A freeform aspheric version of the 1.0X Offner relay design is discussed, with a much larger diffraction-limited field size.

1. Freeform Aspheric Version of the Offner1.0X Relay
David R. Shafer, Luc Gilles
David Shafer Optical Design,56 Drake Lane, Fairfield, CT. 06824 USA
Thirty Meter Telescope Observatory Corp., 100 W. Walnut St, Suite 300, Pasadena, CA 91124, USA
Authors email address:shaferlens@sbcglobal.net, lgilles@caltech.edu

2. 1974 US patent 3,821,763 by
Rod Scott and Perkin-Elmer Corp
ANNULAR FIELD OPTICAL IMAGING SYSTEM
An optical system
might have a “sweet
zone” of good image
quality over some
range of image radii
Inner and outer image zone
radii with good image quality
Rectangular fields can
be fit within the zone
of good imagery

3. ANNULAR FIELD OPTICAL IMAGING SYSTEM
Offner design has
blocked center of field
due to convex mirror
1.0 X Offner design of concentric or
nearly concentric spherical mirrors

4. The diffraction-limited field for an
Offner design may be very narrow.
Then only a small rectangular field
can be fit inside the inner and outer
annular field radii.

5. For an object and image
distance to the concave mirror
of 200 mm the diffraction-
limited (at .5876u) field goes
from 36 to 37 mm off-axis for an
f/3.0 design. That 200 mm
distance is held for the other
f/3.0 designs about to be shown.
Inside this narrow 1.0 mm wide annular field a rectangular field can
be fit that is 11.5 X 0.5 mm, or 6.5 X .75 mm, or 1.0 X 1.0 mm

6. By letting both the concave and
convex mirror be aspheric the
image quality hardly changes at all,
if the design is constrained to be
telecentric. But if telecentricity is
dropped then the convex mirror
(still the aperture stop) slowly
moves away from the concave
mirror. Then the convex mirror gets
smaller and blocks less of the center
of the field. Then the design can
work closer to the optical axis and
get better performance.
With two aspheric mirrors the
f/3.0 design is then diffraction-
limited over a rectangular field of
54 mm X 1.0 mm, or 13 mm X 25
mm, or 15 mm X 15 mm

7. This shows two folding options that allow for scanning

8. If both mirrors are
made freeform aspherics
then the convex mirror
moves even closer to the
object and image plane.
That allows the design to
work even closer to the
axis and the image
quality gets better still.
A rectangular diffraction-limited field going in and
out of the plane of the page can be 115 mm X 1.0
mm, or 50 mm X 5 mm or other aspect ratios.

9. The beam footprint on the convex
mirror for this 115 mm X 1.0 mm field
size design is very elliptical – much larger
in the out of plane direction.

10. If the freeform design is
optimized for a diffraction-
limited field of about 80mm X
1.0 mm then the beam footprint
on the convex mirror is quite
round. That design is shown
here. But any further increases
in field size, still with very good
performance, requires the
design to squeeze in the Y
direction the beam footprint on
the convex mirror so that the
design can work closer to the
axis without vignetting.
That then leads to
this beam footprint
for the 115 mm X
1.0 mm design

11. Design comparison of diffraction-limited field size
Classical f/3 Offner - rectangular field = 11.5 mm x 0.5 mm or 1.0 x 1.0 mm,
for 36 to 37 mm radius annular field
Aspheric f/3 Offner - rectangular field is 56 mm x 1.0 mm or 13mm x 26 mm.
Freeform f/3 Offner - rectangular field = 115 mm x 1.0 mm or 50 mm x 5 mm
Object and image distance to concave mirror = 200 for all designs

12. This freeform
design can be used
as a spectrograph by
making the convex
mirror have a grating
on its surface. That
would have to be on
top of the freeform
aspheric. The design
has a very wide slit
length in the out of
plane direction