"the backdrop against which" is correct and usable in written English.
It is often used to describe the background or context in which something happens or is being viewed. Example: "The economic crisis was the backdrop against which the political unrest and protests took place."
It provided the backdrop against which the Harlem Renaissance was set.
'Terrorism is the backdrop against which we have to operate': Full interview.
Segregation and intimidation were the backdrop against which Anderson's subjects stood — determined, unbowed.
That was the backdrop against which Angelos judged Johnson's handling of the Alomar fine.
But such activity, he argues, is merely the backdrop against which social entrepreneurship should be viewed.
The backdrop against which he preens is a muted array of wood, asphalt, dirt, and woven tweed.
From the blue azure rectangles of nine empty swimming pools to the gasoline stations hugging the freeway, he photographed the backdrops against which human drama is played out.
These maps provide the backdrops against which the dramas of Wilno lives played out: birth, baptism, education, marriage, separation or divorce, guild membership, poor relief, and death and funeral practices.
The backdrops against which Ms. Sheehan stands -- both that of Mr. Bush's what-me-worry vacation and that of Iraq itself -- are perfectly synergistic with her message of unequal sacrifice and fruitless carnage.
This provided the Chinese the perfect backdrop against which to pursue their own initiative, the Asian Infrastructure Investment Bank, and market it to other Western countries, who are themselves keen to attract Chinese business deals and inward investment.
If the TOL topology is taken to represent the history of cell divisions, then it can conveniently be conceived as the organismal backdrop against which the web-like intricacies of genome evolution can be examined (e.g., [ 49, 51]).
