# coding: utf-8

from __future__ import division, print_function, unicode_literals
from lab import *
import uncertainties.umath  as um
import uncertainties.unumpy as unp
import numpy                as np
import matplotlib.pyplot    as plt

# convert micrometer readings to SI unit
length = lambda x,y,z: x*1e-4 + y*1/4*1e-4 + z*1e-6

##
## Part I
##

k  = 60                   # number of wavefronts
l0 = ufloat(633, 1)*1e-9  # laser wavelength

# micrometer calibration
d0 = k*l0/2          # expected value
d  = length(0,3,10)  # measured value
df = d - d0          # offset

# laser wavelength measure
d = sample(length(*i)-df.n for i in [(0,3,9.5), (0,3,10), 
                                     (0,3,10.5), (0,3,10)]).tval()
l1 = 2*d/k

print(mformat('''
# Part I (Fabry-Perot interferometer)
offset: {} μm
λ: {} nm
''', df*1e6, l1*1e9))


##
## Part II
##

df = length(2,0,1) # micrometer offset
k  = 70            # number of wavefronts

# laser wavelength measure
d = sample(length(*i)-df for i in [(2,0,22.5), (2,0,23.5), (2,0,23.5),
                                   (2,0,23.5), (2,0,23), (2,0,23)]).tval()
l2 = 2*d/k

print(mformat('''
# Part II (Michelson interferometer)
λ: {} nm''', l2*1e9))


## compare wavelengths
alpha = check_measures(l1, l2)
l = combine_measures(l1, l2)

print(mformat('''
comparibility test λ₁ - λ₂
  α={:.2f} α>ε: {}
λbest: {} nm
''', alpha, alpha>epsilon, l*1e9))



##
## Part III
##

d    = 3e-2    # air cavity thickness
Patm = 101.3e3 # atmosferic pressure

k = array(17, 20, 17, 18, 19)           # number of wavefronts
P = array(82e3, 83e3, 84e3, 83e3, 84e3) # gauge pressure

m = sample(*(k*l.n/(2*d*P)))

print(mformat('''
# Part III (air refraction index)
m: {} Pa⁻¹
''', m.tval()))


##
## Part IV
##

d = ufloat(6, 1)*1e-3                   # glass pane thickness
t = ufloat(12, 1)*np.pi/180             # angle
k = sample(162, 112, 124, 122).tval()   # number of wavefronts
n = (2*d-k*l) / (2*d-k*l/(1-um.cos(t))) # refraction index

print(mformat('''
# Part IV (glass refraction index)
n: {}
''', n))



##
## Part V
##

# peak position
S = array(8.9, 10.7, 11.7, 12.7, 13.4,
         14.1, 14.7, 15.6, 16.3, 16.7,
         17.3, 18.0, 18.3, 18.9)*1e-2 

# uncertainty
sigmaS = 2e-3

# peak number
n = np.arange(1, len(S))

d  = ufloat(1e-3, 0)          # slit length
L  = ufloat(125.1, 0.5)*1e-2  # screen distance
ti = um.atan(S[0]/L)          # incidence angle

# drop first peak
S = S[1:]

x = np.linspace(0, 13, 200)
peak = lambda n, t, l: L.n*np.sqrt(1/(np.cos(t)-n*l/d.n)**2 - 1)
f, (tio, lo) = curve(n, S, peak, sigmaS, guess=[ti.n, l.n])

plt.xlabel('peak order')
plt.ylabel('distance from center (m)')
plt.errorbar(n, S, sigmaS, color='#604848', linestyle='', linewidth=1.1)
plt.scatter(n, S, color='#a17e3e')
plt.plot(x, f(x), color='#65788f')
plt.show()

alpha = check_measures(l, lo)
beta  = chi_squared_fit(n, S, f, sigmaS)

print(mformat('''
# Part V (ruler diffraction)
λₒ: {} nm
θₒ: {} rad

compatibility test λ - λₒ:
  α={:.2f}, α>ε: {}

χ² test:
  α={:.2f}, α>ε: {}
''', lo*1e9, tio
   , alpha, alpha>epsilon
   , beta,  beta>epsilon))