IVF also threatened our equanimity, Kass wrote, by moving "the mysterious and intimate processes of generation" out of the darkness of the womb and into the bright light of the laboratory, "beyond the shadow of a single doubt". Such harsh, cruel knowledge could be destabilizing...
'Beyond a shadow of a doubt' means 'without the slightest doubt'. Adding 'single' intensifies the expression: 'beyond the shadow even of a single doubt'.
The 'doubt' here would presumably be 'any doubt as to the nature of the processes of generation'. Once those processes are examined in the 'bright light of the laboratory', we can see them as they are.
a single doubt 
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