Simple optical ray tracing library to validate the design of an optical system (lenses positions and sizes, focal lengths, aperture and field stops). Support for Monte Carlo raytracing to estimate transmission efficiency and powers, limited but functional Zemax file loader for lenses, several material dispersion curves included for chromatic aberrations all coming from http://refractiveindex.info
Project description
RayTracing
by the DCCLab group http://www.dcclab.ca, guided by Prof. Daniel Côté.
This code aims to provide a simple ray tracing module for calculating various properties of optical paths (object, image, aperture stops, field stops). It makes use of ABCD matrices and does not consider spherical aberrations but can compute chromatic aberrations for simple cases when the materials are known. Since it uses the ABCD formalism (or Ray matrices, or Gauss matrices) it can perform tracing of rays and gaussian laser beams.
It is not a package to do "Rendering in 3D with raytracing".
The code has been developed first for teaching purposes and is used in my "Optique" Study Notes (french only), but also for actual use in my research. As of January 21st, 2021, there is an extensive, freely accessible, peerreviewed tutorial in Journal of Neurophotonics:
"Tools and tutorial on practical ray tracing for microscopy"
by V. Pineau Noël*, S. Masoumi*, E. Parham*, G. Genest, L. Bégin, M.A. Vigneault, D. C. Côté, Neurophotonics, 8(1), 010801 (2021). *Equal contributions. Permalink: https://doi.org/10.1117/1.NPh.8.1.010801
The published tutorial assumes version 1.3.x. There are video tutorials (in english or french, with english subtitles when in french) on YouTube. We have made no attempts at making high performance code. Readability and simplicity of usage are the key here. It is a module with a few files, and only matplotlib
and numpy
as dependent modules.
Where do I get started?
 If you want to use the module, keep reading.
 If you have a suggestion or a bug report, go to Issues.
 If you want to read and contribute to the code, go to the Wiki for general considerations. We plan to have a roadmap in the near future.
Getting started
The module defines Ray
, Matrix
, MatrixGroup
and ImagingPath
as the main elements for tracing rays. Matrix
and MatrixGroup
are either one or a sequence of many matrices into which Ray
will propagate. ImagingPath
is also a sequence of elements, with an object at the front edge. Specific subclasses of Matrix
exists: Space
, Lens
, ThicklLens
, and Aperture
. Finally, a ray fan is a collection of rays, originating from a given point with a range of angles.
We have tried to separate the calculation code (i.e. the matrices and subclasses) from the drawing code (figures and graphics). One can use the calculation code without any graphics calls.
If you want to perform calculations with coherent laser beams, then you use GaussianBeam
and LaserPath
. Everything is essentially the same, except that the formalism does not allow for the gaussian beam to be "blocked", hence any calculation of stops with aperture are not available in LaserPath
. That part of the code is less developed, but it is nevertheless available.
What's new?
To get information about what is new, currently the best place is the release page on GitHub.
There is a Frequently Asked Questions page.
The article above is fully compatible with all 1.3.x versions. As long as the API does not change, versions will be 1.3.x.
Installing and upgrading
You need matplotlib
, which is a fairly standard Python module. If you do not have it, installing Anaconda is your best option. Python 3.6 or later is required. There are several ways to install the module:
 Simplest:
pip install raytracing
orpip install upgrade raytracing
 If you need to install
pip
, download getpip.py and run it withpython getpip.py
 If you need to install
 If you download the source of the module, then you can type:
python setup.py install
 From GitHub, you can get the latest version (including bugs, which are 153% free!) and then type
python setup.py install
 If you are completely lost, copying the folder
raytracing
(the one that includes__init__.py
) from the source file into the same directory as your own script will work.  Watch the tutorial with subtitles here.
Getting started
The simplest way to import the package in your own scripts after installing it:
from raytracing import *
This will import Ray
, GaussianBeam
, and several Matrix
elements such as Space
, Lens
, ThickLens
, Aperture
, DielectricInterface
, but also MatrixGroup
(to group elements together), ImagingPath
(to ray trace with an object at the front edge), LaserPath
(to trace a gaussian laser beam from the front edge) and a few predefined other such as Objective
(to create a very thick lens that mimicks an objective).
You create an ImagingPath
or a LaserPath
, which you then populate with optical elements such as Space
, Lens
or Aperture
or vendor lenses. You can then adjust the path properties (object height in ImagingPath
for instance or inputBeam for LaserPath
) and display in matplotlib. You can create a group of elements with MatrixGroup
for instance a telescope, a retrofocus or any group of optical elements you would like to treat as a "group". The Thorlabs and Edmund optics lenses, for instance, are defined as MatrixGroups
.
This will show you a list of examples of things you can do (more on that in the Examples section):
python m raytracing l # List examples
python m raytracing e all # Run all of them
python m raytracing e 1,2,4,6 # Only run 1,2,4 and 6
python m raytracing t # Run all the tests. Some performance tests can take up to a minute, but they should all pass.
or request help with:
python m raytracing h
In your code, you would do this:
from raytracing import *
path = ImagingPath()
path.append(Space(d=50))
path.append(Lens(f=50, diameter=25))
path.append(Space(d=120))
path.append(Lens(f=70))
path.append(Space(d=100))
path.display()
You can also call display()
on an element to see the cardinal points, principal planes, BFL (back focal length, or the distance between the last interface and the focal point after the lens) and FFL (front focal length, or the distance between the focal point before the lens and the first interface). You can do it with any single Matrix
element but also with MatrixGroup
.
from raytracing import *
thorlabs.AC254_050_A().display()
eo.PN_33_921().display()
Finally, an addition as of 1.2.0 is the ability to obtain the intensity profile of a given source from the object plane at the exit plane of an OpticalPath
. This is in fact really simple: by tracing a large number of rays, with the number of rays at y and θ being proportionnal to the intensity, one can obtain the intensity profile by plotting the histogram of rays reaching a given height at the image plane. Rays
are small classes that return a Ray
that satisfies the condition of the class. Currently, there is UniformRays
,RandomUniformRays
LambertianRays
and RandomLambertianRays
(a Lambertian distribution follows a cosθ distribution, it is a common diffuse surface source). They appear like iterators and can easily be used like this example script:
from raytracing import *
from numpy import *
import matplotlib.pyplot as plt
# Kohler illumination with these variables
fobj = 5
dObj = 5
f2 = 200
d2 = 50
f3 = 100
d3 = 50
# We build the path (i.e. not an Imaging path)
path = OpticalPath()
path.append(Space(d=f3))
path.append(Lens(f=f3, diameter=d3))
path.append(Space(d=f3))
path.append(Space(d=f2))
path.append(Lens(f=f2, diameter=d2))
path.append(Space(d=f2))
path.append(Space(d=fobj))
path.append(Lens(f=fobj, diameter=dObj))
path.append(Space(d=fobj))
# Obtaining the intensity profile
nRays = 1000000 # Increase for better resolution
inputRays = RandomLambertianRays(yMax=2.5, maxCount=nRays)
inputRays.display("Input profile")
outputRays = path.traceManyThrough(inputRays, progress=True)
# On macOS and Linux, you can do parallel computations
# outputRays = path.traceManyThroughInParallel(inputRays, progress=True, processes=8)
outputRays.display("Output profile")
and you will get the following ray histograms:
Finally, it is possible to obtain the chromatic aberrations for compound lenses (achromatic doublets from Thorlabs and Edmund optics, and singlet lens because the materials are known). The following command will give you the focal shift as a function of wavelength (as a graph or values):
from raytracing import *
thorlabs.AC254_100_A().showChromaticAberrations()
wavelengths, shifts = thorlabs.AC254_100_A().focalShifts()
Documentation
All the documentation is available online.
The class hierarchy for optical elements (with parameters and defaults) is:
You may obtain help by:
 Reading the documentation for the code (API reference).
 Core:
Ray
: a ray for geometrical optics with a height and angle $y$ and $\theta$.Rays
: ray distributions to ray trace an object through the optical system.UniformRays
,RandomUniformRays
,LambertianRays
andRandomLambertianRays
are currently available. See example above.
GaussianBeam
: a gaussian laser beam with complex radius of curvature $q$.Matrix
: any 2x2 matrix.MatrixGroup
: treats a group of matrix as a unit (draws it as a unit too)ImagingPath
: AMatrixGroup
with an object at the front for geometrical opticsLaserPath
: AMatrixGroup
with a laser beam input at the front or a Resonator.
 Optical elements:
Aperture
,Space
,Lens
,DielectricInterface
,DielectricSlab
,ThickLens
 Specialty lenses: Defines a general achromat and objective lens
 Thorlabs lenses: Achromat doublet lenses from Thorlabs.
 Edmund Optics lenses: Achromat doublet lenses from Edmund Optics
 Olympus objectives: A few objectives from Olympus.
 Glasses: A few glasses used by Thorlabs to make achromatic doublets. They all have a single function
n(wavelength)
that returns the index at that wavelength. All data obtained from http://refractiveindex.info.  Zemax ZMX file reader: to read textbased Zemax files of lenses.
 Core:
 typing (interactively):
help(Matrix)
,help(MatrixGroup)
help(Ray)
,help(ImagingPath)
to get the API,  look at the examples with
python m raytracing
 simply look at the code.
python
>>> help(Matrix)
Help on class Matrix in module raytracing.abcd:
class Matrix(builtins.object)
 Matrix(A, B, C, D, physicalLength=0, apertureDiameter=inf, label='')

 A matrix and an optical element that can transform a ray or another
 matrix.

 The general properties (A,B,C,D) are defined here. The operator "*" is
 overloaded to allow simple statements such as:

 ray2 = M1 * ray
 or
 M3 = M2 * M1

 The physical length is included in the matrix to allow simple management of
 the ray tracing. IF two matrices are multiplied, the resulting matrice
 will have a physical length that is the sum of both matrices.

 In addition finite apertures are considered: if the apertureDiameter
 is not infinite (default), then the object is assumed to limit the
 ray height to plus or minus apertureDiameter/2 from the front edge to the back
 edge of the element.

 Methods defined here:

 __init__(self, A, B, C, D, physicalLength=0, apertureDiameter=inf, label='')
 Initialize self. See help(type(self)) for accurate signature.

 __mul__(self, rightSide)
 Operator overloading allowing easy to read matrix multiplication

 For instance, with M1 = Matrix() and M2 = Matrix(), one can write
 M3 = M1*M2. With r = Ray(), one can apply the M1 transform to a ray
 with r = M1*r

 __str__(self)
 String description that allows the use of print(Matrix())

 backwardConjugate(self)
 With an image at the back edge of the element,
 where is the object ? Distance before the element by
 which a ray must travel to reach the conjugate plane at
 the back of the element. A positive distance means the
 object is "distance" in front of the element (or to the
 left, or before).

 M2 = M1*Space(distance)
 # M2.isImaging == True
Examples
You can list several examples python m raytracing l
:
All example code on your machine is found at: /somedirectory/on/your/machine
1. ex01.py A single lens f = 50 mm, infinite diameter
2. ex02.py Two lenses, infinite diameters
3. ex03.py Finitediameter lens
4. ex04.py Aperture behind lens acting as Field Stop
5. ex05.py Simple microscope system
6. ex06.py Kohler illumination
7. ex07.py Focussing through a dielectric slab
8. ex08.py Virtual image at f with object at f/2
9. ex09.py Infinite telecentric 4f telescope
10. ex10.py Retrofocus $f_e$={0:.1f} cm, and BFL={1:.1f}
11. ex11.py Thick diverging lens computed from the Lensmaker equation
12. ex12.py Thick diverging lens built from individual elements
13. ex13.py Obtain the forward and backward conjugates
14. ex14.py Generic objectives
15. ex15.py Model Olympus objective LUMPlanFL40X
16. ex16.py Commercial doublets from Thorlabs and Edmund
17. ex17.py An optical system with vendor lenses
18. ex18.py Laser beam and vendor lenses
19. ex19.py Cavity round trip and calculated laser modes
.... and more complete examples at /somedirectory/on/your/machine
You can run them all with python m raytracing e all
(see them all below) to get a flavour of what is possible (note: in the US, it will give you a flavor of what is possible instead). Notice the command will tell you where the directory with all the tests is on your machine. You will find more complete examples in that examples directory, distributed with the module. For instance, illuminator.py
to see a Kohler illuminator, and invariant.py
to see an example of the role of lens diameters to determine the field of view.
Known limitations
There are no known bugs in the actual calculations, but there are bugs or limitations in the display:
 It is not easy to put several labels on a graph without any overlap. We are still working on it.
 It is also not easy to figure out what "the right size" should be for an arrow head, the font, the position of a label, the size of the "ticks" on the aperture.
 Labelling focal points with appropriate secondary labels should be possible, maybe a superscript?
 The yscale is not always set appropriately when the elements have infinite diameters: the rays will go beyond the element drawn on the figure.
Licence
This code is provided under the MIT License.
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