Does a diffraction grating with a shape form fourier image

  • #1
9
0

Main Question or Discussion Point

i just wanted to get this cleared that a beam falling on a diffraction grating with a shape gives the fourier images of the grating object which can be reobtained by placing a biconvex lens that would converge the rays and form a focussed fourier image at its focal length and the image of the object at other points.
please correct me if i have misunderstood any phenomenon above
and is there any relation between the grating lines and the fourier image? how can i calculate the transfer function of the lens?
 

Answers and Replies

  • #2
blue_leaf77
Science Advisor
Homework Helper
2,629
784
FT relation between object and its image holds true only in far-field region and paraxial rays. The far-field image will give you the FT of the grating object if the used grating upstream was illuminated with plane wave, otherwise the far-field image will be the FT of the field just after the grating (i.e. product between incoming beam and grating transmission function). For the effect of placing a lens, I suggest this file: http://users.ece.utexas.edu/~becker/FOch5-6.pdf

is there any relation between the grating lines and the fourier image?
To obtain this relation you have to calculate the FT of the grating lines arrangement.
 
  • #3
9
0
FT relation between object and its image holds true only in far-field region and paraxial rays. The far-field image will give you the FT of the grating object if the used grating upstream was illuminated with plane wave, otherwise the far-field image will be the FT of the field just after the grating (i.e. product between incoming beam and grating transmission function). For the effect of placing a lens, I suggest this file: http://users.ece.utexas.edu/~becker/FOch5-6.pdf


To obtain this relation you have to calculate the FT of the grating lines arrangement.
any particular good book/reference where i can find how to mathematically? thanks for the help
 
  • #4
blue_leaf77
Science Advisor
Homework Helper
2,629
784
Fundamentals of Photonics by Saleh and Teich
 
  • #5
Andy Resnick
Science Advisor
Education Advisor
Insights Author
7,386
1,838
i just wanted to get this cleared that a beam falling on a diffraction grating with a shape gives the fourier images of the grating object which can be reobtained by placing a biconvex lens that would converge the rays and form a focussed fourier image at its focal length and the image of the object at other points.
<snip>
I'm a little confused by your question- do you mean that the diffraction grating was cut into a particular shape, like a circle or paper doll? Alternatively, by 'shape of the grating' do you mean the groove profile?
 
  • #6
9
0
I'm a little confused by your question- do you mean that the diffraction grating was cut into a particular shape, like a circle or paper doll? Alternatively, by 'shape of the grating' do you mean the groove profile?
groove profile, like a cartoon character on the squares, thats all.
 
  • #7
Andy Resnick
Science Advisor
Education Advisor
Insights Author
7,386
1,838
groove profile, like a cartoon character on the squares, thats all.
Thanks, that helps me understand. For example, you may have a laser pointer attachment that projects a square or cartoon character rather than the 'raw beam', right? That attachment is a 2-D phase grating, but if you want to suppress the undiffracted beam as well as undesired diffraction orders, then the grating is nonperiodic.

In any case, the far-field diffraction pattern is the Fourier Transform of the grating transmission. Shining the diffracted beam onto a positive lens (it doesn't have to be biconvex, but it does have to be a positive lens) simply moves the far-field diffraction pattern from infinity to a user-defined plane that is closer and also converts the angular diffraction pattern into a linear diffraction pattern with a conversion factor that involves the focal length of the lens.

Does this help?
 
  • #8
9
0
Thanks, that helps me understand. For example, you may have a laser pointer attachment that projects a square or cartoon character rather than the 'raw beam', right? That attachment is a 2-D phase grating, but if you want to suppress the undiffracted beam as well as undesired diffraction orders, then the grating is nonperiodic.

In any case, the far-field diffraction pattern is the Fourier Transform of the grating transmission. Shining the diffracted beam onto a positive lens (it doesn't have to be biconvex, but it does have to be a positive lens) simply moves the far-field diffraction pattern from infinity to a user-defined plane that is closer and also converts the angular diffraction pattern into a linear diffraction pattern with a conversion factor that involves the focal length of the lens.

Does this help?
yes, thanks
 

Related Threads on Does a diffraction grating with a shape form fourier image

Replies
0
Views
2K
  • Last Post
Replies
1
Views
857
Replies
0
Views
827
Replies
3
Views
2K
  • Last Post
Replies
1
Views
1K
Replies
1
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
9
Views
3K
  • Last Post
Replies
1
Views
474
  • Last Post
Replies
10
Views
1K
Top