Time and spectral averaging

Kvis combines groups of samples into frames (as configured, Sec. 3.1). The samples are filtered through a buffer to eliminate the data immediately before a transition from lock to semi-lock in the fringe tracker. The size of this buffer is set by lockBufferSize in config.params (Sec. 3.2) and corresponds to the averaging used by the fringe tracker when determining the lock state. Each good sample is dewarped and the bias corrections are applied. For the wide-band channel, an average phase is calculated for the frame. Coherent estimators for each frame are produced for each channel by derotating the fringe quadratures with respect to the WB average phase ($\phi_{{WB}}^{}$). For the spectrometer channels, $\phi_{{WB}}^{}$ is scaled by the ratio of the WB and channel wavelengths.

$$\hat{{X_i\,}}_{{coh}}^{} \langle \hat{{X_i}} \phi_{{WB}}^{} \lambda_{{WB}}^{} \lambda_{i}^{} \hat{{Y_i}} \phi_{{WB}}^{} \lambda_{{WB}}^{} \lambda_{i}^{} \rangle$$ =

$$\hat{{Y_i\,}}_{{coh}}^{} \langle \hat{{X_i}} \phi_{{WB}}^{} \lambda_{{WB}}^{} \lambda_{i}^{} \hat{{Y_i}} \phi_{{WB}}^{} \lambda_{{WB}}^{} \lambda_{i}^{} \rangle$$ = (13)

The coherent value for NUM is given by

$$\hat{{X_i\,}}_{{coh}}^{} \hat{{X_i\,}}_{{coh}}^{} \hat{{N}}$$ (14)

where N_samps is the number of samples in the frame and the incoherent value by

$$\langle \widehat{{NUM}} \rangle$$ (15)

where the average is calculated from the sample values.

In combining frames to form a block the values of NUMI, NUMC and N are simply averaged. The coherent and incoherent values of V² for each channel are given by equation 5. The spectral line channels are combined to form a composite spectrometer visibility

$${\frac{{\sum_i V^2_i W_i}}{{\sum_i W_i}}}$$ (16)

where the weights W_i are set by the user (Sec. 3.1).