## 1 Introduction  
Human health is a priority, and maintaining good health is challenging, especially in today's fast-paced world. Oxidants, reactive oxygen species (ROS), and reactive nitrogen species (RNS) are continuously produced by our bodies, where they play significant roles in immune function and signal transmission. The presence of oxidants is balanced by our body's antioxidant defense system. While endogenous enzymatic and non-enzymatic antioxidant systems provide excellent protection, we sometimes need help from the outside. Antioxidants present in food, particularly in vegetables and fruits, are an important supplement to these systems [1, 2]. Oxidative stress is one of the major causes of various illnesses and can be described as an imbalance between antioxidants and prooxidants (prooxidants promote oxidation) [3]. A natural source of antioxidants is carotenoids, a group of pigments that are widely studied, especially for their impact on human health [4, 5]. Good sources of carotenoids are marine organisms, mainly phytoplankton, but these pigments can also be found in organisms such as crabs, lobster, tuna, shrimp, and salmon, where they contribute to the coloration of these organisms [6]. Lutein belongs to the group of carotenoids known as xanthophylls, yellowish-orange pigments that are synthesized exclusively in plants (dark green vegetables, flowers, cereals) [7,8], as well as in some microalgae, fungi, and bacteria. Because humans cannot synthesize lutein, it must be ingested through food. It contributes to human health through its anti-cataract, anti-inflammatory, antioxidant, anti-arthritis, neuroprotective, bone-remodeling, hepatocyte, cardioprotective, anticancer, and antidiabetic retinopathy activities [9], as well as through its positive effects on cognitive functions [10]. Lutein's influence on eye health has also been extensively researched [11]. Fruits and vegetables are the most common source of lutein (80-90% of all carotenoids derive from these sources). Animal sources include eggs and, to some extent, raw or processed milk [12; 13; 14]. Although lutein is synthesized exclusively in plants, egg yolk is considered a better source of lutein for humans due to its high fat content, which enhances bioavailability [15; 16]. Lutein also has a favorable effect on the health of laying hens by enhancing protection against respiratory infections [17]. Beyond its health benefits for humans, lutein contributes to customers' perception of egg yolk color and hen skin color. In hens' feed mixtures, the crops that make up the mixture are a source of lutein; however, lutein may also be added as an additive. According to EU legislation, between 50 and 80 mg of total carotenoids/kg of complete feed can be included [18]. Since eggs are a good source of lutein and other nutrients, and hen meat is widely used in nutrition, researchers aim to optimize feed composition for laying hens in order to increase the lutein content as well as other nutrients [19]. Many methods are used for the extraction of various bioactive compounds. Soxhlet, maceration, decoction, and liquid-liquid extraction are among the older methods. More recently, modern, instrumentally guided extraction processes have become more common: extraction with supercritical CO2, extraction with ionic solvents, microwave-assisted extraction, and extraction with ultrasound [20; 21]. The most important advantages of these newer techniques are high extraction efficiency and time and chemical savings. The choice of solvent or solvent mixture has a significant impact on the success of extraction of bioactive compounds. Various organic solvents (hexane, acetonitrile, acetone, ethanol, methanol) and water are commonly used. The polarity of the solvent or solvent mixture affects the solubility of the target bioactive compound; therefore, a well-chosen solvent or solvent mixture enhances extraction efficiency [22]. In addition to the solvent mixture, the success of the extraction is influenced by particle size and temperature.