Solved

# How to change the wavefront error?

• 12 replies
• 1379 views

Hi ,

I am trying to design a schwarzschild objective mirror.

I’d like to calculate the each DoF(depth of focus) at RMS wavefront error λ/5, λ/10, λ/15, λ/20.

Where λ is 1.03 micrometer.

When using OPDX operand, what should I fill in the “Hx, Hy, Px, Py” and “Target” section?

This is my first that use the Opticstudio, so I don’t know how to change the wavefront error.

Can any one help me?

### 12 replies

Userlevel 7
+2

Hi YoungDae,

Let me try to rephrase what you want to make sure I understood it well. You would like to evaluate the RMS wavefront error axially, and check when it reaches a certain value such as λ/5, λ/10, or so, and this will be the definition of your depth of focus.

To answer your question first, OPDX will calculate the optical path difference (OPD) for a single ray and you have to tell OpticStudio which one. That is what Hx, Hy, Px, and Py are for. Have a look at the Help File (F1) under: Conventions and Definitions > Normalized Field Coordinates and Conventions and Definitions > Normalized Pupil Coordinates. Hx, and Hy describe the field coordinates with a value between -1 and 1, 1 being for the most extreme fields in your file. Px, and Py, describe the pupil coordinates (where the ray hits the STOP) with a value between -1 and 1, 1 being at the very edge of your STOP. Target is what you want the OPDX operand to aim for. If you give an operand a Weight, and a Target, OpticStudio will use the variables in your system to try and meet those targets. I suggest reading about the introductory articles on the knowledgebase to understand more about the Merit Funciton.

Imagine you have just one field, on-axis, you could have a series of OPDX, with Hx = Hy = 0, and if your system is rotationally symmetric, you could have Px = 0, and have Py vary between 0, and 1, typically what people do is choosing values that are similar to those used in the Gaussian Quadrature, so that you sample more at the outter edges of the pupil. You could have one OPDX with Py = 0.0, one with Py = 0.5, one with Py = 0.8, one with Py = 0.95 for example. Since you want to measure the OPD, ignore the target, and leave the weight at 0. Then you could add a MAXX operand, which will report the maximum value among your different OPDX operands. Finally, what you need to do, and perhaps I would use a ZPL macro for that, is to change the last Thickness of your system, and report the maximum OPD at each point. There’s quite a bit to cover for someone new to OpticStudio. Perhaps you could share your file with us, and we can try to walk you through.

I hope this helps. Take care,

David

Userlevel 7
+3

In addition, it’s a fairly easy matter to determine the DoF for a given design.  You can add a dummy defocus surface in front of the image plane, and then use the Universal Plot feature to create a graph of wavefront error vs. defocus.

Then the DoF at a particular wavefront error can be easily read directly from the graph.

Thanks for your helps.

Whenever I calculate DoF and consider the wavefront error, the spent time is shorter than previous!

Your helps are super efficient to me

Userlevel 7
+3

You’re very welcome.  Quick update: For a Schwarzschild objective it’s better to use RWRE or RWRH operands to compute the wavefront error because of the central obscuration.

Dear Jeff.Wilde

I’m designing a Schwarzschild objective.

So, I would like to use the operand RWRE or RWRH for it.

Could you show me some of examples how to use the operands?

Userlevel 7
+3

Sure, for your problem, after optimization you can calculate the wavefront error vs. defocus using the Universal Plot with RWRE as the operand:

Here is the result for an NA = 0.5 objective at a wavelength of 1.03 um:

As before, you can determine the DoF for a given RMS wavefront error from this graph.

If you are just beginning to learn OpticStudio for lens design, here is a good set of introductory articles:

How to design a singlet lens, Part 1: Setup

How to design a singlet lens, Part 2: Analysis

How to design a singlet lens, Part 3: Optimization

Thank you!

I have one more question.

When I hope to calculate DoF at λ/5, Is the thickness value of dummy defocus surface 2.06e-4(1.030÷5) ?

Below picture is mine

Userlevel 7
+3

The operands compute the RMS wavefront error in waves:

An RMS wavefront error of λ/5 = 0.20 waves.  So try increasing the plot scale for the dummy surface thickness until the RMS error reaches (or exceeds) this value.  Then you can find the DoF.

Thank you for your helps,

I can design a Schwarzschild objective, and then I calculate DoF

Below picture is mine, is it correct at λ/5(0.2Wave)?

Userlevel 7
+3

I can’t validate the design or confirm that you have the correct DoF without a careful review of the complete model.  However, the general approach of using the RWRE operand in the merit function to determine the DoF (relative to a particular wavefront error) should be okay.  You may want to try increasing the sampling value until you reach a reasonably stable value for the wavefront error.

Is it the correct DoF when the wavefront errer is lower than diffraction limit?

If it is correct mean that I said, the DoF is incorrect when the wavefront error is upper than diffraction limit?

If you are OK, please could you validate my design?

Userlevel 7
+3

Unfortunately, I can’t assume responsibility for validation of your design.  However, I think you are on the right track.  Good luck!