subtracting {HEAD ~ the integrated normalized ambient image} from both the integrated first gate image and the integrated second gate image, to yield {TAIL ~ a first and second frame integration} 
to yield
subtracting { HEAD ~ the integrated normalized ambient image } from both the integrated first gate image and the integrated second gate image , to yield { TAIL ~ a first and second frame integration }
OTH HEAD HEAD HEAD HEAD HEAD HEAD HEAD HEAD HEAD OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH REL REL TAIL TAIL TAIL TAIL TAIL TAIL TAIL TAIL TAIL TAIL