Determining Optical Material Parameters With Motion in Structured Illumination
A set of power measurements as a function of controlled nanopositioner movement of a planar film arrangement in a standing wave field is presented as a means to obtain the thicknesses and the dielectric constants to a precision dictated by noise in an exciting laser beam, and the positioning and detector process, all of which can be refined with averaging.

The broad need for determining the optical properties of thin films in a multitude of applications is usually served by ellipsometry. Practical application of ellipsometry generally requires prior constraints, typically in the form of a frequency-dependent model. To provide for a suitable solution of the inverse problem, where film parameters are determined from a set of optical measurements. We present motion in structured illumination as a means to obtain additional information and hence avoid the need for a material response model. Using this approach, inversion for multiple parameters at each wavelength becomes possible, and in a mutual information sense, this is achieved by taking intensity measurements at a known set of displacements in a cavity.
Ellipsometry measures the amplitude ratio and the phase difference between polarized light reflected from the surface of a film and determines the refractive index or thickness by fitting the experimental data to an optical model that represents an approximated sample structure. Generally, a model of the frequency-dependent dielectric constant is used for successful parameter extraction, in order to constrain the inversion. For example, such a model may represent a Lorentzian resonance or impose a Drude model. While simplifying the extraction, this imposes an approximate but not necessarily the correct description. Otherwise, a careful choice of the initial variables is needed in ellipsometry.
There is a long history of using interferometers to determine the relative position of a surface, and to determine the refractive index of gases, and in fuel cells, including water content changes in membrane fuel cells. White-light interferometry has been used to retrieve the thickness of thin films, under the assumption that the frequency-dependent dielectric constant is known.
We present the concept of an interferometer arrangement where intensity measurements as a function of controlled position of the sample, as could be achieved with a piezoelectric positioner, allow extraction of both the thickness and dielectric constant based on transmission measurements. The simple intensity-based measurement required avoids the alignment and multiple polarization data typical of ellipsometry. Here, the film is moved in a structured background field in steps, and the total power due to the background and scattered fields is measured. The method relies on cost-function minimization using a forward model to compare the measurements to a set of forward model data corresponding to different sample structures rather than repeated corrections to the theoretical dielectric function and initial values in order to fit the experimental data.
An illustration of the arrangement used to obtain simulated data is shown in Fig. 1(a). The 1D object to be characterized is located and scanned within a cavity having a low quality (Q) factor that provides the structured field, as illustrated in Fig. 1(b). Two dielectric slabs forming the partially reflective mirrors have a refractive index of 1.5 (simulating crown glass) and a thickness of λ/5/5, with λ being the free-space wavelength, 1.5μ1.5m. The mirrors are separated by 2.7λ (inner face-to-face distance). Note that the length of the cavity was not tuned to resonance. An object of total thickness λ/5/5 is comprised of two layers of different materials: a slab with a known refractive index of 1.5 and a thin film on top with a thickness L and refractive index n. Both L and n are to be determined simultaneously at the single frequency of the measurement, at a free-space wavelength of λ.
This work was performed by Dergan Lin, Vivek Raghuram, and Kevin J. Webb for the National Science Foundation and the Air Force Office of Scientific Research. For more information, download the Technical Support Package (free white paper) below. ADT-09233
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Determining Optical Material Parameters With Motion in Structured Illumination
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Overview
The document presents a research article focused on a novel method for characterizing thin films using structured illumination and motion. This approach aims to enhance the detection of small changes in material properties and geometries by utilizing a structured background field, which is fundamentally different from traditional structured illumination microscopy that primarily aims to improve resolution through enhanced illumination.
The method involves moving a film within a structured background field and measuring the time-average power at a detector as a function of the film's position. This allows for the extraction of information about the film's thickness and dielectric constant through a forward model that compares experimental measurements to theoretical predictions. The technique is designed to be sensitive to very thin films with low refractive index contrasts, and the success rate of detection can exceed 99.99% under optimal conditions.
Key factors influencing the sensitivity and spatial resolution of the measurements include noise from various sources, such as laser amplitude and phase noise, object positioning errors, and detector noise. The article discusses how deterministic errors can be mitigated through careful experimental design and signal processing, while random noise can be reduced by increasing the number of measurements.
The research highlights the potential for achieving deep-subwavelength precision in film characterization, with the spatial resolution being primarily limited by noise rather than the method itself. The authors also suggest that multi-resolution approaches could enhance computational efficiency and help avoid local minima during optimization processes.
Additionally, the document explores the possibility of extending the method to retrieve the imaginary index of refraction by incorporating additional variables into the cost function. The findings indicate that both macroscopic and microscopic information can be obtained through statistical averaging of intensity data, although this may not always require a forward model.
Overall, the article emphasizes the advantages of this structured illumination technique for film characterization, particularly in applications where traditional methods like ellipsometry may be limited. The proposed method offers a promising alternative for accurately determining optical properties in various materials, which is crucial for advancements in fields such as semiconductor technology and materials science.
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