PHP - MongoDB: Retrieve Fields from Sub Document with Field Names in Array

Consider an Array

$lettersArray = [A,C,E,G]

and my MongoDB Collection has the following structure.

{
    Collection : {
        letters:{
            A:{...},
            B:{...},
            ...
            Z:{...}
        }

    }
}

Consider that the Letter Sub document is a part of a larger collection. Hence I am using Aggregation. Right Now I have tried to project -

['$Collection.letters' => ['$elemMatch' => ['$in' => $lettersArray]]

and also tried

['Letters' => ['$in' => [$lettersArray,'$Collection.letters']]

But it didn’t work.

In the End, I want result like the following:

 [
     Collection => [
        letters => [
            A => [...],
            C => [...],
            E => [...],
            G => [...]
        ]
    ]
]

Is there any way to do this?