Understanding Light diffraction

[Misr]

Hello World,
I'm suffering a lot about light diffraction and I need help
I can't really imagine the idea of diffraction
What is an Airy disk?and what does it represent?Does it represent the image of the hole at which diffraction takes place?Is that the reason why the shape of airy disk changes by changing the shape of the hole?
What is the difference between single slit diffraction and Airy disk?and what is the difference between Single slit diffraction(diffraction by using a rectangular hole) and diffraction by using circular hole??

What is a diffraction fringe?the textbook wrote a terrible definition which I can't understand
diffraction fringes are bright regions and dark regions that appear at the edge of the hole image(or may be the book means the airy disk) ,which indicates that light propagates on the two sides of the hole :(((

diffraction shape changes by changing the shape of the hole?why?
Could you illustrate your answer with some pictures
but no videos please because I'm using the dial up connection :(((

 

[Andy Resnick]

There are several equivalent ways to think of an Airy disk: 1) the far-field diffraction pattern of a circular aperture, 2) the Fourier transform of a circle function, 3) the point spread function of a diffraction-limited imaging system that has a circular aperture, 4) the Greens function for a rotationally symmetric optical system (and probably others).

Does that help, at least as a start?

 

[Misr]

That's very complicated I just want to know about some basics

 

[Andy Resnick]

Ok, then let's back up: tell me what you know about 'diffraction'.

 

[Misr]

Okay,that's a very good Idea
I imagine that light diffracts when it passes through an obstacle,When light passes through a slit ,each point on the wave front is considered as a secondary source of waves,waves from those secondary sources interfere with each other , bright fringes are produced from constructive interfere -when two crests meet-,dark fringes are produced from destructive interference , but I was shocked when I read the definition of a diffraction fringe in the textbook, which says as I mentioned earlier ,"diffraction fringes are bright regions and dark regions that appear at the edge of the hole image or the shadow of the barrier(or may be the book means the airy disk) ,which indicates that light propagates on the two sides of the hole"
which image?Does an image of the hole is formed when light passes through it?
could you explain that definition if it is correct or give me a simple definition of a diffraction fringe please
and why does diffraction changes by changing the shape of the hole in this picture?
http://imageshack.us/photo/my-images/193/1522d.jpg/

and what causes light to bend in this way?Is it interference?how?
http://imageshack.us/photo/my-images/832/1000pxrefractiononanape.png/

I always thought of an airy disk as a point of constructive interfernce of waves but now I'm very confused :(
hope I'm clear now
Thanks

 

[Misr]

Okay,that's a very good Idea
I imagine that light diffracts when it passes through an obstacle,When light passes through a slit ,each point on the wave front is considered as a secondary source of waves,waves from those secondary sources interfere with each other , bright fringes are produced from constructive interfere -when two crests meet-,dark fringes are produced from destructive interference , but I was shocked when I read the definition of a diffraction fringe in the textbook, which says as I mentioned earlier ,"diffraction fringes are bright regions and dark regions that appear at the edge of the hole image or the shadow of the barrier(or may be the book means the airy disk) ,which indicates that light propagates on the two sides of the hole"
which image?Does an image of the hole is formed when light passes through it?
could you explain that definition if it is correct or give me a simple definition of a diffraction fringe please
and why does diffraction changes by changing the shape of the hole in this picture?
http://imageshack.us/photo/my-images/193/1522d.jpg/

and what causes light to bend in this way?Is it interference?how?
http://imageshack.us/photo/my-images/832/1000pxrefractiononanape.png/

I always thought of an airy disk as a point of constructive interfernce of waves but now I'm very confused :(
hope I'm clear now
Thanks

 

[Andy Resnick]

Does an image of the hole is formed when light passes through it?

Let's start here. The answer is 'no'- making an image requires a lens. Without a lens present, the image is infinitely far away- that is the meaning of 'far-field' diffraction pattern.

So start with a circular hole illuminated by a perfect plane wave and no lens. If you insert a piece of paper at various distances from the hole, what do you expect to see?

For very short distances, the pattern rapidly changes. However, once the paper is a few thousand wavelengths away (a few millimeters or so for visible light), the pattern on the paper only increases in size- the diffraction pattern itself doesn't really change.

That pattern is what you describe in your first picture.

Is this better?

 

[Misr]

Let's start here. The answer is 'no'- making an image requires a lens. Without a lens present, the image is infinitely far away- that is the meaning of 'far-field' diffraction pattern

Which image?The image of the hole itself or the image of a certain object in front of the light source?
According to this , the definition of my school book is completely wrong
I need a simple definition of an airy disk and a diffraction fringe

For very short distances, the pattern rapidly changes. However, once the paper is a few thousand wavelengths away (a few millimeters or so for visible light), the pattern on the paper only increases in size- the diffraction pattern itself doesn't really change.

ok, what makes the pattern become bigger or smaller by changing distance?

 

[Misr]

Is this better?

Yeah ,certainly but I still need more

 

[Andy Resnick]

Which image?The image of the hole itself or the image of a certain object in front of the light source?
According to this , the definition of my school book is completely wrong
I need a simple definition of an airy disk and a diffraction fringe

Hang on there- the hole *is* the source, as far as this discussion is concerned. That is, the source is a circle of light: inside the circle, the electric field has a single amplitude and phase everywhere, and outside of the circle the electric field is zero.

I tried to give a 'simple' definition already, but your idea of 'simple' is different than mine. That's why we now have to make incremental steps. An 'Airy Disc' is the illumination pattern on a screen that our source above produces when the screen is far enough away. Non-circular holes do not produce Airy Discs, they produce other patterns. If the electric field varies within the circle, you do not get an Airy Disc either. You don't need lenses or images; at this point in the discussion those are distractions.

ok, what makes the pattern become bigger or smaller by changing distance?

Geometry- light rays travel in straight lines. If you like, think about shadows- how does the size of your shadow change as you move closer to a source?

 

[Misr]

Hang on there- the hole *is* the source, as far as this discussion is concerned. That is, the source is a circle of light: inside the circle, the electric field has a single amplitude and phase everywhere, and outside of the circle the electric field is zero.

Yes,I see ,but I'm just confused about the definition in the school book,as I mentioned earlier

Geometry- light rays travel in straight lines. If you like, think about shadows- how does the size of your shadow change as you move closer to a source

I don't know how,could you explain?
then the pattern formed is the shadow of the hole?

 

[Andy Resnick]

Yes,I see ,but I'm just confused about the definition in the school book,as I mentioned earlier


I don't know how,could you explain?
then the pattern formed is the shadow of the hole?

I don't know what book you are using, can you provide any information about it?

The diffraction pattern is not simply a 'shadow'- a shadow is a geometrical optics idea, a diffraction pattern is a more detailed description. In various limits (large holes, long distances, etc), the two descriptions converge to each other.

Diffraction explicitly accounts for the wave nature of light, while geometrical optics does not.

 

[Misr]

I don't know what book you are using, can you provide any information about it?

hmmm,the misleading Egyptian curriculum -sorry to say that

The diffraction pattern is not simply a 'shadow'- a shadow is a geometrical optics idea, a diffraction pattern is a more detailed description. In various limits (large holes, long distances, etc), the two descriptions converge to each other.

Could you explain more about diffraction? You can ignore the idea of the shadow just for now

 

[Andy Resnick]

Could you explain more about diffraction? You can ignore the idea of the shadow just for now

You are on the right track:

I imagine that light diffracts when it passes through an obstacle,When light passes through a slit ,each point on the wave front is considered as a secondary source of waves<snip>

Huygens' principle is the cornerstone of diffraction theory- each point of the wavefront acts as a new source. This, combined with superposition- the total field at a point is the sum of all the individual contributions- tells you the distribution of light 'downstream' from the source.

The general case is extremely difficult to calculate, but with some reasonable assumptions (monochromatic light, a flat aperture for a source, initial plane wave of amplitude '1' within the aperture and '0' elsewhere, etc) the calculation becomes much more simple to perform.

Some basic geometries where a closed-form solution can be readily obtained are a half-plane (diffraction from an edge), a rectangle (sinc(x) = sin(x)/x functions), a circle (Airy disc = J_0(r)/r), a regular array of identical apertures (double slit, multiple slits, etc). Using the assumptions above, the far-field diffraction pattern is given by the Fourier transform of the aperture. For example, if I write the transmission of light through a long slit of width 'b' as f(x) = 1 if |x|<b/2 and 0 if |x|>b/2, then the diffraction pattern is g(w) = b/l*z*sin(w)/w, and 'w' = b*x/(l*z), where 'l' is the wavelength of light, and z the propagation distance. The intensity is the square of the field and is given by [b/l*z]^2*[sin(w)/w]^2

Edit: another assumption is that the intensity does not change in time; diffraction and scattering by short pulses is different due to the finite velocity of light.

 

[Misr]

What kind of knowledge do I need to fully understand this explanation?