Return only the queried element and its parent from a nested document

I have the following Schema Structure

Artist Schema
albums:[Albums Schema]

Album Schema
songs:[Songs Schema]

Now, i want to search by a song id and return the song, its parent album and the artist detail. I don't want to return a song and album other than the one matched. So far i have only been able to restrict it to returning the queried album using the positional or elemMatch but it still returns all the songs . Does anyone know a way of restricting both the song and the album elements to one ?

Examples below are using the mongo shell for convenience but should be straightforward to translate.

Assuming you have a schema similar to:

db.artist.insert({
    name: '"Weird Al" Yankovic',
    albums: [
        {
            name: 'Dare to Be Stupid',
            year: 1995,
            songs: [
                { track: 'A1', name: 'Like a Surgeon' },
                { track: 'A2', name: 'Dare to Be Stupid' },
                { track: 'A3', name: 'I Want a New Duck' },
            ],
        },
        {
            name: 'Polka Party!',
            year: 1985,
            songs: [
                { track: 'A1', name: 'Living with a Hernia' },
                { track: 'A2', name: 'Dog Eat Dog' },
                { track: 'A3', name: 'Addicted to Spuds' },
            ],
        },
    ],
})

You can use the Aggregation Framework to get the expected results:

db.artist.aggregate(

    // First match to reduce the number of candidate documents
    { $match: {
        "albums.songs.name": "I Want a New Duck",
    }},

    // Unwind 'albums' & 'songs' arrays
    { $unwind: "$albums" },
    { $unwind: "$albums.songs" },

    // Limit to matching song & album
    { $match: {
        "albums.songs.name": "I Want a New Duck",
    }}
)

Example result:

{
    "_id" : ObjectId("53defb826ed136423e50d082"),
    "name" : "\"Weird Al\" Yankovic",
    "albums" : {
        "name" : "Dare to Be Stupid",
        "year" : 1995,
        "songs" : {
            "track" : "A3",
            "name" : "I Want a New Duck"
        }
    }
}