LightPipes for Python

https://opticspy.github.io/lightpipes/
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LightPipes for Python is a set of functions for modeling coherent optical devices and light...
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### Install LightPipes with pyFFTW support

Source: https://opticspy.github.io/lightpipes/_sources/install.rst.txt

Install LightPipes with pyFFTW support for potentially faster FFT calculations. This is the recommended way to install if pyFFTW is available and desired.

```bash
sudo pip(3) install LightPipes[pyfftw]
```

--------------------------------

### Compile and Install FFTW

Source: https://opticspy.github.io/lightpipes/_sources/install.rst.txt

Commands to configure, compile, and install the FFTW library from source. This is necessary for pyFFTW installation on systems like Raspberry Pi.

```bash
cd fftw-3.3.9
./configure --enable-threads --enable-shared
make
sudo make install
```

--------------------------------

### Install LightPipes

Source: https://opticspy.github.io/lightpipes/_sources/install.rst.txt

Perform a normal installation of LightPipes. If pyFFTW is not installed, LightPipes will fall back to using numpy FFT.

```bash
sudo pip(3) install LightPipes
```

--------------------------------

### Install matplotlib

Source: https://opticspy.github.io/lightpipes/manual.html

Install the matplotlib package for plotting. This is a prerequisite for visualizing simulation results.

```bash
>>> pip install matplotlib

```

--------------------------------

### Install python3-gi-cairo

Source: https://opticspy.github.io/lightpipes/_sources/install.rst.txt

Install the python3-gi-cairo package, which may be a prerequisite for certain LightPipes functionalities.

```bash
sudo apt install python3-gi-cairo
```

--------------------------------

### Michelson Interferometer Setup and Simulation

Source: https://opticspy.github.io/lightpipes/_sources/MichelsonInterferometer.rst.txt

This code sets up and simulates a basic Michelson interferometer. It defines parameters like wavelength, beam size, grid resolution, arm lengths, and distances, then propagates a Gaussian beam through the setup to observe the intensity pattern on a screen. Use this for a fundamental understanding of the interferometer simulation.

```python
#! /usr/bin/env python
from LightPipes import *
import matplotlib.pyplot as plt

wavelength=632.8*nm #wavelength of HeNe laser
size=15*mm # size of the grid
N=500 # number (NxN) of grid pixels
R=9*mm # laser beam radius
z1=8*cm # length of arm 1
z2=7*cm # length of arm 2
z3=3*cm # distance laser to beamsplitter
z4=5*cm # distance beamsplitter to screen
Rbs=0.5 # reflection beam splitter
tx=0.0*mrad; ty=0.0*mrad # tilt of mirror 1



#Generate a laser beam:
F=Begin(size,wavelength,N)
F=GaussBeam(F, R)

#Propagate to the beamsplitter:
F=Forvard(z3,F)

#Split the beam and propagate to mirror #2:
F2=IntAttenuator(1-Rbs,F)
F2=Forvard(z2,F2)

#Propagate back to the beamsplitter:
F2=Tilt(tx,ty,F2)
F2=Forvard(z2,F2)
F2=IntAttenuator(Rbs,F2)

#Split off the second beam and propagate to- and back from the mirror #1:
F10=IntAttenuator(Rbs,F)
F1=Forvard(z1*2,F10)
F1=IntAttenuator(1-Rbs,F1)

#Recombine the two beams and propagate to the screen:
F=BeamMix(F1,F2)
F=Forvard(z4,F)
I=Intensity(1,F)

s1 =    r'LightPipes for Python ' + LPversion + '\n\n'+
        r'Michelson interferometer'+ '\n'
        
s2 =    r'Michelson.py'+ '\n\n'+
        f'size = {size/mm:4.2f} mm' + '\n'+
        f'$\lambda$ = {wavelength/um:4.2f} $\mu$m' + '\n'+
        f'N = {N:d}' + '\n'+
        f'R = {R/mm:4.2f} mm beam radius of the laser' + '\n'+
        f'z1 = {z1/mm:4.2f} mm length of arm 1' + '\n'+
        f'z2 = {z2/mm:4.2f} mm length of arm 2' + '\n'+
        f'z3 = {z3/mm:4.2f} mm distance from the laser to the beam splitter' + '\n'+
        f'z4 = {z4/mm:4.2f} mm distance from the beam splitter to the screen' + '\n'+
        f'tx, ty = {tx/mrad:4.2f}, {ty/mrad:4.2f} mrad tilt of mirror 2' + '\n'
        r'${\copyright}$ Fred van Goor, June 2020'
        
fig=plt.figure(figsize=(6,9));
ax1 = fig.add_subplot(311);ax1.axis('off')
ax2 = fig.add_subplot(312);ax2.axis('off')
ax3 = fig.add_subplot(313);ax3.axis('off')
ax1.imshow(I,cmap='jet');ax1.set_title('intensity pattern')
ax2.text(0.0,0.6,s1,fontsize=12, fontweight='bold')
ax3.text(0.0,0.50,s2)

plt.show()
```

--------------------------------

### Install pyFFTW package

Source: https://opticspy.github.io/lightpipes/_sources/install.rst.txt

Install the pyFFTW package separately. This can be done before or after installing LightPipes.

```bash
sudo pip(3) install pyFFTW
```

--------------------------------

### Install LightPipes for Python

Source: https://opticspy.github.io/lightpipes/_sources/introduction.rst.txt

Install the latest version of LightPipes for Python using pip. This command is used to get started with the library.

```bash
pip install LightPipes
```

--------------------------------

### Simulate Multi-Hole Diffraction

Source: https://opticspy.github.io/lightpipes/_sources/MultiHoleAndSlit.rst.txt

This example simulates the diffraction pattern produced by light passing through multiple circular holes. Ensure the lightpipes library is installed.

```python
import numpy as np
import lightpipes as lp
from lightpipes. অপটিক্স import * # Import all optics functions

# Define simulation parameters
n = 512 # Number of grid points
size = 10e-3 # Physical size of the grid (meters)
wavelength = 632.8e-9 # Wavelength of light (meters)

# Create a Wavefront object
wave = lp.Wavefront(n, size, wavelength)

# Define the multi-hole aperture
# Example: 3 holes in a line
# hole_radius = 0.5e-3
# hole_spacing = 2e-3
# wave.aperture = lp.MultiHole(wave, hole_radius, hole_spacing, n_holes=3, orientation='horizontal')

# Example: 5 holes in a cross pattern
wave.aperture = lp.MultiHole(wave, radius=0.3e-3, spacing=1.5e-3, n_holes=5, orientation='cross')

# Propagate the wavefront to a distance
# For example, to the far field (using Fraunhofer approximation)
distance = 1.0 # meters
propagated_wave = wave.propagate(distance)

# Visualize the intensity pattern
propagated_wave.intensity().plot(title='Multi-Hole Diffraction Pattern')

# You can also access the intensity data as a numpy array:
# intensity_data = propagated_wave.intensity().data

```

--------------------------------

### Comparing Propagation Methods

Source: https://opticspy.github.io/lightpipes/_sources/manual.rst.txt

This example demonstrates the difference in results between using a small aperture (waveguide-like) and a larger grid for far-field propagation.

```python
from LightPipes import *

size = 100e-3
wavelength = 632.8e-9

# Initialize the field
field = Begin(size, wavelength, 1000)

# Propagate 1m forward
field = Forvard(field, 1.0)

# Filter with an aperture equal to grid size
field = RectAperture(field, size, size)

# Propagate 1m forward again
field = Forvard(field, 1.0)

# Initialize the field with a larger grid
field2 = Begin(size*4, wavelength, 1000)

# Propagate 1m forward
field2 = Forvard(field2, 1.0)

# Filter with an aperture smaller than the grid
field2 = RectAperture(field2, 10e-3, 10e-3)

# Propagate 1m forward again
field2 = Forvard(field2, 1.0)

```

--------------------------------

### Install LightPipes Python Package

Source: https://opticspy.github.io/lightpipes/_sources/install.rst.txt

Use this command to install the LightPipes package from PyPi. If you have both Python 2.7 and 3.+ installed, use pip3 instead of pip.

```bash
pip(3) install LightPipes
```

--------------------------------

### CylindricalLens Example

Source: https://opticspy.github.io/lightpipes/command-reference.html

Demonstrates the application of CylindricalLens with different parameters for focal length, shift, and angle.

```python
>>> F=Begin(size,wavelength,N)
>>> F=CylindricalLens(F,f) #Cylindrical lens in the center
>>> F=CylindricalLens(F,f, x_shift=2*mm) #idem, shifted 2 mm in x direction
>>> F=CylindricalLens(F,f, x_shift=2*mm, angle=30.0*deg) #idem, rotated 30 degrees
```

--------------------------------

### Initialize LightPipes Field

Source: https://opticspy.github.io/lightpipes/manual.html

Starts LightPipes calculations by defining grid size, dimension, and wavelength. Requires importing the LightPipes package and optionally units.

```python
from LightPipes import *
GridSize = 30*mm
GridDimension = 5
lambda_ = 500*nm #lambda_ is used because lambda is a Python build-in function.
Field = Begin(GridSize, lambda_, GridDimension)
print(Field.field)
```

--------------------------------

### Install LightPipes for Python 3

Source: https://opticspy.github.io/lightpipes/install.html

Installs LightPipes for Python 3, typically used on systems like Raspberry Pi.

```bash
sudo pip3 install lightpipes
```

--------------------------------

### Install Cython and ATLAS

Source: https://opticspy.github.io/lightpipes/_sources/install.rst.txt

Install necessary build tools like Cython and the ATLAS library, which are often required for compiling Python packages with C extensions.

```bash
sudo pip3 install cython
sudo apt-get install libatlas-base-dev
```

--------------------------------

### Test LightPipes Installation

Source: https://opticspy.github.io/lightpipes/_sources/install.rst.txt

After installation, run these Python commands to test if LightPipes is working correctly. A successful test will output 'LightPipes for Python: test passed.'

```python
>>> from LightPipes import *
>>> LPtest()
LightPipes for Python: test passed.
>>>
```

--------------------------------

### Install LightPipes for Python 3

Source: https://opticspy.github.io/lightpipes/_sources/install.rst.txt

Final installation command for LightPipes using pip, typically for Python 3. This command should be run after all dependencies are met.

```bash
sudo pip(3) install lightpipes
```

--------------------------------

### Get Help for a Specific Command in LightPipes

Source: https://opticspy.github.io/lightpipes/_sources/support.rst.txt

Use the `help()` function at the Python prompt to get detailed information about specific LightPipes commands. This is useful for understanding command arguments and return values.

```python
from LightPipes import *
help(Begin)
```

--------------------------------

### Far-field Propagation with Rectangular Aperture

Source: https://opticspy.github.io/lightpipes/manual.html

Demonstrates far-field propagation of a rectangular aperture using LightPipes. This example sets up a larger propagation distance and a different initial field size compared to near-field examples. Requires LightPipes and Matplotlib.

```python
from LightPipes import *
import matplotlib.pyplot as plt

Field=Begin(400*mm, 1*um, 512)
Field = RectAperture(20*mm,20*mm,0, 0,0, Field)
Field = Forvard(500*m, Field)
I = Intensity(0,Field)

x=[]
for i in range(512):
    x.append((-20*mm/2+i*20*mm/512)/mm)

fig=plt.figure(figsize=(10,6))
ax1 = fig.add_subplot(121)
ax2 = fig.add_subplot(122)
ax1.imshow(I,cmap='rainbow'); ax1.axis('off')
ax2.plot(x,I[256]);ax2.set_xlabel('x [mm]');ax2.set_ylabel('Intensity [a.u.]')
ax2.grid('on')
plt.show()
```

--------------------------------

### Simulate Interference from Multiple Holes

Source: https://opticspy.github.io/lightpipes/_sources/MultiHoleAndSlit.rst.txt

Demonstrates creating a row of holes and analyzing the interference pattern. This example is useful for understanding diffraction from multiple apertures.

```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()
```

--------------------------------

### Begin

Source: https://opticspy.github.io/lightpipes/command-reference.html

Initializes a new optical field with specified grid size, wavelength, and dimension. Allows for memory optimization by setting the data type.

```APIDOC
## Begin(_size_ , _labda_ , _N_ , _dtype =None_)

### Description
Initiates a field with a grid size, a wavelength and a grid dimension. By setting dtype to numpy.complex64 memory can be saved. If dtype is not set (default = None), complex (equivalent to numpy.complex128) will be used for the field array.

### Parameters
* **size** (_int_, _float_) – size of the square grid
* **labda** (_int_, _float_) – the wavelength of the output field
* **N** (_int_) – the grid dimension
* **dtype** (_complex_, _numpy.complex64_, _numpy.complex128_ (default = None) – type of the field array

### Returns
output field (N x N square array of complex numbers).

### Return type
LightPipes.field.Field

### Example
```python
>>> from LightPipes import *
>>> size = 20*mm
>>> wavelength = 500*nm
>>> N = 5
>>> F = Begin(size, wavelength, N)
```
```

--------------------------------

### Simulate Multi-Slit Diffraction

Source: https://opticspy.github.io/lightpipes/_sources/MultiHoleAndSlit.rst.txt

This example simulates the diffraction pattern produced by light passing through multiple parallel slits. Ensure the lightpipes library is installed.

```python
import numpy as np
import lightpipes as lp
from lightpipes. অপটিক্স import * # Import all optics functions

# Define simulation parameters
n = 512 # Number of grid points
size = 10e-3 # Physical size of the grid (meters)
wavelength = 632.8e-9 # Wavelength of light (meters)

# Create a Wavefront object
wave = lp.Wavefront(n, size, wavelength)

# Define the multi-slit aperture
# Example: 3 slits
# slit_width = 0.2e-3
# slit_spacing = 1.0e-3
# wave.aperture = lp.MultiSlit(wave, slit_width, slit_spacing, n_slits=3, orientation='horizontal')

# Example: 5 slits
wave.aperture = lp.MultiSlit(wave, width=0.1e-3, spacing=0.5e-3, n_slits=5, orientation='vertical')

# Propagate the wavefront to a distance
distance = 1.0 # meters
propagated_wave = wave.propagate(distance)

# Visualize the intensity pattern
propagated_wave.intensity().plot(title='Multi-Slit Diffraction Pattern')

# You can also access the intensity data as a numpy array:
# intensity_data = propagated_wave.intensity().data

```

--------------------------------

### Arbitrary Intensity and Phase Distribution (Python)

Source: https://opticspy.github.io/lightpipes/_sources/manual.rst.txt

This example demonstrates how to create and apply arbitrary intensity and phase distributions to a light beam. It's useful for simulating complex optical elements or wavefront shaping.

```python
import numpy as np
import matplotlib.pyplot as plt
from LightPipes import *

# Parameters
wavelength = 633*nm
size = 10*mm
N = 256 # Grid size

# Initialize Field
F = Begin(size, wavelength, N)

# Create an arbitrary phase distribution (e.g., a simple phase ramp)
# phase_map = np.zeros((N, N))
# for i in range(N):
#     for j in range(N):
#         phase_map[i, j] = (i / N) * 2 * np.pi # Example phase ramp

# Create an arbitrary intensity distribution (e.g., a Gaussian beam)
# intensity_map = np.zeros((N, N))
# center_x, center_y = N // 2, N // 2
# sigma = N / 8
# for i in range(N):
#     for j in range(N):
#         intensity_map[i, j] = np.exp(-((i - center_x)**2 + (j - center_y)**2) / (2 * sigma**2))

# Apply custom phase and intensity filters
# F = Phase(phase_map, F) # Apply custom phase
# F = Intensity(intensity_map, F) # Apply custom intensity

# For demonstration, let's create a simple phase and intensity filter
# Example: A circular aperture for intensity and a quadratic phase for focus
radius = size / 4
phase_center_x, phase_center_y = 0, 0
phase_coeff = 1e-3 # Controls the curvature of the phase

intensity_map = np.zeros((N, N))
phase_map = np.zeros((N, N))

for i in range(N):
    for j in range(N):
        x = (i - N/2) * size / N
        y = (j - N/2) * size / N
        
        # Circular aperture for intensity
        if x**2 + y**2 < radius**2:
            intensity_map[i, j] = 1.0
        else:
            intensity_map[i, j] = 0.0
            
        # Quadratic phase for focusing
        phase_map[i, j] = phase_coeff * (x**2 + y**2)

F = Intensity(intensity_map, F)
F = Phase(phase_map, F)

# Calculate and plot the resulting intensity and phase
I = Intensity(0, F)
Phi = Phase(0, F)

plt.figure(figsize=(12, 5))

plt.subplot(1, 2, 1)
plt.imshow(I, cmap='jet')
plt.title('Intensity Distribution')
plt.xlabel('x index')
plt.ylabel('y index')
plt.colorbar()

plt.subplot(1, 2, 2)
plt.imshow(Phi, cmap='hsv')
plt.title('Phase Distribution')
plt.xlabel('x index')
plt.ylabel('y index')
plt.colorbar()

plt.tight_layout()
plt.show()

```

--------------------------------

### Far-Field Propagation with Forvard

Source: https://opticspy.github.io/lightpipes/_sources/manual.rst.txt

For far-field propagation, the grid size must be significantly larger than the beam to avoid interference from wave guide walls. This example uses a larger grid.

```python
from LightPipes import *

size = 100e-3
wavelength = 632.8e-9

# Initialize the field with a larger grid
field = Begin(size*4, wavelength, 1000)

# Propagate 1m forward
field = Forvard(field, 1.0)

# Filter with an aperture smaller than the grid
field = RectAperture(field, 10e-3, 10e-3)

# Propagate 1m forward again
field = Forvard(field, 1.0)

```

--------------------------------

### Focusing a Lens with Steps Command

Source: https://opticspy.github.io/lightpipes/manual.html

Demonstrates calculating the intensity distribution in the focus of a lens using the `Steps` command for propagation. This example models diffraction, absorption, and refraction effects.

```python
from LightPipes import*
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt

wavelength=632.8*nm;
size=4*mm;
N=100;
N2=50;
R=1.5*mm;
dz=10*mm;
f=50*cm;
n=(1.0 + 0.1j)*np.ones((N,N))

Icross=np.zeros((100,N))
X=range(N)
Z=range(100)
X, Z=np.meshgrid(X,Z)
F=Begin(size,wavelength,N);
F=CircAperture(R,0,0,F);
F=Lens(f,0,0,F);
for i in range(0,100):
  F=Steps(dz,1,n,F);
  I=Intensity(0,F);
  Icross[i][:N]=I[N2][:N]

ax = plt.axes(projection='3d')
ax.plot_surface(X, Z,
        Icross,
        rstride=1,
        cstride=1,
        cmap='rainbow',
        linewidth=0.0,
        )
plt.axis('off')
plt.show()
```

--------------------------------

### Initialize Field with Begin Command

Source: https://opticspy.github.io/lightpipes/_sources/manual.rst.txt

Initializes the optical field. Requires importing LightPipes and defining grid parameters. The Begin command creates a uniform field with intensity 1 and phase 0.

```bash
>>> from LightPipes import *
>>> GridSize = 30*mm
>>> GridDimension = 5
>>> lambda_ = 500*nm #lambda_ is used because lambda is a Python build-in function.
>>> Field = Begin(GridSize, lambda_, GridDimension)
>>> print(Field.field)
[[1.+0.j 1.+0.j 1.+0.j 1.+0.j 1.+0.j]
 [1.+0.j 1.+0.j 1.+0.j 1.+0.j 1.+0.j]
 [1.+0.j 1.+0.j 1.+0.j 1.+0.j 1.+0.j]
 [1.+0.j 1.+0.j 1.+0.j 1.+0.j 1.+0.j]
 [1.+0.j 1.+0.j 1.+0.j 1.+0.j 1.+0.j]]
```

--------------------------------

### Import Bitmap as Filter (Python)

Source: https://opticspy.github.io/lightpipes/_sources/manual.rst.txt

This example shows how to import a bitmap image (like an arrow created in Paint) and use it as a filter to shape the light beam's intensity and phase.

```python
import numpy as np
import matplotlib.pyplot as plt
from PIL import Image
from LightPipes import *

# Parameters
wavelength = 633*nm
size = 10*mm
N = 200 # Grid size should match the bitmap dimensions if possible

# Initialize Field
F = Begin(size, wavelength, N)

# Load the bitmap image (ensure 'arrow.png' is in the same directory or provide the full path)
# The image should be a monochrome bitmap (black and white)
try:
    img = Image.open('arrow.png').convert('L') # Convert to grayscale
    # Resize image if necessary to match N, or adjust N to match image size
    if img.size != (N, N):
        img = img.resize((N, N))
    
    bitmap_data = np.array(img)
    
    # Normalize the bitmap data to be between 0 and 1
    # Assuming black is 0 and white is 255
    bitmap_filter = 1.0 - (bitmap_data / 255.0) # Invert: white areas let light through (1), black areas block (0)

    # Apply the bitmap as an intensity filter
    F = Intensity(bitmap_filter, F)

    # Calculate and plot the resulting intensity
    I = Intensity(0, F)

    plt.figure(figsize=(8, 6))
    plt.imshow(I, cmap='jet')
    plt.title('Intensity after applying Bitmap Filter (Arrow)')
    plt.xlabel('x index')
    plt.ylabel('y index')
    plt.colorbar()
    plt.show()

except FileNotFoundError:
    print("Error: 'arrow.png' not found. Please ensure the bitmap file is in the correct directory.")
except Exception as e:
    print(f"An error occurred: {e}")

```

--------------------------------

### Install numpy

Source: https://opticspy.github.io/lightpipes/manual.html

Install the numpy package for numerical operations, which is used for array manipulation in plotting.

```bash
>>> pip install numpy

```

--------------------------------

### Find Python installation directory (Windows)

Source: https://opticspy.github.io/lightpipes/_sources/install.rst.txt

Command to locate the Python installation directory on Windows systems.

```bash
where python
```

--------------------------------

### Install Matplotlib for Plotting

Source: https://opticspy.github.io/lightpipes/_sources/install.rst.txt

Matplotlib is a required plotting library for most LightPipes applications. Install it using pip.

```bash
pip(3) install matplotlib
```

--------------------------------

### LPhelp

Source: https://opticspy.github.io/lightpipes/command-reference.html

Navigates to the LightPipes documentation website.

```APIDOC
## LPhelp()

### Description
Goes to the LightPipes documentation website.

### Endpoint
https://opticspy.github.io/lightpipes/
```

--------------------------------

### Find Python installation directory (Linux/Mac)

Source: https://opticspy.github.io/lightpipes/_sources/install.rst.txt

Command to locate the Python installation directory on Linux or Mac systems.

```bash
which python
```

--------------------------------

### Spatial Filtering with PipFFT (Python)

Source: https://opticspy.github.io/lightpipes/_sources/manual.rst.txt

This example demonstrates spatial filtering using the PipFFT command, which performs a Fourier transform on the light field. It allows for filtering in the frequency domain before transforming back.

```python
import numpy as np
import matplotlib.pyplot as plt
from LightPipes import *

# Parameters
wavelength = 633*nm
size = 10*mm
N = 256

# Initialize Field with a Gaussian beam
F = Begin(size, wavelength, N)
F = GaussianBeam(F)

# Calculate initial intensity
I_initial = Intensity(0, F)

# Apply a spatial filter in the Fourier domain (e.g., a circular aperture)
# First, perform FFT
F_fft = PipFFT(F)

# Define filter parameters in the frequency domain
# The frequency domain grid size corresponds to 2*pi*lambda/delta_x
# One step in frequency domain corresponds to 2*pi*lambda/grid_size
# Let's apply a circular aperture in the frequency domain
freq_domain_size = size # The size parameter of PipFFT is the physical size of the grid
freq_aperture_radius = 1 / (5 * mm) # Example: filter out high frequencies

# Create a circular mask in the frequency domain
freq_x = np.fft.fftfreq(N, d=freq_domain_size/N)
freq_y = np.fft.fftfreq(N, d=freq_domain_size/N)
X_freq, Y_freq = np.meshgrid(freq_x, freq_y)

freq_mask = np.zeros((N, N))
for i in range(N):
    for j in range(N):
        if X_freq[i, j]**2 + Y_freq[i, j]**2 < freq_aperture_radius**2:
            freq_mask[i, j] = 1.0
        else:
            freq_mask[i, j] = 0.0

# Apply the frequency mask
F_fft_filtered = F_fft * freq_mask

# Perform inverse FFT to get the filtered field
F_filtered = PipFFT(F_fft_filtered) # PipFFT performs both forward and inverse FFT

# Calculate final intensity
I_filtered = Intensity(0, F_filtered)

# Plotting
plt.figure(figsize=(12, 5))

plt.subplot(1, 2, 1)
plt.imshow(I_initial, cmap='jet')
plt.title('Initial Intensity')
plt.xlabel('x index')
plt.ylabel('y index')
plt.colorbar()

plt.subplot(1, 2, 2)
plt.imshow(I_filtered, cmap='jet')
plt.title('Filtered Intensity (Spatial Filter)')
plt.xlabel('x index')
plt.ylabel('y index')
plt.colorbar()

plt.tight_layout()
plt.show()

```

--------------------------------

### Install Numpy

Source: https://opticspy.github.io/lightpipes/_sources/manual.rst.txt

Installs the numpy package, which is used for numerical operations and array manipulation in LightPipes, particularly for plotting results.

```bash
>>> pip install numpy
```

--------------------------------

### LPdemo

Source: https://opticspy.github.io/lightpipes/command-reference.html

Demonstrates the simulation of a two-holes interferometer. Returns a plot of the interference pattern and a listing of the Python script.

```APIDOC
## LPdemo()

### Description
Demonstrates the simulation of a two-holes interferometer.

### Returns
A plot of the interference pattern and a listing of the Python script.

### Return type
matplotlib.image.AxesImage
```

--------------------------------

### Install LightPipes C++ version

Source: https://opticspy.github.io/lightpipes/_sources/install.rst.txt

Install the C++ version 1.2.0 of LightPipes, suitable for environments like Raspberry Pi with Python 3.7.

```bash
sudo pip(3) install LightPipes==1.2.0
```

--------------------------------

### LightPipes Begin Command Signature

Source: https://opticspy.github.io/lightpipes/_sources/support.rst.txt

This is the signature for the `Begin` command, which creates a plane wave. It requires GridSize, Wavelength, and N (grid points).

```bash
Help on built-in function Begin:

Begin(...) method of LightPipes._LightPipes.Init instance
    F = Begin(GridSize, Wavelength, N)

    :ref:`Creates a plane wave (phase = 0.0, amplitude = 1.0). <Begin>`

    Args::

        GridSize: size of the grid
        Wavelength: wavelength of the field
        N: N x N grid points (N must be even)

    Returns::

        F: N x N square array of complex numbers (1+0j).

    Example:

    :ref:`Diffraction from a circular aperture <Diffraction>`

>>>
```

--------------------------------

### Find Python installation directory

Source: https://opticspy.github.io/lightpipes/install.html

Commands to locate the Python installation directory on different operating systems, necessary for finding and editing configuration files.

```bash
where python
```

```bash
which python
```

--------------------------------

### Simulate Poisson's Spot with LightPipes

Source: https://opticspy.github.io/lightpipes/PoissonSpot.html

This script simulates Poisson's spot by creating a uniform plane wave, introducing a circular opaque disk as an obstacle, and performing Fresnel propagation. It then calculates and visualizes the intensity pattern, showing the characteristic bright central spot and diffraction rings. Requires numpy, LightPipes, and matplotlib.

```python
import numpy as np
from LightPipes import *
import matplotlib.pyplot as plt

# Parameters
wavelength=5*um
size=25.0*mm
N=2000
N2=int(N/2)
z=20*cm

# Begin with a plane wave
F = Begin(size, wavelength, N)

# Gaussian laser beam
w0=size/3
F=GaussBeam(F, w0)

# Circular opaque disk (obstacle)
disk_diameter = 6.0 * mm
F = CircScreen(F,disk_diameter/2)

# Fresnel propagation
F = Fresnel(F, z)

# Intensity at the screen
I = Intensity(0, F)

# Coordinates for plotting
x = np.linspace(-size/2, size/2, N) / mm

s1 =    r'LightPipes for Python' + '\n'
s2 =    r'Poisson.py'+ '\n\n'\
         f'size = {size/mm:4.2f} mm' + '\n'
         f'$\lambda$ = {wavelength/um:4.2f} $\mu$m' + '\n'
         f'N = {N:d}' + '\n' +
         f'd = {disk_diameter/mm:4.2f} mm disk diameter' + '\n'
         f'w0 = {w0/mm:4.2f} mm radius Gauss beam' + '\n'
         f'z = {z/cm:4.2f} cm distance from disk' + '\n'
         r'${\copyright}$ Fred van Goor, February 2026'


fig=plt.figure(figsize=(11,6))
fig.suptitle("The spot of Poisson")
ax1 = fig.add_subplot(221);ax1.axis('off')
ax2 = fig.add_subplot(222)
ax3 = fig.add_subplot(223);ax3.axis('off')
ax1.set_xlim(N2-300,N2+300)
ax1.set_ylim(N2-300,N2+300)
ax1.imshow(I,cmap='jet')

ax1.set_title(f'Intensity pattern after {z/cm:4.1f} cm propagation')
X=np.linspace(-size/2,size/2,N)
ax2.plot(X/mm,I[N2]); ax2.set_xlabel('x[mm]'); ax2.set_ylabel('Intensity [a.u.]')
ax2.set_xlim(-1,1); ax2.set_title('The intensity cross-section of the spot')
ax3.text(0.0,1.0,s1,fontsize=12, fontweight='bold')
ax3.text(0.0,0.3,s2)
plt.show()
```

--------------------------------

### Simulate Lens and Fresnel Propagation with Spherical Coordinates

Source: https://opticspy.github.io/lightpipes/manual.html

This example demonstrates simulating optical propagation through a lens and using Fresnel diffraction, comparing results obtained with and without spherical coordinates. It visualizes phase and intensity distributions. Requires LightPipes and Matplotlib.

```python
from LightPipes import *
import matplotlib.pyplot as plt

def TheExample(N):
    fig=plt.figure(figsize=(15,9.5))
    ax1 = fig.add_subplot(221)
    ax2 = fig.add_subplot(222)
    ax3 = fig.add_subplot(223)
    ax4 = fig.add_subplot(224)

    labda=1000*nm;
    size=10*mm;

    f=10*cm
    f1=10*m
    f2=f1*f/(f1-f)
    frac=f/f1
    newsize=frac*size
    w=5*mm;
    F=Begin(size,labda,N);
    F=RectAperture(w,w,0,0,0,F);

#1) Using Lens and Fresnel:
    F1=Lens(f,0,0,F)
    F1=Fresnel(f,F1)
    phi1=Phase(F1);phi1=PhaseUnwrap(phi1)
    I1=Intensity(0,F1);
    x1=[]
    for i in range(N):
        x1.append((-size/2+i*size/N)/mm)  

#2) Using Lens + LensFresnel and Convert:
    F2=Lens(f1,0,0,F);
    F2=LensFresnel(f2,f,F2);
    F2=Convert(F2);
    phi2=Phase(F2);phi2=PhaseUnwrap(phi2)
    I2=Intensity(0,F2);
    x2=[]

    for i in range(N):
        x2.append((-newsize/2+i*newsize/N)/mm)

    ax1.plot(x1,phi1[int(N/2)],'k--',label='Without spherical coordinates')
    ax1.plot(x2,phi2[int(N/2)],'k',label='With spherical coordinates');
    ax1.set_xlim(-newsize/2/mm,newsize/2/mm)
    ax1.set_ylim(-2,4)
    ax1.set_xlabel('x [mm]');
    ax1.set_ylabel('phase [rad]');
    ax1.set_title('phase, N = %d' %N)
    legend = ax1.legend(loc='upper center', shadow=True)

    ax2.plot(x1,I1[int(N/2)],'k--',label='Without spherical coordinates')
    ax2.plot(x2,I2[int(N/2)], 'k',label='With spherical coordinates');
    ax2.set_xlim(-newsize/2/mm,newsize/2/mm)
    ax2.set_ylim(0,100000)
    ax2.set_xlabel('x [mm]');
    ax2.set_ylabel('Intensity [a.u.]');
    ax2.set_title('intensity, N = %d' %N)
    legend = ax2.legend(loc='upper center', shadow=True)

    ax3.imshow(I1);ax3.axis('off');ax3.set_title('Without spherical coordinates')
    ax3.set_xlim(int(N/2)-N*frac/2,int(N/2)+N*frac/2)
    ax3.set_ylim(int(N/2)-N*frac/2,int(N/2)+N*frac/2)
    ax4.imshow(I2);ax4.axis('off');ax4.set_title('With spherical coordinates')
    plt.figtext(0.3,0.95,'Spherical Coordinates, f = 10cm lens\nGrid dimension is: %d x %d pixels' %(N, N), fontsize = 18, color='red')

TheExample(100) #100 x 100 grid

TheExample(1000) #1000 x 1000 grid

plt.show()
```

--------------------------------

### Locate LightPipes Site-Packages Directory

Source: https://opticspy.github.io/lightpipes/_sources/UserDefinedFunctions.rst.txt

Provides Python code to find the 'site-packages' directory where LightPipes is installed. This is necessary for adding custom functions directly to the installation.

```python
import site
print(site.getsitepackages())
```

--------------------------------

### Plot Bessel Annular Slit Example

Source: https://opticspy.github.io/lightpipes/_sources/PoissonSpottoBesselBeam.rst.txt

Generates a plot illustrating the Bessel beam created by an annular slit. This example is useful for visualizing non-diffractive beam properties.

```python
import numpy as np
import matplotlib.pyplot as plt
from lightpipes.beam import CircularAperture, Beam
from lightpipes.propagation import FresnelPropagation

# Parameters
wavelength = 633e-9 # meters
radius = 1e-3 # meters
N = 1024 # grid size
length = 0.1 # meters

# Create a beam
wavelength = 633e-9 # meters
radius = 1e-3 # meters
N = 1024 # grid size
length = 0.1 # meters

# Create a beam
field = Beam(radius=radius, wavelength=wavelength, N=N)

# Create an annular aperture
# Inner radius is 0.5 * outer radius
annular_aperture = CircularAperture(field, radius=radius, inner_radius=radius/2)

# Propagate the beam
propagator = FresnelPropagation(length=length, field=field)
field = propagator.propagate(annular_aperture)

# Plot the intensity
plt.figure(figsize=(8, 6))
plt.imshow(np.abs(field.field)**2, extent=[field.x.min(), field.x.max(), field.y.min(), field.y.max()])
plt.title('Bessel Beam Intensity')
plt.xlabel('x (m)')
plt.ylabel('y (m)')
plt.colorbar(label='Intensity')
plt.show()

```
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