Take a digital photo of each voter as they sign in to vote.
Have the voter sign a card with their (supposed) name and address. Affix the photo to the card.
It’s no hardship for the voter to pick up the card after voting. Or mail a copy to them if they are in too much of a rush.
The card is proof, only, that the person claimed a certain identity for voting.
This would not eliminate all fraud, but might discourage some.
It should not be used as ID for any other purposes.
The digital pic can be used as evidence to prosecute fraud.
The pic can also be run through a facial recognition program to check for people voting at more than one place.