How to use the aotools.fouriertransform.ft2 function in aotools

ndarray: Output complex amplitude
    '''

    N = Uin.shape[0] #Assume square grid
    k = 2*numpy.pi/wvl  #Optical Wavevector

    #Observation plane coordinates
    fX = numpy.arange( -N/2.,N/2.)/(N*d1)

    #Observation plane coordinates
    x2,y2 = numpy.meshgrid(wvl * f * fX, wvl * f * fX)
    del(fX)

    #Evaluate the Fresnel-Kirchoff integral but with the quadratic
    #phase factor inside cancelled by the phase of the lens
    Uout = numpy.exp( 1j*k/(2*f) * (x2**2 + y2**2) )/ (1j*wvl*f) * fouriertransform.ft2( Uin, d1)

    return Uout

#Observation Plane Co-ords
    x2,y2 = numpy.meshgrid( outputSpacing*numpy.arange(-N/2,N/2),
                            outputSpacing*numpy.arange(-N/2,N/2) )
    r2sq = x2**2 + y2**2

    #Quadratic phase factors
    Q1 = numpy.exp( 1j * k/2. * (1-mag)/z * r1sq)

    Q2 = numpy.exp(-1j * numpy.pi**2 * 2 * z/mag/k*fsq)

    Q3 = numpy.exp(1j * k/2. * (mag-1)/(mag*z) * r2sq)

    #Compute propagated field
    outputComplexAmp = Q3 * fouriertransform.ift2(
                    Q2 * fouriertransform.ft2(Q1 * inputComplexAmp/mag,inputSpacing), df1)
    return outputComplexAmp

"""
    N = Uin.shape[0]    #Assume square grid
    k = 2*numpy.pi/wvl  #optical wavevector

    #Source plane coordinates
    x1,y1 = numpy.meshgrid( numpy.arange(-N/2.,N/2.) * d1,
                            numpy.arange(-N/2.,N/2.) * d1)
    #observation plane coordinates
    d2 = wvl*z/(N*d1)
    x2,y2 = numpy.meshgrid( numpy.arange(-N/2.,N/2.) * d2,
                            numpy.arange(-N/2.,N/2.) * d2 )

    #evaluate Fresnel-Kirchoff integral
    A = 1/(1j*wvl*z)
    B = numpy.exp( 1j * k/(2*z) * (x2**2 + y2**2))
    C = fouriertransform.ft2(Uin *numpy.exp(1j * k/(2*z) * (x1**2+y1**2)), d1)

    Uout = A*B*C

    return Uout

"""
    N = Uin.shape[0]    #Assume square grid
    k = 2*numpy.pi/wvl  #optical wavevector

    #Source plane coordinates
    x1,y1 = numpy.meshgrid( numpy.arange(-N/2.,N/2.) * d1,
                            numpy.arange(-N/2.,N/2.) * d1)
    #observation plane coordinates
    d2 = wvl*z/(N*d1)
    x2,y2 = numpy.meshgrid( numpy.arange(-N/2.,N/2.) * d2,
                            numpy.arange(-N/2.,N/2.) * d2 )

    #evaluate Fresnel-Kirchoff integral
    A = 1/(1j*wvl*z)
    B = numpy.exp( 1j * k/(2*z) * (x2**2 + y2**2))
    C = fouriertransform.ft2(Uin *numpy.exp(1j * k/(2*z) * (x1**2+y1**2)), d1)

    Uout = A*B*C

    return Uout

ndarray: Output complex amplitude
    '''

    N = Uin.shape[0] #Assume square grid
    k = 2*numpy.pi/wvl  #Optical Wavevector

    #Observation plane coordinates
    fX = numpy.arange( -N/2.,N/2.)/(N*d1)

    #Observation plane coordinates
    x2,y2 = numpy.meshgrid(wvl * f * fX, wvl * f * fX)
    del(fX)

    #Evaluate the Fresnel-Kirchoff integral but with the quadratic
    #phase factor inside cancelled by the phase of the lens
    Uout = numpy.exp( 1j*k/(2*f) * (x2**2 + y2**2) )/ (1j*wvl*f) * fouriertransform.ft2( Uin, d1)

    return Uout

#magnification
    m = float(d2)/d1

    #intermediate plane
    try:
        Dz1  = z / (1-m) #propagation distance
    except ZeroDivisionError:
        Dz1 = z / (1+m)
    d1a = wvl * abs(Dz1) / (N*d1) #coordinates
    x1a, y1a = numpy.meshgrid( numpy.arange( -N/2.,N/2.) * d1a,
                              numpy.arange( -N/2.,N/2.) * d1a )

    #Evaluate Fresnel-Kirchhoff integral
    A = 1./(1j * wvl * Dz1)
    B = numpy.exp(1j * k/(2*Dz1) * (x1a**2 + y1a**2) )
    C = fouriertransform.ft2(Uin * numpy.exp(1j * k/(2*Dz1) * (x1**2 + y1**2)), d1)
    Uitm = A*B*C
    #Observation plane
    Dz2 = z - Dz1

    #coordinates
    x2,y2 = numpy.meshgrid( numpy.arange(-N/2., N/2.) * d2,
                            numpy.arange(-N/2., N/2.) * d2 )

    #Evaluate the Fresnel diffraction integral
    A = 1. / (1j * wvl * Dz2)
    B = numpy.exp( 1j * k/(2 * Dz2) * (x2**2 + y2**2) )
    C = fouriertransform.ft2(Uitm * numpy.exp( 1j * k/(2*Dz2) * (x1a**2 + y1a**2)), d1a)
    Uout = A*B*C

    return Uout

#magnification
    m = float(d2)/d1

    #intermediate plane
    try:
        Dz1  = z / (1-m) #propagation distance
    except ZeroDivisionError:
        Dz1 = z / (1+m)
    d1a = wvl * abs(Dz1) / (N*d1) #coordinates
    x1a, y1a = numpy.meshgrid( numpy.arange( -N/2.,N/2.) * d1a,
                              numpy.arange( -N/2.,N/2.) * d1a )

    #Evaluate Fresnel-Kirchhoff integral
    A = 1./(1j * wvl * Dz1)
    B = numpy.exp(1j * k/(2*Dz1) * (x1a**2 + y1a**2) )
    C = fouriertransform.ft2(Uin * numpy.exp(1j * k/(2*Dz1) * (x1**2 + y1**2)), d1)
    Uitm = A*B*C
    #Observation plane
    Dz2 = z - Dz1

    #coordinates
    x2,y2 = numpy.meshgrid( numpy.arange(-N/2., N/2.) * d2,
                            numpy.arange(-N/2., N/2.) * d2 )

    #Evaluate the Fresnel diffraction integral
    A = 1. / (1j * wvl * Dz2)
    B = numpy.exp( 1j * k/(2 * Dz2) * (x2**2 + y2**2) )
    C = fouriertransform.ft2(Uitm * numpy.exp( 1j * k/(2*Dz2) * (x1a**2 + y1a**2)), d1a)
    Uout = A*B*C

    return Uout

#Evaluate Fresnel-Kirchhoff integral
    A = 1./(1j * wvl * Dz1)
    B = numpy.exp(1j * k/(2*Dz1) * (x1a**2 + y1a**2) )
    C = fouriertransform.ft2(Uin * numpy.exp(1j * k/(2*Dz1) * (x1**2 + y1**2)), d1)
    Uitm = A*B*C
    #Observation plane
    Dz2 = z - Dz1

    #coordinates
    x2,y2 = numpy.meshgrid( numpy.arange(-N/2., N/2.) * d2,
                            numpy.arange(-N/2., N/2.) * d2 )

    #Evaluate the Fresnel diffraction integral
    A = 1. / (1j * wvl * Dz2)
    B = numpy.exp( 1j * k/(2 * Dz2) * (x2**2 + y2**2) )
    C = fouriertransform.ft2(Uitm * numpy.exp( 1j * k/(2*Dz2) * (x1a**2 + y1a**2)), d1a)
    Uout = A*B*C

    return Uout