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I know this is an old post and you might have found the answer, but, just for the sake of others, I'm posting it here.

Aggregation aggregation = Aggregation.newAggregation(
.match(Criteria.where("name").is("name"))
.project("name")        
    .and(ArrayOperators.Size.lengthOfArray(ConditionalOperators.ifNull("audience").then(Collections.emptyList()))).as("sent")
        
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