In [27]:

    

import matplotlib
matplotlib.use('nbagg')

from zernike import ZernikeVector
import astropy.units as u
import numpy as np


    

In [2]:

    

z = ZernikeVector(Z4=100.0)


    

In [3]:

    

z.array


    

    
Out[3]:





$[0,~0,~100] \; \mathrm{nm}$

In [4]:

    

z['Z55'] = 100.0


    

In [5]:

    

z['Z5'] = 1000.0
z['Z6'] = 100
z['Z12'] = 55


    

In [6]:

    

z.coeffs


    

    
Out[6]:





{'Z04': <Quantity 100.0 nm>,
 'Z05': <Quantity 1000.0 nm>,
 'Z06': <Quantity 100.0 nm>,
 'Z12': <Quantity 55.0 nm>,
 'Z55': <Quantity 100.0 nm>}

In [7]:

    

z.denormalize()
print(z)


    

    




 Z04:       100 nm 	 Defocus (2, 0)
 Z05:     1e+03 nm 	 Primary Astig at 45˚ (2, -2)
 Z06:       100 nm 	 Primary Astig at 0˚ (2, 2)
 Z12:        55 nm 	 Secondary Astigmatism at 0˚ (4, 2)
 Z55:       100 nm

In [8]:

    

z.units = u.nm
z


    

    
Out[8]:





 Z04:       100 nm 	 Defocus (2, 0)
 Z05:     1e+03 nm 	 Primary Astig at 45˚ (2, -2)
 Z06:       100 nm 	 Primary Astig at 0˚ (2, 2)
 Z12:        55 nm 	 Secondary Astigmatism at 0˚ (4, 2)
 Z55:       100 nm

In [9]:

    

z.denormalize()
z.norm_array


    

    
Out[9]:





$[0,~0,~57.735027,~408.24829,~40.824829,~0,~0,~0,~0,~0,~17.392527,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~0,~22.36068] \; \mathrm{nm}$

In [10]:

    

for c in z:
    print(c, z[c])


    

    




Z04 100.0 nm
Z06 100.0 nm
Z05 1000.0 nm
Z55 100.0 nm
Z12 54.99999999999999 nm

In [11]:

    

'Z04' in z


    

    
Out[11]:





True

In [12]:

    

z.denormalize()
z.ignore('Z05')
z.units = u.nm
z.plot_map()
z.peak2valley


    

    















    












    
Out[12]:





$501.19255 \; \mathrm{nm}$

In [13]:

    

z.restore('Z05')
z.plot_map()
z.rms


    

    















    












    
Out[13]:





$325.82856 \; \mathrm{nm}$

In [14]:

    

z.plot_surface()


    

In [15]:

    

b = z.phase_map()


    

In [16]:

    

b[4].max()


    

    
Out[16]:





$1175.8988 \; \mathrm{nm}$

In [17]:

    

z


    

    
Out[17]:





 Z04:       100 nm 	 Defocus (2, 0)
 Z05:     1e+03 nm 	 Primary Astig at 45˚ (2, -2)
 Z06:       100 nm 	 Primary Astig at 0˚ (2, 2)
 Z12:        55 nm 	 Secondary Astigmatism at 0˚ (4, 2)
 Z55:       100 nm

In [18]:

    

ref = ZernikeVector(Z04=-500, Z20=20)


    

In [19]:

    

ref


    

    
Out[19]:





 Z04:      -500 nm 	 Defocus (2, 0)
 Z20:        20 nm 	 X Pentafoil (5, 5)

In [20]:

    

z + ref


    

    
Out[20]:





 Z04:      -400 nm 	 Defocus (2, 0)
 Z05:     1e+03 nm 	 Primary Astig at 45˚ (2, -2)
 Z06:       100 nm 	 Primary Astig at 0˚ (2, 2)
 Z12:        55 nm 	 Secondary Astigmatism at 0˚ (4, 2)
 Z20:        20 nm 	 X Pentafoil (5, 5)
 Z55:       100 nm

In [21]:

    

new = ref - z

new


    

    
Out[21]:





 Z04:      -600 nm 	 Defocus (2, 0)
 Z05:    -1e+03 nm 	 Primary Astig at 45˚ (2, -2)
 Z06:      -100 nm 	 Primary Astig at 0˚ (2, 2)
 Z12:       -55 nm 	 Secondary Astigmatism at 0˚ (4, 2)
 Z20:        20 nm 	 X Pentafoil (5, 5)
 Z55:      -100 nm

In [22]:

    

new * 5


    

    
Out[22]:





 Z04:    -3e+03 nm 	 Defocus (2, 0)
 Z05:    -5e+03 nm 	 Primary Astig at 45˚ (2, -2)
 Z06:      -500 nm 	 Primary Astig at 0˚ (2, 2)
 Z12:      -275 nm 	 Secondary Astigmatism at 0˚ (4, 2)
 Z20:       100 nm 	 X Pentafoil (5, 5)
 Z55:      -500 nm

In [23]:

    

5/ new


    

    
Out[23]:





 Z04: -0.00833 1 / nm 	 Defocus (2, 0)
 Z05: -0.005 1 / nm 	 Primary Astig at 45˚ (2, -2)
 Z06: -0.05 1 / nm 	 Primary Astig at 0˚ (2, 2)
 Z12: -0.0909 1 / nm 	 Secondary Astigmatism at 0˚ (4, 2)
 Z20:  0.25 1 / nm 	 X Pentafoil (5, 5)
 Z55: -0.05 1 / nm

In [33]:

    

new * 2


    

    
Out[33]:





 Z04:  -1.2e+03 nm 	 Defocus (2, 0)
 Z05:    -2e+03 nm 	 Primary Astig at 45˚ (2, -2)
 Z06:      -200 nm 	 Primary Astig at 0˚ (2, 2)
 Z12:      -110 nm 	 Secondary Astigmatism at 0˚ (4, 2)
 Z20:        40 nm 	 X Pentafoil (5, 5)
 Z55:      -200 nm

In [ ]:

    

2 + new


    

In [ ]:

    

set(z.keys() & ref.keys())


    

In [ ]:

    

for k in sorted(z.keys()):
    print(k)


    

In [ ]:

    

(1.0 * u.nm / (1. * u.mm).to(u.nm)).value


    

In [ ]:

    

u.di