gaussian - How do I fit my data to an Airy Function in python? -

my code takes image of pinhole aperture , fits data gaussian. using gaussian fit calculates full-width @ half maximum. tells me resolution of imaging system.

here fit code right now:

according theory pinhole diffraction images, data should correspond airy disk function. completeness want fit data bessel function or airy disk pattern. cannot find packages fit these functions.

here picture using:

you can just make out outer fringes around central bright spot. fringes want account in fit.

import numpy np import scipy.optimize opt import pil pil import imagefilter pylab import *  #defining gaussian def gauss(x, p): # p[0]==mean, p[1]==stdev     return 1.0/(p[1]*np.sqrt(2*np.pi))*np.exp(-(x-p[0])**2/(2*p[1]**2))  im = pil.image.open('c:/documents/user/3000.bmp').convert("l")  #convert array imarr = np.array(im, dtype=float) bg = np.average(imarr)  #find background, subtract imarr = imarr - bg  #get approx coordinates of brightest spot filtering im2 = im.filter(imagefilter.gaussianblur(radius=2)) imarr2 = np.array(im2, dtype=float) tuple = unravel_index(imarr2.argmax(), imarr2.shape)  #find , plot fwhm brightest spot x = np.arange(tuple[1] - 100, tuple[1] + 100, dtype=np.float) y = imarr[tuple[0], tuple[1] - 100:tuple[1] + 100]  y /= ((max(x) - min(x)) / len(x)) * np.sum(y) # renormalize proper gaussian  p0 = [tuple[1], tuple[0]] errfunc = lambda p, x, y: gauss(x, p) - y # distance target function p1, success = opt.leastsq(errfunc, p0[:], args=(x, y))  fit_mu, fit_stdev = p1  fwhm = 2*np.sqrt(2*np.log(2))*fit_stdev print "fwhm", fwhm  plt.plot(x,y) plt.plot(x, gauss(x,p1), lw=3, alpha=.5, color='r') plt.axvspan(fit_mu-fwhm/2, fit_mu+fwhm/2, facecolor='g', alpha=0.5) plt.show()