The document discusses an optimal lens design for an f/1.5 lens with a 30-degree field of view, aiming for high performance by correcting for 3rd, 5th, and 7th-order aberrations. It compares various lens configurations, including 5 and 6 element designs, and emphasizes the importance of optimizing parameters like color correction and vignetting. The author expresses interest in improving a specific 5 lens design that performs well but struggles to incorporate additional lenses without losing performance.

1. An optimum lens design for f/1.5 with a 30 degree diameter field
David Shafer
David Shafer Optical Design
Fairfield, CT. 06824
#203-259-1431
shaferlens@sbcglobal.net

2. In 1994 I showed at I.O.D.C. many
different 6 element designs that can be
corrected to zero for all the 3rd order
Seidel and 5th order Buchdahl
monochromatic aberrations.
The point of that is to see which
designs have the best potential for high
performance. Of course in a real design
real rays and wavefront are optimized,
not 3rd and 5th order aberrations. But if a
design cannot be corrected for all the 3rd
and 5th order then it probably cannot
give the best performance.
The top design here seems to have the smallest 7th-order aberrations of those 6 lens designs
with zero 3rd and 5th order. The 2nd lens is so weak that the 5 lens design shown below it is
almost as good.

3. Both of the designs just shown
can have either a cemented or
airspaced doublet right after the
aperture stop, and need a
substantial index difference
between those two lenses. If all the
3rd and 5th order aberrations are
zero then they still are for any
aperture stop position, but the
position shown gives the best 7th
order aberrations.
In 2013 Duckett showed in Applied Optics two 5
lens designs with all the 3rd and 5th = 0 but where
color cannot be corrected without extra lenses. My
1994 design, above, is clearly one of these designs.
The other one of Duckett’s has the nearly cemented
doublet on the front side of the stop instead of the
rear side. The shaded grey lens here is low index.

4. Neither of these 5 lens designs can be corrected for axial and lateral color, but
a blend of the two designs can be, as shown here below.
The parameters that we want to
optimize for are a speed of f/1.5, a
field diameter of 30 degrees with no
vignetting, distortion correction, color
correction, a focal length of 25 mm
and a total length of 50 mm or less.

5. SF6, SK10, SK10, F2, SK10, SF6
This design has two lens pairs that are cemented and by playing with the glass
types an optimum design is achieved with this polychromatic MTF. The last
lens surface is in contact with the image surface. This shows what can result
from first finding a design correctable for all the 3rd and 5th order aberrations
and axial and lateral color before doing any ray optimization. Then you are
starting very close to a good final solution.

6. A related 6 lens design is shown
here, with essentially the same
polychromatic MTF. Only the first
two lenses are cemented.
So now we are finished, right?
Wrong! We have identified the best
6 lens design for the specs (f/1.5, 30
degree field, length <twice F.L.) given
the particular design method used
(start with all 3rd and 5th order = 0).
But life is not so simple. There are
designs which cannot be corrected
for all the 5th order but which have
very small 7th order and sometimes
they may be preferred.
This 5 lens design
cannot be corrected
for all the 5th order but
has very good
performance and can
be corrected for axial
and lateral color.

7. Since this particular 5 lens design has quite good performance (but not as good
as the best 6 lens designs already shown) you would think that we could just add
another lens to it and get equal or better performance to the 6 lens design already
shown. But it turns out to be very difficult to add a lens to this design and get any
significant improvement. That is quite a mystery. It is a distinctly different lens
form from what has been already shown and it is the best 5 lens design that I
know of.

8. Despite a lot of effort I have not found
a way to add a lens to this design that
gives better performance at the edge of
the field. It is very hard to budge the T
and S polychromatic MTF curves at the
edge of the field compared to where
they are in this 5 lens design.
So it looks like the earlier 6 lens design
that I showed is the best solution. The
prescription is given on the next slide. I
would be very interested if anyone can
improve this 5 lens design shown here,
by adding a lens.

9. SRF RADIUS THICKNESS APERTURE RADIUS GLASS
OBJ -- 3.1250e+19 8.3734e+18 AIR
1 21.012877 V 15.777236 V 14.000000 SF6
2 7.604372 V 4.500000 7.000000 SK10
3 58.984342 V 1.846145 V 7.000000 AIR
AST -26.784478 V 5.780516 V 6.000000 A SK5
5 -35.592464 V 1.307023 V 7.000000 AIR
6 14.535978 V 4.998056 V 8.750000 SK10
7 -43.134942 V 1.247614 V 8.750000 AIR
8 -138.408416 V 11.512612 V 8.500000 SF1
9 -46.768559 V 2.000000 8.500000 AIR
10 -9.626844 V 0.995771 V 6.460581 S SF1
11 -- 0.057580 V 7.000000 AIR
IMS -- -- 7.000000 *
F/1.5, 30 degree diameter field with no vignetting, 25
mm focal length, 50 mm length. Cemented front pair.