Why do you see stars all over the sky at night, but there are no stars during the day?

We can often see an amateur astronomer asking, "Why don't the stars shine during the day?" At this time, if you throw him a sentence "because the sun is shining during the day, little fool", that is not enough. I often wonder how I can explain this seemingly obvious phenomenon. I learned from the philosopher thomas kuhn that if we want to explain scientifically, we must break the inherent inertia of thinking and look at the problem from a new angle.

The story of human eye and color CCD camera

I once asked a question about color CCD camera in SAA forum, and the scientist yohan blake A. Blackwell later answered my question. He explained the principle of this color camera from a very professional point of view, and it was after reading his comments that I suddenly found that the related concepts of signal/noise are closely related to the images of celestial bodies (whether stars or arbitrary celestial bodies) we received.

This is a rather complicated theory. In order to facilitate readers' understanding, I will briefly describe it here without going into details. In short, the ability of human beings to observe the stars during the day is related to the sensitivity of the eyes and the stray light of the observer's environment. Strong sunlight is like background noise in the sky, and the human eye is like a "filter" to deal with scattered light in the atmosphere. So how to relate the ability of human eyes to observe stars with signal-to-noise ratio in professional terms? Here's my explanation.

Personally, I used to be a professional photographer, and I can skillfully use image processing technology to improve the quality of some black-and-white and color photos (including astronomical photos). My teacher often tells me: "Please correct the color balance of this film, weaken its structural sharpness, and highlight the details of this' highlight area' ... I can understand all this!" Finally, I learned how to use fuzzy masking and other skills to achieve these goals. But now things have changed. I am a computer scientist now. Although I am still interested in astrophotography, the current problems need more technical solutions. We painstakingly use computers, image amplifiers, CCD detectors, etc., and constantly try to reduce the "quantum defects" of the image in order to obtain a good image with uniform color, high saturation and minimum noise. In short, this is a real challenge!

I discuss CCD here because we can compare it with the structure of human eyes relatively easily. You already know that they can detect light and process discrete analog signals continuously. After the CCD detector converts photons into digital form (electrons into binary numbers), we can easily operate them on the computer because the two systems "speak" the same language.

In order to find out why we can only see stars in the night sky, I compared human eyes with electronic detectors like CCD and got some interesting results. Explain as follows

Just like CCD camera, the sensitivity of our eyes depends not only on the structural characteristics of the eyeball itself, but also on the ability of our brain (its image acquisition software for CCD camera) to deal with the "noise" in the original signal.

In the previous chapter, we have specially introduced the CCD camera. These "noises" may include the noise of the pickup head (noise introduced in the process of A/D conversion) (note: the pickup head is a device for collecting live sound and then transmitting it to the back-end equipment), the dark current and deviation caused by electronic fluctuations (related to the ambient temperature) and some natural and man-made background sounds (rays in the atmosphere, moonlight, light pollution ...). Although the human eye is not an electronic device, when it must pass through the optic nerve to the brain, Now my question is, what is the connection between human eyes and CCD sensors?

Although I am not a neurophysiologist (generally in the category of neurophysicists, but then again, the eyes are only a partial extension of the brain) and I am not a technical analyst, it seems to me that the first few noises we just mentioned, namely "the noise of the pickup head" and "dark current", have no obvious influence on people's eyes (and brain). When there is no light stimulus, we won't perceive any visual signals, just like the blind ... No matter what the structure and shape of these light signals are, although they do exist, their influence is minimal or even negligible.

Next, let's talk about the influence of "background noise". At night, whether you cancel all flights in the sky or order all jets to stop, the background noise is always there. This noise can hit our retina and other nerve cells in the form of cosmic rays. In rare cases, we can see a flash in our eyes, just like a new star suddenly explodes at night. But it is mainly reflected in the brightness of the sky (active atmospheric atoms emit light), but now light pollution limits our ability to distinguish weak light objects (in busy cities, signals and noises are probably the same intensity, so we rarely have the opportunity to observe stars).

In order to make my theory sound more comprehensive, we should also consider the weather factor. If the observation conditions (turbulence and air transparency) are good, then the signal sources (planets, satellites, stars, galaxies) will send out stronger signals than noise. In short, a simple analysis like this can give a clear answer to the question why we can only observe the starry sky at night. In addition, we can draw a conclusion from this analysis, that is, the intensity of all natural background "noise" is far lower than the signal emitted by stars.

What are the stars like in the daytime?

Application of mathematical logic and physical methods

If we want to find stars in the sun, we need to realize that the environmental conditions during the day are completely different from those at night. The sunshine in the daytime and the brightness of the sky add a lot of "noise" to the radiation signal sent by the stars. At this time, it is impossible to remove these "noises" only by a "filter". In fact, the principle is so simple! Now let's explain this problem in mathematical terms.

Suppose we are doing a meditation experiment (there will be extra imaginary values in the later demonstration), and the content of meditation training is how to observe a star in broad daylight. Sunlight, light from stars and various sounds in nature hit the sensitive cells in our eyes at the speed of 10000 photons per second. What we need to pay attention to is that these data do not separate the signals from all the mixed signals. The visual field of human eyes is about 120, covering a vast sky and a lot of light, and brightness may be included, which we will confirm later [1].

Such a signal is a complex object, which consists of photon wave train and quantum with energy, and is suitable for the laws of quantum physics. According to the laws of quantum physics, we can regard noise as a random quantum. Like CCD camera, the total noise (B) in the signal we are looking for with naked eyes is equivalent to the quantum uncertainty or standard deviation of the relative average brightness. Its expression is defined as the square root of the sum of squares of each noise value (it sounds so difficult! ):

B =？ (noise 12+ noise 22+? ...)< equation1>;

So what is the signal of the stars? We measured this special star and found that our eyes can capture 50 photons from this star in one day. This is how we get the signal of the star: the total signal minus the signal of the sun and other noise signals. In fact, everything is a matter of quantum events, and all noises (equation 1) will be generated:? 10000 or 100 photons per visual unit.

It is now known that there are 50 stellar photons mixed with 9950 other photons, which are composed of light scattered in the field of vision. Light sources include the sun, the sky and some light pollution sources. We can determine the signal intensity of the star, that is, the signal-to-noise ratio or S/B. Applying this relationship to this situation, we find that the ratio S/B = 50/ 100, that is, 0.5. What does this number stand for?

The above is the simulation of the star with increased star number, and its signal-to-noise ratio is between 2: 1 and 16: 1. A similar test was completed on the artificial nebula below.

In this example, the data of 0.5 shows that we can't estimate the magnitude (or brightness) of a star with higher accuracy than 1/0.5, unless it is element 2, and its value is 10 times lower than the acceptable detection threshold of A. CCD detector (the signal-to-noise ratio of each pixel can reach 20 or higher, which is enough to detect a star with a magnitude of 20e per square arc second). But our eyes are not completely similar to CCD sensors, because the structure with retinal function at this value of 0.5 also means that the brightness of stars will be submerged in the background light of the sky, which greatly reduces the signal-to-noise ratio of stars we try to observe during the day. If our stars are displayed on the computer screen, we can hardly see any patterns during the day, leaving us with a blank screen at most.

Now let's try to solve the problem of observing the stars in the sun! What exactly should I do? In fact, we just need to improve the signal-to-noise ratio of the stars. If we use some instruments with a visual field of about 10' or smaller, such as telephoto or binoculars, we will greatly reduce the influence of noise by 10 times or more, thus improving the S/B ratio of stars. We can improve the star's S/B ratio in this way, but at the cost of darkening the background brightness. On the display, the image will become softer, and the star now looks like a small bright spot bathed in a blue-gray halo, which is a typical manifestation of the gradual weakening of the signal, or in other words, it may make the already unstable S/B value smaller.

Because of this way of thinking, we reduce the noise influence in the star signal-to-noise ratio to 50/? 1000 instead of 50/? 10000, now this value is 15 instead of 0.5. Thanks to the "sampling" of 30 times, theoretically, we can distinguish the signals of stars from other signals more easily, so that some stars can be observed during the day and their magnitude can be estimated with the accuracy of115 or 7%. The amplitude is 7%, not a simple multiple of 2!

conclusion

Borrowing from the field of CCD, in fact, the images of our stars are "undersampled" from the beginning and cannot be detected by our visual detectors (eyes). In order to increase the readability of sampling and distinguish our stars in the sun, we must increase the focal length of the telescope in order to obtain images with greater gradient. However, the comparison between eyes and CDD cameras can only go so far, because we can't use eyes like manipulating the focal length reducer, nor can we achieve our goals like using professional methods such as pixel grading and merging (pixel merging). But I never said that we can't subtract the brightness of the sky from the image to increase the signal of the stars captured by the CCD camera, or that we can't process such information in the image processing software. Don't misunderstand me. ...

Thanks to math, we solved this problem!