OCRA Workshop, Toruń, 3 - 5 Sep 2009
K.M. Borkowski, TCfA



A 90 m Transit Radio Telescope:
Offset or Symmetrical?



Similar studies of other possible solutions connected directly or indirectly with the projected RTK telescope were presented in earlier reports:
    1. 80-metre offset paraboloid (June 2006) 
    2. 90-metre offset paraboloid (May 2009)
    3. RT32 with OCRAp/f (pointing and gain) (June 2005)
    4. Follow-up of the above (OCRA-f) (July 2006)
    5. Properties of the RT32 enlarged to 36 m (in Polish; January 2009)



The Tool – OptiCass program


Developed at Centre for Radio Astronomy

Language: Fortran (about 3000 lines)

Method: ray tracing (up to 15 000 rays)
    Doesn't use paraxial technique — its ray tracing is exact
    DFT of amplitude & phase on aperture –> power pattern
    Optimizes through iterations for minimum losses

Input:    25 design and computation parameters

Output: 55 numerical results
             18 analytical results
             graphical presentation

Example of usage (symmetrical 90 m RT):


Note: As seen in the above screen capture, analytical expressions of classical optics give completely wrong result (a few hundred percent) for 'Astigmatic gain loss' due to the assumed very large feed offset (6 m). It signifies just the fact that classical optics expressions are valid for small offsets only.


Graphical output (of the above example):


Notes:
1. There are about 2800 rays traced (coloured dots in the inset at top-right).
2. The value of u = (D/λ)sinΘx = –104.253 corresponds to Θx = –1.33° main beam shift.
3. The plot of distortions is the difference between the pattern shown and one computed for feed in the focus.




Reliability of OptiCass


Early tests have demonstrated that:

For small offsets ray tracing outputs are in very good agreement with closed formulas results (closed formulas are also built-in in OptiCass); see this table.

The path length errors in aperture distribution resulting from subreflector tilt computed for the ALMA 12 m telescope using OptiCass and the J. Ruze's approximate formulas compare very nicely:



More recently:

When the OCRA-p system has been moved 72 cm away from the focus in late August 2009, OptiCass predicted about right improvement in aperture efficiency due to z-offset (towards the subreflector).



RT90 Symmetrical vs Offset


 Circular aperture diameter, D                           90.000 m
 Focal length of primary mirror, f                       50.000 m
 Frequency, ν                                              15.0 GHz
 Height of secondary focus above paraboloid vertex, h    25.000 m
 
 Primary dish type               Symmetrical      Offset paraboloid
 Primary physical size               90 m               90x102 m 
 Secondary diameter(s)                8 m              7.4x9.1 m 
 Secondary projected size             8 m              7.4x8.3 m 
 Secondary subtended angle         21.1 deg              16x18 deg 
 Telescope magnification           4.87                   5.65 
 Effective focal length             243 m                  283 m 
 Feed offset in y [m]          1      6               1      6      
 Optimal z [m]                0.04   3.63            0.02   3.35    
 Secondary tilt y/(x) [deg]   1.28   3.14        1.96/0.03 3.0/-4.2   
 Beem offset [deg]            0.10   1.28            0.03   1.12    
 Minimized gain loss [%]      0.31   20.9            3.80   13.0
     NOTES:
1. The x offset is towards the main dish; y – perpendicularly to it.
2. The high losses are mainly due to aberration (phase errors).
3. For offset paraboloid the horizontal (in y) feed displacements cause both 'vertical' and horizontal beam offsets (see OptiCass graph).
4. At the feed horizontal displacement of 7 m the losses for offset paraboloid can be reduced to about 17 % and then the horizontal beam offset would reach 1.33°.


The beam throw of an offset telescope with the main dish built on the same paraboloid of revolution is comparable to a symmetrical telescope of the same projected diameter.
At larger feed displacements the offset telescope performs somewhat better (has smaller losses).

A transit 90-m offset telescope with f = 50 m would allow for about ±5 minutes (±1.25°) of observing time at the equator with losses not much greater than 13 %.
This would require somewhat more than ±6 m feed lateral movement accompanied by corresponding secondary tilts exceeding ±3 and ±4° in two directions (or rather, alternatively, in one direction with the feed being displaced also in x direction) .



[Last updated: September 7, 2009]