A collimated beam suffers from beam waist. When such a beam falls on grating the dispersion does not appear good. But this problem can be solved by the use of cylindrical lens how?
Hi. If I understand the question right, here is what going on:
Grating deflects each spectral component of your beam at a different angle, but if the beam is broad (even colimated) it takes really long distance before different colors separate, so you can visually see it, so dispersion doesn't look good. Once you put a cylindrical lens with long enough focal length before the grating, each color's central ray (chief ray) is still deviated by the same angle as without the lens, but now each color is being focused. So on your screen, if it is placed at the focal plane of your lens, you will see many spots of different colors. The actual distance between spots is same as without the lens, but now the spots are focused, so the wavelength separation is much more apparent.
To conclude: The dispersion of the system is given ONLY by the properties of the grating, so it remains the same. The resolution gets better, so you can see the colors separately.
After broaded the beam, you can try use a pair of lens or clindrical lens with opposite abberation, the effect will be good.
For a grating of a given grooves density, the resolving power is proportional to the number of grooves intercepted by the incident radiation. If the size of the grating is enough larger than the beam waist diameter (and this usually happens) you can use cylinder lenses as a beam expander in the plane of dispersion. Thus, in this plane, you will obtain a beam larger and more collimated impinging on the grating.
Roberto, in order to talk about resolution, you still need the spectrum to be focused after the grating. the physical size of the spot in every color will indeed have inverse dependence on the beam's size on the grating, and focal length of the focusing optics. The distance between spots of two colors will depend on groove density. You can indeed expand your beam before grating, and than use another lens to focus the dispersed beam, or put your grating in the pupil plane of the lens.
Yes, I agree with you Yuri, (except that the spot size will have direct dependence, and not inverse, on the focal length of the focusing lens). But I was speaking of the resolving power (lambda/Delta lambda), that is an intrinsic property of the grating, and it is not, like the resolution, dependent on the optical and mechanical characteristics of the system in which it is used. For a given groove density, the incident beam should intercept the highest possible number of grooves to improve the theoretical limit of resolution.
Sibashish, At given incident angle (theta) and diffraction agnle (phi), the resolution (R) of grating is proprtional to its length (W). That is R=W(sin(theta)+sin(phi))/lambda. If w=50mm, R=6x10^4 is common. Elliptic beam after a cylindrical lens enhances the resolution of the grating. Shigeo
Sibasish, Basic idea behind my answer is that the spectral linewidth of grating is analogous to the linewidth of the multiple beam interference pattern after multiple slits, which becomes sharper and sharper when the number of relevant slits is increased. Shigeo
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