BIMA Memoranda No. 33 PASSBAND CORRECTION WITH THE BIMA ARRAY Melvyn Wright, 12-Jan-94 SUMMARY This memo describes the current state of the on-line passband calibration, and gives some examples of the astronomical passband calibration for data from the BIMA array. Polynomial fits to each interferometer baseline and correlator window currently provide the most reliable passband calibration. INTRODUCTION Passband calibration is discussed in general in BIMA Memoranda 19 (2-Oct-91) The instrumental passband has contributions from the RF, IF and correlator systems. The RF passband is a slowly varying function of frequency, and includes the relative phase between the antennas. The IF passband includes the dispersion in the analog delay system, and the signal path through the switchyard. The correlator system includes the baseband converters, samplers and the correlator. All systems, except the digital correlator are associated with individual antennas; the digital correlation is made for each antenna pair and can be baseline dependent. We measure the instrumental passband at the start of each INT or MINT observation. The on-line passband correction removes most, but not all of the instrumental frequency response. An additional astronomical passband calibration is obtained from an interferometer observation of a strong achromatic source. This passband observation is usually made for each configuration of the receiver tuning and correlator, at the begining or end of each project. ON-LINE PASSBAND CALIBRATION The on-line passband calibration is made by correlating the IF power from each antenna in turn using the same correlator configuration as in the interferometer observation, and forming the geometric mean for each antenna pair. The on-line passband measures: Pij = sqrt(Gi x Gi* x Cij x Ti) x sqrt(Gj x Gj* x Cij x Tj) = abs(Gi x Gj* x Cij) x sqrt(Ti x Tj) For the source observation, the observed correlation is: Vij = Gi x Gj* x Cij x Sij where Gi is the gain, and Ti the noise temperature for antenna i, * denotes the complex conjugate, Cij is the correlator passband for baseline ij, and Sij is the source correlation function for baseline ij. Gi, Ti, Cij, and Tij are, in general, functions of frequency. The corrected source correlation function is obtained as: Sij = sqrt(Ti x Tj) x abs(Vij / Pij) As discussed in BIMA memo 19, in principle this calibration includes everything except the phase response in front of the switchyard where the IF is split to measure the passband. In practice the switchyard introduces some dispersion, and we also apply corrections to the uv-data for the transmission through the switchyard, and for the response of each analog delay step. The passband stability, measured by sampling the on-line passband at 6 min intervals for 1 hour, shows variations across an 800 MHz bandwidth of typically 2% in amplitude, and 0.2 degrees of phase on time scales of 6 min to one hour. With the correlator LO's all set to the same value, the residual amplitude pattern repeates in each spectral window, whilst the phase pattern is different in each window. This suggests that most of the amplitude residual is coming from the IF, whilst most of the phase residual is in the correlator. ASTRONOMICAL PASSBAND CALIBRATION The source spectra corrected by the on-line passband calibration typically show variations of 20% in amplitude and 5-10 degrees of phase across an 800 MHz bandwidth. Slow variations as a function of antenna and frequency are expected across the RF passband since the the on-line passband calibration is double sideband whilst the astronomical observation is single sideband. However, in practice we often see variations in amplitude and phase as a function of baseline and correlator configuration. In this case, a baseline-dependent passband calibration (UVGAINS, or PASSMAKE) will work better than an antenna-dependent calibration (MFCAL). Since the passband residuals depend on the correlator configuration, the astronomical passband should be made using the same correlator configuration as the source observations. We can improve the SNR and reduce the number of parameters in the passband calibration by fitting polynomials to each sideband, or spectral window. Fitting the vector average of the complex passband data gives unbiased fits. If sinosoidal real, or imaginary passband residuals are evident in a spectral window, then polynomial fits to the amplitude and phase may give smaller residuals, but a steep phase slope within a spectral window may be an intermittent correlator problem, and not be present in the source data to be corrected. In this case fitting a steep phase slope to the passband data will introduce a systematic error in the corrected data. EXAMPLES 1. PASSCAL The script PASSCAL is offered as an example of how to make the astronomical passband calibration. The output is a uv-data file containing averaged passband and polynomial fit. PASSCAL is a csh script to fit a passband to BIMA uv-data using the Miriad task UVGAINS with a polynomial fit to each window. The user specifies a passband uv-file and a reference line used for the antenna gain calibration versus time. The antenna gains are derived from the time-averaged reference line using SELFCAL. The passband is derived from polynomial fits to the vector average, relative to the time-averaged reference line. The user specifies the order of the polynomial fit. The script plots the passband uv-data and fits, and the corrected passband uv-data. To apply the passband gains to other uv-data files, use COPYHD to copy the channel gains (items=cgains,ncgains,ncbase) from the output passband file into the other uv-data files. The channel gains can only be applied if the uv-data use the same correlator configuration. The channel gains are applied automatically by Miriad tasks when plotting (uvplt, uvspec), copying (uvcat, uvcal, uvaver, uvgains), or imaging (invert). However, the channel gains are not interpolated and can only be applied if all the channels are used, i.e. in plotting, or imaging all the channels. To plot or image other line types the channel gains must first be applied by copying the channel gains into the Miriad dataset to be corrected (copyhd), and writing all the channels into a new Miriad dataset (uvcat, uvcal). The passband corrected gain calibrator and source data can then be used to determine the antenna gains versus time and image the source data. (e.g. using AUTOCAL) Examples: To derive the channel gains relative to the 1st wideband channel: passcal mars.12apr pass /xw wide,1 To apply the channel gains to the gain calibrator and source data: copyhd in=pass out=source items=ncgains,cgains,ncbase copyhd in=pass out=calibrator items=ncgains,cgains,ncbase To plot the passband corrected spectra: uvspec vis=source device=/xw To plot the spectra without the passband correction: uvspec vis=source device=/xw options=nopass To plot or map other line types, first write a corrected dataset: uvcal vis=source out=source.pass options=nowide uvcal vis=calibrator out=source.pass options=nowide (items nwgains,nwbase,wgains are needed to correct the wideband) To derive the antenna gains and image the source: autocal calib source /xw wide,1 cal_line 'pol(YY)' The calibrator line in autocal should be the same as used to derive the channel gains. 2. UVGAINS The task UVGAINS has several options for checking the passband: 2.1 reference line The channel or wideband gains can be determined relative to a reference line before averaging the data. This may be the best method in the case of high SNR or rapid antenna gain fluctuations. In this case no gain corrections should be applied: options=nocal,nopol Using a reference line and applying gains does not make sense. The default is no reference line. 2.2 interval Time averaging interval, in minutes. The default is 0. (i.e. no averaging). The channel gains are derived from the first average. The uv-data can be averaged into several intervals to see how cgains or wgains change with time. A large interval averages each occurance of each 'source'. 2.3 options=dsb Fit polynomial to each sideband for double sideband spectra. If there is no evidence for passband variations between the spectral windows, then it is better to use fewer parameters by fitting to each sideband.