我們使用史隆數位巡天的第七次公佈的資料，來估計橢圓星系的真實的軸比和紅位移之間的關聯。使用的資料包含69720 個視張角大於2 角秒，紅移範圍在0.01 至0.3 之間的橢圓星系，每個星系階有g、r、i、z 四個波段的橢圓率的資料。我們將此問題化為一個Fredholm 第一型積分方程，以三軸不等長的橢球作為橢圓星系的模型，並選擇以二維高斯分佈作為橢球軸比的機率分佈函數來解此問題。我們的結果顯示軸比的分佈範圍則隨著紅移增加而減小，而最大機率的中長軸比介於0.77 至0.65 之間，短長軸比介於0.85 至0.74 之間，隨著紅移增加而變化。

We estimate the relations between the true axial ratios and the redshifts of elliptical galaxies. The sample is selected from SDSS DR7, which contains 69720 elliptical galaxies with redshifts from 0.01 to 0.30, angular size larger than 2 arcsec. We consider triaxial ellipsoids to be the model of elliptical galaxies, and adopt Gaussian distributions for the axial ratios to fit the observations. This problem is a question of Fredholm integral equation of the first kind. Our result shows that the real shape of elliptical galaxies distributes in a smaller range as redshift increases, and the most probable axial ratios of middle-to-major are between 0.77 and 0.65, ratios of minor-to-major are between 0.85 and 0.74, change as redshift increases.

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