What's The Point?!

[Southwind17]

As I peruse the night sky from the indulgent comfort of my newly-installed Jacuzzi, I notice that the stars, particularly the brightest, appear to have an apparent diameter. Hard to say, but the brightest observed seems to have an apparent diameter of, say, 1/100 of the Moon, there or thereabouts.

Using UY Scuti as an example (albeit probably not one of the stars observed, but the largest known star), however, we can calculate the apparent diameter as approximately 1/6,600 of the resolving power of the best human eye. In other words, it's a 'dot', or a point source.

Does this mean, then, that the image is detected by only one photosensor within the eye's retina, which is processed by the brain and perceived as larger than it actually is?

 

[casebro]

It means the atmospherics scatters the light of the stars making them look bigger.

 

[Darwin123]

As I peruse the night sky from the indulgent comfort of my newly-installed Jacuzzi, I notice that the stars, particularly the brightest, appear to have an apparent diameter. Hard to say, but the brightest observed seems to have an apparent diameter of, say, 1/100 of the Moon, there or thereabouts
....
Does this mean, then, that the image is detected by only one photosensor within the eye's retina, which is processed by the brain and perceived as larger than it actually is?

Quite a bit larger, actually. The atmospheric turbulence makes the image slide around very fast. The slow response time of the unaided eye interprets this partly as an enlargement of the star.

I conjecture that the diameter that you see in the sky is very close to what is called the 'isoplanic angle' of the star. The isoplanic angle describes the apparent size of the star seen when viewed through atmospheric turbulence.


The effective image of stars is effectively broadened by atmospheric turbulence. The point transfer function of most stars in a hypothetical vacuum is too small for the unaided eye to resolve. Due to atmospheric turbulence, there are little pockets of air with a different temperature and pressure than the ambient air. The light from the star is refracted in different directions.

Thus the image of the star fluctuates in intensity, size, shape, center position due to turbulence. The fluctuations in the image of the star have a wide range of frequencies because the turbulence has a wide range of frequencies.

The energy of turbulence is spread over a wide range of frequencies. Hence the apparent image of the star both moves and changes shape in a way that depends on the response time of the detector. In this case, the detector is the unaided human eye. Atmospheric turbulence basically causes both apparent motion and apparent size in the image.

The low frequency components of atmospheric turbulence cause the ‘twinkle’ in stars. The fluctuations in size and intensity causes the star to ‘move’ back and forth, out and in. The in an out amounts to a change in intensity.

The high frequency components of the atmospheric turbulence causes the apparent diameter of the star to change. If one takes a long exposure photograph of the star, the diameter of the image would largely be determined by the isoplanic angle.

I recommend that the next time you look at the star, you should try to separate in your mind the apparent motion of the star, the apparent diameter of the star and the apparent intensity of the star. I think you will find it difficult as the three effects are convoluted together by the response characteristics of your eye.


http://www.ctio.noao.edu/~atokovin/tutorial/part1/turb.html
‘The long-exposure atmospheric PSF is independent of the viewing direction (isoplanatic), because the turbulence and its structure function are statistically the same everywhere in the field. But the instantaneous atmospheric phase aberrations do depend on the direction: the telescope beam as projected on the atmospheric layer at 10 km shifts by 0.5 m for an angular offset of 10 arcseconds.’

Please note that there are all sorts of indirect ways to tease the vacuum diameter of the image from the image distorted by turbulence. The real diameter of the star is too small to resolve directly with the strongest telescopes. However, there are all sorts of ways to cheat without going into space.

Only the satellite telescopes have been able to take pictures undisturbed by turbulence. One of the ‘minor’ benefits of the Hubble telescope is that it has enabled scientists to validate the angular size of stars extracted from ground data.

https://en.wikipedia.org/wiki/Astro...at_half_maximum_.28FWHM.29_of_the_seeing_disc
‘Without an atmosphere, a small star would have an apparent size, an "Airy disk", in a telescope image determined by diffraction and would be inversely proportional to the diameter of the telescope. However when light enters the Earth's atmosphere, the different temperature layers and different wind speeds distort the light waves, leading to distortions in the image of a star. The effects of the atmosphere can be modeled as rotating cells of air moving turbulently. At most observatories, the turbulence is only significant on scales larger than r0 (see below—the seeing parameter r0 is 10–20*cm at visible wavelengths under the best conditions) and this limits the resolution of telescopes to be about the same as given by a space-based 10–20*cm telescope.’

 

[Molinaro]

As I peruse the night sky from the indulgent comfort of my newly-installed Jacuzzi, I notice that the stars, particularly the brightest, appear to have an apparent diameter. Hard to say, but the brightest observed seems to have an apparent diameter of, say, 1/100 of the Moon, there or thereabouts.

Sounds like you are looking at a planet and not a star.

Venus easily, as well as Mars, Saturn and Jupiter if you have decent vision, are clearly seen as a disk and not a point source of light.

The simple test is: does it twinkle?

Stars twinkle, planets do not. And it is precisely because planets are resolved as a disk of light and not a point source when viewed with the naked eye. Air turbulence can momentarily cause nearly all of the light from a star to bend so that it does not reach your eye. This is the cause of the twinkling.

But for the disk of a planet viewed from here, the light from opposite edges of the disk pass through too wide a column of air for it to entirely be bent away from your eye. Hence, planets do not twinkle.

 

[Southwind17]

The point transfer function of most stars in a hypothetical vacuum is too small for the unaided eye to resolve.

I wonder why NASA didn't raise this when challenged by the CTists about the absence of stars from the Apollo photos?! If this is so why did NASA run the under-exposure argument (not wanting this to become another 'fake Apollo landings' thread)?

 

[Southwind17]

Sounds like you are looking at a planet and not a star.

Nah - I can tell the difference between the two, and even if I couldn't, I sure know that there aren't dozens of planets visible from Earth, as there are stars!

 

[Reality Check]

I wonder why NASA didn't raise this when challenged by the CTists about the absence of stars from the Apollo photos?! If this is so why did NASA run the under-exposure argument (not wanting this to become another 'fake Apollo landings' thread)?

Could that be that the CTists did not state that cameras were naked eyes and so NASA did not need to debunk an argument that was not put forward?

As already pointed out - any apparent diameter that you see for stars is a product of atmospheric turbulence.

 

[Southwind17]

Could that be that the CTists did not state that cameras were naked eyes and so NASA did not need to debunk an argument that was not put forward?

As already pointed out - any apparent diameter that you see for stars is a product of atmospheric turbulence.

To be clear, isn't that the reason we see stars at all? How would our eyes register a point light with essentially zero apparent diameter without an atmosphere to help? in other words, can we see stars from space, and if so, what mechanics of the human eye enable us to do so, given that they're seemingly not resolvable without an atmosphere?

 

[Reality Check]

To be clear, isn't that the reason we see stars at all? ...

Astronauts in the ISS can see stars without any thick atmosphere to cause them to twinkle. Thus no one says that stars are not resolvable to the naked eye without an atmosphere.
An "essentially zero apparent diameter" is not a zero apparent diameter.

ETA: Resolution of human eye: 50” (day) so 17” (night). N.B. This is the resolution between bright objects not of bright objects.

 

[Darwin123]

To be clear, isn't that the reason we see stars at all? How would our eyes register a point light with essentially zero apparent diameter without an atmosphere to help? in other words, can we see stars from space, and if so, what mechanics of the human eye enable us to do so, given that they're seemingly not resolvable without an atmosphere?

The resolution is not the same as the sensitivity. One could see a star without being able to resolve a diameter. Cells on the retina could give a large signal even if the the light struck only one cell. A single crystal on the photographic emulsion could be reduced even if the light struck only one crystal. So the absence of an atmosphere couldn't hide the stars. In fact, it would probably make the starlight look even more intense.

The problem you presented is under what conditions does one perceive a finite diameter on a star. That has more to do with the number of retinal cells excited than the power going to each cell.

Let us consider what the resolution of a stars image would mean for an astronaut on the moon.


We have a finite number of photoreception cells on our retina. This would set one limit of resolution for the unaided eye.

The light from a point source would be focused by an ideal lens/cornea system to a single spot on the retina. If the starlight was so well focused that only one photoreceptor was illuminated by the starlight, that photoreceptor alone would be excited. The light on that one photoreceptor would excite a signal.

The individual photoreceptor may be very highly excited on the moon, because all the power focused into a very small circle of light on the retina. The more power in going to the retina, the brighter the signal. The diffraction of the star light could limit the resolution if the lens/cornea system was ideal. Basically, the wavelength and the diameter of the pupil would then determine the resolution.

The lens/cornea system of the unaided eye is not ideal even for a person with 20/20 vision. A star would probably be focused on a few photodetector cells even without an atmosphere. As long as each cell receives a significant amount of power from the starlight, the light would be seen by the brain. The diameter of the spot focused on the retina would be a component of the apparent diameter of the star.

The turbulence from the atmosphere is the greatest limitation on resolution on the earth. The image of a star as seen from the earth will be darting back and forth over a large region of the retina. There is a minimum exposure time in the unaided eye. Thus, the faster motions of the image will blur the image of the star making it look far greater than it is.

The diffraction and flaws in the lens cornea system would create a finite diameter as seen from the moon. However, the atmosphere of the earth adds a far larger component of diameter for stars seen from the earth.

Ironically, astronomers have been using close up objects to calibrate the image observed through their telescopes. These nearby objects are called guide stars. Their effective diameter is much smaller than that of 'real stars' because the light from a guide star passes through less atmosphere. The effect of atmospheric turbulence increases with the thickness of atmosphere the light passes through.

You were probably thinking of light scatter and absorption from molecules and small particles. That is not the same as turbulence. An aerosol particle could be 10 microns. The effect of an atmospheric particle would be to cause extinction which weakens the star light. Scattered light from the sun would create background light, hiding the star. However, the image of the star in each case won't move or change.

Light scattering and absorption from small stars is what hides stars during the day on earth. However, light scattering can not change the shape or position of the image.


An atmospheric vortex can be several feet wide. So the main effect of the turbulence is a change in angle for the propagating light. The vortex doesn't absorb the light really. It only distorts the image. There would be very little extinction caused by an atmospheric vortex. However, the vortex could greatly change the diameter of the image if the observer is on the surface of the earth.

Turbulence and particles have completely different effects on light. The diameter that you saw was probably broadened by turbulence, not particles.

 

[Southwind17]

The resolution is not the same as the sensitivity. One could see a star without being able to resolve a diameter. Cells on the retina could give a large signal even if the the light struck only one cell. A single crystal on the photographic emulsion could be reduced even if the light struck only one crystal. So the absence of an atmosphere couldn't hide the stars. In fact, it would probably make the starlight look even more intense.

...

Very helpful explanation Darwin - thanks for taking the time

 

[Southwind17]

An "essentially zero apparent diameter" is not a zero apparent diameter.

Moot point, but I think 'apparent' diameter refers to the actual diameter of the [spherical] object from an observer's perspective. What one perceives as the diameter due to the reasons explained in this thread is, I think, different. It would be the apparent diameter, presumably, that one would use for determining whether details are resolvable, as the reasons that give rise to the perceived diameter will only serve to 'distort' the image, thereby worsening the ability to resolve.