/ 
Physics-Ellipsometry-VASE-1.02
/ Physics::Ellipsometry::VASE

NAME

Physics::Ellipsometry::VASE - Variable Angle Spectroscopic Ellipsometry analysis

VERSION

Version 1.01

SYNOPSIS

use PDL;
use PDL::NiceSlice;
use Physics::Ellipsometry::VASE;
use Physics::Ellipsometry::VASE::TMM qw(psi_delta);
use Physics::Ellipsometry::VASE::Dispersion qw(cauchy);
use Physics::Ellipsometry::VASE::EMA qw(ema_bruggeman);
use Physics::Ellipsometry::VASE::Materials qw(load_material interpolate_material);
use Physics::Ellipsometry::VASE::Optimizer qw(differential_evolution);

# Create VASE fitter with built-in delta handling
my $vase = Physics::Ellipsometry::VASE->new(
    layers         => 3,
    circular_delta => 1,       # circular residuals for Delta
    deriv_step     => 1e-3,
    min_deriv_step => 0.01,
);
$vase->load_data('measurement.dat');

# Use built-in dispersion, EMA, TMM
my $cauchy_fn = cauchy(A => 2.1, B => 0.01, C => 0.001);
my $substrate = load_material('ta_pbp.mat');

$vase->set_model(sub { ... });
my $fitted = $vase->fit(pdl [...]);
my $mse = $vase->mse($fitted, nparams => 6);
$vase->plot($fitted, output => 'fit.png');

DESCRIPTION

Physics::Ellipsometry::VASE v1.01 provides a complete framework for spectroscopic ellipsometry analysis including:

  • Transfer Matrix Method (VASE::TMM)

  • Dispersion models: Cauchy, Sellmeier, Tauc-Lorentz, Drude, Genosc (VASE::Dispersion)

  • EMA mixing: Linear, Bruggeman, Maxwell-Garnett (VASE::EMA)

  • Material file loader with eV/nm conversion (VASE::Materials)

  • Parameter bounds and vary/fix control (VASE::Parameter)

  • Global optimizer: Differential Evolution (VASE::Optimizer)

  • Circular Delta residuals in LM fitting

  • Robust LM regularization (diagonal floor prevents singular matrices)

METHODS

new

my $vase = Physics::Ellipsometry::VASE->new(%args);

Constructor. Accepts the following options: layers (number of thin-film layers), circular_delta (enable circular Delta residuals), deriv_step, min_deriv_step, maxiter, eps, lm_reg_floor.

load_data

my $data = $vase->load_data($filename);

Reads ellipsometry data from $filename. The format is auto-detected:

Simple format

Whitespace-separated columns. Lines starting with # are comments; blank lines are skipped.

# Wavelength(nm)  Angle(deg)  Psi(deg)  Delta(deg)
400  70  45.0  120.0
410  70  44.5  121.0
Woollam VASE format

Recognised when line 2 starts with VASEmethod[. The four-line header is parsed and stored as object attributes:

$vase->{sample_name}    # line 1
$vase->{vase_method}    # VASEmethod[...] content
$vase->{original_file}  # Original[...] content
$vase->{units}          # line 4 (e.g. "nm")

Columns 5-6 (sigma_psi, sigma_delta) are extracted into $vase->{sigma} and automatically used as weights during fitting.

Returns a PDL piddle of shape (4, npts) where the columns are wavelength, angle, psi, delta.

set_model

$vase->set_model(\&my_model);

Sets the model function used for fitting. The function receives two arguments:

sub my_model {
    my ($params, $x) = @_;
    # $params - PDL piddle of fit parameters
    # $x      - PDL piddle of shape (npts, 2):
    #           column 0 = wavelength (nm)
    #           column 1 = angle of incidence (degrees)

    my $psi   = ...;  # compute psi   (npts values)
    my $delta = ...;  # compute delta (npts values)

    return cat($psi, $delta)->flat;   # concatenated 1-D piddle
}

The return value must be a flat piddle of length 2*npts with all psi values followed by all delta values.

fit

my $fitted_params = $vase->fit($initial_params);

Performs a Levenberg-Marquardt fit of the current model to the loaded data.

$initial_params is a PDL piddle of starting parameter values. Returns a piddle of optimised parameters.

After fitting, the following attributes are available:

$vase->{covar}  # covariance matrix (PDL)
$vase->{iters}  # number of LM iterations
$vase->{ym}     # model values at the fitted parameters

The fit uses relative-step finite differences for the numerical Jacobian (step size |p_i| * 1e-7 + 1e-10) and converges when the relative change in chi-squared falls below 1e-7, or after 300 iterations.

mse

my $mse = $vase->mse($fit_params, nparams => $n);

Calculates WVASE-convention mean squared error: sqrt(chi2 / (2*npts - nparams)).

plot

$vase->plot($fit_params, %options);

Plots measured data with the model fit overlaid. Requires PDL::Graphics::Gnuplot (loaded on demand).

Options:

output

Filename for the plot image. The format is inferred from the extension: .png, .pdf, .svg, .eps. If omitted, an interactive window is opened.

title

Title string for the plot (default: "VASE Fit Results").

When multiple angles of incidence are present, each angle is plotted as a separate colour-coded series.

EXAMPLES

The examples/ directory in the distribution contains:

fit_linear.pl

Minimal example fitting a linear dispersion model.

vase_test_fit.pl

Cauchy thin-film model with complex Fresnel equations for Ta2O5 on Si.

vase_tauc_lorentz_fit.pl

Tauc-Lorentz oscillator model with numerical Kramers-Kronig integration.

DEPENDENCIES

PDL (≥ 2.0)
PDL::Fit::LM
PDL::NiceSlice
PDL::Graphics::Gnuplot (optional, for plotting)

SEE ALSO

Physics::Ellipsometry::VASE::TMM, Physics::Ellipsometry::VASE::Dispersion, Physics::Ellipsometry::VASE::EMA, Physics::Ellipsometry::VASE::Materials, Physics::Ellipsometry::VASE::Parameter, Physics::Ellipsometry::VASE::Optimizer

PDL, PDL::Fit::LM, PDL::Graphics::Gnuplot

H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications, John Wiley & Sons, 2007.

G.E. Jellison and F.A. Modine, "Parameterization of the optical functions of amorphous materials in the interband region", Appl. Phys. Lett. 69, 371 (1996).

AUTHOR

Jovan Trujillo <jtrujil1 at asu.edu>

LICENSE AND COPYRIGHT

Copyright 2026 Jovan Trujillo.

This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself. See https://dev.perl.org/licenses/ for details.