N RS1 Numerical calculation A Analytical calculation (equation 12) N 1.22 2.24 3.25 4.26 5.26 A 1.22 2.23 3.24 4.24 5.24 * uncertainty = 0.01 vP Table 12. Positions and relative values for the peak in the irradiance distribution vP/ RS1 Numerical calculation Analytical calculation (equation 12) N A N 1.64 2.69 3.71 4.72 5.74 uP N 0.0176 0.0042 0.0016 0.0008 0.0004 peaks A 1.63 2.68 3.70 4.71 5.72 uP A 0.0175 0.0042 0.0016 0.0008 0.0004 peaks * uncertainty = 0.01 vP The figure (12) and the results in Tables 11 and 12 clearly shows the excellent agreement between the numerical computation of the RS1 diffraction integral and the predictions using the Debye approximation. The irradiance distribution has a central bright spot called the Airy disk and it is surrounded by circular bright rings of rapidly decreasing strength which are separated by dark rings as shown in figure (13). Figure (14) shows the radiant flux enclosed with circles of increasing radius in the observation plane. The radiant flux emitted from the aperture pupil must equal the radiant flux through the observation plane because of conservation of energy. By the focussing action of the optical system modelled, most of the energy is concentrated into the Airy disk with 84% of the radiant flux within the first dark ring. Changing the Fresnel number to = 15.80 by increasing the focal length to = NF f 10.00 m does not change the irradiance distribution as a function of the radial coordinate However, the radius of the Airy disk expressed in meters is much vP. larger as shown in figure (15) as compared to figure (12). The location of the first minimum: = 1580 min) = 3.910-6 m NF rP(1st = 15.80 min) = 3.910-4 m NF rP(1st Fig. 14. The radial irradiance in the plane. = 632.8 nm = 0.01 m = 10.00 m = 15.80 = 0.100 a f NF N.A.
N RS1 Numerical calculation A Analytical calculation (equation 12) N 1.22 2.24 3.25 4.26 5.26 A 1.22 2.23 3.24 4.24 5.24 * uncertainty vP = 0.01 Table 12. Positions vP/ and relative values for the peak in the irradiance distribution N RS1 Numerical calculation A Analytical calculation (equation 12) N uP 1.64 2.69 3.71 4.72 5.74 N peaks 0.0176 0.0042 0.0016 0.0008 0.0004 A uP 1.63 2.68 3.70 4.71 5.72 A peaks 0.0175 0.0042 0.0016 0.0008 0.0004 * uncertainty vP = 0.01 The figure (12) and the results in Tables 11 and 12 clearly shows the excellent agreement between the numerical computation of the RS1 diffraction integral and the predictions using the Debye approximation. The irradiance distribution has a central bright spot called the Airy disk and it is surrounded by circular bright rings of rapidly decreasing strength which are separated by dark rings as shown in figure (13). Figure (14) shows the radiant flux enclosed with circles of increasing radius in the observation plane. The radiant flux emitted from the aperture pupil must equal the radiant flux through the observation plane because of conservation of energy. By the focussing action of the optical system modelled, most of the energy is concentrated into the Airy disk with 84% of the radiant flux within the first dark ring. Changing the Fresnel number to NF = 15.80 by increasing the focal length to f = 10.00 m does not change the irradiance distribution as a function of the radial coordinate vP. However, the radius of the Airy disk expressed in meters is much larger as shown in figure (15) as compared to figure (12). The location of the first minimum: NF = 1580 rP(1st min) = 3.910-6 m NF = 15.80 rP(1st min) = 3.910-4 m Fig. 14. The radial irradiance in the plane. = 632.8 nm a = 0.01 m f = 10.00 m NF = 15.80 N.A. = 0.100
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