MongoDB $lookup嵌套文档

我是mongo的新手，正在努力解决以下问题.我有两个系列， struct 如下.就我个人而言，我不知道如何在学校藏品上查找$.在阅读其他帖子时，我肯定会使用ObjectId作为参考，同时也会用到国外领域.

以下是我的 struct :

Alumni:

{
    "_id": "john",
    "items": [
        {
            "name": "John",
            "items": [
                {
                    "school": ObjectId("56de35ab520fc05b2fa3d5e4"),
                    "grad": true
                },
                {
                    "school": ObjectId("56de35ab520fc05b2fa00000"),
                    "grad": false
                }
            ]
        },
        {
            "name": "Johnny"
            // notice no nested items, this doc should still be included in result
        },
        {
            "name": "Jon",
            "items": [
                {
                    "school": ObjectId("56de35ab520fc05b2fa11111"),
                    "grad": false
                }
            ]
        }
     ]
}

Schools

{
    _id: ObjectId("56de35ab520fc05b2fa3d5e4"),
    name: "Some University",
    street: "ABC Boulevard"
}

我想要的是:

{
    "_id": "john",
    "items": [
        {
            "name": "John",
            "items": [
                {
                    "school": ObjectId("56de35ab520fc05b2fa3d5e4"),
                    "grad": true,
                    "schoolInfo":     {
                        _id: ObjectId("56de35ab520fc05b2fa3d5e4"),
                        name: "Some University",
                        street: "ABC Boulevard"
                    }
                },
                {
                    "school": ObjectId("56de35ab520fc05b2fa00000"),
                    "grad": true,
                    "schoolInfo":     {
                        _id: ObjectId("56de35ab520fc05b2fa00000"),
                        name: "Another University",
                        street: "123 Boulevard"
                    }
                }
            ]
        },
        {
            name: "Johnny"
        },
        {
            "name": "Jon",
            "items": [
                {
                    "school": ObjectId("56de35ab520fc05b2fa11111"),
                    "grad": true,
                    "schoolInfo":     {
                        _id: ObjectId("56de35ab520fc05b2fa11111"),
                        name: "Some University",
                        street: "ABC Boulevard"
                    }
                }
            ]
         }
     ]
}

我try 过的问题没有用:

db.alumni.aggregate([
      {$match: {_id: 'john'}}, 
      {$lookup: {
                from: 'schools', 
                localField: 'items.items.school', 
                foreignField: '_id', 
                as: 'schoolInfo'}}
 ])

任何帮助都将不胜感激！