宇宙中質量最大的重力束縛系統——星系團，其形狀、分佈與大尺度結構分佈緊密關聯，因此星系團是研究宇宙結構的重要探針。尤其是星系團的二維投影形狀，為後續探討大尺度結構之內在排列（Intrinsic Alignment）提供了關鍵測量量，我們的研究，即是為測量內在排列效應，整理出純淨的星系團成員，並提供一套量化星系團形狀的流程。
我們的研究使用 South Pole Telescope Sunyaev–Zel’dovich（SPT-SZ）調查的星系團樣本，結合 Dark Energy Survey Year 3 Gold 光學星系目錄，研發出一套針對星系團成員篩選與投影形狀量測的方法。相較於純光學選出的星系團樣本易受視線方向投影效應影響，本研究以 ICM 選出的星系團為基礎，降低由前景與背景星系混入所引入的系統性偏差。對於星系團視線方向上的星系污染，我們先結合紅色序列（Red Sequence）模型選出潛在星系團成員，再於二維星等空間中對潛在星系團成員進行逐點統計扣除（point-by-point, PBP），以獲得純淨的星系團成員樣本。
星系團形狀量測方面，我們利用篩選後之成員星系空間分布，計算二階矩（Second Moment）並估計星系團的橢圓率，作為星系團二維投影形狀的量化指標。
為檢驗成員篩選流程與形狀量測的可靠性，我們利用橢圓化 NFW 模型（ellipse-NFW model）和光度函數（Schechter Luminosity function）產生模擬星系團的空間與光度分佈，並將其與一組真實的隨機背景場混合後，應用逐點扣除演算法，我們多次測量發現橢圓率訊號對少數為在非主軸方向且距離較遠的入侵點相當敏感，因此需要基於逐點扣除的結果，再降低入侵點對形狀量測的貢獻，以降低殘餘污染對橢圓率訊號造成的偏差。
本流程能有效降低星系團之前景、背景的污染對星系團形狀量測的影響，並改善星系團的形狀量測。本研究為測量內在排列訊號的前置作業，建立可靠的成員辨識和星系團形狀量測流程。而我們的方法可拓展至 X-Ray 的觀測資料之基礎，進一步提升星系團形狀量測的可靠性。

Galaxy clusters are the most massive gravitationally bound systems in the universe and are important tracers of large-scale structure. Their two-dimensional projected shapes provide key information for future studies of intrinsic alignment. In this study, we develop a procedure for galaxy cluster member identification and projected shape measurement using SPT-SZ selected galaxy clusters combined with the DES Y3 Gold optical galaxy catalog. Since SPT-SZ clusters are selected through the Sunyaev–Zel’dovich effect, they are less affected by optical projection effects than purely optically selected cluster samples. To reduce foreground and background contamination, we first select potential cluster members using a red sequence model and then apply point-by-point statistical subtraction in magnitude space using background samples constructed from random apertures in the DES footprint. The projected cluster shape is quantified by calculating the second moments of the spatial distribution of the selected member galaxies and deriving the ellipticity. To evaluate the reliability of this procedure, mock galaxy clusters are generated using an ellipse-NFW model and a Schechter luminosity function, then mixed with real background fields. The results show that residual interlopers can strongly affect ellipticity measurements, especially when located at large projected radii. This study establishes a practical framework for cleaner cluster member selection and more reliable galaxy cluster shape measurement.

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