The correct answer is option 4: Abbe J.A. Dubois. Abbe J.A. Dubois was a French Catholic missionary who travelled extensively in India during the early 19th century. In his book "Hindu Manners, Customs and Ceremonies", he made the observation that Hindu women could go anywhere alone without fearing impertinent looks or jokes from idle people. This reflects the relatively high level of respect and freedom enjoyed by Hindu women in Indian society at that time.

Option 1, Francois Bernier, was a French physician and travel writer who visited India in the 17th century. Although he wrote extensively about his experiences in his book "Travels in the Mogul Empire", he did not make this particular observation about Hindu women.

Option 2, Jean-Baptiste Tavernier, was a French gem merchant and traveler who visited India during the 17th century. His travel accounts, recorded in the book "Travels in India", do not provide any mention of Hindu women in relation to their freedom and safety in public spaces.

Option 3, Thomas Roe, was an English ambassador who visited the Mughal Empire in the early 17th century. His diplomatic missions and subsequent writings in "The Embassy