Visibility estimators

The fringe detector uses a four bin algorithm with path length modulation. See Colavita (1999) for a detailed description of this method. The detector array is read 5 times, before the modulation starts and after each quarter-wave of modulation. These reads are called z, a, b, c and d. Each of these reads consists of a number of sub-reads to reduce the effective read-noise. The basic output of the fringe detector, which is called a sample (Sec. 2.2), is the array counts for each channel and these values are read in by Kvis.

For each channel the integrated flux in each bin is calculated as

A = (a - z)/n_s B = (b - a)/n_s

C = (c - b)/n_s D = (d - c)/n_s, (1)

where n_s is the number of non-destructive reads of the detector. The fringe quadratures are then given by

X = C - A

Y = D - B (2)

and the total flux is

N = A + B + C + D. (3)

A measure of the energy is given by

NUM = X² + Y². (4)

From these values we calculate the squared visibility and phase

$${\frac{{\pi^2}}{{2}}} {\frac{{NUM}}{{N^2}}}$$ (5)

$$\phi {\frac{{Y}}{{X}}}$$ (6)