RGB‐Color Image Analysis for Determination of Birefringence of Micro‐Films and Columnar Coatings

Abstract

The birefringence analysis of thin ≈13.33333ptμ$\approx 1\hspace*{3.33333pt}\umu $m SiO2 films deposited via evaporation at a glancing angle of 3.33333pt70∘$\hspace*{3.33333pt}{70}^{\circ}$ to the normal on resist pillar arrays on Si and nanopatterned SiO2 substrates is carried out by spectral and color (red–green–blue [RGB]) imaging modes. Retardance and birefringence of the films deposited over flat and structured regions can be distinguished with only ≈1% difference between neighboring regions for the visible spectral range using RGB numerical analysis of images. The Michel‐Lévy color map is used for color rendering of birefringence to make quantitative measurements by numerical RGB color filtering. It is shown that by using λ/2$\lambda /2$ at 530 nm waveplate inserted at π/4$\pi /4$ angle to the cross polarizer‐analyzer setup, the range of changes in chromaticity xy‐coordinates expands approximately twice upon angular rotation of a birefringent sample. This facilitates a better signal‐to‐noise determination of birefringence. The proposed method with λ/2$\lambda /2$‐plate color shifting can be directly used to determine birefringence from step‐like spectral features in reflection and transmission polariscopy. Direct measurement of birefringence (normalΔn=0.023${\Delta}n=0.023$) and retardance of SiO2 chevron film is carried out using Berek compensator as a benchmark.

Determination of Stokes Vector from a Single Image Acquisition

“…For example, formation of a crystalline phase of organic crystal polyhydroxybutyrate (PHB) from a cooled amorphous melt ($$150^\circ$$C) takes place with a typical front speed of few micrometers per second for a tens‐of‐$$\umu$$m thick bounded spherulite between two transparent plates. [ 22 ] Figure 5 shows an optical image (intensity) and orientation angle $$\theta$$ maps obtained by the best fit. This example shows a complex spiraling crystalline pattern of PHB with the spiraling period of $$\approx 20\nobreakspace \umu$$m revealed via the orientation azimuth.…”

“…A simple cross‐Nicol image with a 530‐nm color shifter $$\lambda$$‐plate can determine slow versus fast orientation. [ 22 ]…”

“…The direction of fast versus slow axis, $$\theta _1$$ or $$\theta _2$$, is determined unequivocally from the cross‐Nicol imaging with complimentary color shifting 530 nm $$\lambda$$‐plate, see, e.g., for the polyhydroxybutyrate (PHB) bounded spherulite organic crystal. [ 22 ]…”

“…A simple cross-Nicol image with a 530-nm color shifter 𝜆-plate can determine slow versus fast orientation. [22] from transmission or reflection even under conditions where feature sizes of ≈ 100 nm of an aligned pattern are ≈ 20 times below the diffraction limit, as shown for the IR chemical fingerprinting wavelengths where nanoscale resolution cannot be reached. [11] Mechanical stress-induced anisotropies can be imaged by change of characteristic wavenumbers in Raman spectroscopy/scattering as demonstrated for sapphire.…”

“…The ambiguity of slow versus fast axis definition is due to tan 2𝜃 = −S 1 ∕S 2 which has solutions 2𝜃 = 2𝜃 − 𝜋 (or 𝜃 = 𝜃 − 𝜋∕2, i.e., the slow or fast axis marked by the dashed line diagonal is not determined unequivocally). A simple cross-Nicol image with a 530-nm color shifter 𝜆-plate can determine slow versus fast orientation [22].…”