Passing an empty array as default value of an optional parameter

If you can make the array the last argument you could also do this:

public void DoSomething(int index, bool wasThirdParam = true, params ushort[] array)

The compiler will automatically pass an empty array if it is not specified, and you get the added flexibility to either pass an array as a single argument or put the elements directly as variable length arguments to your method.

You can't create compile-time constants of object references.

The only valid compile-time constant you can use is null, so change your code to this:

public void DoSomething(int index, ushort[] array = null,
  bool thirdParam = true)

And inside your method do this:

array = array ?? new ushort[0];

(from comments) From C# 8 onwards you can also use the shorter syntax:

array ??= new ushort[0];