Are rainbows holograms?

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A rainbow has many properties associated with holograms. Is the effect of rainbows in clouds essentially holographic?

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I am currently researching holograms and realized that a rainbow has many properties associated with holograms. Obviously there are some differences, but as a student of scalar diffraction theory I see important similarities.
Here is my basic reasoning, but I haven't found anybody discussing the theory of rainbows in this way.
  • Like a hologram, a rainbow is composed of countless nearly identical sources of coherent light, reflected and refracted off water droplets.
  • Like a hologram, a wavefront emerges from the cloud of rain droplets, but what you see are not the individual droplets but a whole image which depends on your relationship to the light source and the cloud. When you move, the rainbow moves.
  • Like a hologram, a given point in the cloud (or a given point on the holographic film) doesn't correspond to a particular part of the rainbow (or the object being holographed). For instance, depending on your perspective, a given region in space may appear red or violet.
Holograms are based off capturing phase relationships of the laser light, whereas a rainbow is diffracting based upon frequency (i.e. magnitude not phase). But both are fundamentally dependent on interference properties in the frequency domain.

I haven't found literature comparing the mathematics of holography with that of rainbows, but it seems a strong case to me.
 
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  • #2
anorlunda
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anorlunda
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And thinking about your primary question, rainbow light is not coherent, and I don't see how it can be described as a hologram.

Holograms are interference patterns.
 
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They are quite different.

Rainbows. to lowest order. are not really caused by interference. They are instead caused by an inflection point in the internal reflection of light in a sphere vs impact parameter. The separation into colors is a dispersion effect. caused by speed variation with color. The secondary bow is caused two internal reflections in the drop.

The higher order effects are more directly related to interference phenomena. But holograms are all about interference. I wish you well but think this an unlikely pursuit.
 
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  • #5
sophiecentaur
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Summary:: A rainbow has many properties associated with holograms. Is the effect of rainbows in clouds essentially holographic?

I haven't found literature comparing the mathematics of holography with that of rainbows,
I could suggest that the reason for that is the fact that the two phenomena are not related. There can be a big temptation to think one is the 'first ' to think of a new idea in Science but you can only justify that feeling when you have already looked at the problem from every which way and have become an 'expert'. If not then the lack of evidence can usually be taken as evidence that the 'new idea' is probably not relevant.

The common term 'diffraction' does actually apply to all optical phenomena and whoever you see light. The drops that form the rainbow are randomly positioned so there can be no observable interference pattern due to any 'repeated' pattern of sources. The rainbow is just due to the addition of the contributions of all the individual droplets at the various angles; dispersion changes the angles but also the individual drops will have a diffraction pattern due to their diameters. That diffraction pattern will be very broad because the droplets are small. The effect would be to blur the image of the Sun, viewed directly but, looking in the direction of the bow there would just be the normal back-scatter of the raincloud. Look at the links, suggested above.

I can't make up my mind whether a uniform square array of water droplets would produce any effect on the bow, due to interference. I think perhaps not but I could imagine a starburst pattern being impressed on the bow - or broad light / dark bands at different angles??
 
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There are of course the sundogs "parhelion" which are caused by hexagonal ice crystals.

1589195501251.png


That diffraction pattern will be very broad because the droplets are small.
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The "supernumery" bands are the direct result of this (you can see the Bessel function !) and would be present even without the color-separating dispersion

1589194438846.png
 
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Just read the insights article.......preaching to the choir!. Nice photo, too..
 
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  • #8
sophiecentaur
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Sundogs: There are two aspects to any diffraction pattern (good old antenna theory is the way into this topic). You have the pattern of the individual element and you have the patterns of the array. It's much easier when the individual elements are either symmetrical or when they hoo 'point' in the same direction because you can multiply the two patterns together. But that's not always possible. The array pattern has fringes with widths sort of related to 1/D (the total aperture of the array) and the individual element patterns tend to have fringes / lobes / etc. which relate to 1/d , the element effective aperture.
When you have a regularly spaced array, the fringes can be very tight but as the array becomes more random, the 'array factor' gets more an more fuzzy, in the end, disappearing altogether. For sundays, I'd suggest that the pattern relates to the angles of the single ice crystals and would slightly be affected by crystal size - hence the non-sharp pattern for a range of crystals in the air. Sharper could mean that the crystals happen to be of nearly similar sizes due to similar formation times (??).
 
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Thanks! I did read that thread and thought it was well written and very interesting. That's what inspired me to post here! I appreciate your reply.
 
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And thinking about your primary question, rainbow light is not coherent, and I don't see how it can be described as a hologram.

Holograms are interference patterns.
Maybe you're right. Although I think there are some subtleties, and I am willing to be convinced in the favor of your point. Nonetheless, I think it is worth discussion.

For instance, the question of the spatial coherence of sunlight is not straightforward.

In "Coherence properties of sunlight" (Agarwal, Gbur, Wolf, 2004, Optics Letters, Vol 29 No 5) the authors calculate Area of coherence= 3.67 x 10^{-3} mm^2, or on the order of a tenth of a millimeter in each dimension. This is consistent with an original calculation they reference originally done in the mid 1800s.

Water droplets in clouds are smaller than this, so they act as a diffraction grating on sunlight, albeit a superposition of randomly oriented difraction gratings, which I might guess leads to the washed out white look of clouds.

Raindrops are bigger, on the order of a 1mm, so that is pushing the boundary of Agarwal's calculation of coherence. Nonetheless, it seems unjustified to make a blanket statement that sunlight (and thus rainbow light) is spatially incoherent. Coherence is a matter of degree.

As a second point, an audio Compact Disk creates interference and rainbows due to reflection, since it is composed of regularly spaced reflectors. Clearly, too, reflection holograms create interference patterns due to reflection. One does not require diffraction in order to generate interference. As an aside, reflection holograms, I believe, can work in white light, though not as good as monochromatic transmission holograms.

So my original point is trying to identify what makes a hologram a hologram. The fundamental physics is not necessarily diffraction, but interference in some form, which is possible with refraction as well (as in an thin oil film). I think the key feature of a hologram is the construction of an entire macroscopic wavefront which is coherent. Hence, a hologram of a person's face is a macroscopic wavefront bouncing off the whole holographic plate and appearing to your eyes as a coherent image.

Thus, is a rainbow not a macroscopic wavefront containing a coherent image of a colored arc in the sky? Is not a CD generating a coherent wavefront across a region of a centimeter or so when you see a rainbow on its underbelly surface?
 
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They are quite different.

Rainbows. to lowest order. are not really caused by interference. They are instead caused by an inflection point in the internal reflection of light in a sphere vs impact parameter. The separation into colors is a dispersion effect. caused by speed variation with color. The secondary bow is caused two internal reflections in the drop.

The higher order effects are more directly related to interference phenomena. But holograms are all about interference. I wish you well but think this an unlikely pursuit.
Thanks, I'll have to think on this. I know that we think of light bouncing off a raindrop at 42 degrees will appear red to our eyes, and so forth. But it seems to me that there is interference involved in the perception of a rainbow.

For instance, when we cut off the right side of a hologram, we can still move our heads to the left to "See around the barrier" and see the image hiding there, that we tried to cut off. Looking at a hologram is like looking through a window. This happens because the light bouncing off the various regions of the film interact in just the right way to recreate the appropriate wavefront. The effect is done as-a-whole, based on relationships across the film (which encode phase relationships in the frequency domain).

Now, if I am looking at a rainbow, and then I remove half of the cloud and make it completely stop raining on the right side of the rainbow, then the right side of the rainbow goes away (I believe). But then if I move myself to the left, obviously the right side of the rainbow will come back into view, because I have moved more into the rain portion and the rainbow moves with me. The point opposite the sun has moved further into the rain portion of the sky (i.e. to the left). This is like "looking around the barrier."

I get that there are differences, but the effect seems to be identical.

It does seem that you are right though. I don't see how interference plays a role.
 
  • #12
sophiecentaur
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Water droplets in clouds are smaller than this, so they act as a diffraction grating on sunlight,
It's not the individual size of the elements that accounts for interference. It is the coherent effect of a number of elements. Where do you think the word "grating" comes from? It is from the regularity of the pattern. A random array is not a grating.
Individual droplets will exhibit a diffraction pattern, from a source of waves. What seems to be accepted is that the term 'interference' relates to the behaviour of an array of diffracting elements. But interference is just a subset of the more general diffraction. Interference patterns can be calculated (approximately) by summing (Σ) the effects of the elements. Diffraction involves Integration (∫) over the whole aperture. I suggest that we should stick to those accepted uses of the terms. If you look at this link in the region around and following p20 you will see the distinction explained pretty well. For the pattern to be achieved, you need a sufficiently coherent source.
 
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But it seems to me that there is interference involved in the perception of a rainbow.
Rainbows are colored for the same reason light passing through a glass prism is colored. Not a diffraction grating nor a thin film. Different physics, same colors......
 
  • #14
anorlunda
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In "Coherence properties of sunlight" (Agarwal, Gbur, Wolf, 2004, Optics Letters, Vol 29 No 5) the authors calculate Area of coherence= 3.67 x 10^{-3} mm^2, or on the order of a tenth of a millimeter in each dimension. This is consistent with an original calculation they reference originally done in the mid 1800s.
Optics is not my field. Is there more than one definition of "coherence"?

Holograms are made from laser light which is both monochromatic, and coherent meaning that all photons have the same phase. Obviously, sunlight is not monochromatic to start with.

https://en.wikipedia.org/wiki/Coherence_(physics) said:
In physics, two wave sources are perfectly coherent if they have a constant phase difference and the same frequency, and the same waveform.
https://en.wikipedia.org/wiki/Holography#Laser said:
In laser holography, the hologram is recorded using a source of laser light, which is very pure in its color and orderly in its composition.
 
  • #15
sophiecentaur
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Obviously, sunlight is not monochromatic to start with.
Of course but it can be regarded as coming from pretty narrow source (0.5°) which is small compared with the angle range from a rainbow. To spot the absorption lines, you would need to collimate the light through a small slit and that would avoid the 'overlap' of the spectra from across the Sun's width.
But it seems to me that there is interference involved in the perception of a rainbow.
Physics doesn't work well with a "seems to me" approach. In as far as diffraction can be said to apply to any situation of light passing through a system then you could perhaps apply the word diffraction to the formation of a rainbow but interference? Never. It fails at every part of the definition of the world.
Just read up about it - so many google hits available and believe that your view could just be wrong.
 
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Thank you for your helpful comments. SophieCentaur, yes, from your points I acknowledge that the idea as I stated it appears to be incorrect, thanks.

I would like to ask for help reviewing this passage from the text I have written. If anyone is willing, please let me know if there is something I've stated below that appears incorrect. Note that for the audience I am writing for, precision is less important than understanding, and of course, accuracy.
Thank you!

"You perceive a rainbow far away in the sky. It always appears directly opposite the sun, when it is both rainy and sunny at the same time. And it always appears at an angle of forty-two degrees in the sky. The rainbow seems like an “object out there,” with a left side, a right side, and a middle.

But what if I remind you that when you try to drive past the rainbow it moves along with you? You’d say “Oh yes, that’s true. A funny thing, too!” If you chase the end of the rainbow in order to find a pot of gold, you know that the end of the rainbow recedes away from you as you approach it. There is something really subtle going on with the light from a rainbow. It is clearly different from the trees or mountains moving past your window, for you can never catch up to a rainbow.

Throughout this book we shall explore the idea that a rainbow—and light in general—does not exist in the normal space you are used to but in frequency space, or the frequency domain. We’ll use both these terms interchangeably. When you move your body in space, the entire rainbow moves across the background with you, as if it were an object flying through space alongside you. Yet another person down the road sees the rainbow in a different place. When you look at a patch of sky and see red, the other person looking at the same patch of sky might see yellow, or violet, or just blue sky. In fact, just about any place in that region of the sky can appear to be part of the rainbow for somebody looking from the right direction.
It seems that the rainbow you see must not really be an “object,” in the usual sense, but rather a pattern. A rainbow emphasizes the relationships between different parts of space, just as much about you as it is about the water in the sky and the position of the Sun shining the light. There is no physical thing sitting in the sky that is red, orange, yellow, green, blue, indigo, and violet. Rather, it is a collective pattern of light traveling from the Sun behind you to the raindrops floating in front of you, then bouncing to your eyes. Think of it as a relationship. A rainbow is not a thing but a motif, an expression of the organization of light."
 
  • #17
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Thank you for your helpful comments. SophieCentaur, yes, from your points I acknowledge that the idea as I stated it appears to be incorrect, thanks.

I would like to ask for help reviewing this passage from the text I have written. If anyone is willing, please let me know if there is something I've stated below that appears incorrect. Note that for the audience I am writing for, precision is less important than understanding, and of course, accuracy.
Thank you!

"You perceive a rainbow far away in the sky. It always appears directly opposite the sun, when it is both rainy and sunny at the same time. And it always appears at an angle of forty-two degrees in the sky. The rainbow seems like an “object out there,” with a left side, a right side, and a middle.

But what if I remind you that when you try to drive past the rainbow it moves along with you? You’d say “Oh yes, that’s true. A funny thing, too!” If you chase the end of the rainbow in order to find a pot of gold, you know that the end of the rainbow recedes away from you as you approach it. There is something really subtle going on with the light from a rainbow. It is clearly different from the trees or mountains moving past your window, for you can never catch up to a rainbow.

Throughout this book we shall explore the idea that a rainbow—and light in general—does not exist in the normal space you are used to but in frequency space, or the frequency domain. We’ll use both these terms interchangeably. When you move your body in space, the entire rainbow moves across the background with you, as if it were an object flying through space alongside you. Yet another person down the road sees the rainbow in a different place. When you look at a patch of sky and see red, the other person looking at the same patch of sky might see yellow, or violet, or just blue sky. In fact, just about any place in that region of the sky can appear to be part of the rainbow for somebody looking from the right direction.
It seems that the rainbow you see must not really be an “object,” in the usual sense, but rather a pattern. A rainbow emphasizes the relationships between different parts of space, just as much about you as it is about the water in the sky and the position of the Sun shining the light. There is no physical thing sitting in the sky that is red, orange, yellow, green, blue, indigo, and violet. Rather, it is a collective pattern of light traveling from the Sun behind you to the raindrops floating in front of you, then bouncing to your eyes. Think of it as a relationship. A rainbow is not a thing but a motif, an expression of the organization of light."
Hmm. There appear to be errors in what you have written, and what sounds like a bit of pseudoscience. What exactly is the target audience?

For example, I don't think this is correct:

>we shall explore the idea that a rainbow—and light in general—does not exist in the normal space you are used to but in frequency space, or the frequency domain.

and this:

>When you move your body in space, the entire rainbow moves across the background with you, as if it were an object flying through space alongside you.

A rainbow is fundamentally a reflection. Much like you can see the reflection of your car in building windows along the roadway -- it moves with you, but it's obvious why (because it's your reflection in the windows as you are moving). I'm not sure it adds any value to try to make this mystical somehow.

And if you want to write about them, be sure to look into all of the different kinds of rainbows, since there are other types beyond the simple one that we see most commonly...

https://en.wikipedia.org/wiki/Rainbow
 
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"You perceive a rainbow far away in the sky. It always appears directly opposite the sun, when it is both rainy and sunny at the same time. And it always appears at an angle of forty-two degrees in the sky. The rainbow seems like an “object out there,” with a left side, a right side, and a middle.

But what if I remind you that when you try to drive past the rainbow it moves along with you? You’d say “Oh yes, that’s true. A funny thing, too!” If you chase the end of the rainbow in order to find a pot of gold, you know that the end of the rainbow recedes away from you as you approach it. There is something really subtle going on with the light from a rainbow. It is clearly different from the trees or mountains moving past your window, for you can never catch up to a rainbow.

Throughout this book we shall explore the idea that a rainbow—and light in general—does not exist in the normal space you are used to but in frequency space, or the frequency domain. We’ll use both these terms interchangeably. When you move your body in space, the entire rainbow moves across the background with you, as if it were an object flying through space alongside you. Yet another person down the road sees the rainbow in a different place. When you look at a patch of sky and see red, the other person looking at the same patch of sky might see yellow, or violet, or just blue sky. In fact, just about any place in that region of the sky can appear to be part of the rainbow for somebody looking from the right direction.
It seems that the rainbow you see must not really be an “object,” in the usual sense, but rather a pattern. A rainbow emphasizes the relationships between different parts of space, just as much about you as it is about the water in the sky and the position of the Sun shining the light. There is no physical thing sitting in the sky that is red, orange, yellow, green, blue, indigo, and violet. Rather, it is a collective pattern of light traveling from the Sun behind you to the raindrops floating in front of you, then bouncing to your eyes. Think of it as a relationship. A rainbow is not a thing but a motif, an expression of the organization of light."
You seem to be having more problems with language than science, at least for my reading skills. directly opposite the sun has no frame of reference for opposition. Ditto, forty two degrees, and I've no idea where you got left, right, middle from. A rainbow may seem to be receding if you're moving towards it, but certainly not away from you, which would imply that the relative distance would be opening.

A rainbow indicates a specific angular relationship between a (parallel'ish, white) light source, water droplets (or reasonable facsimile) and an observer, but it is not the relationship, itself. A lake with somebody consistently on top of the water indicates that the person knows how to swim (or has a flotation device), but does not make that person the lake. Mommy, daddy and baby may be a "family", but the baby is not a family.

Et cetera.

You've got a few nice turns of phrases in there, but don't seem to be familiar enough with the words you're using - within context of the phenomenon - to be articulate. If it were the Homework section, people (okay, maybe just me) would be telling you to check over your own work before asking others to do so.

Out of curiousity, is there a metaphor/simile/analogy:pick-one that you're trying to portray ? or, just wondering if one will appear.
 
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