Optical Arrangements


The experimental setup for studying the diffuse backscattering of polarized light is illustrated in Figure 2. The laser is a linearly polarized red HeNe laser (wavelength lambda = 632.8 nm) with an approximate output power of 7.5 mW. The absolute direction of polarization was measured using knowledge of Brewster's Law and marked on the face of the laser. Brewster's angle, also called the polarization angle, is the angle whose tangent is the ratio of the transmitting index of refraction to the incident index of refraction \cite{hecht}. At this angle, the reflected light is always linearly polarized perpendicular to the plane of incidence. It follows that when the incident light is linearly polarized in the plane of incidence, there is essentially no reflection. In determining the polarization of the laser, the laser was directed at a vertical glass slide at Brewster's angle, approximately 57 degrees. At the orientation at which a photodetector indicated the least amount of reflectance, the laser was polarized in the plane of incidence, which in this setup became the vertical direction.

For linearly polarized light, the laser was simply rotated, whereas for circularly polarized light a quarter-wave plate was placed in front of the laser (Polarization Optic 1). The laser light travels parallel to the table until reflected straight downwards by a first surface mirror (Mirror 1) at 45 degrees, relative to the table. The laser passes through a small three millimeter diameter hand-drilled hole in the second mirror (Mirror 2) to strike the surface of the sample, which fills a 7 cm diameter sample container to a depth of about 4 cm. The backscattered light reflects off the bottom of Mirror 2, also an uncoated first surface mirror, and passes through a lens (Lens 1, focal length 30 cm, diameter 10.5 cm). The light then passes through a linear polarizer or quarter-wave plate as needed (Polarization Optic 2), and a small adjustable lens attached to the CCD camera body (Lens 2), and strikes the CCD element of the camera. The laser, linear polarizers, and quarter-wave plates are mounted on rotation stages for easy use.


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During the selection of the mirrors, it was necessary to test that the intensity of the reflected light was independent of the polarization of the incident beam, as intensity control is a key factor in interpreting the image data correctly. This was easily done using a photodetector and voltmeter. Each polarization optic also had to be tested to locate the correct orientations that would result in the desired direction of electric field. The linear polarizers were placed in front of the linearly polarized laser when the laser was arranged to produce light polarized in the plane parallel to the table. This direction was labelled the $x$-axis or horizontal axis for future consistency. A photodetector attached to a voltmeter placed after the polarizer could indicate the orientation of the polarizer which admitted the least about of light. At this orientation, the polarizer was labelled to be oriented to admit only electric fields parallel to y-axis or vertical axis. The quarter wave plates were more difficult to characterize. One at a time, they were placed directly in front of the laser, which was turned to produce vertically polarized light. After the wave plate was a linear polarized already tested, turned to allow only horizontally polarized light. At the point where a photodetector indicated the least amount of laser light passed through both elements, the quarter-wave plate did not have any effect on the polarization of the light. Therefore it was oriented so that electric field was parallel to either the fast or slow axis of the plate. While knowing which axis was truly parallel to the vertical electric field of the polarized laser light would allow the handedness to be known of the circularly polarized admitted light, it is not essential to find this out. Our definition of any axis or direction is completely arbitrary; there is no standard for naming directions of polarization.

Some standards were adopted in order to have a consistent procedure for the experimentation. It was decided that the polarization of the laser would be determined as if the viewer was standing behind the laser looking towards the rest of the setup. The polarizers and quarter wave plates would also be uniformly arranged so the 360 degree rotation stage would face away from the laser.

While the image created by the scattered light focused through the large lens (Lens 1 in Figure 2) is accurate in orientation, the image is magnified because the image distance is approximately twice the object distance. In Figure 3, a piece of graph paper was placed in the setup where the scattering medium usually is, at the same height as the typical sample height. A sheet of white paper was placed at the image plane (where the image comes into focus) and a ruler was placed next the paper as a scale for later reference. The graph paper at the sample position was illuminated with a strong light and a conventional consumer-type digital camera (Sony Mavica) was used to take a picture of the image projected on to the white paper screen. The graph paper contained the usual 1/4-inch square boxes, and the image shows one box at the image plane as approximately 1/2-inch square, as expected.


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Figure 4 also shows an image of a ruler placed in the image plane, but this time the picture was taken with the Electrim scientific CCD camera (see below) in the standard position used in the experiments, with the camera carefully focused on the ruler. The box around the ruler shows the actual borders of the image, and hence -- together with Figure 3 -- establishes a calibration of the field of view at the surface of the sample.


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