Diode in 6N138 optocoupler
The reverse biased diode is the photodiode (PD) .  

The Darlington transistor is there to amplify the current. It also has a high variation of hFE current gain.   Each of these are rated in CTR or current transfer ratio as the loss x hFE product can often be &lt; 100%

When we need accurate current to voltage sensing of light we just choose a PD and series resistor to measure the voltage rise (R=V/I gain) with some tradeoff on risetime.  When we need high gain and high speed, then we choose specialized digital opto chips. 

Perhaps you may consider the 10MHz BW https://www.digikey.com/product-detail/en/lite-on-inc/6N137/160-1791-ND/1969175