Procducing Science Quality Rotation Corrected Power Spectra
B Pohl. E. Anderson
National Solar Observatory, National Optical Astronomy Observatories, 950 N. Cherry Ave., Tucson, AZ 85726 USA
We describe modifications to the Gong Reduction and Analysis Package software that generates rotation-corrected l-nu diagrams. Previously, these diagrams were only used as quality assurance indicators for downstream reductions. The modified approach produces a science quality product by taking into account the rotation coefficients as a function of n and l, by performing the rotation correction in the Fourier domain (rather than on the power spectra) thereby minimizing the interpolator overshoot, and by removing the effects of the two-point difference filter used to detrend the time series of images.
Our standard method of rotation-correction uses a single set of Legendre coefficients to compute the frequency shift. The new approach determines the shift as a function of l and frequency. This is accomplished by first computing the shift value and pixel locations for each n ridge of a given l.
These x-y pairs (the dots in figure 1) are passed to a simple piecewise linear fit routine that determines the overall shift as a function of frequency (the solid line in figure 1.)
The standard method of rotation correcting the power spectra suffers from interpolator overshoot producing negative values (particularly at low l) due to the large mode amplitudes and small mode spacing. Shifting in the Fourier domain before converting to power eliminates this error.
The one-minute integration plus our spatial two-point difference filter applied to the time series of images introduces a gradient in the power spectra. This effect can be removed by multiplying the following equation to each row of the power spectra.
N= Total pixel bins, n=currenct pixel (1,2,3..N)
since this function approaches infinity as n approaches 0, we selected a cutoff value of 133 microhertz (just below the intersection of the lowest n ridge with the l=0 axis) below which the function rolls off to 1.
Comparisons between the enhanced and standard rotation correction methods show significant improvements. Figure 2 demonstrates a gain in power and signal to noise at the target peak. The lower frequency leaks gain power while the higher leaks lose power, showing improved spatial leakage symmetry around the target mode.
In conclusion, we have successfully created an algorithm for producing rotation-corrected, m-averaged l-nu spectra of improved scientific quality.
The National Optical Astronomy Observatories are operated by the the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the National Science Foundation.