I tried to fit the curve of the dataset. I used 'Nonlinearmodelfit' function to get the specific fitted equation. Yes, I can get the result, but I am wondering there is a way to improve the result.
This is the dataset, basically {Angle, Intensity}
data={{0.,4852.},{0.0872665,3128.},{0.174533,2686.},{0.261799,6450.},{0.349066,15532.},{0.436332,28730.},{0.523599,42838.},{0.610865,52648.},{0.698132,51744.},{0.785398,66190.},{0.872665,71260.},{0.959931,73682.},{1.0472,67820.},{1.13446,53786.},{1.22173,36626.},{1.309,26750.},{1.39626,28354.},{1.48353,26258.},{1.5708,19888.},{1.65806,19844.},{1.74533,16350.},{1.8326,15732.},{1.91986,12062.},{2.00713,9996.},{2.0944,15350.},{2.18166,17160.},{2.26893,21986.},{2.35619,19248.},{2.44346,22100.},{2.53073,20096.},{2.61799,16962.},{2.70526,15510.},{2.79253,14280.},{2.87979,11278.},{2.96706,7664.},{3.05433,5452.},{3.14159,3114.},{3.22886,1712.},{3.31613,1860.},{3.40339,3510.},{3.49066,7498.},{3.57792,19636.},{3.66519,38690.},{3.75246,56766.},{3.83972,68802.},{3.92699,64136.},{4.01426,74730.},{4.10152,83330.},{4.18879,63400.},{4.27606,48962.},{4.36332,35622.},{4.45059,22414.},{4.53786,15704.},{4.62512,11696.},{4.71239,10184.},{4.79966,9836.},{4.88692,11946.},{4.97419,11496.},{5.06145,13668.},{5.14872,18054.},{5.23599,31018.},{5.32325,37838.},{5.41052,47124.},{5.49779,55154.},{5.58505,46564.},{5.67232,34936.},{5.75959,27916.},{5.84685,22714.},{5.93412,15792.},{6.02139,12696.},{6.10865,8584.},{6.19592,8166.}}
And, These below are the model and parameters that I used.
Model= a + b*Cos[x] + c*Cos[2x] + d*Cos[3x] + e*Cos[4x] + f*Cos[5x] + g*Cos[6x] + h*Sin[x] + i*Sin[2x] + j*Sin[3x] + k*Sin[4x] + l*Sin[5x] + m*Sin[6x]
coeff = {a, b, c, d, e, f, g, h, i, j, k, l, m};
nlm = Normal[NonlinearModelFit[data, model , coeff , x, MaxIterations -> 1000]];
Thank you