Example 02: Fit concave hyperboloid

This example shows how to fit a concave hyperboloid to simulated data using the XMF library.

import numpy as np
import xmf

# 1. Define lateral coordinates
x_range = 200e-3
y_range = 20e-3
x_num = 201
y_num = 21

x1d = np.linspace(-x_range/2, x_range/2, x_num)
y1d = np.linspace(-y_range/2, y_range/2, y_num)
x2d, y2d = np.meshgrid(x1d, y1d)

# 2. Set mirror parameters
# 2.1. Shape parameters
abs_p = 30
abs_q = 0.3
theta = 30e-3

# 2.2. Pose parameters
x_i = -1e-3
y_i = -2e-4
z_i = 3e-7
alpha = 2e-6
beta = 1e-5
gamma = 0.5e-3

# 2.3. True parameters as dictionary
true_params_dict = {
    'p': abs_p,
    'q': abs_q,
    'theta': theta,
    'x_i': x_i,
    'y_i': y_i,
    'z_i': z_i,
    'alpha': alpha,
    'beta': beta,
    'gamma': gamma
}

# 3. Set measurement noise
height_measurement_noise_std = 0.5e-9
slope_measurement_noise_std = 100e-9

# 4. Demonstarte the fitting
# 4.1. Set input parameters as dictionary
input_params_dict = {
    'p': abs_p,
    'q': abs_q,
    'theta': theta
}

# 4.2. Set the optimization flag dictionary
opt_dict = {
    'p': False,
    'q': False,
    'theta': False
}

# 4.3. Generate the surface
z2d = xmf.generate_2d_curved_surface_height(xmf.standard_concave_hyperboloid_height, x2d, y2d, abs_p, abs_q, theta, x_i, y_i, z_i, alpha, beta, gamma)
# 4.4. Adding noise to mimic the measured data
z2d_measured = z2d + np.random.randn(z2d.shape[0], z2d.shape[1])*height_measurement_noise_std
# 4.5. Fit the surface shape
z2d_res, z2d_fit, opt_params_dict, opt_params_ci_dict, _ = xmf.fit_concave_hyperboloid_height(x2d, y2d, z2d_measured, input_params_dict, opt_dict)
# 4.6. Show fitting results
xmf.fig_show_2d_fitting_map(x2d, y2d, z2d_measured, z2d_fit, z2d_res, true_params_dict, opt_params_dict, opt_params_ci_dict, 'Concave Hyperboloid')