What is relation between 得 and 他 in these sentences?
cause : （他）对竹子非常熟悉 

effect: 他闭上眼睛，心理就有竹子的影子

使得 can express causal relation. If you read the sentence this way, maybe it is more comprehensive.

Example 1: 热使得气体膨胀 Heat makes gases expand, where:

cause : 热 

effect: 气体膨胀

Example 2: 因为你的说明，使得我弄清楚怎么一回事 Your explanation makes me clear, where:

cause : 你的说明 

effect: 我弄清楚怎么一回事