# Quantitative Evaluation of the Effectiveness of Erbium Glass Laser Therapy for Acne Scars
## 1 Introduction
In recent years, imaging technologies have played a pivotal role in evaluating the efficacy of various treatments by providing precise, objective assessments of skin parameters. These methods not only enhance our understanding of the underlying structural changes but also allow for the quantitative tracking of therapeutic progress, bridging the gap between clinical outcomes and patient satisfaction. The Antera 3D\({}^{\circledR}\) system is an advanced imaging device designed for the acquisition and analysis of skin conditions. It operates based on multipoint skin illumination and computer-assisted three-dimensional surface reconstruction. By analyzing differences in images captured at various wavelengths and illumination angles, the system providesdetailed spatial and spectral analysis. This analysis allows for the precise mapping of melanin, hemoglobin, pores, and wrinkles, offering insights into surface structure and volumetric changes. The Antera 3D(r) system employs reflectance mapping across seven different wavelengths, covering the entire visible spectrum. This approach allows for a precise analysis of the skin's colorimetric properties, which are predominantly determined by two key chromophores: melanin and hemoglobin. The acquired spectral images are converted into skin spectral reflectance maps, with the skin surface's shape used to compensate for variations in light intensity caused by changing illumination angles. Then, the reflectance data are transformed into skin absorption coefficients, which are used to quantitatively determine the concentrations of melanin and hemoglobin via mathematical correlation with the known spectral absorption data of these chromophores. For the analysis of skin texture, a filter is applied to the reconstructed 3D surface of the skin, which differentiates between depressions and elevations relative to a normalized reference shape (a surface free of roughness). By removing the normalized reference shape, the presentation of the skin's roughness is obtained. Skin texture is defined by the average roughness (Ra), which represents the mean value of all deviations from the normalized reference surface, irrespective of the vertical direction. \[Ra=\frac{1}{n}\Sigma\frac{n}{i}=\left|z_{i}-z_{iNRS}\right|\]  
* \(n\) is the number of pixels in the selected area;
* \(Z_{i}\) and \(Z_{iNRS}\) represent the elevations of both the reconstructed skin surface and the normalized reference surface at the \(i\)-th pixel [12; 13; 14]. High-frequency ultrasonography (HFUS) is a valuable diagnostic tool in dermatology, enabling the detailed evaluation of skin structure and parameters. Operating at frequencies above 20 MHz, HFUS provides high-resolution imaging, allowing for the analysis of various skin layers, including the epidermis, dermis, and subcutaneous tissue. This technique also facilitates the assessment of skin echogenicity, which reflects changes in collagen and elastin content [15; 16]. In our study, we employed both the Antera 3D(r) imaging system and high-frequency ultrasonography (HFUS) to comprehensively evaluate the efficacy of erbium glass laser treatment for acne scars.