Br Gamma data from both UT951216 and UT951217 show an apparently periodic signal covering the full wavelength range of the spectrum. As can be seen from Figure 3.6 this signal does not disappear by removing the ripple of period 2 present in the the spectrum and due to the sampling procedure.
Figure 3.6: Top panel - Extracted spectrum of
the positive beam for the standard star BS1251 at Br Gamma. Bottom panel -
Same as top panel after de-rippling. One can easily see that an apparently
periodic signal remains superimposed to the spectrum of the star.
Given that at this wavelength region there are no lines capable of producing such a pattern, its source must be the instrument itself. The explanation for the observed pattern is interference resulting from the Circular Variable Filter (CVF).
A typical interference pattern is observed in the flat field frame for the Br Gamma wavelength region (top panel of Figure 3.7) as a set of slanted lines. For comparison, the flat field corresponding to the Pa Beta observations of UT951215 is shown in the bottom panel of Figure 3.7. The interference pattern is not present at Pa Beta.
Figure 3.7: Top panel - Flat field frame for the Br Gamma
data obtained in UT951217. The fringing pattern is seen as a set of
slanted lines running from top to bottom. Bottom panel - Flat filed
frame for the Pa Beta data obtained in UT951215. In this case there is
no evidence for the presence of any fringes.
This interference pattern should clearly be eliminated. If the signal
was periodic with a single
period then it could be easily removed using Figaro's IRFLAT task
.
A single period is not found though and Fourier techniques had to be
used in order to identify possible periods in the signal. Figure
3.8 shows the modulus of the Fast Fourier Transform (FFT) for
the spectrum shown on the bottom panel of Figure 3.6.
Figure 3.8: FFT modulus of the flattened
and zero mean spectrum of BS1251's positive beam.
As it happens, the frequency peaks between 
and
, where 
/Period is the Nyquist
Frequency, correspond to the interference
signal. By filtering this signal out, one effectively removes the
interference pattern from the original spectrum. As an example, Figure
3.9 shows the spectrum of the positive beam of BS1251 after
filtering.
Figure 3.9: BS1251's
positive beam spectrum after filtering the interference pattern out.
The filtering was carried out using standard Figaro tasks. The procedure used was as follows:
idiv myspect response_cvf_brg_p myspect_p
istat myspect_p reset accept
icsub myspect_p @$HOME/adam/GLOBAL.STAT_MEAN myspect_p_0
r2cmplx myspect_p_0 myspect_p_0i
fft myspect_p_0i myspect_p_0ifft
cmplx2m myspect_p_0ifft myspect_p_0fftm
cmplxmult myspect_p_0ifft cfilt_cvf_brg myspect_p_0ifftf
bfft myspect_p_0ifftf myspect_p_0if{\it myspect}
cmplx2r myspect_p_0if myspect_p_0f
xcopy myspect_p_0f myspect_p_0 myspect_p_0f
icadd myspect_p_0f @$HOME/adam/GLOBAL.STAT_MEAN myspect_p_f
imult myspect_p_f response_cvf_brg_p myspect_pf_sp_p_f
The spectrum that needs to be filtered is myspect. The
identification of periodicities in data strings using Fourier
Transforms, requires the mean of the data string to be zero. Otherwise,
the peaks in the modulus of the Fourier Transform responsible for the
periodic structure may be swamped by the large scale structure in the
data string. The interference pattern is filtered out from the spectrum
with mean zero that results from myspect. The Figaro commands
IDIV, ISTAT and ICSUB operate on myspect transforming it into a
spectrum with zero continuum level. R2CMPLX transforms the real data
string in a complex data string. FFT computes the Fast Fourier Transform
and CMPLX2M its modulus. The actual filtering is performed by CMPLXMULT, which
multiplies the FFT of the zero mean myspect by a band reject
filter, where the reject bands (values set to zero) are 
and
. The result of the multiplication is
inverse FFTed by BFFT. A real string of data is obtained by CMPLX2R, the
original x-axis information is restored with XCOPY and the original
large scale shape is restored with ICADD and IMULT. At this stage the
filtering process of myspect is concluded and the CVF fringing removed.
The interference pattern removed from the spectrum in Figure 3.6 is shown in the top panel of Figure 3.10. As can be seen from this figure, the fringes for that particular spectrum imply fluctuations that can be as large as 5% about the mean level. The amplitude of the interference pattern depend on the intensity of the observed source though. The fringe pattern removed from the Br Gamma spectrum of DN Tau is shown in the bottom of Figure 3.10 as an example. The amplitude of the signal is now about 4% at maximum although it is in general slightly lower than that.
Figure 3.10: Top panel - Fringes obtained for the
Br Gamma spectrum of BS1251 obtained by the filtering procedure
described in the main text. Bottom panel - same as top panel for the Br
Gamma spectrum of DN Tau.
The interference pattern observed along the dispersion direction is not expected to be periodic in wavelength. Interference fringes resulting from an optical component with a fixed finite thickness are periodic in wavenumber space and therefore not in wavelength space. The wavelength range in the observed spectra is however small enough to allow one to consider that the signal is nearly periodic along the dispersion direction, i.e. in wavelength space. If a large wavelength range had been observed it would not have been possible to use the above procedure to remove the interference fringes.
The typical periods found in the interference pattern are of about 20
pixels and 8 pixels (resulting from the frequencies 
and 
). The Br Gamma
wavelength
calibration imply that 20 pixels correspond to a wavelength interval of
while 8 pixels correspond to a wavelength
interval of 
. Such ``periods'' correspond to
thicknesses of the optical component causing the fringes of about 1mm
and 2.5mm. These are indeed typical of the CVF in CGS4.