A recent article shows the use of a curved image in a three mirror freeform design and the performance benefits that brings. Here I duplicate their results but get better image quality without their "fancy" surface description or a toric image. surface

1. Dave Shafer
David Shafer Optical Design
Fairfield, CT 06824
203-259-1431
shaferlens@sbcglobal.net
A three mirror freeform design study with a curved image

2. In Optics Express, June
2017, these authors
described a three
mirror freeform
telescope with a curved
image detector array.

3. Their design is
100 mm circular
aperture, 250 mm
focal length (f/2.5)
and a square field
of 7.2 X 7.2 degrees
I have done my
own version of this
design, shown here.
The image quality is
slightly better with
the stop on the first
mirror, shown here,
than on the second
mirror.

4. The worst field point in the 7.2 X 7.2 degree field of my f/2.5
design has an r.m.s. OPD of .080 waves. This is with a curved image
detector array with a convex spherical radius of 460 mm. There is
very clearly an advantage to having a curved image, both for image
quality and mirror sizes. But I see no advantage for this design of
having a toric image surface, unlike the author’s claim.
Furthermore I used a conventional X-Y polynomial for the freeform
surfaces. With that and a spherical image surface I get better image
quality than the author’s results with Legendre polynomials, which
they find superior to other types, and their toric image surface.
What is the explanation for this discrepancy?

5. In my opinion there is a simple explanation for the difference. That is
that I have been a full-time lens designer for the past 53 years and that
included many years doing high NA EUV designs with 6 freeform mirrors.
There are several optimization “tricks” that I have developed during my
long career that give me better results than designers with much less
experience. That probably explains my better image quality on this
design and with no advantage to a toric image surface.
But I also don’t see any advantage to the several different surface
descriptions that have been widely written about during the last few
years by several authors. I find the simple X-Y polynomials quite
adequate. However that might only be the case for 2 and 3 mirror
systems. With the 6 mirror freeform designs I have found that
optimization does not proceed as well as I would like and then there
might be some advantage to orthogonal surface form descriptions.