The author of the collection of poems called `Golden Threshold` is Sarojini Naidu, making Option 3 the correct answer.

Sarojini Naidu was a prominent Indian poet and political activist who played a significant role in India`s independence movement. She was also known as the Nightingale of India due to her melodious and evocative poetry.

`Golden Threshold` is one of Sarojini Naidu`s most well-known works. It was published in 1905 and was her debut collection of poems. The collection explores themes of love, nature, and spirituality, and showcases Naidu`s mastery of lyrical and vivid language.

Sarojini Naidu`s poetic style is characterized by her use of rich imagery, musicality, and the incorporation of Indian mythology and cultural references. Her poems often celebrate the beauty of India`s landscapes and traditions while also addressing social and political issues of her time.

It is important to note that the other options listed in the question are not correct:

- Option 1: Aruna Asaf Ali was an Indian independence activist and politician, but she is not associated with the collection of poems `Golden Threshold.`

- Option 2: Annie Besant was a prominent British socialist, women`s rights activist, and supporter of Indian independence. However, she was not the author of `Golden Threshold.`

- Option 4: Vijayalakshmi Pandit was an Indian diplomat and politician but was not known for her poetry or the collection `Golden Threshold.`

Therefore, the correct answer is Option 3: Sarojini Naidu.