Zernike fitting

Zernike polynomial play important roles in various optics branches Where C is the coefficient for each order Z. Therefore, we can get C for every W we measure by intergration.

Defocus = np.sqrt(3)*(2*r**2-1)  
HPA = np.sqrt(6)*r**2*np.cos(2*u)  # horizontal primary astigmatism
PSA = np.sqrt(5)*(6*r**4-6*r**2 + 1)  # primary spherical abberation
HSA = np.sqrt(10)*(4*r**2-3)*r**2*np.cos(2*u)  #  horizontal secondary astigmatism

def fitting(Z,n):
    fitlist = []
    l = len(Z)
    x2 = np.linspace(-1, 1, l)
    y2 = np.linspace(-1, 1, l)
    [X2,Y2] = np.meshgrid(x2,y2)
    r = np.sqrt(X2**2 + Y2**2)  
    u = np.arctan2(Y2, X2)   
    for q in range(n):
            ZF = "Formula of different order Z"
            Z_tot = Z * ZF
            Z_tot[r > 1] = 0
            C = sum(sum(Z_tot))*2*2/l/l/np.pi   
            fitlist.append(np.around(a,3))
    for i in range(l):
        for j in range(l):
            if x2[i]**2+y2[j]**2>1:
                Z_new[i][j]=0

    return fitlist , Z_new

Angle calculation

In order to do the three dimentional reconstruction, the representation angle of each frame should be estimate

  • With uniform distribution, RBC can be seen as biolens and estimate its angle using Zernike polynomials which are used to describe wavefront aberrations
  • Here I use differnt order to discribe different angle
    • Horizontal secondary astigmatism for 90 degree estimation
    • Defocus + Primary spherical abberation for 0 degree estimation
    • Defocus + Horizontal for other frame between each section of 0~90

  • For 90 degree and 0 degree, we find out local maximum of C of different Z to define
  • For other angle
    • From simulation, we find out the Coefficient of the combination of Defocus and Horizontal primary astigmatism is related to cos square curve by rotating ideal discocyte shape
    • The formula to transform C value to angle would be 
        np.abs(np.rad2deg(np.arccos(np.sqrt(C)))

  • After anle transformation of each 0~90 section, combine them and caliberate to 0~360 cycle

  • To accerlerate, Multiprocessing calculation is using 
    def run(self):
  fitting_data , phimap_stack = self.read_rbc(self.isdash)
  pool = mp.Pool(6)
  zc_list = [pool.starmap(self.zernikeFitting,fitting_data)]
  pool.close()
  pool.join()

Updated: