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JamesJames
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I've been reading some stuff on Fourier Optics (Johnson, Optics) and have become quite interested in how Fourier transforms can be used to explain so much. But I have stumbled on something thta is confusing me.
Two students perform a "Fourier Optics" experiment to explore Fourier transform analysis in relation to Experimental Physics. The He-Ne laser used in the experiment is focused onto a 10 micrometer pinhole with adjustable micrometer screws. Three identical lenses are provided inorder to realize 4f-focussing. They all have a focal length of 350 mm. The first lens acts as a condenser to provide a parallel uniformly illuminated beam. The second lens produces a Fourier image in the focal plane (where low pass filtering can be applied using an aperture). The third lens is used to convert the modified Fourier image again into a normal filtered inverted image.
A grid shaped ruling was placed between the condenser and imaging lens. The image was to be observed in the Fourier plane as well as in the image plane. Slits of different widths were placed in the focal plane to cut out high Fourier components first in the horizontal and then in the vertical planes.
Here’ s my question: Would it be possible to completely remove one set of lines and if the slit was rotated in the Fourier plane by 45 degrees what would be observed?
Here’ s the way I see it: A slit of certain width can used to block higher frequency components. The slit could be aligned with a vertical axis, and completely shuts out frequency components along another axis. The produced image in the Image plane would consist of only horizontal lines, since the diffractive pattern of Ronchi rulings is perpendicular to the plane of the rulings.
Next, the students inserted an image slide into the holder and a low pass filter was used to remove the graininess. Here’s what I think: I have read and understood that a low-pass filtered image would be blurred, but preserves the low frequency broad smooth regions of dark and bright and losing the sharp contours and crisp edges. Mathematically, low-pass filtering is equivalent to an optical blurring function.
How could mathematical analysis (just a broad description of the procedure) be used to explain the recorded images?
James
Two students perform a "Fourier Optics" experiment to explore Fourier transform analysis in relation to Experimental Physics. The He-Ne laser used in the experiment is focused onto a 10 micrometer pinhole with adjustable micrometer screws. Three identical lenses are provided inorder to realize 4f-focussing. They all have a focal length of 350 mm. The first lens acts as a condenser to provide a parallel uniformly illuminated beam. The second lens produces a Fourier image in the focal plane (where low pass filtering can be applied using an aperture). The third lens is used to convert the modified Fourier image again into a normal filtered inverted image.
A grid shaped ruling was placed between the condenser and imaging lens. The image was to be observed in the Fourier plane as well as in the image plane. Slits of different widths were placed in the focal plane to cut out high Fourier components first in the horizontal and then in the vertical planes.
Here’ s my question: Would it be possible to completely remove one set of lines and if the slit was rotated in the Fourier plane by 45 degrees what would be observed?
Here’ s the way I see it: A slit of certain width can used to block higher frequency components. The slit could be aligned with a vertical axis, and completely shuts out frequency components along another axis. The produced image in the Image plane would consist of only horizontal lines, since the diffractive pattern of Ronchi rulings is perpendicular to the plane of the rulings.
Next, the students inserted an image slide into the holder and a low pass filter was used to remove the graininess. Here’s what I think: I have read and understood that a low-pass filtered image would be blurred, but preserves the low frequency broad smooth regions of dark and bright and losing the sharp contours and crisp edges. Mathematically, low-pass filtering is equivalent to an optical blurring function.
How could mathematical analysis (just a broad description of the procedure) be used to explain the recorded images?
James