def fit(data, num_terms=16, rms_norm=False, round_at=6):
''' Fits a number of Zernike coefficients to provided data by minimizing
the root sum square between each coefficient and the given data. The
data should be uniformly sampled in an x,y grid.
Args:
data (`numpy.ndarray`): data to fit to.
num_terms (`int`): number of terms to fit, fits terms 0~num_terms.
rms_norm (`bool`): if true, normalize coefficients to unit RMS value.
round_at (`int`): decimal place to round values at.
Returns:
numpy.ndarray: an array of coefficients matching the input data.
'''
if num_terms > len(zernmap):
raise ValueError(f'number of terms must be less than {len(zernmap)}')
# precompute the valid indexes in the original data
pts = m.isfinite(data)
# set up an x/y rho/phi grid to evaluate Zernikes on
x, y = m.linspace(-1, 1, data.shape[1]), m.linspace(-1, 1, data.shape[0])
xx, yy = m.meshgrid(x, y)
rho = m.sqrt(xx**2 + yy**2)[pts].flatten()
phi = m.arctan2(xx, yy)[pts].flatten()
# compute each Zernike term
zernikes = []
for i in range(num_terms):
func = z.zernikes[zernmap[i]]
base_zern = func(rho, phi)
if rms_norm:
base_zern *= func.norm
zernikes.append(base_zern)
zerns = m.asarray(zernikes).T
# use least squares to compute the coefficients
coefs = m.lstsq(zerns, data[pts].flatten(), rcond=None)[0]
return coefs.round(round_at)
def image_dist_epd_to_na(image_distance, epd):
"""Compute the NA from an image distance and entrance pupil diameter.
Parameters
----------
image_distance : `float`
distance from the image to the entrance pupil
epd : `float`
diameter of the entrance pupil
Returns
-------
`float`
numerical aperture. The NA of the system.
"""
image_distance = guarantee_array(image_distance)
rho = epd / 2
marginal_ray_angle = abs(m.arctan2(rho, image_distance))
return marginal_ray_angle
def cart_to_polar(x, y):
'''Return the (rho,phi) coordinates of the (x,y) input points.
Parameters
----------
x : `numpy.ndarray` or number
x coordinate
y : `numpy.ndarray` or number
y coordinate
Returns
-------
rho : `numpy.ndarray` or number
radial coordinate
phi : `numpy.ndarray` or number
azimuthal coordinate
'''
rho = m.sqrt(x**2 + y**2)
phi = m.arctan2(y, x)
return rho, phi
def zernikes_to_magnitude_angle(coefs, namer):
"""Convert Fringe Zernike polynomial set to a magnitude and phase representation."""
def mkary(): # default for defaultdict
return m.zeros(2)
# make a list of names to go with the coefficients
names = [namer(i, base=0) for i in range(len(coefs))]
combinations = defaultdict(mkary)
# for each name and coefficient, make a len 2 array. Put the Y or 0 degree values in the first slot
for coef, name in zip(coefs, names):
if name.endswith(('X', 'Y', '°')):
newname = ' '.join(name.split(' ')[:-1])
if name.endswith('Y'):
combinations[newname][0] = coef
elif name.endswith('X'):
combinations[newname][1] = coef
elif name[-2] == '5': # 45 degree case
combinations[newname][1] = coef
else:
combinations[newname][0] = coef
else:
combinations[name][0] = coef
# now go over the combinations and compute the L2 norms and angles
for name in combinations:
ovals = combinations[name]
magnitude = m.sqrt((ovals**2).sum())
if 'Spheric' in name or 'focus' in name or 'iston' in name:
phase = 0
else:
phase = m.degrees(m.arctan2(*ovals))
values = (magnitude, phase)
combinations[name] = values
return dict(combinations) # cast to regular dict for return
def test_cart_to_polar(x, y):
rho, phi = coordinates.cart_to_polar(x, y)
assert np.allclose(rho, sqrt(x**2 + y**2))
assert np.allclose(phi, arctan2(y, x))