Ultra-broad spectral band catadioptric design

Dave ShaferDavid Shafer Optical Design

Goals –

• Excellent aberration correction across a very broad spectral range, including the UV region

• Very small obscuration

• Few elements

• Long working distance

• Good tolerances

Design Method

• Separate the different design tasks from each other and try to work on them independently

• Fix low-order problems first

• Consider alternate solutions

• Be willing to go back and start over again

Low-order requirements

(Does not include image quality)

• Small obscuration

• External aperture stop

• Telecentric image

• Long working distance with .60 NA

• 6 mm focal length, .5 mm image diameter

• Flat image (Petzval correction)

• First-order color correction

This meets all of the low-order requirements except flat image and first-order color correction

Aperture stop

Field lens

Silica lenses

Color correction problem

• For deep UV spectral range only two glasses are practical – silica and calcium fluoride

• For a very large spectral range, secondary color is too large in an all-refractive color-corrected lens group

• So use catadioptric type of design where low-order color can be corrected with just silica

• Then higher-order color can be fixed with a small use of calcium fluoride

• Try to maximize use of mirror power and minimize use of lens power = minimizes amount of color to be corrected

Opposite color from silica lenses

(But not nearly enough to cancel)

All silica

Color from strong power is enough to cancel color from lens group but is too strong – get TIR (total internal reflection) from outer rays and terrible aberrations. We need to split this into two weaker power elements.

TIR (total internal reflection)

Low-order axial color cancels, small lens gives low-order lateral color cancellation. More mirror power and less lens power than before.

Design has less power in positive lens group than before = less color to be corrected

Design evolution for color correction

If these + and – power silica lenses were thin and in contact then higher-order color would also cancel when low-order color cancels. But the + and – lenses have a considerable airspace between them and that causes a small amount of higher-order color that does not cancel.

Primary color is corrected, and secondary color is 7.5u focus shift over the .365u to 1.0u spectral band. Much too large! Axial depth of focus at .60 NA is +/- .5u at .365u and +/- 1.5u at 1.0u

What we need is both the + lens group and the – lens group to have slightly different dispersion characteristics than just having all silica lenses. We can get that by using a mix of silica and calcium fluoride in both groups.

Calcium fluoride

All silica lenses

Two lenses switched from silica to calcium fluoride

Top focus shift is about 7.5u over .365u to 1.0u band, while bottom is about 1.5u focus shift

Different scale

The Petzval radius of this design is 5.8 mm and it is almost entirely due to the small convex mirror. If all the image aberrations were perfectly corrected the image would still have a radius of 5.8 mm and that is much too curved to be acceptable. The image size is +/- .25 mm and the sag of a 5.8 mm image curvature over that image diameter is 5.4u. If we choose the focus correctly we can split this to be an out of focus error of +/- 5.4u divided by 2, or +/- 2.7u. But the depth of focus of a .60 NA system (see previous slide) is +/- .5u at .365u and so the +/- 2.7u number is more than 5X too large. We need a Petzval image radius that is at least 5X longer than the 5.8 mm of this design, or at least 30 mm. And that does not leave anything for residual color focus error. So we have to correct for Petzval aberration very well.

Notice that we are working our way through these low-order design tasks with no attempt yet to optimize image quality. If low-order problems cannot be fixed then there is no point in worrying about higher-order image quality.

There are two ways to correct the Petzval curvature of the design. One way is to replace the small convex mirror, which is the source of almost all of the Petzval curvature, with a lens/mirror element that has the same power but no Petzval curvature. The negative lens part of this element has opposite Petzval to the convex mirror part and they can cancel out.

Mirror surface

Mangin mirror replacement for tiny spherical convex mirror

The other way to correct the system for Petzval is to add some strong negative lens power to the small diameter part of the design. We will try this first and then look later at the other idea from the last slide. In a 1.0X afocal magnification situation like this the negative lens is stronger than the sum of the positive lenses and so the combined Petzval curvature is that of the negative lens – and is what we need for our design. But we need a lot of this and it makes for strong power lenses and aberration problems. It makes for lateral color problems so we need to use calcium fluoride and silica together to fix that in this Petzval curvature corrected design. It also causes chief ray correction problems.

Strong powers can cause spherical aberration of the chief ray and that makes for telecentricity errors over the image diameter. This has to be corrected and can be quite large if not fixed.

Design fixed for Petzval image curvature, lateral color, and telecentricity variation over the image diameter.

Petzval correction part

Calcium fluoride

Calcium fluoride

Top picture shows design rays at edge of the field at .55u and bottom picture shows rays at .365u. This shows quite dramatically the importance of getting lens drawings that show rays at both of the upper and lower wavelength boundaries in any broad spectral band design. This design is corrected for spherical aberration of the chief ray (monochromatic variation in telecentricity over the image diameter) but there is still a lot of chromatic aberration of the chief ray – way too much!!

.55u rays

.365u rays

If we trace just the chief ray we can see that most of the axial color of the chief ray must be coming from here, where the ray height is the largest. So that part of the design must be changed some to fix this problem.

Unfortunately changing that part of the design, to fix chromatic aberration of the chief ray (telecentricity variation with wavelength), makes lateral color problems and the design starts to get quite complicated. The conclusion is that the method used to correct Petzval (some strong negative lenses) makes for a lot of other problems. We will work on this a little more and then we will go back and look at the alternate Petval correcting solution (a Mangin lens/mirror element) from many slides ago.

Lesson – always be prepared to start over again when you run into problems.

Notice that we are still working with low-order aberrations, like color of the chief ray. Until all the low-order aberrations are fixed there is no point in doing image quality optimization

After a lot of design work a solution was found that fixed the chromatic variation of telecentricity without hurting the lateral color correction. This required several new lenses of calcium fluoride.

All the positive lenses here are calcium fluoride

Calcium fluoride

New – negative/positive doublet instead of positive/positive

This design was polychromatic Strehl optimized and is diffraction-limited over the image diameter from .365u to 1.0u. The chromatic telecentricity variation over the spectrum is about one degree. The next step is to try to simplify the design.

It was found that the big calcium fluoride element can be replaced with silica if this smaller lens is made to be calcium fluoride. The result has the same good performance and looks like this picture.

A focus near a lens surface needs to be looked at but is just a small detail now, for later work.

The very weak power silica lens/mirror element was replaced with a simple mirror and with about the same performance. The resulting design meets all of the initial requirements. There is no need to go back and look at the other alternate method of correcting Petzval (replacing the small convex mirror with a Mangin lens/mirror element), since this design ended up quite good.

Simple mirror

Mangin lens/mirror element

Final design – no large calcium fluoride lenses (shown in red here). 20% diameter obscuration. 12 mm working distance. 0.50 mm field size and .60 NA.

.365u through 1.0u

Notice that we ended up with almost all of the .60 NA being due to the mirror power. There is very little lens power and that helps the color correction a lot.

Next step – slowly lower the short wavelength, from.365u towards .254u and this will be very difficult to do. Extra lenses will be needed. But first let us look at the alternate Petzval correction design approach, to see if this has better short wavelength potential.

Simpler design – fewer lenses and weaker lenses. But one large calcium fluoride lens. About the same shorter wavelength potential

.365u through 1.0u

Mangin lens/mirror element

• The Mangin mirror replacement for the convex secondary mirror results in a simpler design, so why would we not choose it?

• The shape of that Mangin lens/mirror element and the need for some glass edge run-off when the piece is made will result is somewhat higher obscuration than that of the design with the convex secondary mirror. That could be a reason to choose the other design.

• This whole presentation assumes no prior knowledge of patents on similar designs. With some prior knowledge you would start right out with a configuration that has almost no lens power – the opposite of the Slide #5 starting point here.

• So this is mostly intended to show what the process of design is like, for teaching purposes.