Table I
First Five Zeros of J1(x) − ɛJ1(ɛx)
| zeros |
---|
|
|
---|
ɛ | 1st | 2nd | 3rd | 4th | 5th |
---|
|
|
---|
0 | 3.8317 | 7.0156 | 10.1735 | 13.3268 | 16.4706 |
0.5 | 3.1444 | 7.1832 | 10.9646 | 12.9529 | 15.8734 |
0.8 | 2.6665 | 6.1204 | 9.5941 | 13.0705 | 16.5473 |
Table II
First Five Zeros of J2(x) − ɛ2J2(ɛx)
| zeros |
---|
|
|
---|
ɛ | 1st | 2nd | 3rd | 4th | 5th |
---|
|
|
---|
0 | 5.1356 | 8.4172 | 11.6198 | 14.7959 | 17.9598 |
0.5 | 4.8226 | 8.6723 | 11.8723 | 14.4595 | 17.7965 |
0.8 | 4.2311 | 7.7454 | 11.2282 | 14.6975 | 18.1552 |
Table III
First Three Radii of the Zeros, Maxima, and the Smallest Radius for Which E > 0.9 of the Airy Disk Diffraction Pattern for ɛ = 0, λ = 600 nm
| R × 104(mm) |
---|
|
|
---|
| zeros | maxima | |
---|
|
|
| |
---|
N | 1st | 2nd | 3rd | 1st | 2nd | 3rd | E(>.9) |
---|
|
|
| |
---|
1.5 | 10.98 | 20.10 | 29.14 | 14.71 | 24.11 | 33.29 | 18.00 |
2 | 14.64 | 26.80 | 38.86 | 19.62 | 32.15 | 44.38 | 23.00 |
2.5 | 18.30 | 33.50 | 48.57 | 24.52 | 40.19 | 55.48 | 29.00 |
3 | 21.95 | 40.20 | 58.29 | 29.42 | 48.23 | 66.58 | 35.00 |
3.5 | 25.61 | 46.90 | 68.00 | 34.33 | 56.27 | 77.67 | 40.00 |
4 | 29.27 | 53.60 | 77.72 | 39.23 | 64.30 | 88.77 | 48.00 |
4.5 | 32.93 | 60.29 | 87.43 | 44.14 | 72.34 | 99.87 | 52.00 |
5.6 | 40.98 | 75.03 | 108.81 | 54.93 | 90.02 | 124.28 | 64.00 |
6.3 | 46.10 | 84.41 | 122.41 | 61.79 | 101.28 | 139.81 | 72.00 |
8 | 58.54 | 107.19 | 155.44 | 78.47 | 128.61 | 177.54 | 92.00 |
11 | 80.50 | 147.39 | 213.73 | 107.89 | 176.83 | 244.11 | 130.00 |
16 | 117.09 | 214.38 | 310.88 | 156.93 | 257.21 | 355.08 | 190.00 |
22 | 161.00 | 294.77 | 427.46 | 215.78 | 353.67 | 488.23 | 260.00 |
Table IV
First Three Radii of the Zeros, Maxima, and the smallest Radius for Which E > 0.9 of the Airy Disk Diffraction Pattern for ɛ = 0.3, λ = 600 nm
| R × 104(mm) |
---|
|
|
---|
| zeros | maxima | |
---|
|
|
| |
---|
N | 1st | 2nd | 3rd | 1st | 2nd | 3rd | E(>.9) |
---|
|
|
| |
---|
1.5 | 10.03 | 21.82 | 27.86 | 14.53 | 24.55 | 32.77 | 24.00 |
2 | 13.37 | 29.09 | 37.15 | 19.38 | 32.74 | 43.70 | 32.00 |
2.5 | 16.72 | 36.36 | 46.43 | 24.22 | 40.92 | 54.62 | 39.00 |
3 | 20.06 | 43.63 | 55.72 | 29.07 | 49.10 | 65.54 | 47.00 |
3.5 | 23.40 | 50.91 | 65.01 | 33.91 | 57.29 | 76.47 | 56.00 |
4 | 26.75 | 58.18 | 74.29 | 38.76 | 65.47 | 87.39 | 64.00 |
4.5 | 30.09 | 65.45 | 83.58 | 43.60 | 73.66 | 98.32 | 72.00 |
5.6 | 37.45 | 81.45 | 104.01 | 54.26 | 91.66 | 122.35 | 68.00 |
6.3 | 42.13 | 91.63 | 117.01 | 61.04 | 103.12 | 137.64 | 100.00 |
8 | 53.50 | 116.36 | 148.59 | 77.51 | 130.94 | 174.79 | 128.00 |
11 | 73.56 | 159.99 | 204.31 | 106.58 | 180.05 | 240.33 | 180.00 |
16 | 106.99 | 232.71 | 297.17 | 155.02 | 261.89 | 349.57 | 250.00 |
22 | 147.12 | 319.98 | 408.62 | 213.15 | 360.09 | 480.66 | 350.00 |
Table V
First Three Radii of the Zeros, Maxima, and the Smallest Radius for Which E > 0.9 of the Air Disk Diffraction Pattern for ɛ = 0.5, λ = 600 nm
| R × 104(mm) |
---|
|
|
---|
| zeros | maxima | |
---|
|
|
| |
---|
N | 1st | 2nd | 3rd | 1st | 2nd | 3rd | E(>.9) |
---|
|
|
| |
---|
1.5 | 9.01 | 20.58 | 31.41 | 13.82 | 24.84 | 34.01 | 30.00 |
2 | 12.01 | 27.44 | 41.88 | 18.42 | 33.13 | 45.35 | 40.00 |
2.5 | 15.01 | 34.30 | 52.35 | 23.03 | 41.41 | 56.69 | 49.00 |
3 | 18.02 | 41.16 | 62.82 | 27.63 | 49.69 | 68.02 | 59.00 |
3.5 | 21.02 | 48.02 | 73.29 | 32.24 | 57.97 | 79.36 | 72.00 |
4 | 24.02 | 54.88 | 83.76 | 36.84 | 66.25 | 90.70 | 80.00 |
4.5 | 27.02 | 61.74 | 94.23 | 41.45 | 74.53 | 102.04 | 88.00 |
5.6 | 33.63 | 76.83 | 117.27 | 51.58 | 92.75 | 126.98 | 112.00 |
6.3 | 37.83 | 86.43 | 131.93 | 58.03 | 104.35 | 142.85 | 124.00 |
8 | 48.04 | 109.75 | 167.53 | 73.68 | 132.50 | 181.40 | 160.00 |
11 | 66.06 | 150.91 | 230.35 | 101.32 | 182.19 | 249.42 | 220.00 |
16 | 96.09 | 219.50 | 335.05 | 147.37 | 265.01 | 362.79 | 320.00 |
22 | 132.12 | 301.82 | 460.70 | 202.63 | 364.39 | 498.84 | 430.00 |
Table VI
First Three Radii of the Zeros, Maxima, and the Smallest Radius for Which E > 0.9 of the Airy Disk Diffraction Pattern for ɛ = 0.7, λ = 600 nm
| R × 104(mm) |
---|
|
|
---|
| zeros | maxima | |
---|
|
|
| |
---|
N | 1st | 2nd | 3rd | 1st | 2nd | 3rd | E(>.9) |
---|
|
|
| |
---|
1.5 | 8.06 | 18.50 | 28.99 | 12.71 | 23.25 | 33.62 | 53.00 |
2 | 10.15 | 24.67 | 38.65 | 16.95 | 30.99 | 44.83 | 70.00 |
2.5 | 13.44 | 30.84 | 48.31 | 21.19 | 38.74 | 56.04 | 88.00 |
3 | 16.12 | 37.00 | 57.97 | 25.42 | 46.49 | 67.25 | 108.00 |
3.5 | 18.81 | 43.17 | 67.63 | 29.66 | 54.24 | 78.45 | 124.00 |
4 | 21.50 | 49.34 | 77.29 | 33.90 | 61.99 | 89.66 | 140.00 |
4.5 | 24.19 | 55.50 | 86.96 | 38.14 | 69.74 | 100.87 | 160.00 |
5.6 | 30.10 | 69.07 | 108.21 | 47.46 | 86.79 | 125.53 | 196.00 |
6.3 | 33.86 | 77.71 | 121.74 | 53.39 | 97.63 | 141.22 | 224.00 |
8 | 43.00 | 98.67 | 154.59 | 67.80 | 123.98 | 179.32 | 280.00 |
11 | 59.12 | 135.68 | 212.56 | 93.22 | 170.47 | 246.57 | 390.00 |
16 | 86.00 | 197.35 | 309.17 | 135.59 | 247.96 | 358.65 | 560.00 |
22 | 118.25 | 271.35 | 425.11 | 186.44 | 340.94 | 493.14 | 780.00 |
Table VII
First Three Radii of the Zeros and Maxima of the Airy Disk Diffraction Pattern for N = 1.5, λ = 600 nm
| R × 104(mm) |
---|
|
|
---|
| zeros | maxima |
---|
|
|
|
---|
ɛ | 1st | 2nd | 3rd | 1st | 2nd | 3rd |
---|
|
|
|
---|
0 | 10.98 | 20.10 | 29.14 | 14.71 | 24.11 | 33.29 |
0.1 | 10.85 | 20.42 | 28.64 | 14.71 | 24.12 | 33.27 |
0.2 | 10.50 | 21.21 | 27.80 | 14.67 | 24.23 | 33.08 |
0.3 | 10.03 | 21.82 | 27.86 | 14.53 | 24.55 | 32.77 |
0.4 | 9.52 | 21.49 | 29.71 | 14.25 | 24.92 | 32.92 |
0.5 | 9.01 | 20.58 | 31.41 | 13.82 | 24.84 | 34.01 |
0.6 | 8.52 | 19.53 | 30.50 | 13.29 | 24.20 | 34.57 |
0.7 | 8.06 | 18.50 | 28.99 | 12.71 | 23.25 | 33.62 |
Table VIII
First Three Radii of the Zeros and Maxima of the Airy Disk Diffraction Pattern for N = 4, λ = 600 nm
| R × 104(mm) |
---|
|
|
---|
| zeros | maxi ma |
---|
|
|
|
---|
ɛ | 1st | 2nd | 3rd | 1st | 2nd | 3rd |
---|
|
|
|
---|
0 | 29.27 | 53.60 | 77.72 | 39.23 | 64.30 | 88.77 |
0.1 | 28.92 | 54.45 | 76.38 | 39.23 | 64.33 | 88.72 |
0.2 | 28.00 | 56.57 | 74.12 | 39.13 | 64.62 | 88.22 |
0.3 | 26.75 | 58.18 | 74.29 | 38.76 | 65.47 | 87.39 |
0.4 | 25.38 | 57.31 | 79.22 | 37.99 | 66.44 | 87.80 |
0.5 | 24.02 | 54.88 | 83.76 | 36.84 | 66.25 | 90.70 |
0.6 | 22.72 | 52.08 | 81.33 | 35.44 | 64.54 | 92.19 |
0.7 | 21.50 | 49.34 | 77.29 | 33.90 | 61.99 | 89.66 |
Table IX
First Three Radii of the Zeros and Maxima of the Air Disk Diffraction Pattern for N = 8, λ 600 nm
| R × 104(mm) |
---|
|
|
---|
| zeros | maxima |
---|
|
|
|
---|
ɛ | 1st | 2nd | 3rd | 1st | 2nd | 3rd |
---|
|
|
|
---|
0 | 58.54 | 107.19 | 155.44 | 78.47 | 128.61 | 177.54 |
0.1 | 57.84 | 108.91 | 152.76 | 78.45 | 128.65 | 177.44 |
0.2 | 55.99 | 113.15 | 148.25 | 78.25 | 129.24 | 176.45 |
0.3 | 53.50 | 116.36 | 148.59 | 77.51 | 130.94 | 174.79 |
0.4 | 50.77 | 114.61 | 158.43 | 75.98 | 132.88 | 175.59 |
0.5 | 48.04 | 109.75 | 167.53 | 73.68 | 132.50 | 181.40 |
0.6 | 45.44 | 104.16 | 162.65 | 70.87 | 129.07 | 184.38 |
0.7 | 43.00 | 98.67 | 154.59 | 67.80 | 123.98 | 179.32 |
Table X
First Three Radii of the Zeros and Maxima of the Airy Disk Diffraction Pattern for N = 22, λ = 600 nm
| R × 104(mm) |
---|
|
|
---|
| zeros | maxima |
---|
|
|
|
---|
ɛ | 1st | 2nd | 3rd | 1st | 2nd | 3rd |
---|
|
|
|
---|
0 | 161.00 | 294.77 | 427.46 | 215.78 | 353.67 | 488.23 |
0.1 | 159.07 | 299.50 | 420.08 | 215.74 | 353.80 | 487.96 |
0.2 | 153.98 | 311.15 | 407.68 | 215.19 | 355.40 | 485.23 |
0.3 | 147.12 | 319.98 | 408.62 | 213.15 | 360.09 | 480.66 |
0.4 | 139.61 | 315.18 | 435.69 | 208.93 | 365.43 | 482.88 |
0.5 | 132.12 | 301.82 | 460.70 | 202.63 | 364.39 | 498.84 |
0.6 | 124.96 | 286.45 | 447.29 | 194.90 | 354.95 | 507.03 |
0.7 | 118.25 | 271.35 | 425.11 | 186.44 | 340.94 | 493.14 |