# Welcome to the Sir George Airy diffraction Pattern Bessel function interpolation problem
#  Data from the bessel function table given below will be used to interpolate the Airy function, I = I0 [2*J1(r)/r]^2
#          r	        J0(r)	         J1(r)	         J2(r)
# 0	1	0	0
# 1	0.765198	0.440051	0.114903
# 2	0.223891	0.576725	0.352834
# 3	-0.260052	0.339059	0.486091
# 4	-0.39715	-0.0660433	0.364128
# 5	-0.177597	-0.327579	0.0465651
# 6	0.150645	-0.276684	-0.242873
# 7	0.300079	-0.00468282	-0.301417
# 8	0.171651	0.234636	-0.112992
# 9	-0.0903336	0.245312	0.144847
# 10	-0.245936	0.0434727	0.25463

# The relative intensity (I/I0) as a function of r across the airy diffraction pattern is given by the following data points
0	-1.#IND
0.1	1.23808
0.2	1.18535
0.3	1.13277
0.4	1.08039
0.5	1.02829
0.6	0.976549
0.7	0.92523
0.8	0.874411
0.9	0.824168
1	0.774578
1.1	0.725721
1.2	0.677676
1.3	0.630524
1.4	0.58435
1.5	0.539236
1.6	0.495268
1.7	0.452532
1.8	0.411118
1.9	0.371114
2	0.332612
2.1	0.290973
2.2	0.252294
2.3	0.216683
2.4	0.184179
2.5	0.154765
2.6	0.128387
2.7	0.104954
2.8	0.0843521
2.9	0.0664481
3	0.0510938
3.1	0.0376991
3.2	0.026708
3.3	0.017933
3.4	0.011173
3.5	0.00621842
3.6	0.00285546
3.7	0.000869884
3.8	5.00661e-005
3.9	0.000189762
4	0.00109043
4.1	0.00244874
4.2	0.00414733
4.3	0.00605225
4.4	0.00804626
4.5	0.0100277
4.6	0.0119095
4.7	0.0136184
4.8	0.0150945
4.9	0.01629
5	0.0171693
5.1	0.0172631
5.2	0.0170475
5.3	0.0165545
5.4	0.0158199
5.5	0.014882
5.6	0.0137802
5.7	0.0125537
5.8	0.0112414
5.9	0.00988036
6	0.008506
6.1	0.00700355
6.2	0.00559364
6.3	0.00430804
6.4	0.00317124
6.5	0.00220062
6.6	0.00140678
6.7	0.000794043
6.8	0.000360885
6.9	0.000100579
7	1.79011e-006
7.1	4.55269e-005
7.2	0.000209175
7.3	0.000473936
7.4	0.000819824
7.5	0.00122611
7.6	0.00167178
7.7	0.00213593
7.8	0.00259821
7.9	0.00303922
8	0.00344089
8.1	0.00368125
8.2	0.0038545
8.3	0.00395877
8.4	0.00399426
8.5	0.00396297
8.6	0.00386845
8.7	0.00371559
8.8	0.0035104
8.9	0.00325986
9	0.00297175
9.1	0.00265451
9.2	0.00231715
9.3	0.00196907
9.4	0.00162006
9.5	0.00128011
9.6	0.000959423
9.7	0.00066829
9.8	0.000417056
9.9	0.000216061
10	7.55952e-005

# The relative intensity calculated using a cubic Hermite interpolation algorithm
0	1
0.1	0.997329
0.2	0.9895
0.3	0.976793
0.4	0.959484
0.5	0.937852
0.6	0.912176
0.7	0.882732
0.8	0.849799
0.9	0.813655
1	0.774578
1.1	0.733101
1.2	0.68986
1.3	0.64529
1.4	0.599827
1.5	0.553903
1.6	0.507956
1.7	0.462418
1.8	0.417725
1.9	0.374311
2	0.332612
2.1	0.293082
2.2	0.255929
2.3	0.221208
2.4	0.188977
2.5	0.159293
2.6	0.132214
2.7	0.107798
2.8	0.0861005
2.9	0.0671801
3	0.0510938
3.1	0.0377189
3.2	0.0267565
3.3	0.0179999
3.4	0.0112421
3.5	0.00627646
3.6	0.00289604
3.7	0.000894045
3.8	6.36592e-005
3.9	0.000198061
4	0.00109043
4.1	0.00247066
4.2	0.00414552
4.3	0.00602349
4.4	0.00801307
4.5	0.0100227
4.6	0.011961
4.7	0.0137362
4.8	0.0152571
4.9	0.0164319
5	0.0171693
5.1	0.0174565
5.2	0.017371
5.3	0.0169563
5.4	0.0162563
5.5	0.0153144
5.6	0.0141744
5.7	0.01288
5.8	0.0114746
5.9	0.0100021
6	0.008506
6.1	0.00706037
6.2	0.00571749
6.3	0.00448843
6.4	0.00338427
6.5	0.00241606
6.6	0.00159487
6.7	0.000931787
6.8	0.000437864
6.9	0.000124176
7	1.79011e-006
7.1	4.95928e-005
7.2	0.000223911
7.3	0.000501978
7.4	0.000861025
7.5	0.00127828
7.6	0.00173099
7.7	0.00219637
7.8	0.00265166
7.9	0.00307409
8	0.00344089
8.1	0.00372777
8.2	0.00392859
8.3	0.0040478
8.4	0.00408987
8.5	0.00405924
8.6	0.00396038
8.7	0.00379775
8.8	0.00357579
8.9	0.00329897
9	0.00297175
9.1	0.00261436
9.2	0.00224968
9.3	0.00188609
9.4	0.00153196
9.5	0.00119569
9.6	0.000885658
9.7	0.000610248
9.8	0.000377845
9.9	0.000196833
10	7.55952e-005

# The cross section of the scattering has a zero at : 3.83371