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Zernike coefficients computation

  • 16 December 2022
  • 3 replies
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Hello everyone,

 

I am a new user of Zemax OpticStudio and have a few questions about the Zernike coefficients. I have to use the Zernike coefficients in order to align an optical system with 3 lenses and I want to model it with OpticStudio.

  • How are the coefficients calculated in OpticStudio ? In theory, they have to be computed in the exit pupil plane but I understood that they are computed in the surface that is selected in the Zernike Standard Coefficient window, for example the image plane, so I am wondering how OpticStudio computes the coefficients.
  • I need to know the evolution of a certain coefficient with respect to a certain disalignment, let’s say a lens tilt, do I have to make OpticStudio recompute the image plane each time I disalign the lens ?
  • If I want to experimentally make the measurement of the Zernike polynomials with a wavefront sensor, should I place it in the exit pupil plane (which is not easy to find I think but I can be wrong) or should I put it in the plane where the beam is the size of the sensor ? And is it possible in OpticStudio to model the disalignment of a wavefront sensor/model a wavefront sensor directly ?
  • Reading the Help section, I found out that when using the Merit Function Editor, I need to compute the Zernike coefficients one order higher than the highest coefficient I need or so, and I am not quite sure why or what it precisely means.

Thank you very much for your help !

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Best answer by Sandrine Auriol 20 December 2022, 13:32

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Userlevel 6
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Hi @alice.renaux !

Thank you for posting on the forum.

  • The coefficients are calculated at the exit pupil, because this is where we compute the wavefront. The wavefront reference is given here:
    Note that the coefficients consider a uniform sampling.
    If the surface is not the image plane, have a look at this section “Evaluating results at intermediate surfaces” of our help files.
  • This will be automatic. When you disalign, the software will recompute the wavefront.
  • Have a look at that article https://support.zemax.com/hc/en-us/articles/4406838460819-Modelling-of-a-Shack-Hartmann-Sensor-for-eye-aberration-evaluation.
    To find the exit pupil position, you can use a solve:
  • For the Merit Function, where did you read that you need to compute the Zernike coefficients one order higher than the highest coefficient you need? I need to check this.

Hello,

 

Thank you very much for your answer, it is very clear !

  • Concerning the number of Zernike coefficients to compute, I couldn’t find the page again but it was because in order to compute an accurate coefficient, Zemax has to compute the whole order of the coefficient or something (I don’t know if this is exact but it is what I understood).
  • If I am manually disaligning an optical system, are the ZERN operands in the merit function computed in the same way as the Zernike Standard Coefficients computed in the Anlyze => Wavefront window ?
  • And do I have to turn the Ray-Aiming feature on when disaligning an optical system on purpose ?

Again, thank you very much for your help !

Userlevel 6
Badge +2

Hi @alice.renaux !

  • Yes the ZERN coefficients are computed in the same way. 
  • The Zernike coefficients consider a uniform sampling so yes I would turn on ray-aiming. There is a post discussing this here: 

     

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