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# Why my Nominal criterion value (Spot Radius) in the tolerance report is different than the RMS spot radius reported in the Spot Diagram?

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Dear All,

I am conducting a tolerance for an optical system and setting the criterion to be RMS Spot Radius.

The nominal criterion value is 1.7815 while the actual spot radius value is a lot smaller than this value as shown in the snippet below.

I did some search and found this discussion here but I really did not understand what I should do with my current merit function editor. The Merit Function value is 0.00420 as shown in the snippet below.

Any idea on what I am missing here?

Thank you

Kind Regards,

Naif

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Best answer by MichaelH 12 February 2024, 17:22

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Userlevel 7
+2

@Naif.Alsalem,

Can you show the settings of your Spot Diagram? Its the button in the upper-left corner of the Spot Diagram window.

Take care,

David

Dear Naif.Alsalem,

I guess you get confused trying to compare “Spot Radius ( RMS, GE, etc. ) with the Merit Fucntion value ( Nominal criterion ). Since Merit Function represents the weighted deviation of all operands, there is no direct correlation between Nominal Criterion and Spot Radius. A lower merit function just indicates a well-optimized system and does not provide the operands value itself.

Also keep in mind that “Nominal Criterion” is the initial value of Merit Function before tolerancing the lens. I hope this information will help to clarify your question.

Kind regards,

Christian

Userlevel 6
+2

Hi Naif,

The reason why your Nominal Criteria and your Merit Function Value differ is because the Nominal Criteria is using Gaussian Quadrature, 4 rings, 8 arms and your Merit Function is using a 64x64 rectangular grid.  I would suggest setting both the # Monte Carlo Runs and # Monte Carlo Save to 1 and check the new MC_T0001.zmx file that is saved.  It will have the modified MFE which shows the value reported for the Nominal Criteria.  Once you have everything verified, then you can run 1000 (or more) Monte Carlos for your tolerance analysis.

@Naif.Alsalem,

Can you show the settings of your Spot Diagram? Its the button in the upper-left corner of the Spot Diagram window.

Take care,

David

Hi David,

Many thanks for taking the time to reply. I think it is solved now by modifying the Pupil Integration settings in the merit function Wizards to be 4 rings and 8 arms.

Thank you again.

Take care.

Naif

Dear Naif.Alsalem,

I guess you get confused trying to compare “Spot Radius ( RMS, GE, etc. ) with the Merit Fucntion value ( Nominal criterion ). Since Merit Function represents the weighted deviation of all operands, there is no direct correlation between Nominal Criterion and Spot Radius. A lower merit function just indicates a well-optimized system and does not provide the operands value itself.

Also keep in mind that “Nominal Criterion” is the initial value of Merit Function before tolerancing the lens. I hope this information will help to clarify your question.

Kind regards,

Christian

Hi Christian,

Thank you very much for clarifying this. Very informative.

Best Regards,

Naif

Hi Naif,

The reason why your Nominal Criteria and your Merit Function Value differ is because the Nominal Criteria is using Gaussian Quadrature, 4 rings, 8 arms and your Merit Function is using a 64x64 rectangular grid.  I would suggest setting both the # Monte Carlo Runs and # Monte Carlo Save to 1 and check the new MC_T0001.zmx file that is saved.  It will have the modified MFE which shows the value reported for the Nominal Criteria.  Once you have everything verified, then you can run 1000 (or more) Monte Carlos for your tolerance analysis.

Hi Michael,

Thank you very much for taking the time to reply. It is not solved by modifying the merit function Pupil Integration to the settings you outlined in your reply. I then ran the MC, saved it (only one iteration as you showed in your snippet) and then ran the needed MC. It worked smoothly.

In another tolerance analysis, I followed the same but then ran into an error message that you (or others in this thread) may know how to tackle? The error message indicate that the tolerance analysis cannot proceed because some surface in my LDE is under a merit function constraint! What is the best practice to tackle this? Loosening my tolerance values?

Here is a snippet of the msg:

I can put this in another new question if it is proper to do so.

Thank you again.

Kind Regards,

Naif

Userlevel 6
+2

Hi Naif,

The `HYLD` operand is designed for optimizing the shape of an optical system by minimizing the power (aberration) each lens contributes to the overall system; this is achieved by minimizing the angle of incidence for all rays across the surface.  If you minimize the AOI, you desensitize your entire system.

When you’re tolerancing, your system is “fixed” in its design form, you’re just apply small perturbations and then changing a small number of compensators to maximize performance; the compensators that you are changing are not the minimization of AOI across the surface.  So, `HYLD` and tolerancing are inherently contradictory.

This error only occurs when you choose “Merit Function” for the Criterion in the Tolerancing window.  If you have a custom Merit Function you want to use for Tolerancing, I suggest you rebuild your DMFS with Best Nominal Performance checked: