The two main eye biometrics are iris recognition and retina recognition (aka retinal scan). These are not going to work from an ordinary photo of someone's face. I have used iris recognition at about ten feet away and this article claims it can be done at 40 feet!
Eye recognition, or identification of a person from an image of their eyes alone (i.e., without seeing their iris or retina), has such a high error rate that it is not done. You may find the following paper of interest:
Nawaz Ripon, K. S., Ershad Ali, L., Siddique, N., & Ma, J. (2019). Convolutional Neural Network based Eye Recognition from Distantly Acquired Face Images for Human Identification. 2019 International Joint Conference on Neural Networks (IJCNN), Neural Networks (IJCNN), 2019 International Joint Conference On, 1–8. doi:10.1109/IJCNN.2019.8852190
For more information on iris recognition see pp 10-11 of this tutorial, and pp 12-13 for retinal scan.
An excerpt from Retinal vs. Iris Recognition: Did You Know Your Eyes Can Get You Identified? by Danny Thakkar:
The posterior portion of human eye forms retina. It
is made of a light sensitive tissue. When light passing through cornea
and lens reaches retina, neural signals are generated and transferred
to the brain via the optic nerve. Retina is a thin layer of tissue
formed by neural cells. Capillaries responsible for blood supply of
this layer forms a pattern that can be used for personal
identification. This pattern of blood capillaries is believed to be
unique in each individual due to huge possibility of variation how
these capillaries run on the surface of retina. Since retina is
located at the posterior portion inside the human eye, special
equipment is required to scan this pattern. Retina recognition is one
of the least deployed biometric methods because of high cost of the
implementation and its highly invasive nature that may cause some user
discomfort. Still, it is used is very high security applications like
military and high level government access due to its accuracy and high
level of security.
Retina recognition systems make use of low energy infra-red light to
scan the retinal pattern. Blood vessels absorb infrared light while
surrounding tissues reflect it. This reflection is detected by the
retina recognition system and image of this pattern is captured. This
image is further enhanced to make is usable for the recognition
algorithm. Retina template is generated once the image is taken
through recognition algorithm; this template is associate with a
subject’s demographic data and stored. The process so far is called
enrolment. The subject’s identity can be verified anytime by scanning
a new retinal sample and matching it against the stored template.
Iris recognition Iris is the ring shaped colored portion in a human
eye and is visible from outside with naked eye. It is made of muscle
tissue that adjusts the size of pupil and controls how much light can
enter the eye. Amount of melatonin pigment in iris is responsible for
different colors that human eyes take. Folds in iris muscles
throughout the ring create a pattern with great amount of details.
Formation of this pattern is completely random and there is no rule
how it will turn out in an individual’s eye. However, once this
pattern is created during the foetal development, it stays the same
throughout the life. An individual’s irises are unique and
structurally distinct, even iris of same individual does not match.
All these attributes make them good enough for personal recognition.
Details of iris can be captured with any high quality digital camera,
however, modern recognition systems make use of near infrared (NIR:
700–900 nm) instead of visible light to capture details. Since iris
recognition can be established with high quality camera and
recognition software, it can be setup on any computing device;
however, dedicated recognition systems are more common due to
performance and security reasons. Iris recognition systems use a
camera to capture details of the iris and this image is enhanced by
the image enhancement algorithms. Once the image is usable enough, it
is processed by the recognition algorithms, which extracts unique
features to generate a biometric template. Associating identity data
with this template establishes identity of the subject in question,
which can be used for identity verification in future.