On the Polarization Diversity of Aperture Array Antennas for SKA Wide-Field Polarimetry

Transcription

1 On the Polarization Diersity of Apertre Array Antennas for KA Wide-Field Polarimetry ob Maaskant and Tobia Carozzi May 04, 00 BYU orkshop, Proo, Utah In part based on a discssion ith: Karl Warnick, Brian effs, Marianna Iashina, and tefan Wijnholds

2 pecifications on Polarization Prity for the qare Kilometre Array KA MMO 00, preliminary specifications for the KA (007, page 4) Plsar timing experiments Calibrated polarization prity has to be at the leel of 40 db at the center of the field. poch of eionisation (o) and Cosmic Magnetism experiments A prity of at least 30 db oer the entire field is reqired (leakage of intensity signal into the other tokes parameters, after calibration and mosaicing). xperiments ill be needed to erify the leel of polarization prity that can be achieed at the pt of polarization-optimized beam formers. - Polarization prity can be improed to irtally any leel by compromising the? - Polarization prity shold be a positie nmber? - George eald: max. 0.5% (-3 db) of the total intensity is alloed to leak into the other tokes parameters (oer the entire FoV) - o are these nmbers related to standard I definitions on cross-polarization?

3 I tandard Definitions on Cross-Polarization Cross-Polarization Discrimination (XPD): The ratio of the poer leel at the pt of a receiing antenna, nominally co-polarized ith the transmitting antenna, to the pt of a receiing antenna of the same gain bt nominally orthogonally polarized to the transmitting antenna ŷ xˆ T y ŷ x- and transmitting antennas x- and receiing antennas XPD y P P y x Cross-Polarization Isolation (XPI): The ratio of the anted poer to the nanted poer in the same receier channel hen the transmitting antenna is radiating nominally orthogonally polarized signals at the same freqency and poer leel x- and transmitting antennas T T x y xˆ ŷ ŷ xˆ x- and receiing antennas XPI y P y P y T T y x ŷ xˆ

4 A adio Polarimeter inc ˆ + ˆ ones matrix (amaker, Bregman, alt)

5 XPD Characterization of the adio Polarimeter Determination of the ones matrix (, 0) inc û 0

6 Characterization of the adio Polarimeter Determination of the ones matrix XPD XPD (, ) 0 inc ˆ 0 XPI The ones matrix, the XPDs and the XPIs depend on the eight ectors and the chosen reference frame XPI

7 A adio Polarimeter inc ˆ + ˆ ( ) ( ) * * A adio Polarimeter V * ( ) ( ) *

8 A adio Polarimeter inc ˆ + ˆ ( ) ( ) * * V Measrement eqation (amaker, Bregman, alt) Ideally: GI V ( ) ( ) * *

9 o ideal is the ones matrix? Condition nmber of measres ho close e achieed the sitation that GI. Important hen e aim to sole inc ith high accracy κ ( ) + The ones polarimeter s intrinsic cross-polarization ratio (Tobia Carozzi): IX κ ( ) ˆ κ ( ), κ, [ 0] û κ [ 0 ] IX ( ) IX xample: ones matrix hich rotates and scales the polarization ectors 0. 5 XPD 0. 5 IX [ ] [ ] IX measres the independency of a -D basis, XPD does not. ˆ ˆ

10 MBAC Tile (all 7x7 TA sed in simlations) CBFM: - from 0833 WG basis fnctions don to 5560 CBFs - total exection time (single core) is 34 min. 3 sec. Z 0 50 Ohm

11 and as a fnction of angle (sampled at the beam centers) - Polarization ellipses are shon in black - û and ˆ chosen according to Ldig s 3 rd definition - Weights are chosen to receie maximm poer (CFM)

12 imlated XPD and IX XPD [db] κ ( ) + IX κ ( )

13 oint optimization for both and Polarization Prity (, 0) inc û deterministic CW signal {, } sig sig self term sig leakage (cross) term

14 oint optimization for both and Polarization Prity (, ) 0 inc ˆ {, } sig sig leakage (cross) term sig self term

15 oint optimization for both and Polarization Prity K. Warnick proposes a constraint optimization to determine the optimal eights: I (calibrated system), then minimize noise Calibrated for hat reference coordinate system and? û ˆ B. effs proposes to consider the leakage term as an additional noise term in the max optimization: ( ) sig max + sig Weights depends on the sorce strength sig sig sig sig Minimize condition nmber of the matrix to maximize the sensitiity of the polarization measrement min ( κ ( )) {, } κ

16 oint optimization for both and Polarization Prity {, sig } on-deterministic signal ( ) ( ) * sig has a rank of to for partially polarized aes, ith eigenectors: e and e Brce Veidt s method: (based on max. method) e e * sig sig For npolarized sorce, the realized pt oltage ectors can hae arbitrary rotation, so calibration is still reqired?

17 Open Qestions Which pair of eight ectors hae to be chosen to simltaneosly optimize for good polarization characteristics and high? Maybe e need to look into robst beamformer algorithms that are insensitie to first-order pertrbations in or system? Does Brce Veidt s method yield good and stable polarimetric properties for each beam? o important is polarization stability oer the FoV before calibration? o does an error on the tokes parameters translate into reqirements for the XPD, XPI, and IX? What reference frame shold be taken for û and ˆ? (this qestion may be of less importance hen all the are beam formed, otherise the intrinsic polarization properties mst be good enogh)