A.I. and Welch, W.J.: 1994, Annual Rev. Astr. Astroph. 31, 297
Tyson , R.K.: 1991, "Principles of Adaptive Optics", Acad. Press, NY

-----------------------------------------------------------------------

FIGURE CAPTIONS (Figures could be send separately by the request) 

Fig. 1 The ATCA 22-m antenna design (side view). The head part of the 
laser theodolite system, LTS, is located at a blind spot of the 
secondary mirror. Other LTS part consist of 160 retroreflectors 
attached to the each primary mirror panel.

Fig. 2 The CA 22-telescope primary mirror panel location (one quarter of 
the PM) is shown. The first four rings correspond to the PM 15-m 
inner part (solid panels). Two other (outer) rings consist of the 
perforated panels. The retroreflector, RR, is attached to the left 
outer corner of each panel (open circles).

Fig. 3 RF path length errors due to gravity deflections of the Haystack 37-m
telescope primary mirror (before upgrade). Astigmatism, the sag of
panels between rings, and the local effects near the shear studs are
all illustrated in this Figure. 
Note: This map should be replaced by the complete set of the 
corresponding surface error distributions of the CA antennas.

Fig. 4 Ray path when the distortion Sigma-Zp of the primary mirror (PM) 
is corrected by the secondary mirror (SM) surface local shift
(designations see von Hoerner 1976).

Fig. 5 Design of the Haystack 37-m telescope deformable secondary mirror.
Note that this design specifically corresponds to the error
distribution shown at Fig. 3. 

===========================================================================

                A P P E N D I X  1.  H o w   l o n g ?


A1.1. On-line mode

The estimated time required for the first on-line mode device design and
development is 30 months. This time range includes the 6-12 months project
design (PD), 12 months feasibility study (FS), 12 months DSM structure
development (SD), 24 months software development (SW), 3 months AT/DSM
device installation phase (DI) and 3 months test control (TC) stage, see
Table A1. 

Table A1. A schedule of the first AT/DSM on-line device design & development 
          (1 - 6 phases as defined above)
__________________________________________________________________________________________
Month No: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
------------------------------------------------------------------------------------------
1. PD     1 2 3 4 5 6 7 8 9 10 11 12 
2. FS                 1 2 3  4  5  6  7  8  9 10 11 12
3. SD                                 1  2  3  4  5  6  7  8  9 10 11 12
4. SW                 1 2 3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
5. DI                                                                     1  2  3   
6. TC                                                                              1  2  3
------------------------------------------------------------------------------------------

The next five devices would be produced practically simultaneously and
could be installed within next two years. 

A1.2. Off-line mode

The estimated time required for the first off-line mode device design
and development is 24 months. This time range includes the 9 months
project design (PD), 6 months feasibility study (FS), 12 months DSM
structure development (SD), 12 months software development (SW), 3 months
AT/DSM device installation phase (DI) and 3 months test control (TC)
stage, see Table A2. 

Table A2. A schedule of the first AT/DSM off-line device design & development 
          (1 - 6 phases as defined above)
 _________________________________________________________________________
 Month No: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 
 -------------------------------------------------------------------------
 1. PD    1 2 3 4 5 6 7 8 9
 2. FS                1 2 3 4   5  6  
 3. SD                      1   2  3  4  5  6  7  8  9 10 11 12
 4. SW                1 2 3 4   5  6  7  8  9 10 11 12 
 5. DI                                                  1  2  3   
 6. TC                                                           1  2  3
 -------------------------------------------------------------------------

The next five devices would be produced practically simultaneously and
could be installed within next two years. 

=======================================================================


                A P P E N D I X  2.  H o w  m u c h ?


A2.1 On-line mode

Costs amount of the AT/DSM device (on-line mode) is 3.15 M$ for the 
first one and about 2.2 M$ for the each next one. 

A2.1.1. Cost of the first AT/DSM on-line device consists of

                Project design                  -  0.210 M$
                Feasibility Study (prototype)   -  0.450
                Active SM                       -  0.800
                SM back-up structure            -  0.450
                Laser theodolite system (LTS)   -  0.450
                Other hardware                  -  0.200
                Software                        -  0.140
                Installation work               -  0.140
                Other expenses                  -  0.310
                                        ---------------------
                Total financial investment      -  3.150 M$
                                        ---------------------                   
   Total financial investment for six CA antennae
                (on-line DSM)                   - 14,500 M$ (per 4.5 years)


A2.1.2. Human resource investment of the first AT/DSM on-line device 
consist of

        Project design                          -  3.0 p-y
        Electronics tech/eng time 
        to construct AT/DSM                     -  6.0
        Engineering firmware development        -  6.0
        AT/DSM software development             -  2.0
        Installation, testing etc.              -  2.0
                                        --------------------
        Total human resource investment         - 19.0 p-y
                                        ---------------------
        Total human resource investment
        for six CA antennae (on-line DSM)       - 44.0 p-y


A2.2. Off-line mode

Costs amount of the AT/DSM device (off-line case) is 2.1 M$ for the 
first one and about 1.3 M$ for the each next one.

A2.2.1. Cost of the first AT/DSM off-line device consists of

                Project design                  -  0.140 M$
                Feasibility Study (prototype)   -  0.250
                Active SM                       -  0.800
                SM back-up structure            -  0.450
                Other hardware                  -  0.100
                Software and holography         -  0.070
                Installation work               -  0.070
                Other expenses                  -  0.210
                                       ---------------------
                Total financial investment      -  2.100 M$
                                       ---------------------    
        Total financial investment for six CA antennae
                (off-line DSM)                  -  8.600 M$ (per 4 years)

A2.2.2. Human resource investment of the first AT/DSM off-line device 
consist of

        Project design                          -  1.0 p-y
        Feasibility Study                       -  0.5
        Electronics tech/eng time 
        to construct AT/DSM                     -  2.0
        Engineering firmware development        -  4.0
        Software development and holography     -  1.0
        Installation, testing etc.              -  1.0
                                        --------------------
        Total human resource investment         -  8.5 p-y
                                        --------------------
        Total human resource investment
        for six CA antennae (off-line DSM)      - 31.0 p-y 


A2.3. Additional remarks

It seems to be interesting to compare known costs of the CA
telescope (0.2 efficiency at 7 mm), the VLA antenna (corresponding
efficiency 0.25, Rupen 1996) and IRAM 30-m telescope (efficiency near 0.6,
see IRAM Newsletter No 24, 1996). What is an expenditure difference of
these cm and mm type telescopes? Reduced to 22-25 m size the estimated
value should be about 30 M$, and it could be considered as an additional
cost of the mm-wave "direct" performance. Let's compare this value with
the cost of the AT/DSM system proposed here. 

Also, it should be stressed that a highly profitable product could be 
developed, based on the AT/DSM device consisting of the active SM, high 
precision distance measurement unit and other relevant hardware and
software. We could expect a considerable demand of such effective and
relatively low cost mm-wave upgrade of the space network, military and
civilian radar and communication antennae and, first of all, many radio
telescopes around the world. 

===================================================================
The End