VASE.pm - Variable Angle Spectroscopic Ellipsometry Analysis
A Perl library for fitting optical models to variable angle spectroscopic ellipsometry (VASE) data using the Levenberg-Marquardt algorithm.
What is Ellipsometry?
Ellipsometry is an optical technique that measures the change in polarization of light upon reflection from a sample surface. It provides information about the optical properties (refractive index, extinction coefficient) and thickness of thin films and multilayer structures. The measured parameters are:
- Psi (Ψ): Related to the amplitude ratio of p- and s-polarized light
- Delta (Δ): Phase difference between p- and s-polarized light
Variable angle measurements provide additional constraints for more accurate model fitting.
Features
- Flexible Model Definition: Define custom optical models as Perl functions
- Robust Fitting: Uses Levenberg-Marquardt algorithm via PDL::Fit::LM
- Multi-layer Support: Configurable for single or multi-layer optical systems
- Standard Data Format: Reads common ellipsometry data file formats
- PDL Integration: Leverages Perl Data Language for efficient numerical computations
Requirements
- Perl 5.x
- PDL (Perl Data Language)
- PDL::Fit::LM (for Levenberg-Marquardt fitting)
- PDL::NiceSlice (for matrix slicing syntax)
Installation
# Install PDL and required modules
cpan PDL PDL::Fit::LM
# Clone or download this repository
# No additional installation needed - use with perl -I.
Quick Start
use strict;
use warnings;
use PDL;
use VASE;
# Create VASE object
my $vase = VASE->new(layers => 1);
# Load experimental data
$vase->load_data('data/sample.dat');
# Define a simple linear model
sub linear_model {
my ($params, $x) = @_;
my ($a, $b, $c, $d) = list $params;
my $wavelength = $x->(:,0); # Extract wavelength column
my $psi = $a - $b * $wavelength;
my $delta = $c + $d * $wavelength;
return cat($psi, $delta)->flat;
}
$vase->set_model(\&linear_model);
# Perform fit with initial parameters
my $initial_params = pdl [65, 0.05, 80, 0.1];
my $fit_params = $vase->fit($initial_params);
# Display results
my ($a, $b, $c, $d) = list $fit_params;
print "Fitted parameters:\n";
print "Psi: $a - $b * wavelength\n";
print "Delta: $c + $d * wavelength\n";
Data Format
Input files should contain whitespace-separated columns:
# Wavelength(nm) Angle(deg) Psi(deg) Delta(deg)
400 70 45.0 120.0
410 70 44.5 121.0
420 70 44.0 122.0
430 70 43.5 123.0
- Lines starting with
#are treated as comments - Blank lines are ignored
- Columns: wavelength (nm), incident angle (degrees), Psi (degrees), Delta (degrees)
API Reference
Constructor
my $vase = VASE->new(%args);
Parameters:
layers: Number of layers in the optical model (default: 1)model: Optional model function (can be set later withset_model())
Methods
load_data($filename)
Loads ellipsometry data from a file.
$vase->load_data('experimental_data.dat');
Parameters:
$filename: Path to data file
Returns: PDL piddle containing the loaded data
set_model($model_function)
Sets the optical model function for fitting.
$vase->set_model(\&my_model);
Parameters:
$model_function: Code reference to model function
fit($initial_params)
Performs Levenberg-Marquardt fitting of the model to loaded data.
my $fitted_params = $vase->fit($initial_params);
Parameters:
$initial_params: PDL piddle with initial parameter guesses
Returns: PDL piddle containing fitted parameters
Model Function Requirements
Model functions must follow this signature:
sub model_function {
my ($params, $x) = @_;
# Extract parameters
my $param1 = $params->(0);
my $param2 = $params->(1);
# ... etc
# Extract input variables
my $wavelength = $x->(:,0); # Column 0: wavelength
my $angle = $x->(:,1); # Column 1: incident angle
# Calculate Psi and Delta based on your optical model
my $psi = ...; # Your Psi calculation
my $delta = ...; # Your Delta calculation
# Return concatenated and flattened result
return cat($psi, $delta)->flat;
}
Key Points:
- Input
$paramscontains fit parameters as a PDL piddle - Input
$xcontains independent variables (wavelength, angle) - Must return flattened PDL with [Psi_values, Delta_values]
- Use PDL NiceSlice syntax:
$x->(:,0)for column extraction
Example Models
Linear Model
sub linear_model {
my ($params, $x) = @_;
my ($a, $b, $c, $d) = list $params;
my $wavelength = $x->(:,0);
my $psi = $a - $b * $wavelength;
my $delta = $c + $d * $wavelength;
return cat($psi, $delta)->flat;
}
Polynomial Model
sub polynomial_model {
my ($params, $x) = @_;
my ($a0, $a1, $a2, $b0, $b1, $b2) = list $params;
my $wavelength = $x->(:,0);
my $psi = $a0 + $a1 * $wavelength + $a2 * $wavelength**2;
my $delta = $b0 + $b1 * $wavelength + $b2 * $wavelength**2;
return cat($psi, $delta)->flat;
}
Angle-Dependent Model
sub angle_dependent_model {
my ($params, $x) = @_;
my ($n, $k, $thickness) = list $params;
my $wavelength = $x->(:,0);
my $angle = $x->(:,1);
# Complex optical calculations using both wavelength and angle
# (This would require implementing Fresnel equations)
return cat($psi, $delta)->flat;
}
Running Examples
# Run the included example
perl -I. test_fit.pl
# Note: Use -I. to include current directory in module search path
File Structure
├── VASE.pm # Main library module
├── test_fit.pl # Example usage script
├── data/
│ ├── sample.dat # Sample data file
│ ├── Jovan_Ellipsometer/ # Equipment-specific datasets
│ └── OTS_on_SiO2/ # Material-specific datasets
└── .github/
└── copilot-instructions.md
Tips for Model Development
- Start Simple: Begin with linear or polynomial models to verify data loading and fitting
- Physical Constraints: Ensure your model produces physically reasonable values
- Parameter Bounds: Consider reasonable ranges for your initial parameter guesses
- Convergence: The Levenberg-Marquardt algorithm is sensitive to initial conditions
- Multi-angle Data: Use angle-dependent models when you have variable angle measurements
Contributing
This library is designed for research applications in optical characterization. Feel free to extend the model library or improve the fitting algorithms.
License
[Add your license information here]