Multi- holes and slits.
-----------------------

In this example we demonstrate the use of a number of holes or slits in a row.
In this way it is possible to make a grating. There are two wavelengths in the beam which demonstrates 
the use of a grating as a spectrometer. The intensities of the two fields can be simply added after separate propagations.

.. code:: python

    #! python3
    import numpy as np
    import matplotlib.pyplot as plt
    from LightPipes import *
    """
        MultiSlit.py
        Demonstrates the RowOfFields command. Two wavelengths are used to show 
        the principles of a grating.
        
        cc Fred van Goor, June 2020.
    """
    wavelength=1000*nm
    Dlambda=150*nm
    size=11*mm
    N=2000
    N2=int(N/2)

    SlitSeparation=0.5*mm
    f=30*cm
    Nslits=20
    SlitHeight=5*mm
    SlitWidth=0.1*mm
    Nheight=int(SlitHeight/size*N)
    Nwidth=int(SlitWidth/size*N)
    Fslit=np.ones((Nheight,Nwidth))
    F1=Begin(size,wavelength,N)
    F1=RowOfFields(F1,Fslit,Nslits,SlitSeparation)
    Islits=Intensity(F1)
    F1=Lens(F1,f)
    F1=Forvard(F1,f)
    F11=Interpol(F1,size,N,magnif=4)
    Iscreen1=Intensity(F11)
    F2=Begin(size,wavelength+Dlambda,N)
    F2=RowOfFields(F2,Fslit,Nslits,SlitSeparation)
    F2=Lens(F2,f)
    F2=Forvard(F2,f)
    F22=Interpol(F2,size,N,magnif=4)
    Iscreen2=Intensity(F22)
    F3=BeamMix(F11,F22)
    Iscreen3=Intensity(F3)
    print(F22.lam/nm)

    X=np.arange(N)
    X=(X/N-1/2)*size/mm
    s= r'LightPipes for Python,' + '\n' +\
      r'MultiSlit.py'+ '\n\n'\
      r'size = {:4.2f} mm'.format(size/mm) + '\n' +\
      r'$\lambda$ = {:4.2f} nm'.format(wavelength/nm) + '\n' +\
      r'$\Delta\lambda$ = {:4.2f} nm'.format(Dlambda/nm) + '\n' +\
      r'N = {:d}'.format(N) + '\n' +\
      r'width of the slits: {:4.2f} mm'.format(SlitWidth/mm) + '\n' +\
      r'height of the slits: {:4.2f} mm'.format(SlitHeight/mm) + '\n' +\
      r'separation of the slits: {:4.2f} mm'.format(SlitSeparation/mm) + '\n' +\
      r'number of slits: {:d}'.format(Nslits) + '\n' +\
      r'focal length lens: {:4.2f} cm'.format(f/cm) + '\n\n' +\
      r'${\copyright}$ Fred van Goor, May 2020'
      
    fig=plt.figure(figsize=(10,6))
    ax1 = fig.add_subplot(221)
    ax2 = fig.add_subplot(222);#ax2.set_ylim(bottom=900,top=1100)
    ax3 = fig.add_subplot(223)
    ax4 = fig.add_subplot(224)
    ax1.imshow(Islits,cmap='gray',aspect='equal');ax1.axis('off'); ax1.set_title('Screen with slits')
    ax2.imshow(Iscreen1+Iscreen2,cmap='jet',aspect='equal');ax2.axis('off'); ax2.set_title('Intensity distribution at the focus of the lens')
    #ax2.margins(x=0, y=-0.45)
    ax3.plot(X,(Iscreen1+Iscreen2)[N2]); ax3.set_xlabel('x [mm]'); ax3.set_ylabel('Intensity [a.u.]'); ax3.set_title('Cross section of intensity at the focus')
    ax4.text(0,0,s); ax4.axis('off')
    plt.show()

.. plot:: ./Examples/Interference/MultiSlit.py

Below we demonstrate interference from a row of holes.

.. code:: python

    #! python3
    import numpy as np
    import matplotlib.pyplot as plt
    from LightPipes import *
    """
        MultiHole.py
        Demonstrates the MultiHole command. Two wavelengths are used to show 
        the principles of a grating.
        
        cc Fred van Goor, June 2020.
    """
    wavelength=1000*nm
    size=30*mm
    N=800
    N2=int(N/2)

    HoleSeparation=2*mm
    z=300*cm
    Nholes=6
    size_hole=1*mm
    HoleDiameter=0.5*mm

    Ndiameter=int(HoleDiameter/size*N)
    Nhole=int(size_hole/size*N)
    Fhole=Begin(size_hole,wavelength,Nhole)
    Fhole=CircAperture(Fhole,HoleDiameter/2)

    F=Begin(size,wavelength,N)
    F=RowOfFields(F,Fhole,Nholes,HoleSeparation)
    Iholes=Intensity(F)
    X=np.arange(N)
    X=(X/N-1/2)*size/mm
    F=Lens(F,z)
    F=Fresnel(F,z)
    Iscreen=Intensity(F)

    s= r'LightPipes for Python,' + '\n' +\
      r'MultiHole.py'+ '\n\n'\
      r'size = {:4.2f} mm'.format(size/mm) + '\n' +\
      r'$\lambda$ = {:4.2f} nm'.format(wavelength/nm) + '\n' +\
      r'N = {:d}'.format(N) + '\n' +\
      r'diameter holes: {:4.2f} mm'.format(HoleDiameter/mm) + '\n' +\
      r'separation of the holes: {:4.2f} mm'.format(HoleSeparation/mm) + '\n' +\
      r'number of holes: {:d}'.format(Nholes) + '\n' +\
      r'focal length lens: {:4.2f} cm'.format(z/cm) + '\n\n' +\
      r'${\copyright}$ Fred van Goor, May 2020'
      
    fig=plt.figure(figsize=(10,6))
    ax1 = fig.add_subplot(221)
    ax2 = fig.add_subplot(222);# ax2.set_ylim(bottom=130,top=170)
    ax3 = fig.add_subplot(223)
    ax4 = fig.add_subplot(224)
    ax1.imshow(Iholes,cmap='gray',aspect='equal');ax1.axis('off'); ax1.set_title('Screen with holes')
    ax2.imshow(Iscreen,cmap='jet',aspect='equal');ax2.axis('off'); ax2.set_title('Intensity distribution at the focus of the lens')
    ax3.plot(X,Iscreen[N2]); ax3.set_xlabel('x [mm]'); ax3.set_ylabel('Intensity [a.u.]'); ax3.set_title('Cross section of intensity at the focus')
    ax4.text(0,0,s); ax4.axis('off')
    plt.show()

.. plot:: ./Examples/Interference/MultiHole.py