DMM: Diode Checking: Measurement Current

[ElektronikLabor]

When you use an multimeter to measure the threshold voltage of a diode, the multimeter sends a small current through the diode and measures the Voltage across it. Correct me if I'm wrong.
Are there any standards how big this current should be? On the most modern DMMs it's seems to be 1mA. Is it always so?

[Elantramax1]

What about the Voltage? I am in the market for a Good DVM for Automotive repair. And read customer reviews about the V on some meters not being high enough. It was usually the Meters with the AA batteries vs. the 9V units. The Bosch I am considering shows (In manual) Good Diode at .4-.9v. And a Bad 1.0-3.0. I am looking at an Innova 3340. The Manual shows Diode check .6ma. But shows open V at 2.8