Database

db={"FirstCollection":[{_id:"601d07fece769400012f1280",FieldName:"Summary",Type:"Chapter"},{_id:"601d07fece769400012f1281",FieldName:"Summary1",Type:"Chapter"}],"SecondCollection":[{_id:"601d11905617082d7049153a",SurveyId:"601d118e5617082d70491539",TemplateName:"",Elements:[{_id:"601d07fece769400012f1280",FieldName:"Employee",Type:"Chapter",Children:[{_id:"5fd06931f3b6810001fc960d",FieldName:"Summary",Type:"Section"},{_id:"5fd06931f3b6810001fc961d",FieldName:"Summary1",Type:"Section"}]},{_id:"601d07fece769400012f1281",FieldName:"Contract",Type:"Chapter",Children:[{_id:"5fd06931f3b6810001fc960d",FieldName:"Summary",Type:"Section"},{_id:"5fd06931f3b6810001fc961d",FieldName:"Summary1",Type:"Section"}]}]}]}

Query

db.FirstCollection.aggregate([{"$lookup":{"from":"SecondCollection","let":{"fieldname":"$FieldName"},"pipeline":[{"$match":{"$expr":{"$in":["$$fieldname",{$reduce:{input:"$Elements.Children.FieldName",initialValue:[],in:{$concatArrays:["$$this","$$value"]}}}]}}},{"$project":{"SurveyId":1}}],"as":"SurveyInfo"}}])

Result