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Synthesizing and fitting coherent anti-Stokes Raman spectra (CARS) in Python

Project description

CARSpy Documentation Status

Synthesizing and fitting coherent anti-Stokes Raman spectra in Python.


Having no access to the source codes of any of the existing CARS programs, I started this project simply as a way to learn more about CARS. I ended up spending a lot of time sifting through literatures from the past decades, trying to figure out what were done to analyze experimental CARS spectra and how they were implemented. The latter proved rather challenging as specific implementations weren’t always laid out in sufficient (mathematical) details to facilitate comprehension and replication (e.g., things as trivial as units for different constants weren’t always made clear in some publications).

In an effort to put together a fully-functioning CARS fitting program, I thought it would perhaps benefit other CARS practitioners (especially the newcomers) if I open source my implementations. I hope to also benefit from this transparency and openness to public scrutiny. Although the “draft” code (not available in this public repo) already lives up to my original purpose (least-square fit of experimental broadband CARS spectra), it is most likely not error-free and has a lot of room left for improvement. Therefore, I plan to rewrite the important modules (spectrum synthesis and least-square fit) and slowly bring all features (see below) up to date. I am also looking forward to feedbacks and potential collaborators from the community.


Nitrogen is currently the only species implemented/tested in carspy. Other common species will be added in the future (or can be readily introduced via customization).

Quick start

$ pip install carspy

See installation guide for alternative methods.

Live demonstration

To try out the basic functions of carspy, head over to the Live demo, which is a webapp built with Plotly/Dash and hosted on Heroku to showcase how CARS spectrum could be synthesized and fitted with carspy. The computation/loading speed is largely limited by the cloud server and Internet speed. For a much better performance, download or fork the carspy app repository and run the app locally.

  • Synthesize CARS spectrum
  • Least-square-fit of a synthesized spectrum


  • CARSpy (stands for Coherent Anti-Stokes Raman Spectroscopy):
carspy structure
  • The CARS model:
cars model


  • The default chemical equilibrium solver based on cantera can be replaced by custom functions.
  • Voigt profile is implemented via numerical convolution of a Gaussian profile with the Raman lines.
  • Extended exponential gap model is not yet implemented.


  • Readily extendable for species other than N2 and for other CARS setup other than typical broadband CARS.
  • Option to incorporate equilibrium composition using an external chemical equilibrium calculator (such as cantera), such that temperature is the only fitting parameter for thermometry.
  • Vibrational and rotational nonequilibrium: vibrational temperature can be varied independently from rotational temperature.

Comparisons with CARSFT


Figure 1 Synthesized CARS spectra in N2 at 1 atm, 2400 K, with a pump linewidth of 0.5 cm-1, using Voigt lineshape and cross-coherence convolution.


Figure 2 Synthesized CARS spectra in N2 at 10 atm, 2400 K, with a pump linewidth of 0.5 cm-1, using modified exponential gap law (MEG) and cross-coherence convolution.


There seems to exist a number of compiled versions of CARSFT that have likely been modified (in a hardcoded way) to suit specific purposes (e.g., artificially inflated nonresonant background and/or Raman linewidth).

The version used for the comparisons here was likely optimized for dual-pump CARS, such that several important settings (isolated line, single/double convolution, MEG, etc) don’t behave consistently. Small tweaks during the configuration setup (e.g., modifiers) were necessary to create theoretically correct spectra in CARSFT.


The above features currently present in the draft code will be gradually improved and included in the main branch. Here is a tentative plan:

  • (Done) Module for synthesizing CARS spectra (optional with cantera)
  • (Done) Module for least-square fit (optional with lmfit)
  • (Done) Parallel processing example with joblib
  • (Mid-term) EMEG and XMEG for high-pressure combustion environments
  • (Long-term) Enrich documentation
  • (Long-term) Other common diatomic species
  • (Long-term) Dualpump/Wide CARS


Please consider citing this repository if you use carspy for your publications as:

  author = {Yin, Zhiyao},
  title = {CARSpy: Synthesizing and fitting coherent anti-Stokes Raman spectra in Python},
  year = {2021},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{}}


  • A copy of the NRC report (TR-GD-013_1989) was kindly provided by Dr. Gregory Smallwood and his colleagues at NRC, which has significantly eased the difficulty of understanding some of the key theories in synthesizing CARS spectra.
  • This package was initially created with Cookiecutter and the audreyr/cookiecutter-pypackage project template.

Change Log

0.6.1 (2021-07-07)

  • Fix the discontinuity problem in the asymmetric Voigt profile

0.6.0 (2021-07-05)

  • Add a peak-finding function for calibrating the spectrometer based on Ar or Hg spectra.
  • Implement a fitting routine for the slit function based either on asymmetric Gaussian or Voigt profiles.

0.5.0 (2021-05-17)

  • Add link to a standalone web application that demonstrates the basic functions for synthesizing CARS spectra

0.4.2 (2021-03-12)

  • Add missing json data files to the package.

0.4.1 (2021-03-10)

  • Implement an asymmetric “super” Voigt function for better fitting slit function.

0.4.0 (2021-03-03)

  • Implement least-square fitting routine with lmfit (optional).
  • Add documentations for the least-square fitting module.
  • Add usage examples for both synthesizing and fitting CARS spectra.

0.3.0 (2021-02-25)

  • Implement optional function for calculating local gas composition at chemical equilibrium using cantera.
  • Add documentations for secondary modules.
  • Add bibtex style references in documentations.

0.2.1 (2021-02-14)

  • Change Sphinx theme.
  • Add existing modules to docs.
  • Fix format errors in docstrings.

0.2.0 (2021-02-13)

  • Implement modules for synthesizing N2 CARS spectra.

0.1.0 (2021-02-13)

  • First release on PyPI.

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