Elasticsearch - Calculate Delay between Timestamps

Question

How can I calculate the delay between timestamps without logstash, but with script_fields?

e.g. for this documents:

{
 "_source": {
  "name": "test1",
  "timestamp": "2021-12-30 12:30:00"
 }
}
{
 "_source": {
  "name": "test1",
  "timestamp": "2021-12-30 12:30:01"
 }
}
{
 "_source": {
  "name": "test1",
  "timestamp": "2021-12-30 12:30:03"
 }
}

I want to have a new field called "time_taken", so the expected documents should look like this:

{
 "_source": {
  "name": "test1",
  "timestamp": "2021-12-30 12:30:00"
 }
}
{
 "_source": {
  "name": "test1",
  "timestamp": "2021-12-30 12:30:01",
  "time_taken": "1"
 }
}
{
 "_source": {
  "name": "test1",
  "timestamp": "2021-12-30 12:30:03",
  "time_taken": "2"
 }
}