Abstract In-situ observation of crystal growth in transparent media allows us to observe solidification phase change in real-time. These systems are analogous to opaque systems such as metals. The interpretation of transient 2-dimensional area projections from 3-dimensional phase change phenomena occurring in a bulky sample is problematic due to uncertainty of impingement and hidden nucleation events; in stereology this problem is known as over-projection. This manuscript describes and demonstrates a continuous model for nucleation and growth using the well-established Johnson-Mehl-Avrami-Kolmogorov model, and provides a method to relate 3-dimensional volumetric data (nucleation events, volume fraction) to observed data in a 2-dimensional projection (nucleation count, area fraction). A parametric analysis is performed; the projection phenomenon is shown to be significant in cases where nucleation is occurring continuously with a relatively large variance. In general, area fraction on a projection plane will overestimate the volume fraction within the sample and the nuclei count recorded on the projection plane will underestimate the number of real nucleation events. The statistical framework given in this manuscript provides a methodology to deal with the differences between the observed (projected) data and the real (volumetric) measures.

中文翻译：

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解释来自原位 3 维等轴成核和生长的投影图像数据的理论分析

摘要 透明介质中晶体生长的原位观察使我们能够实时观察凝固相变。这些系统类似于不透明的系统，例如金属。由于撞击和隐藏成核事件的不确定性，从大样本中发生的 3 维相变现象解释瞬态 2 维面积投影是有问题的；在体视学中，这个问题被称为过度投影。本手稿使用完善的 Johnson-Mehl-Avrami-Kolmogorov 模型描述并演示了成核和生长的连续模型，并提供了一种将 3 维体积数据（成核事件、体积分数）与 2 -维投影（成核计数，面积分数）。进行参数分析；在成核连续发生且方差相对较大的情况下，投影现象显示出很重要。通常，投影平面上的面积分数会高估样品内的体积分数，而投影平面上记录的核数会低估实际成核事件的数量。本手稿中给出的统计框架提供了一种方法来处理观察到的（预测）数据与实际（体积）测量之间的差异。