SMA Optics

SMA OPTICS

1. Basic requirements

The optics for the SMA are required to satisfy the following functional and performance requirements:

The optics should be designed for maximum possible illumination efficiency. For scalar feeds, the maximum theoretical illumination efficiency excluding blockage can be made as high as 87% with minimal variation across each receiver band by using an imaging beam waveguide design.
Loss due to factors such as beam truncation, distortion at focusing mirrors, and absorption and reflection at windows and mirrors should be held to a few percent. A reasonable goal is to hold the net loss due to all such factors to ten percent or less.
Of eight possible receivers, two at a time will be active simultaneously, using polarization diplexing. The cryostat housing the receivers should operate in a fixed orientation relative to gravity.
Warm and ambient loads will be provided for receiver calibration. These should be located in the optics train as near to the sky as possible. They should be capable of switching rapidly in and out of the beam (~0.5 sec. or less) in order to minimize dead time in the calibration cycle.
Provision will be made for polarimetry using overlapping receiver bands at 345 GHz; a quarter-wave plate will be available for converting the two linear polarization channels to circular polarization. Cross-polarization introduced by focusing optics should be kept small relative to the cross-polar leakage for the wire grid polarizer used for separating receiver channels, which is expected to be about -35 dB.

Figure 1 - Schematic diagram of the SMA beam waveguide

2. SMA optics concept

A schematic diagram of the SMA beam waveguide is shown in Fig.1. Two focusing mirrors combined with one lens form an imaging beam waveguide which images the aperture of the receiver feed horn onto the secondary mirror. The focusing mirrors are common to all receivers, while the lenses and feeds are separately optimized for each receiver band. To the extent that the aperture field at the feed is independent of frequency, the illumination at the subreflector is likewise frequency-independent. The overall magnification from the feed aperture to the secondary mirror is chosen to maximize the antenna gain. For scalar feeds, this corresponds to an image of the feed horn aperture at the secondary mirror with 10.0 dB edge taper.

The virtual image formed behind the receivers serves as a common source plane for the receiver beam at all frequencies. Its size and position were chosen based on two considerations. First, the beam at the lowest frequencies was assumed to have flat phase at the receiver cryostat window in order to minimize the size of the low-frequency receiver optics and of mirror M5. Second, locating the image plane well behind the receiver with negative phase curvature results in a beam size at the feed lens and cryostat window which decreases with frequency. This allows the lenses and windows to be smaller and hence thinner, helping to compensate for the increase of absorption loss with frequency.

Receiver calibration loads and the 345 GHz quarter-wave plate will be located around the intermediate image between mirrors M4 and M5.

Figure 2 - Antenna optics layout

3. Optics layout

The overall layout of the beam waveguide and the receiver optics package is shown in Fig. 2. A more detailed view of the layout of the beam waveguide mirrors within the receiver cabin is shown in Fig. 3. The Z-shaped configuration of the beam waveguide mirrors was adopted to minimize the incidence angles at focusing mirrors M4 and M5. Compared with the earlier scheme in which the 90° turn in the optical path was made at M5, this configuration has lower cross-polarization (~4 dB at 345 GHz), simpler alignment, and slightly improved efficiency.

Figure 3 - Beam waveguide mirrors

The receiver optics layout is shown in Fig. 4. Four identical sets of optics are used for the four low-frequency receivers, and four identical sets for the high-frequency receivers. (A discussion of the allocation of receiver bands and the receiver pairing scheme is contained in the Project Book entry for Receivers.) Because of the large number of receivers, the optics have been kept as simple as possible. The LO injection scheme for the low-frequency receivers uses a simple mesh coupler. It is anticipated that sufficient LO power will be available at these frequencies to limit the signal loss using this scheme to 1% or less. Since available LO power for the high-frequency bands will be more limited, the LO for these bands will be coupled to the mixer using a Martin-Puplett diplexer. It is worth noting that because of the wide IF bandwidth of the SMA, the performance of the mesh coupler is actually superior to that of the Martin-Puplett when sufficient LO power is available.

Positions, focal lengths and sizes of all of the optical elements are specified in Table 1. Feed horn parameters are specified in Table 2. Sizing of the optics for acceptable truncation loss and analysis of the beam waveguide efficiency were carried out using multi-mode beam propagation and mirror analysis code developed for the SMA.

Figure 4 - Receiver optics layout. 20 dB truncation contours for the receiver beam are shown at 216 GHz for the low-frequency optics and at 460 GHz for the high-frequency optics.

Table 1 - Parameters for optical elements

     element      position   focal   focal    focal   angle of   major    minor  
                     on     length   length   length  incidence diameter diameter 
                   optical   [mm]    on sky     on                [mm]     [mm]  
                   axis z             side   receiver [degrees]                  
                    [mm]†             [mm]     side                              
                                               [mm]                              

                                                                          
optics common to all bands                                                

    secondary      8307.2   -149.94 -145.44   4847.5      0       350            

       M3          3891.7    flat                        45       212      150   

       M4          3456.6   309.78   4228.7   334.27    24.93     165      150   

       M5           2161    726.57   1166.9   1925.4    24.93     331      300   

       M6           1761     flat                        45       354      250   

  combiner grid     1207     flat                        45       269      190   

                                                                          
low-frequency receiver optics                                             

 turning mirror      812     flat                        45       219      155   

 turning mirror      469     flat                       24.1      131      120   

  LO injection      294.9    flat                       24.1      110      100   
    mesh/grid                                                                    

 cryostat window    ~109     flat                         0        76            
  (176-256 GHz)                                                                  

 cryostat window    ~109     flat                         0        76            
  (250-360 GHz)                                                                  

  lens (176-256       0       120     2394    126.3       0        75            
      GHz)                                                                       

  lens (250-360       0       100     1060    110.4       0        70            
      GHz)                                                                       

                                                                          
high-frequency receiver optics                                            

 combiner mirror    1032     flat                        45       212      150   

  LO injection       657     flat                        45       148      105   
      grid                                                                       

 turning mirror      487     flat                        45       127      90    

LO diplexer grid  377, 177   flat                        45       113      80    

  roof mirrors       277     roof                         0        74      74    

 cryostat window    ~109     flat                         0        70            
  (320-420 GHz)                                                                  

 cryostat window    ~109     flat                         0        65            
  (400-520 GHz)                                                                  

 cryostat window    ~109     flat                         0        60            
  (600-720 GHz)                                                                  

 cryostat window    ~109     flat                         0        50            
  (780-920 GHz)                                                                  

  lens (320-420       ‡        ‡       ‡        ‡         ‡        ‡             
      GHz)                                                                       

  lens (400-520       0       80      706      90.2       0        55            
      GHz)                                                                       

  lens (600-720       0       70      600      79.2       0        45            
      GHz)                                                                       

  lens (780-920       ‡        ‡       ‡        ‡         ‡        ‡             
      GHz)

† z = 0 is defined by the nominal position of the top surface of the radiation shield in the receiver dewar.

‡ To be determined

Table 2 - Scalar horn parameters

    band     position of    aperture   length from  input guide   input guide  
   [GHz]       aperture      radius      apex to       width        height     
               plane on       [mm]       aperture       [mm]         [mm]      
               optical                     [mm]                                
                axis z                                                         
                [mm]†                                                          

 176 - 256       -104         6.27        52.75        1.150         0.276     

 250 - 360      -88.6         5.34        35.65        0.800         0.191     

 320 - 420        ‡            ‡            ‡            ‡             ‡       

 400 - 520      -72.6         4.37        22.26        0.558         0.130     

 600 - 720      -64.2         3.87        16.86        0.373         0.091     

 780 - 920        ‡            ‡            ‡            ‡             ‡

† z = 0 is defined by the nominal position of the top surface of the radiation shield in the receiver dewar.

‡ To be determined (feed for 780 - 920 GHz may not be a scalar horn)

4. Other specifications and performance estimates

Combined truncation and absorption loss at receiver feed lenses. (Lens diameters are chosen to minimize the combined truncation and absorption loss. All other optics have been sized so that the truncation loss at the lenses is the main contribution to the overall truncation loss.)
```
	4% at 216 GHz
	4.5% at 345 GHz (250 - 360 GHz receiver)
	8% at 460 GHz
	Loss at higher frequencies will depend on final choice of lens materials.
	
```

Martin-Puplett diplexers for high-frequency LO injection:

	At IF center:
	    LO port noise rejection: 25 dB or better
	    Signal loss: ~0.3%
	At 1GHz offset:
	    LO port noise rejection: 10 dB
	    Signal loss: 10%

Beam waveguide mirrors M4 and M5:

	Coupling loss at M4 for beam from scalar feed: 0.25% at 175 GHz
	    0.05% at 400 GHz
	    0.02% at 900 GHz
	Coupling loss at M5 for beam from scalar feed: 0.9% at 175 GHz
	    0.15% at 400 GHz
	    0.08% at 900 GHz
	    (Coupling loss includes phase loss, spillover, and geometric loss due to off-axis incidence.)
	Cross-polarization contribution from M4 and M5 at 345 GHz:
	    null on axis, -38 dB maximum cross-polar to copolar ratio at 3 dB points of the copolar beam

Illumination taper at secondary edge: 10.0 dB
Illumination efficiency neglecting blockage and truncation: 87% for scalar feeds
Geometric illumination distortion on propagation from secondary to primary:
```
	+2% at primary edge, -2% at primary center
	
```
Illumination efficiency net of quadrupod and subreflector blockage, including geometric distortion: 80.5%

Scott Paine rev. 7/5/95