Probe functions & aberrations

[dnjohnstone]

There are some probe function things here, that we should think about supporting: https://github.com/ePSIC-DLS/epsic_tools/pull/15/files

E.g. aberration function:

def FuncAberrUV(u,v,aberrcoeff):

# this function needs comments

# input:
# u: Kx
# v: Ky

u2 = u*u
u3 = u2*u
u4 = u3*u

v2 = v*v
v3 = v2*v
v4 = v3*v

# aberr are in unit of meter.
C1   = aberrcoeff[0] # defocus
C12a = aberrcoeff[1] # 2 stig
C12b = aberrcoeff[2] # 2 stig
C23a = aberrcoeff[3] # 3 stig
C23b = aberrcoeff[4] # 3 stig
C21a = aberrcoeff[5] # coma 
C21b = aberrcoeff[6] # coma
C3   = aberrcoeff[7] # Spherical abb
C34a = aberrcoeff[8] # 4 stig
C34b = aberrcoeff[9] # 4 stig
C32a = aberrcoeff[10] # star
C32b = aberrcoeff[11] # star

# output:  chi function. in unit of meter*radian.  multiply by 2pi/lambda to get dimensionless
func_aberr =  1/2*C1*(u2+v2)\
        + 1/2*(C12a*(u2-v2) + 2*C12b*u*v)\
        + 1/3*(C23a*(u3-3*u*v2) + C23b*(3*u2*v - v3))\
        + 1/3*(C21a*(u3+u*v2) + C21b*(v3+u2*v))\
        + 1/4* C3*(u4+v4+2*u2*v2)\
        + 1/4* C34a*(u4-6*u2*v2+v4)\
        + 1/4* C34b*(4*u3*v-4*u*v3)\
        + 1/4* C32a*(u4-v4)\
        + 1/4* C32b*(2*u3*v + 2*u*v3)\

return func_aberr