*1.2. Haemoglobin Spectrophotometry*

HCS and physical examination of exposed tissues such as palpebral conjunctiva or nail beds both rely on how humans perceive colors related to the optical spectrum [19]. To better analyze and handle this phenomenon from a computer vision point of view, a chemical insight is required. Spectrophotometry in chemistry is defined as quantitative measurements of the reflective or absorption properties of a material from a wavelength perspective. The spectra of the hemoglobin molecule vary based on whether it is bound to oxygen, carbon monoxide or nothing; the the latter is also called deoxygenated Hb [20].

We relied on experimental literature data [21] for the absorption spectra of hemoglobin used for both plots in Figure 1. The absorption coefficient *μHb a* for HbO2 and Hb is calculated as follows:

$$
\mu\_a^{Hb}(\lambda) = \frac{2.303 \times \varepsilon\_{Hb}(\lambda) \left[\frac{L}{cm \times mol}\right] \times 150 \left[\text{g/L}\right]}{M\_{Hb} \left[\text{g/mol}\right]},
\tag{1}
$$

where *eHb*(*λ*)[ *L cm*×*mol* ] is the Hb molar extinction coefficient and *MHb*[*g*/*mol*] is the Hb gram molecular weight, assuming a concentration of 150 grams per liter.

**Figure 1.** Plots visualizing optical absorption and reflectance of Hb and HbO2, vertical dashed lines are related to human perception of colors associated with (*λ*). (**a**) Molar extinction coefficient () related to absorbance over wavelength (*λ*) considering 15 g/dL of hemoglobin concentration and 1 cm cuvette. (**b**) Derived reflectance plot of absorbance under same constants.

Over the years, the palpebral conjunctiva has been a good spot to diagnose anemia, representing a highly vascular area characterized by several capillaries. In [22] a multi-layered tissue model is proposed and investigated to approximate the lower eyelid with seven layers: conjunctival epithelium, tarsal plate, orbicularis oculi, subcutaneous tissue, dermis, epidermis and stratum corneum on the outside of the eyelid tissue. The conjunctiva is perfused from the ascending branch of the posterior conjunctival artery. The presence of interweaving capillary networks penetrating several layers of the model, with the mucous membrane being highly transparent, allows for model approximations for the digital image domain. As already visually described by Figure 1, Hb and HbO2 both absorb wavelengths from 275 to about 550 nm corresponding to a visible spectrum from purple to light green. Each frequency above 600 nm is highly reflected, matching with colors from orange to dark red. A typical human eye is known to be aware of wavelengths in a range from 380 to 740 nm. The cytoplasm of the red blood cell is rich in hemoglobin, that being responsible for the reddish appearance of exposed tissues and blood in general. Laboratory-based experiments conducted in [23,24], inspired us to start from those results to accomplish segmentation and digital image analysis related to hemoglobin.
