The moon illusion is a visual deception when people perceive the angular diameter of the Moon/Sun near the horizon larger than that of the one higher in the sky. Some theories have been proposed to explain this illusion, but not any is generally accepted. Although several psychophysical experiments have been performed to study different aspects of the moon illusion, their results have sometimes contradicted each other. Artists frequently display(ed) the Moon/Sun in their paintings. If the Moon/Sun appears near the horizon, its painted disc is often exaggeratedly large. How great is the magnitude of moon illusion of painters? How different are the size enlargements of depicted lunar/solar discs? To answer these questions, we measured these magnitudes on 100 paintings collected from the period of 1534–2017. In psychophysical experiments, we also investigated the moon illusion of 10 test persons who had to estimate the size of the lunar/solar disc on 100 paintings and 100 landscape photographs from which the Moon/Sun was retouched. Compared to the lunar/solar disc calculated from reference distances estimated by test persons in paintings, painters overestimated the Moon's size on average Q = 2.1 ± 1.6 times, while the Sun was painted Q = 1.8 ± 1.2 times larger than the real one, where Q = rpainted/rreal is the ratio of the radii of painted (rpainted) and real (rreal) Moons/Suns. In landscape photos, test persons overestimated the Moon's size Q = 1.6 ± 0.4 times and the Sun was assumed Q = 1.7 ± 0.5 times larger than in reality, where Q = rtest/rreal is the ratio of the radius rtest estimated by the test persons and the real radius rreal of Moons/Suns. The majority of the magnitude of moon illusion Q = 1.6, 1.7, 1.8, 2.1, 2.8, 2.9 measured by us are larger than the Q-values 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.8 obtained in previous psychophysical experiments due to methodological differences.

中文翻译：

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绘画和风景照片中月亮错觉的心理物理学研究

月亮错觉是一种视觉欺骗，当人们认为地平线附近的月亮/太阳的角直径大于天空中较高的月亮/太阳的角直径时。已经提出了一些理论来解释这种错觉，但没有一种理论被普遍接受。尽管已经进行了几次心理物理学实验来研究月球幻觉的不同方面，但它们的结果有时相互矛盾。艺术家经常在他们的画作中展示（编辑）月亮/太阳。如果月亮/太阳出现在地平线附近，它的彩绘圆盘通常会夸大其词。画家的月亮错觉有多大？所描绘的月球/太阳盘的尺寸放大有多大不同？为了回答这些问题，我们对 1534 年至 2017 年期间收集的 100 幅画作进行了测量。在心理物理学实验中，我们还调查了 10 名测试人员的月亮错觉，他们必须估计 100 幅绘画和 100 幅风景照片中月球/太阳圆盘的大小，其中月亮/太阳经过修饰。与绘画中测试者估计的参考距离计算出的月球/太阳盘相比，画家平均高估了月球的大小 Q = 2.1 ± 1.6 倍，而绘制的太阳比实际大 Q = 1.8 ± 1.2 倍，其中Q = rpainted/rreal 是绘制 (rpainted) 和真实 (rreal) 月亮/太阳的半径之比。在风景照片中，测试人员高估了月球的大小 Q = 1.6 ± 0.4 倍，并且假设太阳比实际大 Q = 1.7 ± 0.5 倍，其中 Q = rtest/rreal 是测试人员估计的半径 rtest 的比值和月球/太阳的真实半径 rreal 。