Translation:We can see the scientist because she emits photons.
I cannot understand the structure of this phrase: othlmey tlhuDmo' is because she emits photons tej is scientist and wIleghlaH is 'we can see her'.
What puts me off is the ghaH, why is it there?
If you put a comma in, it becomes 'otlhmey tlhuDmo' tej, ghaH wIleghlaH "because the scientist emits photons, we can see her".
The pronoun ghaH "her" is optional; you can add it or omit it as you like.
So the reason why it's there is because the speaker chose not to omit it.
One could also say wIleghlaH maH or even ghaH wIleghlaH maH for the second sentence.
Uhm... At the second round maybe I have a better breakdown of the phrase:
Because the scientist emits photons we can see her
and ghah is used for emphasis... I was not expecting it in the object position though.
Normally, we would try not to place two nouns next to each other like that - it makes you look for a conjunction or expect a genitive (or possessive) meaning. I would normally put a comma there to separate the two clauses and make it more obvious. In actuality, it is a great skill to develop to also begin to consider if the two nouns might actually be from two different phrases or clauses. This Skill is past the half way point, it might be a good time to make you practice that.
I am a very experienced reader and speaker of Klingon, and I found that sentence difficult to parse. I could only figure it out by going over it several times, not because it was understandable the first time.