The Evolution Of A New High NA Broad-Spectrum Catadioptric Design

David Shafer

David Shafer Optical Design

My 1996 US patent 5,488,229

There are many designs that are based on this 1996 patent, which has several nice features:

Very small obscuration Capable of high NA Very broad spectrum with only one glass type Large field size compared to microscopes Few elements

A typical more complicated design version is this .90 NA one with a 1.0 mm field diameter and good performance over a very broad spectrum in the deep UV.All the lenses are silica except in the small field lens group, which has some calcium fluoride lenses.

Two problems:

The tolerances in this field lens group are extremely tight

The design does not have an external aperture stop

Mirror

A 1.0 mm field size might not seem like very much, except to this ant here, but it is much larger than the field size of purely refractive high NA microscope objectives.

There are .90 NA design versions like this one, with only silica elements, that have good performance from the deep UV through the near IR, but only for a small field size. Tolerances are good. Secondary lateral color limits the field size and can only be fixed by having a silica/calcium achromat for the small field lens. Then the field size can be large but the very tight tolerances return.

US patent 7,307,783

US patent 6,560,011

There are all-silica design versions only corrected for a narrow band in the deep UV, like the .193u line, but which are .95 or even .97 NA with field sizes of 1 to 3 mm. An external pupil can be provided, like here.But in a broad spectral band design in the deep UV it is hard to make an external pupil except by a long length relay or a complex addition of silica and calcium fluoride lenses.

Goals for a new design of this general type

• High NA

• Broad spectrum with good performance

• Large field size

• Avoid very tight tolerances (new feature)

• Provide an external aperture stop (new feature)

• Relatively few elements

• Only on glass type

The ideal would be a simple design, without much complexity

From my US patent 7,646,533

An extra mirror relay section leads to a new design that is very simple and has an external pupil. It can provide very high NA, like this .97 NA design with a .80 mm field diameter with good wavefront at .266uIncidence angles and tolerances are better than designs without an extra relay section. All same glass type and there is no color correction.

Aperture stop

Field lens

By reducing the field size by ½ it is possible to push the external stop further out, but this is not the best way to move that external pupil and there is a big penalty in field size.

.97 NA, .40 mm field size, .266u

Aperture stop

By adding a few lenses to make a pupil relay, with an intermediate image, the external exit pupil can be made much further away from the closest lens, for those applications that need that. There is no loss in field size but there is still no color correction.

Aperture stop

.97 NA, .80 mm field diameter, .266u

40 mm diameter

Field lens

• How can we provide color correction for these deep UV all-silica designs that have an external pupil?

• Main problem is lateral color and secondary lateral color

• What can be done with just silica?

By a lot of design work the top design was changed to make it corrected for axial and lateral color over a narrow bandwidth, with just silica. The result is the bottom design. The very thick lens is not practical so it was split in two to give the design on the next slide. The design has good wavefront quality over a +/- 1 nm bandwidth of an un-narrowed .193u laser line, at .90 NA over a 1.0 mm field diameter.

Uncorrected for axial and lateral color

Corrected for axial and lateral color

All silica, color corrected for narrow bandwidth around .193u.

.90 NA, 1.0 mm field diameter, .193u un-narrowed laser bandwidth

70 mm diameterAperture stop

The design is well-corrected over a +/- 1 nm bandwidth at .193u. When it is evaluated at +/- 2 nm we see, above here, secondary color as the main aberration.

In an all-silica design can we do anything about secondary axial and lateral color without using a second glass type?

Let’s see what can be done with the 4 mirror configuration, using OSLO’s ASA program to search for solutions.

One should always look for multiple solutions, even in very simple systems. Before we look at four-reflection designs what do we know about simple two-reflection designs?

2.1X relay

2.1X relay

There are two different solutions for this kind of design, both with good high NA correction on-axis (only) over a broad spectrum. On left above it is a plano-convex element and a negative meniscus shell. On the right it is the reverse of this. The design on the left has better spherochromatism, secondary color, and Petzval. It needs a long glass path. Both designs are all BK7.

.70 NAin air .70 NA

in air

Design with all same glass can be corrected for 3rd and 5th order spherical aberration, axial color, and 3rd order spherochromatism. A .70 NA design with a 50 mm diameter concave mirror is diffraction-limited on-axis (only) from .365u to 2.0u, with just BK7 glass.

We will now take a short side-trip to explore some interesting 1.0X relay designs

Two systems back to back makes a high NA 1.0X broad spectrum relay. By symmetry coma cancels as well as lateral color and distortion. Field lenses correct for astigmatism and Petzval. A .60 NA design with a 25 mm diameter concave mirror is diffraction-limited over a 1.0 mm field diameter from .365u through 1.0u.

All BK7 glass

Field lenses

.60 NA, 1.0 mm field diameter, .365u- 1.0u

To get a double telecentric design and also correct for Petzval requires two sets of field lenses – one set at the intermediate image and one set at the front and back end of the system.

Aperture stop

.60 NA, 1.0 mm field, .365u – 1.0u

The alternate two reflection solution can also be made into a 1.0X relay. It has much less glass path and is shorter but the color correction is not quite as good. Here it has the same performance as the .60 NA design shown earlier, but only by going from .40u to 1.0u instead of .365u to 1.0u. Again it is all BK7 glass.

.60 NA, 1.0 mm field, .40u -1.0u

By splitting the field lenses the .60 NA design, with reduced spectrum of .45u to 1.0u, can be raised to .75 NA with a 1.0 mm field diameter and a 25 mm diameter concave mirror.

Even very simple designs often have 2 or more alternate solutions. Here is a two reflection design with an intermediate image here.

This design is .60 NA, 3.0X magnification, and is diffraction-limited on-axis from .365u through 2.0u with just BK7 lenses

25 mm diameter

Conclusion so far –

1) There are several simple designs with only one glass type that have good high NA correction over a very broad spectral band, but only on-axis.

2) By using 1.0X symmetry and some field lenses we can make large field designs that are high NA and broad spectrum, but only in a 1.0X relay design

3) We need something more complicated to get a good design with a collimated external pupil

4) Let’s try the OSLO design program’s ASA (adaptive simulated annealing) routine to search for something new.

All silica, color corrected for narrow bandwidth around .193u.

.90 NA, 1.0 mm field diameter, .193u un-narrowed laser bandwidth

70 mm diameterAperture stop

Let’s try this general type of configuration and look for a broader spectral band solution

What are the effects of having an extra mirror relay in the design? Let us first look at the simplest possible system of this type, with just a parallel plate, a mirror, and two lenses, with no extra mirror relay.

Color from parallel plate is imaged by field lens onto collimating lens. This corrects for primary and secondary axial color (Offner theory) and primary lateral color. We also correct for Petzval.

All same glass

Extra mirror relay adds Petzval, so lens has to be smaller and stronger to compensate. Smaller lens needs less glass plate thickness to correct for its color. Field lens is also stronger.

No external pupil

Having the extra mirror relay not be 1.0X but instead be 1.5X or more makes the lens gets smaller still, due to the slow f#, and the glass plate thickness gets quite small to correct for the color of the lens.

No external pupil

Starting point for OSLO’s ASA program design search = 4 reflections, parallel plates, two field lenses and one collimating lens.

Field lens

Field lens

Aberrations to be corrected = paraxial primary and secondary axial color and primary and secondary lateral color, and Petzval, with all same glass type. No rays, no 3rd-order except Petzval. Design will be forced to have an external pupil!

External pupil

1) Of the many local minima that the ASA search program finds, only about 1 out of 20 will be one of the few exact solutions that exist, with values of zero for the aberrations being corrected.

2) Then conventional optimization can be used to add correction of other aberrations. Eventually polychromatic Strehl optimizationis used.

3) But the best results can only be achieved if the design is capable of exact correction of primary and secondary axial and lateral color.

4) In an optimized design the paraxial color will not be zero, due to aberration balancing, but the color must be completely controllable, as in 3) above.

OSLO’s ASA program finds several exact solutions to primary and secondary axial and lateral color, and zero Petzval, with all BK7 glass. But most of these designs cannot then be corrected for spherical aberration, coma, and astigmatism and spherochromatism without more design complexity.

No attempt was made here to control obscuration. We are just looking to see what the design configurations are that give exact solutions.

Exact solution Collimated pupil

Some ASA solutions, like this one, are not quite exact and have some residual secondary axial and lateral color. When Strehl optimized they can only work over a broad spectrum at smaller NA values, like .40 NA here.

All BK7 glass

There is one exact solution (zero primary and secondary axial and lateral color, and no Petzval) with only 5 lenses. When Strehl optimized it can only work at about .45 NA for a 1.0 mm field size broad spectrum band.

Intermediate image

Flat Collimated pupil

50 mm diameter

All BK7 glass

Telecentric .70 NA, 1.0 mm field diameter, diffraction-limited from .365u – 1.0u, 1.0 mm working distance, 20% diameter obscuration

The design can be scaled down by 50% and still have good performance over a 1.0 mm field diameter, but with an increased obscuration of 25% diameter.

25 mm diameter

Telecentric .70 NA, 1.0 mm field diameter, diffraction-limited from .365u – 1.0u

All BK7 glass

Telecentric .70 NA, 1.0 mm field diameter, .365u – 1.0u

All BK7 glass

Design with 4 intermediate images!!

50 mm diameter

The best design form can be made to work in the deep UV. Because of the increased UV dispersion and the short wavelength it is necessary to reduce the NA in this all silica design.

Telecentric .60 NA, 1.0 mm field diameter, diffraction-limited from .22u through .30u. 1.0 mm working distance

50 mm diameter

External pupil

New elements

By adding some more elements the NA can be raised to .88 NA in this design with a 1.0 mm field diameter that is good from .365u through to 1.0u

50 mm diameter mirrors

All BK7 glass

.88 NA design, 1.0 mm field, .365u – 1.0u,20% diameter obscuration

In some design versions it is possible to get 5 axial focus crossing points, with just one glass type, giving extremely high-order color correction.

.365u through 1.0u with all BK7 glass

Correction for paraxial primary, secondary, tertiary, and quaternary axial color

By adding a very small water immersion lens to the front of the system and increasing the obscuration to 25% diameter it is possible to get a 1.15 NA design with a 1.0 mm field size that works well from .365u to .70u, with all BK7 glass. There is an external pupil.

External pupil

50 mm diameter

This tiny immersion lens would be hard to mount. A better design is shown next, without that lens but with NA reduced to 1.05 and with no external pupil.

1.05 NA water immersion, 1.0 mm field diameter, .365u-.70u, all BK7 glass

20% diameter obscuration

No external pupil

50 mm diameter optics

.50 mm thick layer of water for immersion

1.05 NA water immersion, 1.0 mm field diameter, .365u-.70u, all BK7 glass

20% diameter obscuration

If an external pupil is not required then a simpler design with higher performance is possible, like this .90 NA, 1.0 mm field, .365u-1.0u design

All BK7 glass

.90 NA polychromatic MTF, .365u – 1.0u with 20% diameter obscuration

• It does not seem to be possible to improve these very good designs by adding a second glass type

• The limiting aberrations are mostly chromatic variation of very high-order aberrations.

• That limits the deep UV bandwidth that is possible in an all-silica design. It is smaller than what can be done in a CMO design, but still very broad.

• But there seem to be many good design solutions and maybe the best one has yet to be found.

Questions?