## 3-way beam combiner

Fringe parameters are the complex visibility, the squared visibility
amplitude, and the total count rate. These can be computed from
**bincounts** using the functions
`fringevis`,
`fringevissq`, and
`fringenphot`.
`
v=fringevis(bincounts(1,*,*,*))`

v2=fringevissq(bincounts(1,*,*,*))

help,v,v2

*
V COMPLEX = Array[32, 42300]*

V2 DOUBLE = Array[32, 42300]

A complex variable has real and imaginary parts, they can be plotted as follows.

`
window,xsize=400,ysize=400`

plot,float(v(0,*)),imaginary(v(0,*)),psym=3,xrange=[-50,50],yrange=[-50,50]

Instead of computing the modulus of the complex visibility, we use a different estimator for the
*squared* amplitude. The reason for this is not trivial, but has to do with obtainig an
*unbiased* estimate of of the amplitude.
`
window_slide
plot,v2(0,*),psym=3
`

## 6-way beam combiner

Note that the data shown below are actually using only three
stations, but the encoding and hardware used were the new
NPOI six-station configuration.
### Fringe spectrum analysis

Here I analyse the (squared) fringe amplitude of channel 1
as a function of k,
the Fourier (frequency) variable conjugate to the Bin index.
From the fringe frame data for a scan I derive the photonrate N
and then, after subtracting the mean photonrate/bin level, I derive
X^2+Y^2-N by direct Fourier transform, using 2*pi*j*k/64 as the
phase interval. Nominator and denominator (N^2) are then averaged 500
samples at a time, then divided, and averaged again. The result is
multiplied with 4/sinc(k/n)^2 for normalization. I have verified with
simulated fringe frames that this procedure results in the correct
squared visibility amplitudes.
Using the observer star and obs log sheets to figure out which
tracking was selected and which stations were pointed at the
star, I check whether I find fringe frequency peaks at positions
(i.e. values of k) consistent with that information.

Here is the configuration information from which we can see
what baselines correspond to which values of k:

print,genconfig.stationid
E02 AC0 AE0 AW0 W07 AN0
print,genconfig.fringemod
7 1 6 5 2 8
5 3 7 4 1 8
print,genconfig.baselineid
E02-AE0 AE0-AW0 AN0-AW0 AN0-AE0 E02-AN0 E02-AW0
E02-AC0 AC0-AW0 W07-AW0 W07-AC0 E02-W07 E02-AW0

The fringemod parameter indicates the values of k, the first line above
corresponding to the first spectrometer. The baselines by spectrometer
are also given above.

Here is the fringe frequency spectrum for scan 6 on 2001-10-16 while E02, AC0, and AW0
were tracking a star. The spectrum below shows that we indeed see peaks
at k=3 (AC0-AW0), 5 (E02-AC0), and 8 (AW0-E02)

The one-second averaged closure phase derived for the three
baselines in this spectrometer is shown below. It is of good
quality and clearly free of atmospheric phase noise.

The third baseline occurs twice in this configuration, and the same
triple, but in a sense independent from the first one, can be
computed and is shown here.