Looking for sutta reference on entering into Jhana

Following are the stages **Ajahn Brahm** mentions in his book **Mindfulness, Bliss and Beyond**, to enter in to Jhana. 1. Present moment awareness 2. Silent present moment awareness 3. Silent present moment awareness on the breath 4. Fully sustained awareness on the breath 5. Fully sustained attention on beautiful breath 6. Experiencing the beautiful Nimmita 7. Jhana I am looking for sutta reference for the same. Additional question- do progression through all these stages compulsary to experiencing the Jhana? Specifically Pitisukha and Nimmitta. Can one dodge the stages and enter the meditative absorption of Jhana?