Dewarping

If the path-length modulation does not match the wavelength of the channel, a correction must be applied to the fringe quadratures. For a stroke length in radians of s, where s = 2$\pi$ is a matched stroke, the dewarped values are given by

$${\frac{{s}}{{2\pi}}} \left(\vphantom{ \frac{X+Y}{\beta} + \frac{X-Y}{\alpha} }\right. {\frac{{X+Y}}{{\beta}}} {\frac{{X-Y}}{{\alpha}}} \left.\vphantom{ \frac{X+Y}{\beta} + \frac{X-Y}{\alpha} }\right)$$ X_c =

$${\frac{{s}}{{2\pi}}} \left(\vphantom{ \frac{X+Y}{\beta} - \frac{X-Y}{\alpha} }\right. {\frac{{X+Y}}{{\beta}}} {\frac{{X-Y}}{{\alpha}}} \left.\vphantom{ \frac{X+Y}{\beta} - \frac{X-Y}{\alpha} }\right)$$ Y_c =

$${\frac{{\gamma}}{{2 \alpha}}}$$ N_c =

$${\frac{{\alpha \pi}}{{s}}}$$ NUM_c = (11)

where X, Y, N are the measured quantities and the constants are given by

$$\alpha$$ = 2 sin(s/4) - sin(s/2)

$$\beta$$ = 1 - cos(s/2)

$$\gamma$$ = 2 sin(s/2)

$$\left(\vphantom{ \frac{s}{2 \pi} }\right. {\frac{{s}}{{2 \pi}}} \left.\vphantom{ \frac{s}{2 \pi} }\right)^{2}_{} \left(\vphantom{ \frac{1}{\alpha^2} + \frac{1}{\beta^2} }\right. {\frac{{1}}{{\alpha^2}}} {\frac{{1}}{{\beta^2}}} \left.\vphantom{ \frac{1}{\alpha^2} + \frac{1}{\beta^2} }\right)$$ G = (12)

The second term in equation 11 for NUM takes the place of the kN term in equation 9. This dewarping correction is applied to all data (fringe tracking and calibration) before the bias corrections discussed in Sec. 2.4 are applied. This results in a unbiased estimate of the visibility. Whether or not the dewarping correction is applied is controlled by the doDewarp parameter (Sec. 3.1).