Fitting a 2D Gaussian function using scipy.optimize.curve_fit - ValueError and minpack.error

Question

I intend to fit a 2D Gaussian function to images showing a laser beam to get its parameters like FWHM and position. So far I tried to understand how to define a

Answer 1

To expand on Dietrich's answer a bit, I got the following error when running the suggested solution with Python 3.4 (on Ubuntu 14.04):

def twoD_Gaussian((x, y), amplitude, xo, yo, sigma_x, sigma_y, theta, offset):
                  ^
SyntaxError: invalid syntax

Running 2to3 suggested the following simple fix:

def twoD_Gaussian(xdata_tuple, amplitude, xo, yo, sigma_x, sigma_y, theta, offset):
    (x, y) = xdata_tuple                                                        
    xo = float(xo)                                                              
    yo = float(yo)                                                              
    a = (np.cos(theta)**2)/(2*sigma_x**2) + (np.sin(theta)**2)/(2*sigma_y**2)   
    b = -(np.sin(2*theta))/(4*sigma_x**2) + (np.sin(2*theta))/(4*sigma_y**2)    
    c = (np.sin(theta)**2)/(2*sigma_x**2) + (np.cos(theta)**2)/(2*sigma_y**2)   
    g = offset + amplitude*np.exp( - (a*((x-xo)**2) + 2*b*(x-xo)*(y-yo)         
                        + c*((y-yo)**2)))                                   
    return g.ravel()

The reason for this is that automatic tuple unpacking when it is passed to a function as a parameter has been removed as of Python 3. For more information see here: PEP 3113