Here is a schematic for a possible solution. Since you still haven't said, I've assumed you are using the 5V version of the Q50 and that 8-bit resolution is sufficient. You will need to increase the PWM frequency if you want the settling time to be lower than a few seconds.
The transistor passes the power (up to 250mA) to the HV multiplier. The op amp cannot supply enough current by itself.The high voltage output is on the right hand side of the schematic. The positive side is marked "+ 0-5 kV", and the negative side is marked Gnd. The negative side is common with Arduino ground. If you wanted negative output instead of positive output, then you would need to use model Q50N and change the arrangement of the voltage divider.
Please explain the voltage requirements for the lense. Have you a specification or datasheet for the lense?The +9V is where you connect the incoming power. You need to provide 9V or a little more at 250mA. You can use the same supply to power the Arduino if the supply can handle the extra current for the Arduino + anything running from its 5V supply.
Can the roles of the resistors prior to the op-amp and the role of the op-amp be explained in more detailed? The resistors coming off the HVM i am assuming is to make safe the connection back to arduino ground?
1. You need a buffer because an Arduino can only supply 40mA per output pin, whereas the 5V version of the HV multiplier requires up to 250mA.2. However, there are very few op amps that can supply as much as 250mA output current. That is why I suggested using an op amp and NPN transistor as the buffer.3. You cannot connect the input of the buffer direct to an Arduino output pin, because the Arduino does not have an internal DAC to drive any output pins with a variable voltage, and you must not try to drive the HV multiplier with PWM. That is why I included the RC network at the input to the buffer.
10-bit: 12-bit external DAC + possible op amp + emitter follower.11-bit: 12-bit external DAC + possible op amp + emitter follower + 12-bit external ADC.The "possible op amp" would be needed unless you are using the 5V version and it is lightly loaded.
When using a DAC, would that be connected to the Arduino output, and then to the rest of the circuit?
Also if another Arduino board was to be used (such as Due, which has a DAC) does that remove the need for an external DAC?