What if you can project an advertisement on the moon?

From an advertising point of view, the moon is undoubtedly a prime location. Its huge influence is unmatched by other forms of advertising. However, for the petty bourgeoisie and literati Mo Ke on the planet, it is an outright nightmare. For example, a poet just chanted the phrase "Bright Moon at Sea", but he saw several words written on the moon: "xx hospital, specializing in infertility". I am afraid that the full poem will soon disappear .

But let's first see how feasible this idea is from the technical point of view.

First, the information in the advertisement should be discernible to the naked eye. Advertisements that require telescopes are not very meaningful. Under this premise, how much information can lunar advertisements contain?

The moon is the largest celestial body in the night sky (visually), and it often gives us a feeling of "large area", especially when it is near the horizon. It should seem no problem writing dozens of words on it. However, this is not the case.

The smallest object that the human eye can distinguish depends on the angle at which this object is projected on the retina (ie, the angle of view). In theory, this minimum viewing angle is 0.3-0.4 points (1 point is 1/60 of 1 degree). However, this requires vision beyond 2.0. As an advertisement for the majority of people, we certainly cannot choose the audience based on the pilot's criteria. We might as well start the analysis with 1.0 vision.

What if you can project an advertisement on the moon?

The standard of visual acuity 1.0 is: you can see letters with a viewing angle of 5 points; the minimum stroke or minimum interval viewing angle is 1 (Visual Acuity by Michael Kalloniatis and Charles Luu). According to this data, we can define the pixel size of the advertising screen as a 1-point viewing angle.


So, how many pixels can be displayed on the moon? In other words, what is the resolution of the moon?

The moon's orbit around the earth is an ellipse, which means that its size in the sky is not constant, and the angle of view
varies between 29′20 ”–34′6 ''. In order to make a simple estimate, we will take an integer of 30 minutes (0.5 degrees).


Each pixel has a viewing angle of 1 point, so the diameter of the moon can only be 30 pixels, the entire moon can only display about 700 pixels. Therefore, the resolution of the moon is actually very low.

Because the minimum length of the letters is 5 points of view, we can display all English letters in a 5 x 6 dot matrix font. The information displayed in this way can be seen by most people, but the quality of such display is very low. Considering the huge cost of moon advertising, such a poor picture quality is certainly disappointing.
 
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This resolution is sufficient for most people with ordinary eyesight, but it is still rough for a few people with good eyesight (such as 1.5 or 2.0), and they can see obvious pixels. We can shrink the pixels to increase the resolution.

If the pixel viewing angle is defined as 0.5 points, then more than 2,800 pixels can be displayed on the moon. Although the number of pixels is still far behind the smart watch, but even for pilots, this resolution has exceeded Apple's Retina Display (Retina Display) standard).

In the high-resolution mode of 0.5-pixel, the same size letters can use 10 x 12 dot matrix fonts, the picture quality has been significantly improved.

The image below shows the effect of these two resolution fonts in the night sky.

The moon in the picture is 1 cm in diameter on my computer monitor. If you look at it from a distance of 1.15 meters, the angle of view is 0.5 degrees, as large as the moon in the night sky. In this example, I increased the contrast. Whether a real ad can achieve such a contrast depends on the method of generating pixels.

It is worth noting that from the perspective of the earth, the moon is a two-dimensional circle, and we want all pixels to be squares of the same size. However, the lunar surface is a sphere, and only a few pixels in the middle are approximately square. For pixels farther from the center, if we want them to be displayed as squares, we must consider the perspective effect.
 
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