"focusing carefully" is correct and usable in written English.
You can use it when you want to emphasize precision and attention to detail. For example, "I spent an hour focusing carefully on the task before me."
Piotr takes Molly's camera, focuses carefully, and takes pictures.
Eckersley promised that the new study will focus carefully on established data protection principles.
This time I focused carefully on the gunman, on whether he aimed downward precisely at the target.
But his writing here was sharply focused, carefully shaped and attuned to coloristic possibilities of the piano, violin and cello.
Mr. Brendel is known for carefully focused, carefully thought out displays of struggle and stamina, like his Beethoven sonata cycle at Carnegie Hall in the 1980's.
Jurors also said they focused carefully on testimony by Mr. Skakel's sister, Julie, who they said had unwittingly discredited his alibi.
Where the blues as played by the Allman Brothers is sprawling and expansive, this music is intimate, tightly focused, carefully arranged but never stiff.
The tutor carefully guides the students (all at the same point in their learning) through a scripted session that will focus carefully on the grammar and vocabulary they're learning just then.
Ms. Morkoski continued in that spirit, offering a focused, carefully shaped account of Messiaen's Préludes (1930), a student work that shows him finding his own approach to dissonance and sonic imagery within a language still heavily influenced by Debussy.
… Proposals to expand the number of visas for STEM fields should focus carefully and flexibly on those fields that can be shown to be experiencing excess demand relative to supply in the U.S. labor market".
With these perspectives in mind, researchers looked more closely at the collective, imaginary and emotional nature of participatory action captured in the video clip and then focused carefully on these through the use of a series of screen capture snapshots of transitory moments (Figs. 1, 2, 3, 4 and 5).
