) diagrams were computed using the GRTOOLS software in
the GRASP package (Anderson 1992).
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PS reprint
W. E. Williams, C. Toner
National Solar Observatory, National Optical Astronomy Observatories,1
Tucson, AZ 85719
1The National Optical Astronomy Observatories are operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperative agreement with the National Science Foundation
The GONG (Global Oscillation Network Group) project was devised to study the internal structure of the sun by long-term, continuous observations of solar acoustic oscillation modes. GONG will observe the sun nearly constantly for three years, from six sites placed around the globe. Solar acoustic oscillation modes are studied by spatial and temporal analysis of radial velocity images computed from intensity triplet images in NiI 677nm. A site survey indicates that two or more sites will be on line at most times, with a network duty cycle of about 90%.
Beginning on February 17, 1995 and following, images were obtained from the first instrument deployed at El Teide in the Canary Islands. Images from each site were added to the data stream as the instruments were deployed. On October 3, 1995, the final GONG network instrument came on-line in Udaipur, India. The data presented here spans from May 7 to June 11, 1995 and includes data from Learmonth, Australia, El Teide and the Big Bear, California instrument, temporarily at Tucson, Arizona.
The data analysis method is based on that of Duvall & Harvey, 1986. After obviously bad data have been removed from the processing stream, the remaining data is processed for helioseismic mode amplitudes and arranged into time series for analysis. Each image was remapped, temporally filtered, and a spherical harmonic transform was computed. The mode coefficients from the spherical harmonic transform were put into time series using the SUNTRANS software in the GRASP package (Williams 1992).
The site days were merged into longer time series using a
weighted average based on the Modulation Transfer Function
(MTF), a function of the spatial wave number, and its
estimated error. The MTF and its error were estimated
from the intensity images using the algorithm of Toner &
Jefferies (1993). The merging scheme is described in
Williams et al. 1995. Power series and mode degree-frequency
() diagrams were computed using the GRTOOLS software in
the GRASP package (Anderson 1992).
We have found that, for the same image, mode coefficients from some mode degrees may be retained within the time series, while those for other mode degrees should be discarded. The physical phenomena contributing to certain aspects of the image quality give insight into the MTF's possible applications in image quality assessment. We note that errors in the estimated limb-darkening parameters propagate into the MTF because the MTF is recovered by division of the model limb darkening in the Fourier domain. These errors affect all spatial scales, i.e., all mode degrees.
Although the criteria used to accept or reject
data are based on physical phenomena, the precise limits of application
in mode degree and numerical values of MTF's and their errors were
determined empirically. Criteria described below were determined
by applying proposed criteria to the mode coefficients and then computing
the mode degree-frequency diagram (
diagram), a common analysis
tool in helioseismology. A solar 
diagram is shown in Figure 1.
The 
diagrams for various criteria were then examined
for minimal reduction in signal combined with a visible reduction in
background noise, and those giving the most acceptable results used.
Since the magnitude of the MTF falls off towards smaller spatial scales (higher mode degree l), random noise (e.g., instrument noise, photon noise, etc.) and seeing variations which blur the limb increase the MTF error to a greater fraction of the MTF itself. Thus, for each mode degree l, any mode coefficient for a time sample at a single mode degree which was less than twice the maximum MTF error found for that l during the site day was discarded.
Of particular importance in the study of velocity images, rapid changes in scattering modify the apparent large scale solar rotation component of the measured velocity field, preventing the accurate removal of large-scale non-oscillatory velocity fields and leaving a residual large spatial scale velocity signal in the data. Thus, for very low mode degree, any mode coefficient for a time sample and l where the MTF value is more than 2% below the average of the twenty highest MTF values for the site day at that l is discarded. This is used for l<20, an empirically determined limit. This criterion removed images with pronounced effects of ``clouds'', atmospheric particles, etc.
Application of the rejection criterion based on the relative magnitudes
of the MTF and the MTF error, reduces the noise in the high l
region of the 
diagram. This MTF error criterion is now in
routine use in the GONG data processing pipeline. The 
diagram in Figure 1
shows the high quality of the first results
from the GONG network. Note, however, that there is still
noticeable noise at very low l (l<5). This is most apparent in
the enlarged area of the P mode region shown on the right.
Figure 1: 
diagram for a 36 day merged time series, images
from three sites, May 7--June 11, 1995. The MTF error criterion
has been applied to the input time series of mode coefficients.
The enlargement on the right shows part of the P mode region of
the diagram, where the signal is strong.
Figure 1: PS 2.0 Mb
The scattering criterion used to remove the effects of
clouds has been applied to the time series, yielding
the 
diagram shown in Figure 2.
The very low l noise is considerably reduced, even down to l=0.
The grey scale line artifact, most apparent at low frequency, is
due to unresolved differences in normalization between the time
series at l values above and below l=20. Note, however,
that in the P mode region where the signal is high, shown
enlarged on the right, the artifact is not noticeable.
Figure 2: 
diagram for a 36 day merged time series, images
from three sites, May 7--June 11, 1995. In addition to the MTF
error criterion, the low l scattering criterion has been applied
to the input time series of mode coefficients. The enlargement on
the right shows part of the P mode region of the diagram, where
the signal is strong.
Figure 2: PS 2.0 Mb
The use of the MTF function in image quality assessment has allowed the reduction of background noise in specific parts of the mode degree-frequency diagram and minimization of the impact of clouds and scattering on the downstream data products of the GONG project. Application of the low l scattering criterion is still under development.
Duvall, T. L., & Harvey, J. W. 1986, in Seismology of the Sun and the Distant Stars, ed. D. Gough (Dordrecht: Reidel), 105
Toner, C. G., & Jefferies, S. M. 1993, ApJ, 415, 852
Williams, W. E. 1992, SUNTRANS: Spherical Harmonic Transform and Transpose Package in GONG Alpha GRASP Version 92.1, J. Pintar, NOAO/ NSO GONG project document
Williams, W. E., Toner, C. G., & Hill, F. 1995, in Fourth Sono Workshop Helioseismology, ed. J. T. Hoeksema, V. Domingo, B. Fleck, & B. Battrick, ESA SP-376, 2, 185