PURPOSE: To show simultaneously the Fourier components that pass through the filter and the image.

DESCRIPTION: A laser beam illuminates a fine mesh, with the resultant light passing through a slit onto a beam-splitting mirror. This beam can be viewed directly or it can be focussed by a 20 cm focal length convex lens through a 10X microscope objective lens which displays the result on a screen. Two demonstrations are performed with this setup:

Demo 1: Place the mesh in the laser beam and project its image on the screen at about ten feet with the slit wide open. Flip in the mirror to see all Fourier components. Close the slit until only the central line of dots are seen, then flip in the mirror again. The image is a set of horizontal lines; the vertical lines have been filtered out. See how the images change when the slit is slowly opened and closed.

Demo 2: Rotate the mesh 45 degrees with the slit open, so the image rotates 45 degrees. No horizontal or vertical lines are observed. Flip in the mirror to show that the Fourier components have also rotated. Close the slit until only the central line of dots from Demo 1 are passing through, then flip in the mirror. Observe that the image is a set of horizontal lines. Observe changes in the image when different portions of the Fourier components are passing through.

Cautions: (1) The location of the slit must be far enough from the mesh that far field diffraction has occurred. (2) The position of the microscope objective with respect to the lens and the screen is very critical. Adjust this position carefully until a reasonably sharp image of the mesh is projected onto the screen.


REFERENCES: (PIRA 6Q20.30) See Demonstration Reference File for papers describing spatial filtering and applicatiuon to this experiment.

EQUIPMENT: Laser cart, slide with mesh, symmetric slit, insertable mirror (in lieu of beam splitter) 30cm focal length convex lens, 10X microscope objective lens, screen.

SETUP TIME: 20 min.

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