Cameras and Lenses
Of lenses and diffractive gratings
I know there are some very clever optics experts here in the forum so I post this question hoping we get some discussion and may be an answer. I was reading some standard text on optics (Hecht) and these question came to my mind:
Q1: Imagine that a narrow beam of white light hits a diffraction grating (transmission type) and gets diffracted into various angles depending on diffraction mode and wavelength. If we put a lens after the grating, can the lense get these differacted beams and focus them back into ONE SPOT?
My answer: I think it should since an ideal lens sould bring light rays into the same focus regardless of wavelength. Since all the differacted rays originate from some spot on the grating, they should come to same focus after the lens.
Q2 (extention of question 1): Imagine that we form an image on a transmission type diffractive grating. Can we reconstruct the image again after the grating using another lens?
My answer: I think it should be posible except for some light loss and some color fringes near the edges of the image since the second lens can not pick up all the diffracted rays for those areas.
Am I wright or wrong? Just trigured my curiosity.. I hope you guys find it interesting and help me with the answer! 
Hi Omid;
I do not think a lens will be able to converge the elements. Been a long time since I studied gratings though.
Gratings work by dispersing the individual wavelengths (factors controlled by the pitch of the grooves, number density of grooves and incident angle) into progressive angle increments. These are spread in wavelength order and not angle to optical axis like an image. Since none of the wavelengths (except one) are parallel to the optical axis, they will not be refracted to a common point by a single refractive index.
A 500/lmm grating will spread a shorter distance, but brighter than a 1000/lmm grating, and easier to see, but harder to measure exact wavelength.
If you look through a simple spectroscopy you will see a spread out line. The eye will not try to focus back to a spot and I do not think a single refractive lens will either.
If I have time, I will try to set this up tonight when I get home and focus with a 200 mm lens and take a picture for you.
Also, if you PM me your address, I can send you a cheap 500/lmm or 1000/lmm film grating to experiment with.
I picture attached is with a camera lens, but I do not remember if there was a relay lens inline or not.
Thanks for your quick answer Ron!
I got so curious that I went home at lunch time and started testing my theory with a CD (= a reflective grating) and a lens. I couldn't focus the rainbow colors reflected from the CD back into a "white" spot using a lens but it still doesn't refute the theory.
Maybe my mistake is that a diffractive grating doesn't work on a "narrow beam" basis (as shown in my top drawing). The diffraction principle is that a "wide beam" should hit the whole surface of the DOE, then get differacted at various angles?? But then even if this is true, each diffracted color (say blue) emerges at a certain dgree. Let's assume that clue goes to +- 30 degreea and red to +-15 degrees. Isn't there a common "hypotetical emegance point" that we can say both of these beams came from? If there is such a point then a lens sould be able to pick both rays up and focus them at the same point.
now I am fully confused...
