Calculation of the nematic entropy using digital images

Abstract

In this work we will use digital images to compute the entropy dependence on temperature of a nematic lyotropic sample. The set of images comprehend the entire temperature range between a reentrant nematic isotropic phase transition, at a low temperature, and a usual nematic isotropic phase transition at a higher temperature. We will show that, inside the nematic phase, the image entropy profile agrees accurately with the entropy given by the Maier-Saupe model. As far as we know, this is the first time that the entropy of a lyotropic nematic phase is evaluated by this method, which introduces a way to measure their macroscopic variables. Namely, being that the entropy is a thermodynamical potential, this result implies that digital images can be used to compute mean values of nematic random variables.

Studies of Image Processing and Refractive Index in Blue Phase

“…The mean square deviation (σ ) for the mean values of the image frame color tones is a fundamental statistical parameter determined by means of this technique. The parameter σ plays an important role in the identification of phase transition points in agreement with other experimental techniques [6,[8][9][10][11][12]. The polarized light optical microscopy connected to the CCD camera is used to observe the isotropic (I), blue phases (BP) and cholesteric (N * ) phases for cholesteryl oleyl carbonate (COC).…”

Quantifying Human Visible Color Variation from High Definition Digital Images of Orb Web Spiders

“…The high complexity and variability in composition of color signals is best suited for an unsupervised algorithm that segments labeled pixels according to the color represented by similar pixel values from a digital image, preventing a bias by selecting preset threshold values [17]. Usupervised algorithms are commonly used for digital image processing [18–20]. While the comprenhensive toolbox for image calibration and analysis described in [21] provides a set of techniques for digital image processing, it is best suited to perform specialized measurements towards estimating colors in non-human visual systems, including tools to linearize digital images and to map signal to animal cone-catch values, ultimately allowing for more objective measurements from digital images that are independent of the human visual system.…”

“…Both image measurements have been used in different applications of image processing to evaluate the quality of digital images [24], and chemical properties extracted from digital images [20], among others. The energy quantifies the average intensity of the pixels and the entropy quantifies the uncertainty of information provided by the image; when entropy of a digital image increases, the information associated to the image is closer to random, when it decreases, it is less random [18–20]. …”