Abstract
The vignetting effect in the Soft X-ray Telescope (SXT) onboard Yohkoh is studied using a two-dimensional distribution of the effective area in the field of view taken from a pre-launch experiment. Our initial estimation of the vignetting in SXT was carried out by fitting the data with a second-order polynomial function. The results show that a two-dimensional vignetting effect in SXT is not rotationally symmetric, particularly in the \(y\)- (north–south) direction, which is probably due to the offset of SXT’s optical center from the location of its CCD center. We adopted a combined functional form consisting of a second-order polynomial function and a Gaussian function to take this asymmetric distribution of the effective area into account. We also considered the steep gradient of the effective area variation at the region near the vignetting center for the case of higher photon energy with this form. We completed a two-dimensional description of the vignetting effect in SXT by a spline surface fit using the “cleaned” effective area data whose noise was reduced satisfactorily by the fitting of our combined function.
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Acknowledgements
Yohkoh was a Japanese ISAS (presently ISAS/JAXA) mission, collaborating with NASA/US and PPARC (presently STFC)/UK, and its scientific operation was conducted by the international science team organized in ISAS. Yohkoh/SXT was prepared by the Lockheed Palo Alto Research Laboratories, the National Astronomical Observatory of Japan, and the University of Tokyo with the support of NASA and ISAS.
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Appendices
Appendix A: 1D Fitting by Second-Order Polynomial Function
Figures 7 and 8 show the results of fitting for a low-energy effective area in the rows and the columns, respectively, when the SOPF is applied. The error bars overplotted on the distribution of the SXT effective area show that the differences in three sets of low-energy data (Al-K and C-K) are very small. Figure 7 shows that the SOPF curves fit the data in a satisfactory way for all of the rows. The maximum points of the symmetric SOPF curves are located very close to the CCD center. Figure 8 shows that the accuracy in the fitting of the SOPF in the columns is poor, especially on the right side of the maximum locations, which is probably due to the fact that the distributions in the \(y\)-direction are not symmetric. Furthermore, the maximum locations of the fitted curves are always shifted to the right with respect to the CCD center.
Results of fitting the SOPF to the averaged low-energy effective area in the rows. The diamonds indicate the distributions of the SXT effective area and the solid lines are the fitted SOPF curves. The error bars overplotted on the symbols show the differences between the Al–K and C–K data. Dotted lines indicate the \(x\)-coordinates of the maximum locations of the SOPF curves.
Results of fitting the SOPF to the averaged low-energy effective area in the columns. The diamonds indicate the distribution of the SXT effective area and the solid lines are the fitted SOPF curves. The error bars overplotted on the symbols show the differences between the Al–K and C–K data. Dotted lines indicate the \(y\)-coordinates of the maximum locations of the SOPF curves.
Figures 9 and 10 show the results of fitting of the SOPF for high-energy effective area in the rows and the columns, respectively. Although the distributions look symmetric in all of the rows, the overall accuracy in the fitting in Figure 9 is poor compared to the low-energy case, which must be due to low photon statistics of high-energy data. In particular, the accuracy in the fitting is worse near the maximum, which is due to the steep gradient of the distribution near the vignetting center. The fitted SOPF curves show that the maximum locations are very close to the \(x\)-coordinate of the CCD center. Figure 10 shows that the accuracy of the fitting in the columns looks much poorer than the results for low-energy cases.
Results of fitting the SOPF to the high-energy effective area in the rows. The diamonds are the distribution of the SXT effective area and the solid lines are the fitted SOPF curves. The dotted lines indicate the \(x\)-coordinates of the maximum locations of the curves.
Results of fitting the SOPF to the high-energy effective area in the columns. The diamonds are the distribution of the SXT effective area and the solid lines are the fitted SOPF curves. The dotted lines indicate the \(y\)-coordinates of the maximum locations of the curves.
Appendix B: 1D Fitting by Combined Gaussian Plus Polynomial Function
Figures 11 and 12 show the results of fitting for low-energy effective area in the rows and the columns, respectively, when our combined function is applied. In Figure 11 the fitting has been performed with high accuracy in all the rows, and as a result we obtain 49 cleaned data from the grid positions of the rows. Figure 12 shows the distributions of the cleaned data in the columns, together with the results of fitting of the combined function. In the figure, the curves of the combined function successfully fit the cleaned data with high accuracy.
Results of fitting the combined function to the low-energy effective area in the rows. The diamonds are the distribution of the averaged SXT effective area. The solid lines are the fitted curves of the combined functions and the triangles are the estimated values of the effective area at the grid positions.
Results of fitting the combined function to the columns for low energy. The squares are the estimated values of the effective area after suppressing the noise by the fittings of the rows. The solid lines are the fitted curves of the combined functions and the triangles are the estimated values of the effective area at the grid positions.
Figures 13 and 14 show the results of fitting for high-energy effective area in the rows and the columns, respectively. Figure 13 shows that although the data look noisier than the low-energy case, the combined functions fit the data successfully by suppressing the effect of noise in the rows. The degree of fitting of the combined function to the data is also very good near the vignetting center. Figure 14 shows that the curves fit the cleaned data satisfactorily with very small differences.
Results of fitting the combined function to the high-energy effective area in the rows. The diamonds are the distribution of the SXT effective area. The solid lines are the fitted curves of the combined functions and the triangles are the estimated values of the effective area at the grid positions.
Results of fitting the combined function to the columns for high energy. The squares are the estimated values of the effective area after suppressing the noise by the fittings of the rows. The solid lines are the fitted curves of the combined functions and the triangles are the estimated values of the effective area at the grid positions.
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Shin, J., Sakurai, T. The Vignetting Effect of the Soft X-Ray Telescope Onboard Yohkoh: II. Pre-Launch Data Analysis. Sol Phys 291, 705–725 (2016). https://doi.org/10.1007/s11207-016-0845-x
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DOI: https://doi.org/10.1007/s11207-016-0845-x