What is the ruling concerning Zina of the eye if one is married (such as looking at pornography)? Is there a punishment for it and/or is there an atonement for it?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

It is confirmed that the Prophet said: “Allah has written for the child of Aadam his/her share of Zina (fornication and adultery) which he/ she commits inevitably. The Zina of the eye is the sight (i.e. to gaze at what is forbidden), the Zina of the ears is the hearing (i.e. listening to what is forbidden), the Zina of the tongue is the speech (i.e. saying what is forbidden), the Zina of the hand is the touching (i.e. illicit touching), the Zina of the feet is the walking (i.e. to forbidden places) and the heart desires and wishes, while the private part ratifies that or denies it.” [Al-Bukhari and Muslim]

This Hadeeth indicates that looking at what Allah has forbidden is Islamically considered as Zina and it is prohibited. This is why Allah ordained us to lower our gaze. Allah Says (what means): {Tell the believing men to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts, etc...) that is purer for them. Verily, Allah is All-Aware of what they do. And tell the believing women to lower their gaze (from looking at forbidden things) and protect their private parts (from illegal sexual acts)...} [Quran 24:30-31] This order to lower the gaze applies to both married and single people. However, there is no punishment in this worldly life and no Hadd (i.e. the corporal punishment determined by the Islamic Law) for whoever commits this kind of Zina.

As regards the Hereafter, it is a sin and which Allah punishes whoever commits it and does not repent from it unless Allah forgives him.

Allah knows best.