A spectrophotometric transmission spectroscopy and a single integrating sphere system were utilized to estimate spectrophotometric characteristics of these two groups of ink diluted samples. These considered as basic requirements to apply inverse adding-doubling algorithm for optical characterization. Furthermore, using a low concentration of dilution samples may predict pure optical coefficients of undiluted samples based on a linear relationship between coefficients and volume concentration. As can be seen from Figs. (4-a) and (6-a), Parker ink optical coefficients have different trends in comparison to Pelikan ink. Figures (4-a) depicts the correlation of absorption coefficient and wavelength of blue ink, that has a structural behavior. For shorter wavelengths, a direct relationship between absorption and wavelength could be shown. Then, over a wavelength spectrum ranged from 616 nm and 675 nm, an inverse relationship could be distinguished. Regarding the scattering coefficient that has a similar profile to the absorption property of blue ink, a quantitative disagreement could be shown. Generally, a single scattering approximation was mainly used to predict India ink scattering property [5–8]. Thus, a linear decremental behavior of ink scattering coefficient with wavelength has been applied. In that context, Madeson et al investigated the optical properties of India ink and clarified the possibility for aggregation of smaller carbon particles to form many different compositions with irregular shapes and dimensions . Thus, scattering property of such media could not predicted previously but demands optical characterization. Accordingly, blue ink albedo could be calculated based on their optical coefficients, Fig. (4-b). Obviously, Pelikan albedo (dash-dotted) has a structured behavior and varied from 0.03 at 675 nm to 0.366 at 583 nm even more so it remained relatively stable over a sub-range from 533 nm to 637 nm around 0.3. Over that, Pelikan albedo decreased gradually with increased wavelength that to be in correspondence to the previous works [6–8]. All previous works aimed to retrieve the optical characteristics of Pelikan ink, carried out over the wavelength range above 594 nm. Over that range, a relative compatibility of albedo behavior could be recognized in which an inverse relationship with wavelength was shown. Furthermore, the differences of albedo values could be attributed to the scattering property discrepancy. That can be caused by the aggregation of smaller carbon particles that results in a variety of ink components' dimensions and shapes. Furthermore, the preparation of ink samples was not associated with ultrasound application that could prevent the aggregation of carbon particles. On the other hand, inter batch variation can cause a significant variability for optical characteristics that may affect albedo values [5, 7, 14].
On the other hand, Parker black ink absorption property has shown a stable relationship over the shorter wavelengths that varied from 500 nm to 616 nm. After that, an inverse correlation with wavelength could be observed. Scattering coefficient of black ink is inversely proportional to increased wavelength, Fig. (6-a). Thus, a large probability of attenuation photon with shorter wavelengths could be predicted, which could be noticed from transmission spectra. Furthermore, a decremental behavior of Parker scattering profile turned out to be in correspondence to the single scattering approximation. Furthermore, scattering profile may be considered as a median case between Ryleigh and Mie scatterings, which could be confirmed by a relative small dependency on wavelength that simulate a case between these limitations. However, the discrepancy between Pelikan and Parker scattering profile and the selective applicability of using that approximation for prediction could be returned to ink brand. In other words, the application of ultrasound before optical characterization is essential but depends on the ink brand and ingredients. Then, black ink coefficients could be used to estimate albedo values, Fig. (6-b). That showed a linear relationship with increased wavelength and ranged from 0.381 at 500 nm to 0.13 at 637 nm gradually. Thus, the behavior of Parker albedo with wavelength turned out to be in accordance to the literature despite a quantitative disagreement . Quantitative variety could be explained by the irregularity of Parker ink ingredients and its disagreement compositions in comparison to other ink brands [5, 10]. To the best of our knowledge, Parker ink has not been examined for optical phantom construction. Although there is an incompatibility at the absorption spectrum of Parker ink, the behavior of absorption has been in agreement with cancerous stomach and esophagus besides hemoglobin absorption spectra over a wide wavelength range [15, 16]. Figures (7) represents comparing diluted ink samples' absorption property with these tissues. Otherwise, Pelikan absorption spectrum has different behavior in comparison to the previous tissues. Therefore, using Parker ink may be useful to simulate absorption property of some biological media and this compatibility can make Parker ink to be a better candidate in constructing optical phantoms [15, 16].