As far as I'm concerned, the essentials of jazz are: melodic improvisation, melodic invention, swing, and instrumental personality.
Think about the photo before and after, never during. The secret is to take your time. You mustn't go too fast. The subject must forget about you. Then, however, you must be very quick.
Imitation, if it is not forgery, is a fine thing. It stems from a generous impulse, and a realistic sense of what can and cannot be done.