Imagine that you have a cosine transmission grating (i.e. a transparency whose a

Question

Imagine that you have a cosine transmission grating (i.e. a transparency whose amplitude transmission profile is cosinusoidally varying between 0 and 1) with a spatial period of 0.01mm. The grating is illuminated by monochromatic plane waves of lambda = 500nm. The grating is in the object plane of a 4f spatial filter with 2m focal length lenses. a) Discuss the diffraction pattern and design a filter for the Fourier plane that will pass only the first order diffraction peaks. Give numbers for the design. b) What will the image look like in the image plane with that filter in place?

Explanation / Answer

The diffraction pattern will be the Fourier transform of the aperture chosen.

So, the intensity distribution on the screen will be the fourier transform of the intensity distribution at the aperture.

Fourier transform, general tells out the range of continuous frequencies present in the given signal.

Since the spatial frequency of the input intensity is distinct and singular therefore, the fourier transform will be a dirac delta function at that spatial frequency. So, for this experiment, the image obtained will be a singular line denoting that there exists only one spatial frequency in the aperture.

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