Fine threads of film in a measure on backstreet? (9)

I believe the answer is:

filaments

I'm a little stuck... Click here to teach me more about this clue!

'fine threads' is the definition.
'filaments' can be an answer for 'threads' (I've seen this in another clue). I'm not certain of the 'fine' bit.

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for filaments that I've seen before include "Slender threads in light-bulbs" , "they glow in the dark" .)

I've seen this clue in the Sydney Morning Herald.

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