def num_int_a_ring(r1,r2,order,position,tal_at_pos,normvec): # numerical integrate the results in a ring # r1: inner radius # r2: outer radius # order: order of zernikes # position: even order positions # tal_at_pos: tallies at even orders # normvec: normalization vectors # integral: numerical integrals R = 0.392 N = 1000 rlist = np.linspace(r1,r2,N+1) dr = (r2-r1)/N zn_mode = np.zeros((len(rlist),len(position))) for j in range(0,len(rlist)): full_zn_vals = capi.calc_zn(order,rlist[j]/R,0) for k in range(0,len(position)): zn_mode[j,k] = full_zn_vals[position[k]] tal_at_pos_mat = np.mat(tal_at_pos) normvec_mat = np.mat(normvec) tal_at_pos_mat = np.multiply(tal_at_pos_mat,normvec_mat) estimate = zn_mode*np.transpose(tal_at_pos_mat) estimate= np.squeeze(np.asarray(estimate)) integral = 2*np.pi*np.trapz(np.multiply(estimate,rlist),rlist) return integral
def fet_func(w, coeff, pos):
R = 0.392
order = 2 * (len(pos) - 1)
# print(order)
y = np.zeros(len(w))
for i in range(0, len(w)):
# print(i)
full_zn_vals = capi.calc_zn(order, w[i] / R, 0)
# print("b",len(full_zn_vals))
# print("a",len(pos))
rn_at_pos = get_val_at_pos(pos, full_zn_vals)
y[i] = np.sum(np.multiply(coeff, rn_at_pos))
return y
def get_fet_est(radmid,position,order,tal_at_pos,normvec):
# get the FET estimations at the middle of each rings
# radmid: middle positions
# order: order of zernikes
# position: even order positions
# tal_at_pos: tallies at even orders
# normvec: normalization vectors
# fet_est_norm: normalized results to get the shape
zn_mode = np.zeros((len(radmid),len(position)))
R = 0.392
for j in range(0,len(radmid)):
full_zn_vals = capi.calc_zn(order,radmid[j]/R,0)
for k in range(0,len(position)):
zn_mode[j,k] = full_zn_vals[position[k]]
tal_at_pos_mat = np.mat(tal_at_pos)
normvec_mat = np.mat(normvec)
tal_at_pos_mat = np.multiply(tal_at_pos_mat,normvec_mat)
estimate = zn_mode*np.transpose(tal_at_pos_mat)
fet_est = np.squeeze(np.asarray(estimate))
fet_est_norm = fet_est/np.linalg.norm(fet_est)
return fet_est_norm