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# What is the reference sphere for a system with an off-axis field?

Hello!

I just wanted to ask, what exactly is the reference wavefront that OpticStudio uses when computing the wavefront error of a system with an off-axis field?

I’ve read several posts talking about the reference wavefront, and to my understanding, the reference wavefront for an off-axis field is a sphere with a center that lies on the chief ray, and the sphere intersects the optical axis at the exit pupil plane.

I’ve read that the radius of the reference sphere is equal to the distance between the focal plane (image plane) and the exit pupil plane (this number is given by the exit pupil position in Prescription Data, multiplied by -1). However, for off-axis fields, I don’t think this is the case. I think the radius for the reference sphere is the distance between where the chief ray intersects the exit pupil plane and where the chief ray intersects the focal plane. This distance would be larger than the exit pupil position.

For example, I have an image below which illustrates where the reference wavefront (in orange) is located for a Double Gauss system:

### 2 replies

@Jeff.Wilde

Hi Jeff, thanks so much for your help! The second discussion you linked, regarding OPD and transverse ray aberrations, was particularly interesting and helpful.

Thank you,

Matthew

Userlevel 7
+3

@matthew :

Yes, you are right, the radius of the reference sphere is the distance from the reference point location on the image plane (OpticStudio uses the real chief ray intercept for the primary wavelength) to the location where the real chief ray intercepts the exit pupil plane (which should be very close to the origin of the exit pupil plane, although pupil aberration can cause the chief ray to miss the center of the stop / exit pupil unless ray aiming is turned on).

This post may help:

Even more detail related to using the OPD to find transverse ray aberrations is discussed here:

Regards,

Jeff