Interferometry Analysis Software (IAS)

Interferometry Analysis Software (IAS) is a dedicated tool for studying gas jets, vapor, and plasma. IAS uses a new algorithm and GUI to analyze interferograms. It can retrieve the accumulated phase shift and apply Abel inversion to estimate the density profile of targets (gas, vapor, or plasma).

Summary

• Introduction
• Installation
• How to use it
  • Main Screen
  • Interferograms
  • Options
• How it works
• Examples
• Authors
• Acknowledgment
• License
• Citation
• Reference

Introduction

The development of diagnostic tools is significant for a better understanding of laser-plasma interactions [1]. An accurate diagnostic is crucial, as instabilities in both target and laser pulses can result in low reproducibility of processes and impair the quality of the intended interaction [2]. Among the various non-perturbing optical methods that can be used to diagnose a gaseous target [3-6], interferometry is a very accurate technique capable of quantifying tiny optical path differences and, therefore, suitable for measuring density variations of gases [7, 8] and laser-induced plasmas [1]. The main drawback of the technique is that it returns the integrated phase along the light path, requiring deconvolution methods for retrieving the target density profile. The software IAS was developed due to the need for a new diagnostic tool to aid in the characterization of supersonic gas jets, vapor, and plasmas, quickly and reliably. IAS was developed from two other software developed by our research group (Interferometry Analysis - Gas-Jet and Interferometry Analysis - LIP). The current version of IAS was developed after several tests and re-evaluations of the density and uncertainty calculations of the targets. IAS is a part of two complementary works: - Studies to implement a laser-plasma accelerator infrastructure laser isotopic separation at the Nuclear and Energy Research Institute (IPEN), in Brazil. - Studies to implement a laser isotopic separation process for nuclear medicine application in the project of Brazilian Multipurpose Reactor (RMB).

Installation

The Interferometry Analysis Software (IAS) was developed in Python 3.11. The use of this algorithm requires the installation of the following packages: NumPy [9], Scipy [10] and PyAbel [11] for data processing, Pillow [12] and Scikit-image [13] for the processing of interferogram images, Matplotlib [14] to plot results, and FreeSimpleGui to create the user's template.

Users also can create a single .exe file using the pyinstaller package through the following terminal command:

pyinstaller --onefile -w IAS_V1.0.0.py

Users who do not use Python IDEs can utilize the software through the executable file available for download HERE.

Note: Users can install IAS with 2 resolutions as default:

IASV1.0.0res45x45 - Version with width and height equal to 45% of the monitor resolution.

IASV1.0.0res80x80 - Version with width and height equal to 80% of the monitor resolution.

How to use it

The Interferometry Analysis Software (IAS) has a graphical interface to facilitate its use, and this section provides a simple review of the software's functions and how to employ them.

Main Screen

The Software Main Screen (Fig. 1) can be divided into 3 main parts: Interferograms, Options, and LIP Profile. Each of these parts will be detailed below.

| | |:--:| | Fig.1. Software Main Screen |

Interferograms

• 1. [Interferogram (Target)] interferogram frame.

  • [Open File(s)] Open interferogram(s) file(s) with the presence of a gaseous target. Image file extensions should preferably be .png or .snp. (Newport proprietary format) for Newport CCD. However, all image extensions (.gif, .jpg, .bmp, etc) can be used. The path to the opened file is shown in the text box immediately above. For more than one file has been opened, two types of analysis can be made:
  • One reference file and n target files, or;
  • n reference file and n target files. > Warning > For different numbers of reference and target files, the IAS code utilizes just a single reference file. > IAS only works with grayscale image files.
    
  • [Rotate] The image rotation in degrees. Positive degrees promote counterclockwise rotation.
    
  • [Original Size] Original dimensions of the image file (width, height). > Note The interferogram shown is scaled to screen size for users' viewing only. However, all processes to determine the plasma density profile are done with the original dimensions of the image file.

• 2. [Interferogram (Ref.)] Scaled reference interferogram.

  • [Open Ref.] Open an undisturbed interferogram file. Image file extensions should preferably be .png or .snp. However, all image extensions (.gif, .jpg, .bmp, etc) can be used. The path to open the file is shown in the textbox above. Unlike interferogram gas jet files, the algorithm allows the insertion of only one reference file. > Warning
    > IAS only works with grayscale image files.

• 3. [Analyse Data] From this command button, the software will apply data processing to generate the accumulated phase-shift map, the radial phase-shift map, and the map of the molecular density distribution of the gaseous target.

• 4. [Clear] Button to clear input and output data.

Options

• 5. [Select Area] Parameters frame for users select the interferogram area to apply the algorithm. The selected area is defined by a rectangle with edges defined by X and Y coordinates. The user can select an area using the mouse click over the image or the combo box [Y Coord] and [X Coord]. > Note: The mouse's first click defines the first value of the X and Y triangle coordinates, and the second click defines the end coordinates of the triangle. Case, the initial X (or Y) is bigger than the final X (or Y), these values will be exchanged.
  • [BG Phase Fit] This parameter defines the values used to construct the background of the accumulated phase $\phi$.
  • For Gas/Vapor targets this value is set based on a percentage of smaller phase values in the selected area, and this background is defined by a 2D plane (default is 5%).
  • For Plasmas, this parameter defines the border size border used to construct the background of the accumulated phase $\phi$. The borders are defined based on a percentage of the selected area, and the background is obtained using a 4th-order 2D polynomial fitting from the selected border as shown in Fig. 2.a and 2.b. The Fig. 2.c and 2.d shows the accumulated phase shift without the fitted background.

| | |:--:| | Fig. 2. a) 3D phase-shift map from plasma with rising background; b) 2D phase-shift map from plasma with background; c) 3D phase-shift map and; d) 2D corrected phase-shift map from plasma without background. |

• 6. [Input Parameteres] Frame to set the experimental parameters used to acquire the interferogram. These parameters are:

  • [Scaling Factor] Interferogram scale in micrometers/pixel (default is $1.000 \mu m /pixel$).
  • [Laser Wavelength] ($\lambda$) and [Laser FHWM] ($\Delta\lambda$) in nm (default is $395\pm0$ nm, respectively).
  • [Gas/Vapor] This frame can only reach Gas/Vapor targets.
  • The list box of some types of gases: H₂, N₂, He and Ar (default is N₂) and [Polarizability] ($\alpha$) in angstrom³. This parameter usually refers to the tendency of matter to acquire an electric dipole moment when subjected to an electric field (default is 1.710 A³ for N₂). > Note > The polarizability value is automatically filled in after selecting the gas type. If the user wants to use gases that are not yet listed, the gas/vapor polarizability value can be entered manually.

• 7. [Analysis Parameters] Parameters frame to analyze the interferogram.

  • [FFT Filter Frequency]: The [Vert. (ν_x)] and [Hor. (ν_x)] parameters are set automatically by the algorithm and these positions define which frequencies ($\pm\nux$) and ($\pm\nuy$) (Horizontal Vertical) will be used to apply the Inverse Fourier Transform and build the phase map of the target.
  • [Filter Range] ($\Delta\nu$) frequency spread of the Gaussian frequency filter in pixel. The initial $\Delta\nu$ depends on the image dimension but can changed by the user. These parameters are given in pixels > Note: For Plasmas the algorithm sets the frequencies that generate a negative phase map. Because the refractive index of the plasma is less than 1. This is an intrinsic characteristic of plasmas. However, the relative's positive and negative frequencies depend on interferogram files.
  • [Gaussian Blur] ($\sigma{blur}$) Spread of the bi-dimensional Gaussian image filter. The standard deviation of the Gaussian filter ($\sigma$) defined by the user is equal for all axes. The [Gaussian Blur] improves the target symmetry. > Note: The ($\sigma{blur}$) is automatically calculated from FFT maps, but users can set this value manually.
  • [Axisymmetric Orientation] Definition of the axis of symmetry (or axisymmetric) to apply the Inverse Abel Transform. The axisymmetric can be Horizontal or Vertical (default is Horizontal for Plasmas and Vertical for Gas/Vapor targets) and the [Axisymmetric Position] is a pixel position on the accumulated phase map to apply the Abel inversion. This position is only for horizontal or vertical orientations. For None (Hor. our Vert) orientations the IAS code doesn't apply Abel Inversion. In this case, the density of the target is retrieved by approximation [15].

Target Profile

• 8. [Stages]: Stages frame allows the visualization of each result of the algorithm.

  • [Fourier Transform] This FFT Frequency map (Fig. 3.a) is built from the Fourier Transform of the target interferogram. The frequency positions highlighted in the FFT Frequency map are automatically identified from pixel columns sum (vertical) and pixel lines sum (horizontal). The selected frequency is marked with a red line over a pixel line (or column) identifying the ($\pm\nux$) and ($\pm\nuy$). > Note: The user can change this [Vert. (ν_x)] and [Hor. (ν_x)] manually. But, the IAS code automatically identifies the frequencies when values equal '0'.
  • [Gaussian Filter] The Gaussian filter map (Fig. 3.b) is applied to generate the phase map. This filter is built from the selected frequencies ($\pm\nux$, $\pm\nuy$) and the range frequency $\Delta\nu$ (Fig. 3.d).
    

|| |:--:| | Fig. 3. (a) 2D and (b) 1D frequency domain obtained by the interferogram Fourier Transform with the selected frequency to be filtered; (c) Gaussian filter to be applied on the selected frequency; (d) 1D frequency domain with range frequency to apply the Gaussian filter. |

For the next three steps, users can view the 2D maps or 1D curves with standard deviation using the [Standard Deviation] checkbox.

• [Acc. Phase-shift] Accumulated phase-shift ($\phi$) of the plasma (in rad) retrieved from the interferograms.

|| |:--:| |Fig. 4. (a) 2D accumulated phase-shift map and (b) 2D standard deviation map; (c) 1D accumulated phase curves and (d) standard deviation of one curve. All phase values are given in rad.|

• [Radial Phase-shift] Radial phase-shift ($\varphi_r$) map in $rad/\mu m$ obtained after applying an Inverse Abel Transform from Accumulated Phase-shift map ($\phi$).

|| |:--:| |Fig. 5. (a) 2D radial phase-shift map and (b) 2D standard deviation map; (c) and (d) accuracy between 1D radial phase-shift and normalized phase-shift curves. All radial phase values are given in rad/μm.|

• [Density Profile] molecular density distribution ($N$) of the Gas-Jet in $cm^{−3}$ built from the radial phase-shift ($\varphi_r$) and [Laser Wavelength] ($\lambda$).

|| |:--:| |Fig. 6. (a) 2D plasma density map and (b) 2D standard deviation map; (c) 1D plasma density curves and (d) standard deviation of one density curve. All density values are given in cm‾³ .|

• 9. [1D Profile] This button enables a 1D frame (Item 15 in Fig. 1) with options for the user to visualize the curves of each selected stage for different positions on the chosen symmetry axis.
• 10. [2D Profile] This button enables the visualization of each [Stage] in 2D images.
• 11. [Uncertainty of Measurement] This checkbox enables the visualization of the uncertainty of the accumulated phase, radial phase, and density for 1D and 2D profiles.
• 12. [Result Frame] In this frame, the user can verify the results of each data processing stage. The results can be seen in 1D or 2D. Results in 2D have different colormaps [Colormap]. >Note: default and default_r colormaps are made specifically for IAS. Other colormaps are in matplotlib database.
• 13. [Save Plot] This button allows the user to save the visualized plot as an image file (.png, .jpg, .bmp, etc).
• 14. [Save Data] This button allows users to save the 2D array that generated the visualized plot as a .dat or .txt file.
• 15. [1D Profile] This Frame allows the visualization of 1D profiles (accumulated phase, radial phase, and density) for different positions over the Axisymmetry.

How it works

A detailed description of the algorithm will be presented in a future article. However, the summarized data processing by the software algorithm is described by the flowchart shown in Fig. 7:

|| |:--:| | Fig. 7. Scheme of the algorithm data processing. |

In the scheme of the algorithm data processing (Fig. 7): I_Target and I_Reference are the intensity functions of the bi-dimensional fringes fields obtained from the target and the reference interferograms, respectively. The hats denote the Fourier transform of the intensities, N^gas is the gas jet density calculated from its refractive index, n, and polarizability, $\alpha$, using the Lorentz-Lorenz relation [14,15].

Examples

In the Examples folder of this repository, the user will find two examples of interferogram targets: - Example 1: Supersonic Gas jet - Example 2: Laser-induced Plasma

These interferograms were obtained using a Mach-Zehnder-like interferometer, as discussed in [16].

Authors

Interferogram Analysis Software (IAS) was developed by researchers of the High-Power Ultrashort Pulse Lasers Group from the Center for Lasers and Applications (CLA) and project of Brazilian Multipurpose Reactor (RMB) from the Instituto de Pesquisas Energéticas e Nucleares (IPEN).

• Jhonatha Ricardo dos Santos
• Armando Valter Felicio Zuffi
• Giovanni Souza
• Nilson Dias Vieira Junior
• Edison Puig Maldonado
• Ricardo Elgul Samad

Acknowledgment

The author Jhonatha Ricardo dos Santos also acknowledges the IPEN, CNEN, FINEP, PATRIA, and RMB.

License

Interferogram Analysis Software (IAS) is licensed under the MIT license.

Copyright (c) 2024 Jhonatha Ricardo dos Santos

Citation

You can find the DOI for the latest version at Zenodo.

Reference

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