Considerations in the placement of phase calibration tones

In the use of tones to calibrate unwanted instrumental phases for very long baseline interferometry experiments, certain problems exist which are related to the placement of these phase calibrator tones. (1) A bias exists in an analytically generated stopping function used during correlation if its frequency satisfies the following condition; f = (f sub s)x(m)/n, where f sub s = sampling frequency, m = any integer, and n = any odd integer. (2) Due to the quantized representation of sine waves in the stopping function, odd harmonics of the fundamental frequencies are generated. Several mechanisms are available through which these harmonics can cause errors in the residual phase extracted from the recorded tones. (3) When multiple tones are injected into a pass band, intermodulation products can occur. The magnitude of these effects is discussed along with strategies designed to avoid them.