Schmidt’s 1934 three lens replacement for an aspheric plate, and some new variations

David ShaferDavid Shafer Optical DesignFairfield, CT. 06824#203-259-1431shaferlens@sbcglobal.net

Recently a fascinating story from lens design history was chronicled in this journal article here, about how Schmidt designed and built in 1934 a three lens replacement for the aspheric plate in a f/1.0 Schmidt camera.

This system designed and built system by Schmidt in 1934 was 10 years before the two and three lens replacements for an aspheric Schmidt plate that were described by Houghton in this 1944 patent. Schmidt died unexpectedly and was never able to publish his results, which have been unknown until very recently. Later Buchroeder in 1972 published some Houghton type of designs.

Here we will compared the performance of this kind of design with a different design that has much better color aberrations.Schmidt’s f/1.0 design

had the triplet be completely symmetrical and made of the same glass type. The image is curved.

Reference design, f/1.0, 10 degree full field, for comparisons

BK7 lenses

Spherical mirror

On-axis+/- 5 degrees off-axis

The design correction benefits some from departing from symmetry for the triplet as well as having some larger lens airgaps than in the Schmidt design, and that was done here. The f/1.0 optimized design ray traces are shown here for .5876u, .4861u, and .6563u.

There is higher order spherical aberration, spherochromatism, and oblique spherical aberration off axis. There is essentially no benefit to trying different glasses.

200 mm F.L.

Schmidt’s 3 lens corrector –positive, negative, positive.

Alternate design, not as good –negative, positive, negative

In both designs all lenses are BK7 and there is little to be gained by different glasses

In 1983 (SPIE Vol. 0399 -“Optical Design With Air Lenses”) I showed how the two lens Houghton corrector can be replaced with two nearly zero power meniscus lenses to get a well-corrected alternate design. And there are theoretical reasons why the resulting pair of lenses moves much closer to the spherical primary mirror, giving a much shorter design than the Houghton design. The lens thickness in this kind of design is an important parameter that affects axial and lateral color as well as higher-order spherical aberration.

A 3rd lens added to these solutions gives these two new ones.

Compared to our reference design, the solution on the top left is somewhat worse in performance while the top right solution is better.

This is a different solution region than this one, and its has much weaker lens powers and much better correction. Lens thickness is important for good correction, while it makes no difference in the other solution on the right. This solution on the top left starts to be close

to the Baker Super-Schmidt design shown on the lower left here, but that is considerably longer and has one or more aspherics.

As the design length is allowed to increase and the lenses become thicker the correction keeps improving

It turns out that there is a variety of three lens solutions, all the same glass, and all spherical surfaces. This one has much better performance than our reference design.

The best design of all, with three lenses, is this one here – where 2 of the 3 lenses are seen in double pass. It is related to our original reference design, pioneered by Schmidt.

Despite the similarity to our reference design (positive, negative, positive lenses, no meniscus lenses, no lens thickness sensitivity), no “automatic design” program is going to find this new solution - using the double-pass idea - from the reference design starting point.

Reference design

New design

On-axis

On-axis

+/- 5 degrees

+/- 5 degrees

Same scale on plots

The new design has better monochromatic correction than the reference design and much better chromatic correction, with almost zero spherochromatism.

All of these design have a curved image

If we put in a field flattening lens right in front of the image to get a flat image these two designs are about the same in performance. The accessibility of the image is different in these two designs.

Getting a flat image by means of a field lens right at the image turns out to reduce the performance differences of the various designs shown here. Probably the best flat image design, with regard to the aberration correction, length, image location, and weak lens curves is this one shown here.

200 mm F.L., F/1.0, 10 degrees full field, flat image, color corrected, all BK7 glass

200 mm, f/1.0, 10 degree full field, flat image

On-axis+/- 5 degrees off axis

.5876u, 4861u, .6563u

This would make a nice f/1.0 camera for astrophotography, with an image chip

35 mm image diameter size

A flat image design that is almost as good in correction but is a little longer and does not have as good an image location is this one here – basically the Schmidt 3 lens type of design with a field lens added at the image. It has considerably stronger curves than the previous design.

In summary, Schmidt’s 1934 design makes a good starting point for finding other simple catadioptric designs. Of course adding more lenses to the design, or aspherics, will further improve performance beyond these examples here.