Hello, I have a question and I hope you can help me solve it.

How is Infrared technology used to measure distance with the APD9930 and APDS9960 sensors?

Attached Datasheet:

 

It shines an IR LED outwards and detects the reflection when there is an object in front of it.

Bob

 

Those units do not detect "distance",
they detect "objects" up to ~100mm away.
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Did you read the datasheets you posted? There is a decent explanation on page 10