Some designs are shown with a single glass type plus diffractive or metasurfaces which bring 4 or even 5 wavelengths to the same focus. Induced color is the explanation.

1. Some color correction studies with diffractive or meta-materials surfaces
Dave Shafer
Here are some results about color correction when highly dispersive diffractive
surfaces or meta-
surfaces are used in
an optical design,
when combined with
only one glass type.
First we want a
comparison with
conventional
achromats. We will
have as the baseline a
100 mm focal length
f/2.5 design and start
with a single SK5 glass lens.
Its paraxial focus shift from
.45u to .65u is shown next
and it has 2.1 mm of axial
focus shift.
Next we make a
conventional achromat by
adding a F2 flint glass
element and correct
primary color. The residual
color then is a 83u focus shift over the .45u to .65u range, shown below here.

2. This 83u of secondary color in
a conventional design is what
our next designs will be
compared to. There have
been many published studies
that show the benefits of
adding a diffractive surface to
a conventional achromat so
that secondary color can be
corrected and what is left is
tertiary color. If that is done
here the result is a doublet
with a diffractive surface and
+/- 6u of cubic tertiary axial
color.
But I want to see what can
be done with just a single glass
type and diffractive surfaces.
If the single SK5 lens shown in
the beginning here has its
color corrected by a diffractive
surface then the result is secondary axial color of 250u, about 4X larger than the
conventional achromat case. And this secondary color, over the .45u to .65u
range is of opposite sign to conventional secondary color.
Next we consider a more complicated design, with an intermediate image.

3. With completely
uncorrected color
from these two
positive lenses of
SK5 glass the axial
focus shift is 6 mm,
or 3X larger than
that from just the
first lens alone.
Next we put a
diffractive surface
on either lens and
correct this large amount of primary color. The result is about 600u of secondary
color over the .45u to .65u range, or a 10X reduction compared to the 6 mm of
primary color. Next we put a diffractive surface on both lenses and it then turns
out that secondary color can be corrected – kind of a big surprise. The 600u of
secondary color can be corrected and the result is about +/- 60u of tertiary color,
as shown below. The diffractive surface powers on the two lenses are of
opposite signs and on both lenses they give very much more color than either of
the glass lenses they are on. My conclusion is that this must be a design where
induced color plays a very
important role. And this is
only possible because of the
intermediate image
configuration. The amount
of primary color, in arbitrary
units, in this design is as
follows. On the first lens
there is 3.9 units of primary

4. color from the diffractive surface and 1.1 units from the lens, both of the same
sign. On the second lens the diffractive surface has -6.4 units of primary color
and the lens has +1.3 units. So for both lenses the diffractive color is much more
than that of the lens and there is a lot of color inside the design. Yet the design
can be corrected for both primary and secondary color, due to induced color
effects. The residual tertiary color is about +/- 60 u over the .45u to .65u range
and that can be compared to the +/- 6u of tertiary color when a diffractive surface
is used in combination with a doublet lens of SK5 and F2 glasses.
The next step is to put a third lens into the design, also of SK5 glass, and see
what this new design variable can do. There are two different types of 3 element
designs of interest. This shows one of them, where all three lenses have a
diffractive surface on them. With the extra variable it is possible to bring 4
wavelengths to the same focus, so tertiary color is corrected.
This is quite remarkable, with just one glass type and diffractive surfaces that
introduce a very large amount of color inside the design. But what is really
amazing is the next design, also with three lenses with diffractive surfaces.

5. Here the 3rd
lens
is quite a bit
smaller and the
system length is
much shorter. The
design brings 5
wavelengths to
the same axial
focus and the
residual color is
very small. But
this design has a
very large amount
of lateral color
and would not
have any practical
use.
A design with 4
axial focus
crossing points
that is corrected
for primary lateral
color is shown
next. The middle
lens is just a flat
plate, with a diffractive surface on it. There is still a lot of secondary lateral color
now that primary lateral color is corrected.

6. The point of this whole exercise here is to show that even with the very
dispersive medium of diffractive surfaces and just a single glass type, with a very

7. large amount of color inside the design, it is still possible to get very broad band
focus shift correction. The same conclusion would apply to metasurface designs if
it turns out that they have the same dispersion properties as diffractive surfaces.
Cleary if so much can be done with just one glass type much more can be done
if two glass types are used.