Thanks guys. As a beginner, it's much easier for me to isolate the tube out and measure it directly. My theory is that if the voltage bias of the tube is correct, then it should be working properly. Otherwise, there's something wrong with the tube itself. I'm not convinced that I need to measure the low voltage circuit to infer the problem indirectly.
If I understand it correctly, the brightness can be controlled by adjusting either V(H1, H2) or V(K, G1). Since the tube is working fine except the brightness, the voltage bias that could go wrong would be these two.
However, looking at my measurement, I didn't see anything wrong with these two voltages.
+ When I turn the intensity knob from min to max, V(K, G1) dropped from 68v to 42v, and the maximum brightness happens at about 60v. So the the dimness could not be because of this voltage is too high or too low.
+ The voltage of the filament is 6.7v. though a bit higher that the 6.3v in the spec, it looks good enough.
The other voltages also look good, V(K, P1) ~= 550v, V(K, G2) ~= 2.1kv.
I also measured the voltage change of V(K, G1), V(K, P1) and V(K, G2) when I turned the intensity knob. Only V(K, G1) changed and the other two were stable.
My conclusion is, the tube is bad. Let me know if I made any stupid error in the above reasoning.
I am going to do more experiments on the tube, e.g. increase the filament voltage, zap it, etc.