Option 1 - Thomas Roe: Thomas Roe was an English diplomat and ambassador to the Mughal Empire during the reign of Jahangir. He was not in India during the reign of Shahjahan, so this option is incorrect.

Option 2 - William Hawkins: William Hawkins was an English sailor and adventurer who traveled to India in the early 17th century. He visited the court of Jahangir but not the court of Shahjahan, so this option is also incorrect.

Option 3 - Ibn Batuta: Ibn Batuta was a Moroccan scholar and explorer who visited India during the reign of Muhammad bin Tughluq in the 14th century, which was much earlier than the reign of Shahjahan. Therefore, this option is incorrect.

Option 4 - Manucci: Niccolao Manucci was an Italian soldier and adventurer who arrived in India during the reign of Shahjahan. He became a trusted advisor and physician to the Mughal emperor. This option is correct.

Therefore, the correct answer is option 4, Manucci.