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How to Use the Zernike Sag Surface to Model an All-Reflective System
- By Mark Nicholson
- Published 14 August 2007
- System Modeling
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How to Use the Zernike Sag Surface to Model an All-Reflective System
This is a companion article to How To Model a 'Black-Box' Optical System Using Zernike Coefficients. Please read that article and understand its contents before proceding with this article.
As discussed in that article, Zernike data represents a measurement of the performance of an optical system at a specific field and at a specific wavelength. Because information about the glasses, radii of curvature, aspheric coefficients etc are not part of the Zernike data, there is no way to scale Zernike data to a different field or wavelength. For this reason, in general you will need a set of Zernike data for each (field, wavelength) pair you want to model performance at. These can be entered into ZEMAX by either having a separate file for each (field, wavelength) combination or (more likely) a separate configuration for each (field, wavelength) pair.
However, if you are working with an all-reflective design, then you can use the Zernike Standard Sag surface to describe the aberrations of the optical system. The advantage is that this then works at all wavelengths for a given field, as all-mirror systems do not suffer chromatic aberration. The Zernike Sag surface is used instead of the Zernike Phase because diffractive power is different than the reflective power as the wavelength changes. One wave of phase is one wave at any wavelength, but one wave of sag at 0.5 microns is only half a wave at 1.0 microns.
For example, consider a Yolo telescope like so:
(This file is included in the zip file at the bottom of this page). This unobscured telescope produces a wavefront like so:
Now, to make an equivalent system using the Zernike sag surface, we just need the exit pupil position and diameter, as in the previous article. This data is:
Exit Pupil Diamater = 701.681 mm
Exit Pupil Position = 9484.22 mm
Still following the previous article, a first-order equivalent system can be produced as follows:
In which the entrance pupil diameter of the system is set to the exit pupil diamater of the original Yolo, and the focal length of the paraxial lens is set to the same value as the exit pupil position. This gives us a first order system with the same reference sphere radius as the original.
We then export the Zernike data in units of sag. The macro that performs this is similar to that provided in the original article, but adds an extra scaling factor
which is then used to scale the Zernike data into sag units prior to saving to disk:
The Zernike data is then imported into the Zernike Standard Sag surface using the Import tool, and the same wavefront error and other ray-tracing results can be seen:
Both the original and Zernike-equivalent files are in the zip file at the bottom of this page. If you add further wavelengths, you will see that both files give the same results at any wavelength. Detailed transmission and other polarization data will not be equivalent, however, as the Zernike file has no knowledge of the coatings used in the original file, and there is still no way to predict how the behavior of the telescope will change with field: a set of Zernike coefficents per field is still needed.
As discussed in that article, Zernike data represents a measurement of the performance of an optical system at a specific field and at a specific wavelength. Because information about the glasses, radii of curvature, aspheric coefficients etc are not part of the Zernike data, there is no way to scale Zernike data to a different field or wavelength. For this reason, in general you will need a set of Zernike data for each (field, wavelength) pair you want to model performance at. These can be entered into ZEMAX by either having a separate file for each (field, wavelength) combination or (more likely) a separate configuration for each (field, wavelength) pair.
However, if you are working with an all-reflective design, then you can use the Zernike Standard Sag surface to describe the aberrations of the optical system. The advantage is that this then works at all wavelengths for a given field, as all-mirror systems do not suffer chromatic aberration. The Zernike Sag surface is used instead of the Zernike Phase because diffractive power is different than the reflective power as the wavelength changes. One wave of phase is one wave at any wavelength, but one wave of sag at 0.5 microns is only half a wave at 1.0 microns.
For example, consider a Yolo telescope like so:
(This file is included in the zip file at the bottom of this page). This unobscured telescope produces a wavefront like so:
Now, to make an equivalent system using the Zernike sag surface, we just need the exit pupil position and diameter, as in the previous article. This data is:
Exit Pupil Diamater = 701.681 mm
Exit Pupil Position = 9484.22 mm
Still following the previous article, a first-order equivalent system can be produced as follows:
In which the entrance pupil diameter of the system is set to the exit pupil diamater of the original Yolo, and the focal length of the paraxial lens is set to the same value as the exit pupil position. This gives us a first order system with the same reference sphere radius as the original.
We then export the Zernike data in units of sag. The macro that performs this is similar to that provided in the original article, but adds an extra scaling factor
which is then used to scale the Zernike data into sag units prior to saving to disk:
The Zernike data is then imported into the Zernike Standard Sag surface using the Import tool, and the same wavefront error and other ray-tracing results can be seen:
Both the original and Zernike-equivalent files are in the zip file at the bottom of this page. If you add further wavelengths, you will see that both files give the same results at any wavelength. Detailed transmission and other polarization data will not be equivalent, however, as the Zernike file has no knowledge of the coatings used in the original file, and there is still no way to predict how the behavior of the telescope will change with field: a set of Zernike coefficents per field is still needed.
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