A method for polishing an end face of a plastic optical fiber (2, 10) that is surrounded by a ferrule made of metal or ceramic, comprising: (a) concurrently abrading an end face of the plastic optical fiber and an end face of the ferrule for a first time duration using a first abrasive film comprising abrasive particles having particle sizes in a first range having upper and lower bounds, wherein, during step (a), the end face of the plastic optical fiber and the end face of the ferrule are pressed against the first abrasive film with a first pressure, wherein step (a) comprises rotating the first abrasive film at a first speed while the end faces are stationary; (b) after the first time duration has expired, abrading the end faces for a second time duration using a second abrasive film comprising abrasive particles having particle sizes in a second range having upper and lower bounds, wherein the upper bound of the second range is less than the lower bound of the first range, wherein, during step (b), the end face of the plastic optical fiber and the end face of the ferrule are pressed against the second abrasive film with a second pressure, wherein step (b) comprises rotating the second abrasive film at a second speed while the end faces are stationary; and (c) after the second time duration has expired, abrading the end faces for a third time duration using a suspension comprising abrasive particles suspended in a liquid on a surface of a polishing pad, wherein the suspended abrasive particles have particle sizes in a third range having upper and lower bounds, wherein the upper bound of the third range is less than the lower bound of the second range, wherein, during step (c), the end face of the plastic optical fiber and the end face of the ferrule are pressed against the polishing pad with a third pressure, wherein step (c) comprises rotating the polishing pad at a third speed while the end faces are stationary, wherein the first duration is greater than the second duration, and the third duration is greater than the first duration, wherein the third pressure is less than the first pressure and less than the second pressure, wherein the first speed is greater than the second speed, and the third speed is less than the second speed. (a) concurrently abrading an end face of the plastic optical fiber and an end face of the ferrule for a first time duration using a first abrasive film comprising abrasive particles having particle sizes in a first range having upper and lower bounds, wherein, during step (a), the end face of the plastic optical fiber and the end face of the ferrule are pressed against the first abrasive film with a first pressure, wherein step (a) comprises rotating the first abrasive film at a first speed while the end faces are stationary; (b) after the first time duration has expired, abrading the end faces for a second time duration using a second abrasive film comprising abrasive particles having particle sizes in a second range having upper and lower bounds, wherein the upper bound of the second range is less than the lower bound of the first range, wherein, during step (b), the end face of the plastic optical fiber and the end face of the ferrule are pressed against the second abrasive film with a second pressure, wherein step (b) comprises rotating the second abrasive film at a second speed while the end faces are stationary; and (c) after the second time duration has expired, abrading the end faces for a third time duration using a suspension comprising abrasive particles suspended in a liquid on a surface of a polishing pad, wherein the suspended abrasive particles have particle sizes in a third range having upper and lower bounds, wherein the upper bound of the third range is less than the lower bound of the second range, wherein, during step (c), the end face of the plastic optical fiber and the end face of the ferrule are pressed against the polishing pad with a third pressure, wherein step (c) comprises rotating the polishing pad at a third speed while the end faces are stationary,