Schematic of the experimental arrangement showing the spatial filter and beam expander for the laser, the single or double slit to create the aperture function, the filtering slit to transmit the appropriate portion of the diffraction/interference pattern, and the line camera for measuring the diffraction produced by the aperture function.
Double slit irradiance and electric field patterns, both normalized to their maximum values. The aperture functions are created by filtering this pattern. The distance from the double slit to the filtering slit is 197 ± 1 mm. The half-sine aperture function (b to c to d) and the cosine aperture function (c to d to e) both span the 0.25-mm width of the filtering slit. Creating the full-sine aperture function (a to b to c to d to e) requires moving the filtering slit to one-half the distance given above.
The inverted cosine aperture function was created using a 0.80-mm wide single slit with the 0.25-mm wide filtering slit located 156 ± 1 mm away. The parameters were selected to produce a minimum field at the center of the pattern that is 0.62 of the maximum field. The fitted curve is given by for and A(x) = 0 elsewhere, with b = 0.25 mm, , and .
Normalized irradiance for each of the aperture functions measured. Each curve is normalized to one and displaced by one vertical unit so that the irradiance from each aperture function can be compared. The dotted vertical lines are the first zeroes of the uniform aperture function irradiance. The dashed vertical lines at the top of the figure are the first irradiance zeroes for a uniform aperture having a width of 0.125 mm (see discussion in text).
The solid line and the dotted line show how the electric fields of the full-sine aperture function and the half-sine aperture function, respectively, behave within the filtering slit. The electric field zeroes at the center of the filtering slit combined with the edges of the filtering slit create an effective slit width that is one-half the width of the filtering slit.
Aperture Function Characteristics. All aperture functions are defined for the region and are zero elsewhere. The zero-to-zero central irradiance widths are given analytically by and are calculated in position space using the parameters in the experiment to be (see text); values have uncertainties of ± 0.03 mm. The ratio column gives the ratio of the first secondary maximum to the maximum irradiance observed.
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