Conditions for Coronal Observations at the Lijiang Observatory in 2011

The sky brightness is a critical parameter for estimating the coronal observation conditions for a solar observatory. As part of a site-survey project in Western China, we measured the sky brightness continuously at the Lijiang Observatory in Yunnan province in 2011. A sky brightness monitor (SBM) was adopted to measure the sky brightness in a region extending from 4.5 to 7.0 apparent solar radii based on the experience of the Daniel K. Inouye Solar Telescope (DKIST) site survey. Every month, the data were collected manually for at least one week. We collected statistics of the sky brightness at four bandpasses located at 450, 530, 890, and 940 nm. The results indicate that aerosol scattering is of great importance for the diurnal variation of the sky brightness. For most of the year, the sky brightness remains under 20 millionths per airmass before local Noon. On average, the sky brightness is less than 20 millionths, which accounts for 40.41% of the total observing time on a clear day. The best observation time is from 9:00 to 13:00 (Beijing time). The Lijiang Observatory is therefore suitable for coronagraphs investigating the structures and dynamics of the corona.

This work was supported by grants from NSFC (11078004, 11533009, 11503084, 11603074), and from the Key Laboratory of Geospace Environment, CAS, University of Science & Technology of China, and from Huairou Solar Observing Station, National Astronomical Observatories Chinese Academy of Sciences. We are grateful to Peter Kovesi for his codes of the phase congruency algorithm (Kovesi, 2000).

Authors and Affiliations

1. Yunnan Observatories, Chinese Academy of Sciences, Kunming, 650011, China

   M. Y. Zhao, Y. Liu, X. F. Zhang, T. F. Song & Z. J. Tian

2. Key Laboratory of Geospace Environment, Chinese Academy of Sciences, University of Science & Technology of China, Hefei, 230026, China

   M. Y. Zhao, Y. Liu, X. F. Zhang & T. F. Song

3. Department of Physics and Astronomy, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

   Y. Liu, A. Elmhamdi & A. S. Kordi

4. Chongqing University College of Optoelectronic Engineering, Chongqing, 400044, China

   T. F. Song

Corresponding author

Correspondence to M. Y. Zhao.

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.

Appendix: Edge-Detection Algorithm

We adopted a method that is based on the phase-congruency principle to detect the edges of the SBM images. This method can be traced back to the experiment of Oppenheim and Lim (1981). This experiment shows that the amplitude spectrum of an image can be modified considerably, even swapped with that from another image, and the features from the original image will still be seen clearly as long as the phase information is preserved. Morrone et al. (1986) and Morrone and Owens (1987) developed a local energy model for feature detection via phase congruency. This model assumes that the compressed-image format should be high in information and low in redundancy. It searches for patterns of order in the phase component of the Fourier transform. A phase congruency function [\(PC(x)\)] at each point \(x\) in the signal can be defined as

where \(A_{n}\) represents the amplitude of the nth Fourier component, and \(\phi_{n}(x)\) represents the local phase of the Fourier component at position \(x\). The relationship between phase congruency, local energy [\(E(x)\)], and the sum of the Fourier amplitudes can be seen geometrically in Figure 8. \(PC(x)\) is a measure of the variance of the phase values of the signal, which takes on values of between zero and unity, and it provides an illumination and spatial-magnification invariant measure of feature significance (Kovesi, 1995).

Polar diagram showing the Fourier components at a location [\(x\)] in the signal [\(F(x)\)] plotted head to tail. This figure is adapted from Kovesi (1999).

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Phase congruency is a rather awkward quantity to calculate, and the Fourier transform is not good for determining local frequency information. As an alternative, Kovesi (1995) described a way of calculating phase congruency using Log-Gabor wavelets. The Log-Gabor function was proposed by Field (1987), who suggested that natural images are better coded by filters that have Gaussian transfer functions when viewed on the logarithmic frequency scale. The transfer function can be constructed as

where \(\omega_{0}\) is the filter center frequency, and \(k/\omega_{0}\) controls the filter bandwidth. Because of the singularity in the log function at the origin, the corresponding functions in the spatial domain, which are a pair of filters in quadrature (see Figure 9), can be obtained by a numerical inverse Fourier Transform. The appearance is similar to Gabor functions, although their shape becomes much sharper as the bandwidth is increased. Therefore, Log-Gabor wavelets can be constructed with arbitrary bandwidth, and the bandwidth can be optimized to produce a filter with minimal spatial extent (Kovesi, 2000).

Example of Log-Gabor functions [\(Y = G(X)\)] in the spatial domain, which are obtained by a numerical inverse Fourier Transform of Equation 2. (a): Real part. (b): Imaginary part.

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Kovesi (1995) extended the one-dimensional Log-Gabor filters into two dimensions by applying a Gaussian spreading with respect to several preference directions. In order to circumvent the complexity of combining phase congruency information over different orientations, Felsberg and Sommer (2000) presented a vector-valued filter that is odd and has an isotropic energy distribution; then the whole theory of local phase and amplitude can directly be applied to images. In the frequency domain, this filter can be formed by combining the Log-Gabor filter with its Riesz transform,

where \(F\) is the Log-Gabor transfer function (Equation 2), \((u_{1},u_{2})\) are the coordinates in the frequency domain, and \(\mathrm{i}\) is the imaginary unit. The vector \({\boldsymbol {H}}=(H_{1},H_{2})\) is isotropic and odd because \(\sqrt{H_{1}^{2}+H_{2}^{2}}=1\) and \({\boldsymbol {H}}(-u_{1},-u_{2})=-{\boldsymbol {H}}(u_{1},u_{2})\). These two filters represent a quadrature phase-shifting operation in the two orthogonal directions of the image (Kovesi, 2012). To obtain local phase and amplitude information, the image \(I\) is convolved with the Log-Gabor filter \(f\) and the two Reisz transform filtered version of \(f\), \(h_{1}f\), and \(h_{2}f\). Then the triple \((I*f,I*h_{1}f,I*h_{2}f)\) forms a multi-dimensional generalization of the analytic signal, which is called the monogenic signal, where \(\text{the asterisk}\) denotes convolution. The local amplitude of the monogenic signal is

and the local phases can be represented in the standard spherical coordinates

Figure 10 depicts this process. The output from convolution with the Log-Gabor filter \(f\) corresponds to the real component of the analytic signal and the convolutions with the Reisz transform filters [\((h_{1}f,h_{2}f)\)] correspond to the imaginary component of the analytic signal. Eventually, phase [\(\phi\)] and amplitude [\(A\)] at multi-scales are used to calculate the phase congruency through Equation 1.

Local phase and amplitude of monogenic filters, constructed following Kovesi (2012).

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The monogenic signal also contains information about the local orientation of an image, namely, phase \(\theta\). Therefore, it can be used to perform nonmaxima suppression according to the Canny edge-detection algorithm (Canny, 1986). The Canny edge-detection algorithm uses a pair of convolution masks to estimate the gradients of an image in the \(x\)-direction and \(y\)-direction, then computes the gradient orientation and magnitude. An edge point is defined to be a point whose gradient magnitude is locally maximum along the direction of the gradient. This process, which results in ridges that are one pixel wide, is called nonmaxima suppression. By analogy, we can constrain the phase congruency to a local maximum across the direction defined by the local orientation [\(\theta\)]. The Canny edge-detection algorithm also uses a hysteresis thresholding to process the nonmaxima suppression image. Hysteresis thresholding adopts two thresholds [\(T_{1}\) and \(T_{2}\)]: any pixel in the nonmaxima suppression image that has a value greater than \(T_{1}\) is presumed to be an edge, and any pixels that are connected to this edge pixel and have a value greater than \(T_{2}\) are also selected as edge pixels.

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