As far as I understand, Zernike standard coefficients and Zernike standard phase coefficients are related by Forier transform.
Is there a way to input the zernike standard coefficients directly to the system and not the phase? I can’t find a zernike standard coefficient surface type.
Best answer by MichaelH
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+2
Hi Baraka,
I believe that surface is the Zernike Standard Sag. The Help File for this surface reads:
The Zernike Standard Sag surface is defined by the same polynomial as the Even Aspheric surface (which supports planes, spheres, conics, and polynomial aspheres) plus additional aspheric terms defined by the Zernike Standard coefficients.
I’m not sure I understand the link with Fourier transforms. As far as I understand, Zernike coefficients are a mathematical way to decompose a surface in an orthogonal basis. Now, in OpticStudio, if you wish to decompose your surface sag into Zernike coefficients, you’ll use the Zernike Standard Sag. But if you wish to decompose your wavefront (which is also a surface in 3D) into Zernike coefficients, you’ll use the Zernike Standard Phase. The same distinction is made for the Grid Sag and Grid Phase surface, where the Help File reads:
This surface is nearly identical to the Grid Sag surface (see “Grid Sag”). The key differences are:
- The units of sag are radians of phase instead of units of length.
...
I hope this helps, and take care,
David
Hello David,
Thank you so much for your reply. I am trying to express a wavefront by defining values for zernike coefficients. The problem is, if I use the zernike standard phase, the values are not the same as the zernike standard coefficients.
For example, if I enter a defocus coefficient value of 0.01, the zernike standard coefficients are totally different. I also made sure that I am using a collimated source. it might be that the zernike standard coefficeients are being fitted but it even flips the sign of the coefficient, and in some cases, it introduces even different coefficients values which I set to zero in the zernike standard phase part.
Thank you in advance for your time
+2
Hi Baraka,
There are several surfaces in OpticStudio which have a Norm Radius column; this is a scale factor for coefficients which make optimization and athermalization faster/more stable. The default Norm Radius for all surfaces is always 100, but this should be changed to either the Clear Semi-Diameter (coefficients scaled to edge of surface; useful for stable coefficients when athermalizing) or 1 (scaling is turned off, coefficients are lens units, and can be useful when comparing something like Extended Asphere to Even Asphere). For Zernike (orthonomal) surfaces, the Norm Radius should always be set to the Clear Semi-Diameter.
Changing this value to 5 to match your EPD, you get the Z4 term of 0.00999525, which with a recursive fitting algorithm is within the expected error range of 1E-2.
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