VHF Dipole effects on P-Band Beam Characteristics

Transcription

1 VHF Dipole effects on P-Band Beam Characteristics D. A. Mitchell, L. J. Greenhill, C. Carilli, R. A. Perley January 7, 1 Overview To investigate any adverse effects on VLA P-band performance due the presence of the VHF dipoles, we compare the beam characteristics of antennas and 17 equipped with VHF dipoles to the inherent variation among P-band systems on the array as a whole. We find that the P- band beam properties in the presence of VHF dipoles, in particular beam ellipticity, width, and centration, are close to the mean established without VHF dipoles in place. Differences are small compared to the inherent variations experienced by P-band users. Observations Our analysis compares data from a set of VLA P-band holography rasters observed with and without VHF dipoles in place. During these scans, the dipoles were electrically shorted. (Shorting is controlled via SYS ROT files; the default state for the array shorts the dipoles.) Two P-band control data sets were used to determine the statistical distribution of P-band performance. These are the data from the 7 July observations summarized in the first two rows of Table 1. All other data sets have VHF systems attached to antennas and 17. Two types of VHF dipoles were used: (1) a short dipole with a 1 cm stand-off from the P-band dipole and () a long dipole with a 1. cm stand-off. (Long and short dipoles differ in length by only. cm. The prototype dipoles whose performance has already been reported used the same stand-off as the present long dipoles, and their lengths were 1. cm shorter.) Each holography raster comprises an oversampled grid of points (between and 33 square) with an angular spacing λ/3d or.7. Some distortion in the regularity of the grid occurred at high elevations, but this was taken into account in our analysis. Four ten-second integrations were vector averaged for each raster point. Observation VHF Dipoles Central Source Grid Additional Date on Antennas Frequency Size Antennas & 17 7 July No dipoles 3. MHz 3C17 1,3,,,7,11,1,1,, 3,,,7,1 (ref) 7 July No dipoles 3. MHz 3C17 1,3,,,7,11,1,1,, 3,,,7,1 (ref) 17 November Long dipoles 37. MHz 3C 1 1 (ref) 1 December Short dipoles 37. MHz TauA (ref) December Short dipoles 37. MHz CasA (ref) December Short dipoles 33. MHz CasA (ref) Table 1: P-Band Observation Parameters. 1

2 3 Analysis After standard calibration and holography processing, each set of data was vector averaged and fitted to a two dimensional Gaussian distribution. The Levenberg-Marquardt method of χ optimization was used to fit for six parameters of the natural logarithm of the Gaussian defined in (1); the amplitude ln(a); the beam center (x, y ), where coordinates x = sin 1 (l) and y = sin 1 (m); the width (σ x, σ y ); and the measure of diagonal distortion (ρ). Each holography raster provided a quasi-regular grid of curves. Model beams were fit directly to the data, while regridding and interpolation were applied to obtain contour plots. { ( 1 (x x ) beam(x, y) = A exp (1 ρ ) σ x + (y y ) σ y ρ(x x )} )(y y ). (1) σ x σ y Chapter 1 of [1] gives an in-depth discussion of the fitting algorithm and associated formal errors. If we assume that the measurement errors are normally distributed and that the fitted parameters are fairly independent (e.g., that ρ is small), then the RMS in a parameter is given by the standard fitting uncertainty in that parameter multiplied by χ ν. The spread along each axis of the beam is given by σ x and σ y, with the full width at half maximum (FWHM) given by σ x (1 ρ ) ln() and σ y (1 ρ ) ln() along the l and m axes respectively. Fitted beams are shown below and at cfa- Table gives a summary of the spread of these parameters for the observations in Table 1. While the fits for antennas with VHF dipoles attached are within the natural variation among antennas in general, the FWHM values do tend to lie slightly below the mean value. At the same time the variation in the FWHM values also appears to be reduced. The fitted ρ-values and the variation of the beam centers do not seem to be systematically affected by the presence of the VHF dipoles. The FWHM data in table are shown graphically in figure 1. The data taken while VHF dipoles were attached are shown as points below histograms of the two control data sets from 7 July. The histograms were constructed by averaging together standard Gaussian distributions of the form y = dx/(σ π) exp 1/(x ˆx)/σ, using the FWHM values of each of the 7 July fits. The fitted FWHM values were used as the means (ˆx), and the FWHM fit uncertainties as the standard deviations (σ). These Gaussians have integrals of unity, so the area under a curve represents the likelihood of a given FWHM value, based on that data. The figure demonstrates within the uncertainties inherent to the P-band receivers that the VHF dipoles (in particular the short dipoles) neither broaden nor distort the P-band beams. Figures through show holography contours for both polarizations of antennas and 17 with and without VHF dipoles attached. The real and imaginary components of each data set were individually interpolated onto a regular grid using cubic Shepard interpolation (see SCILAB documentation at and then combined. The grid spacing was set to.7, approximately one raster step. The -3dB contour of each fit is also shown. Figures through 1 show holography data with beam cuts for antennas and 17. For a complete set of images, and logarithmic scaling, see Summary The VLA P-band beams in the presence of VHF dipoles have not shown any excess distortion, outside of the natural P-band beam variation, with the exception that the beam width seems to have been reduced by a few percent. In particular the short VHF dipoles show stable, well centered, circular beams.

3 Observation χ ρ Pos n Beam FWHM FWHM FWHM FWHM & Antenna Angle center sin 1 (l) sin 1 (m) minor axis major axis Long dipole 37. MHz l, m LL.. +.1,.1.3 ±.9.1 ± ±.1. ±.11 RR ,.. ±.17. ±..19 ±.19. ±.3 17 LL ,..3 ±.. ±.7.3 ±.7. ±. 17 RR , +..1 ±.1.3 ±.1.9 ±.1. ±.1 mean (st.dev).13.3 σ=(.1,.). (.1). (.).3 (.1). (.3) Short dipole 37. MHz l, m LL , +..1 ±..1 ±.. ±.. ±. RR , ±..1 ±.. ±.. ±. 17 LL ,.1.3 ±.9. ±.1.9 ±.9. ±.1 17 RR , ±.1. ±.1.9 ±.1.3 ±.1 mean (st.dev).3. σ=(.,.).3 (.). (.).9 (.).7 (.) Short dipole 37. MHz l, m LL ,..7 ±.. ±.3. ±.3.7 ±. RR , ±..9 ±..9 ±.3.7 ±. 17 LL ,..7 ±..7 ±.3.7 ±.3.7 ±. 17 RR , ±.. ±.. ±..7 ±.7 mean (st.dev).. σ=(.3,.).73 (.).7 (.9).7 (.).79 (.) Short dipole 33. MHz l, m LL , ±.1.9 ±.13.7 ±.13. ±.1 RR ,..7 ± ±.1. ±.1. ±.1 17 LL ,.. ±.19. ±.1. ±.1. ± RR , +..3 ±.17.1 ±.1.3 ±.17.3 ±.1 mean (st.dev).. σ=(.,.). (.).3 (.7).9 (.). (.3) No dipole 3. MHz l, m LL , ±.1.1 ± ±.11.1 ±.1 RR ,.1. ±..33 ±..7 ±..7 ±. 17 LL , +.. ±.1.7 ±..3 ±.1. ±.1 17 RR , ±.17.3 ±.11.3 ±.1.9 ±.1 mean (st.dev).1. σ=(.1,.1).3 (.3). (.7).3 (.). (.3) No dipole all antennas: mean (st.dev).1 +. σ=(.1,.1).7 (.).1 (.).1 (.1). (.) No dipole 3. MHz l, m LL ,.1.33 ±.9.37 ±.1. ±.9.3 ±.1 RR , ±.1.73 ±.1. ±.1. ± LL , +.3. ±.17.7 ±.1. ±.1.7 ±.1 mean (st.dev) σ=(.,.1). (.1).73 (.3). (.). (.) No dipole all antennas: mean (st.dev) σ=(.,.1).7 (.1).7 (.).9 (.11). (.) Table : P-Band Holography Summary. Numbers following ± symbols represent one standard deviation confidence of fit levels, scaled by the reduced χ (χ ν). All angular data are in units of. 3

4 Proportion l Axis Proportion Minor Axis no dipole, 3MHz no dipole, 3MHz no dipole, & 17 long dipole, 37MHz short dipole, 37MHz short dipole, 37MHz short dipole, 33MHz FWHM FWHM Proportion m Axis Proportion Major Axis FWHM FWHM Figure 1: Demonstration of limited impact by shorted VHF dipoles. Parameter likelihood histograms of FWHM values for VLA P-band receivers, constructed from the 7 July data, when there were no VHF dipoles on any antennas. All data were used except for corrupted rasters from receivers 1-LL, 1-LL, 3-RR and 7-LL at 3MHz and -RR and 1-LL at 3MHz. Shown below the histograms are fitted FWHM values from observations at P-band for which VHF dipoles were attached to the antennas. Different VHF dipole types and frequencies are shown on different lines. Each line contains a mark for each polarization of antennas and 17. Note that the green X s show the inherent spread in beam size for these antennas sans VHF dipoles.

5 References [1] W. H. Press, B. P. Flannery, S. A. Teukolsky & W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, 19 antenna : short diople, 19.3 MHz rho =.3, position angle = 1.1 deg antenna 17: short diople, 19.3 MHz rho =., position angle = 1. deg antenna : long diople, 19. MHz rho =.1, position angle =. deg Figure : P-band holography contours (LL polarization) for antenna. The fitted FWHM contour is

6 antenna : short diople, 19.3 MHz rho =., position angle = 9.9 deg antenna 17: short diople, 19.3 MHz rho =., position angle =. deg antenna : long diople, 19. MHz rho =.1, position angle =.3 deg Figure 3: P-band holography contours (RR polarization) for antenna. The fitted FWHM contour is

7 antenna 17: short diople, 19.3 MHz rho =., position angle = 1. deg antenna 17: long diople, 19. MHz rho =., position angle =.3 deg antenna 17: short diople, 1. MHz rho =.3, position angle =. deg antenna 17: short diople, 19. MHz rho =., position angle =. deg Figure : P-band holography contours (LL polarization) for antenna 17. The fitted FWHM contour is 7

8 antenna 17: short diople, 19.3 MHz rho =., position angle =. deg antenna 17: long diople, 19. MHz rho =.1, position angle = 39.1 deg antenna 17: short diople, 1. MHz rho =.7, position angle =.7 deg antenna 17: short diople, 19. MHz rho =., position angle = 77. deg Figure : P-band holography contours (RR polarization) for antenna 17. The fitted FWHM contour is

9 rho =., position angle =. deg l= Cut Fit: N{.1,1.7} deg, FWHM= m= Cut Fit: N{.1,1.} deg, FWHM= Fit: N{.,1.} deg, FWHM=. Fit: N{.,.99} deg, FWHM= rho =., position angle = 11. deg l= Cut Fit: N{.,1.} deg, FWHM= m= Cut Fit: N{.,.9} deg, FWHM= Fit: N{.,1.9} deg, FWHM=. Fit: N{.,.93} deg, FWHM= Figure : Shorted, long dipoles, 37. MHz, Antenna, Reference. The fitted FWHM contour is

10 rho =.3, position angle = 73. deg l= Cut Fit: N{.,1.} deg, FWHM= m= Cut Fit: N{.1,1.11} deg, FWHM= Fit: N{.,1.11} deg, FWHM=. Fit: N{.,1.} deg, FWHM= rho =., position angle =.3 deg l= Cut Fit: N{.9,1.} deg, FWHM= m= Cut Fit: N{.,1.} deg, FWHM= Fit: N{.,1.7} deg, FWHM=. Fit: N{.,1.} deg, FWHM= Figure 7: Shorted, short dipoles, 37. MHz, Antenna, Reference 3. The fitted FWHM contour is

11 rho =., position angle =. deg l= Cut Fit: N{.,1.1} deg, FWHM= m= Cut Fit: N{.11,1.1} deg, FWHM= Fit: N{.,1.17} deg, FWHM=.7 Fit: N{.,1.1} deg, FWHM= rho =., position angle = 73.7 deg l= Cut Fit: N{.,1.1} deg, FWHM= m= Cut Fit: N{.13,1.1} deg, FWHM= Fit: N{.,1.1} deg, FWHM=.7 Fit: N{.,1.1} deg, FWHM= Figure : Shorted, short dipoles, 37. MHz, Antenna, Reference 9. The fitted FWHM contour is

12 rho =., position angle = 71. deg l= Cut Fit: N{.1,.97} deg, FWHM= m= Cut Fit: N{.,1.} deg, FWHM= Fit: N{.,1.} deg, FWHM=. Fit: N{.,.97} deg, FWHM= rho =., position angle = 9. deg l= Cut Fit: N{.,.9} deg, FWHM= m= Cut Fit: N{.9,1.} deg, FWHM= Fit: N{.,1.} deg, FWHM=. Fit: N{.,.97} deg, FWHM= Figure 9: Shorted, short dipoles, 33. MHz, Antenna, Reference 9. The fitted FWHM contour is

13 rho =., position angle = 1. deg l= Cut Fit: N{.,.91} deg, FWHM= m= Cut Fit: N{.3,.} deg, FWHM= Fit: N{.,.91} deg, FWHM=.1 Fit: N{.,.1} deg, FWHM= rho =., position angle =.9 deg l= Cut Fit: N{.1,.99} deg, FWHM= m= Cut Fit: N{.,1.} deg, FWHM= Fit: N{.,1.} deg, FWHM=.7 Fit: N{.,.97} deg, FWHM= Figure 1: No VHF dipoles, 3. MHz, Antenna, Reference 1.

14 rho =., position angle =. deg l= Cut Fit: N{.,1.} deg, FWHM= m= Cut Fit: N{.1,1.} deg, FWHM= Fit: N{.,1.11} deg, FWHM=. Fit: N{.,1.1} deg, FWHM= rho =., position angle = 3.1 deg l= Cut Fit: N{.,1.7} deg, FWHM= m= Cut Fit: N{.1,1.7} deg, FWHM= Fit: N{.,1.} deg, FWHM=. Fit: N{.,1.} deg, FWHM= Figure 11: Shorted, long dipoles, 37. MHz, Antenna 17, Reference. The fitted FWHM contour is

15 rho =., position angle = 39. deg l= Cut Fit: N{.1,1.9} deg, FWHM= m= Cut Fit: N{.3,1.} deg, FWHM= Fit: N{.,1.11} deg, FWHM=. Fit: N{.,1.} deg, FWHM= rho =.1, position angle = 39. deg l= Cut Fit: N{.13,1.7} deg, FWHM= m= Cut Fit: N{.1,1.7} deg, FWHM= Fit: N{.,1.} deg, FWHM=.3 Fit: N{.,1.} deg, FWHM= Figure 1: Shorted, short dipoles, 37. MHz, Antenna 17, Reference 3. The fitted FWHM contour is

16 rho =.1, position angle = 1.7 deg l= Cut Fit: N{.,1.13} deg, FWHM= m= Cut Fit: N{.9,1.17} deg, FWHM= Fit: N{.,1.17} deg, FWHM=.7 Fit: N{.,1.13} deg, FWHM= rho =., position angle = 17.3 deg l= Cut Fit: N{.1,1.1} deg, FWHM= m= Cut Fit: N{.1,1.1} deg, FWHM= Fit: N{.,1.} deg, FWHM=.7 Fit: N{.,1.13} deg, FWHM= Figure 13: Shorted, short dipoles, 37. MHz, Antenna 17, Reference 9. The fitted FWHM contour is

17 rho =., position angle = 9. deg l= Cut Fit: N{.,.9} deg, FWHM= m= Cut Fit: N{.1,1.} deg, FWHM= Fit: N{.,1.} deg, FWHM=. Fit: N{.,.9} deg, FWHM= rho =., position angle = 1.3 deg l= Cut Fit: N{.,1.3} deg, FWHM= m= Cut Fit: N{.,1.} deg, FWHM= Fit: N{.,1.3} deg, FWHM=.3 Fit: N{.,1.} deg, FWHM= Figure 1: Shorted, short dipoles, 33. MHz, Antenna 17, Reference 9. The fitted FWHM contour is

18 rho =.1, position angle = 1. deg l= Cut Fit: N{.,1.19} deg, FWHM= m= Cut Fit: N{.3,.9} deg, FWHM= Fit: N{.,1.1} deg, FWHM=. Fit: N{.,.9} deg, FWHM= rho =.1, position angle = 7. deg l= Cut Fit: N{.7,1.} deg, FWHM= m= Cut Fit: N{.,1.} deg, FWHM= Fit: N{.,1.} deg, FWHM=.9 Fit: N{.,1.} deg, FWHM= Figure 1: No VHF dipoles, 3. MHz, Antenna 17, Reference 1. The fitted FWHM contour is shown in black.

19 rho =.1, position angle =. deg l= Cut Fit: N{.3,1.17} deg, FWHM= m= Cut Fit: N{.,1.} deg, FWHM= Fit: N{.,1.} deg, FWHM=. Fit: N{.,1.} deg, FWHM= rho =.1, position angle = 1. deg l= Cut Fit: N{.3,1.1} deg, FWHM= m= Cut Fit: N{.,1.1} deg, FWHM= Fit: N{.,1.1} deg, FWHM=.7 Fit: N{.,1.1} deg, FWHM= Figure 1: No VHF dipoles, 3. MHz, Antenna 17, Reference 1. The fitted FWHM contour is shown in black.