To solve this problem, we need to determine during which phase the centriole undergoes duplication.$\newline$Let's analyze the cell cycle phases:$\newline \bullet$G$_1$-phase: This is the first gap phase where the cell grows and prepares for DNA replication. Centriole duplication does not occur here.$\newline \bullet$S-phase: This is the synthesis phase where DNA replication occurs. Importantly, centriole duplication also takes place during this phase.$\newline \bullet$G$_2$-phase: This is the second gap phase where the cell prepares for mitosis. Centriole duplication is already completed by this phase.$\newline \bullet$Prophase: This is the first stage of mitosis where chromatin condenses into visible chromosomes, but centriole duplication has already occurred before this phase.$\newline \bullet$Metaphase: This is a stage in mitosis where chromosomes align at the metaphase plate, and centriole duplication is not relevant here.$\newline$Based on this analysis, centriole duplication occurs during the S-phase.$\newline$Therefore, the correct option is Option 1: S-phase.