Mirror set for Kutter 150mm f24


The Gregorian turned out badly corrected due to a measuring error during figuring. Discussions about the Kutter design, and working through various Kutter models in OSLO, concluded in the plan to make a 150mm F24 system with a toroidal primary.
This page describes the making of the set of mirrors:

  • Primary: 155mm x 21mm disk, Concave toroid with target Roc = 4400mm and 4385mm
  • Secundary: 130mm x 15mm disk, 72mm mirror cut out, Convex sphere with target RoC = -4400mm

First, the secondary is partly cored out, about 50% from the front side and 30% from the back. After roughing in the cut is filled with casting plaster, to get smoother curve match at the edges.

Cutting the secondary


9-Mar-2013 Roughing in the curve, Primary on Top (PoT), was done with #150 grit to prevent excess sub-surface damage to the glass. The curve is quite shallow, so time-wise this is not a problem. RoC was monitored with a spherometer.

Starting the grind

The surface was smoothed with 20 wets of #340 grit, Secondary on Top (SoT), until tested sufficiently spherical with a marker pen. Then further smoothing was done with 8 wets of #600 grit, SoT. After this a flash-polish was done, using polishing pads. The reason for this is to measure the RoC more precisely than possible with the spherometer. It turned out to be a bit long, 4520mm where 4400mm was the design target.

Flash polish

After measuring the base disks for the polishing laps were cast on top of the mirror blanks. As usual, the used material is a hard type of casting plaster.
To shorten the RoC a bit 4 more PoT wets of #600 were applied. Then the surface was good enough to proceed with the last grit, #1200. In total 7 long wets were applied, of which the final three were extended to obtain a very smooth surface. The red-out test shows a maximum reflection angle of close to 40°, which is good enough to start polishing.
Before building the pitch laps, another flash polish was done on the primary, so a final RoC measurement could be made. This measurement still yields an RoC of 4520mm, and this means that it is hard to bend the RoC with #600 or higher grades of grit. It also means that we have to re-calculate the system.


The polishing laps cast with plaster a few days ago are best primed before applying the layer of pitch. The priming is done by painting the laps with a generous layer of Richards' Secret Sealer Sauce, which is basically pitch dissolved in turpentine.

Richards' Secret Sealer Sauce

Building the lap is all about timing. The pitch needs to have the right substance after heating, a thick syrup. The lapbase is wrapped in McGyver tape, functioning as pitch retainer. The mirror is painted with Cerium Oxide slurry. Then the pitch is poured out on the lap base, and just when it starts to solidify the painted mirror is pressed on. This moment is fairly crucial, too soft pitch causes a mess and too hard pitch causes bad contact.

Pitchpot Lapbase
Painted mirror Poured

After initial pressing the tape is removed, the lap is cooled and the excess pitch is cut away. Then it is time for the first 30 minutes of polishing.

First press First polish

17-Mar-2013 Two hours of polishing later, the mirror looks quite clear: time for a first Foucault test. This is not so easy, since mirror and knife edge are 4.5 meters apart. First off, it is hard to find suitable space in the house. The long focal length also makes it quite hard to find the slit image, and angular behaviour gets a little touchy. On the other hand, the motions in the z-direction react very slowly.
First result shows a turned down edge and a distinct central hill. This means that the strokes need to be widened, MOT.

22-Mar-2013 It's a trap easily stepped into, the mirror looks polished out but at the knife edge it shows serious surface problems: this simply means you need to polish longer. After almost two additional hours of polishing the surface looks a lot better. Profile is moving towards the usual oblate, or rolled up edge, with a ridge on the 30% zone. Apparently it requires a couple of hours more. Radius of curvature is now 4532mm.
The large 45x45mm pitch tiles have also been cut in 4 to make the lap conform easier in my cold garage. Pressing with warmed-up mirror for half an hour before starting the polishing session.

23-Mar-2013 An hour of circulars with 25% overhang. Test reveals two spheres, central 60% radius has a 2mm longer RoC than the outer 40%. Probably better to go back to 1/3 CoC strokes with some side motion. The surface is smooth though, so I guess we're almost done. Before that I need to fix some missing and damaged pitch tiles, since the toroidisation does not allow rotation of mirror and tool.

Recut lap tiles New lap

24-Mar-2013 The pitch layer has separated from the plaster base at some points, due to gas-bubble forming. No idea what caused this but at some places the tiles were lifted 5mm or so. So I rebuilt the lap today and cut it in for half an hour. Surface has become more oblate, so coming session will be longer and wider TOT mostly.

3-Apr-2013 Some retouching sessions later, there is just the smallest central dimple and turned down edge left. Both are better visible under Foucault, but it is almost impossible to make a picture. Ronchi is more forgiving, althou also quite hard to nail down very well:

Ronchi with laser Ronchi with white light Foucault 24/03

On the left is an image made with a laser source, inside RoC. In the middle an image with white light, outside RoC. On the right the only foucault image that turned out reasonably well, status as of 24-Mar which is now improved. The Ronchi images suffer from diffraction effects, in fact you see three superimposed images which are slightly shifted.
A few more ToT sessions are still required in order to get the edge flat. The last one, with widened strokes (1/3 x 1/3) apparently worked well.

Fringes 14/04

14-Apr-2013 Primary is spherical, secondary as well but with a slightly longer RoC. Need to give it some more rounds ToT before starting the toroidization fun for the primary.

Startest setup front view Startest setup back view Image of laser source

17-Apr-2013 In the meantime I tried the setup for doing a startest at RoC. This test is needed to measure the difference in RoC and finally also to do a null test on the finished toroid. For this purpose a drawtube holding an eyepiece was mounted underneath the laser diode and the XYZ stage. The setup is shown from the front and the back. On the second photo you can see the mirror in the distance (4.5m) on top of the washing machine.
Then I tried to capture the image of the laser source, as seen through the 32mm eyepiece. It is slightly out of focus, but the magified cut-out shows that the source is actually a small slit. The image probably also shows some astigmatism due to the fairly large lateral separation between souce and image. When using this test to evaluate the amount of toroidization, there will be a vertical line for horizontal focus and a horizontal line for vertical focus. The distance along the Z-axis between these two points should be 15mm.

Figuring the primary

8-May-2013 With the secondary almost done, it is time to plan the toroidization of the primary. There are several sources indicating how to achieve a toroid without the use of a warping harness, and this is the way I plan to do it as well. The method boils down to the controlled introduction of the astigmatism that you normally try to avoid, by not randomly and mutually rotating the mirror and tool. Also, the figuring strokes are applied in two directions only, being the directions of the perpendicular diameters corresponding with maximum and minimum RoC.

Compared to a Yolo, the amount of correction required for this Kutter is only limited. Nevertheless, as a starting point I use the figuring plan for a Yolo secondary, as published in the early 90's by e.g. James Mulherin and Lukas Howald. I do not use a jig (Jose Sasian) to fix mutual orientation, but merely mark the mirror and tool to maintain this.

The basic steps are as follows:
Step Stroke Test
A Initial strokes to get to the desired RoC difference.
Use MOT in the direction of the short RoC to further shorten it.
Use TOT in the direction of the long RoC to further lengthen it.
Stroke length is around 2/3 D, stroke width is approximately 1/4 D.

Followed procedure:
  • 20 strokes, then change the mutual orientation 180°,
  • 20 strokes, then rotate both pieces orientation 180°,
  • 20 strokes, then change the mutual orientation 180°,
  • 20 strokes, alternate MOT - TOT and repeat.
Cross test, measure distance between long and short RoC.
The target is 15mm.
B Compared to step A the strokes are gradually shortened to 1/2 D and then 1/3 D. This will smoothen the curves while consolidating the RoC difference. Cross test, lines should get better definition.
Slightly overshoot target RoC difference.
C Lengthen both RoC, by doing TOT mostly, 1/3 D in both directions.
The RoC difference is reduced and the quality of the curve improved. Primarily, the low edges of the short RoC diameter are blended with the deeper center.
Cross test, lines should still get sharper.
D Final retouching, concentrate on short RoC and corresponding edge. Ellipsoid null test, startest with 50cm source-image separation should show no astigmatism.

The resulting effect of the figuring strokes can be visualized according to this sketch:

Polish Toroid

The direction of the short RoC diameter is indicated with an S. The Low and High areas are of course relative to the average spherical curve. The shape of the ovals and the effectiveness of the polishing action is determined by parameters like strokelength and -width and the ratio between ToT and MoT sessions.

20-May-2013 Finalized the secondary to spherical and close enough RoC. The final fringe image is shown below:

Fringes 20/04

The convex secondary mirror has a slightly longer RoC than the Primary, but this one is going to change as well during toroidisation. You can count about 9 fringes over the 65mm radius of the convex disk, indicating a sagitta difference of less than 2.5μ. The difference in RoC is therefore less than 25mm. It is however important to know the RoC fairly precise, since it determines the dimensions of the telescope, for example the location of the focal plane.

22-May-2013 Before starting the toroidisation, I re-matched the primary and its tool by means of pressing and a short ToT session. Also I put on marks to indicate orientation of tool and glass.

Toroidization setup

Exact measurement of the RoC gets down to 4523mm. Therefore the secondary must be approximately 4550mm. Results in OSLO are similar after tuning the toroid short RoC to 4508mm and adjusting the focal plane position. Bottom line is that the required RoC difference for optimum correction is still 15mm.

27-May-2013 Today the first attempt at toroidization was made. After half an hour of Phase A strokes, not much had happened:

long 30 minutes A

The image shows the magnified image of a laser diode at (long?) RoC. So progress seems rather slow, lets go for another 60 minutes:

long 90 minutes A short 90 minutes A

Concluding, there are two line images of the point source, one vertical and another horizontal. The RoC locations are approximately 15mm apart. These lines are not very well defined, probably due to a rough mirror surface. Also the laser point source is too small and too coherent, resulting in a lot of interference effects. For some reason this is most visible in the vertical line, but this may have to do with the elongeted laser aperture.
The way forward is now to smooth the surface by doing shorter strokes, i.e. to start Phase B. Also, a different point source will be needed in order to suppress the interference and get better readings. The point source is made by hammering a dimple in a piece of sheet aluminium with a sharp steel point on hardwood support. The bump on the back side is sanded away until a tiny hole appears. The light source is provided by a diffused LED.

2-Jun-2013 Two 30 min sessions with B strokes decreased the apparent RoC difference to 5mm. Conclusion is also that the pinhole is lousy, making judgment hard to do.

9-Jun-2013 Three 30 min sessions with A strokes increased the differential RoC to 13mm. Pinhole is now made with one from a stack of alu foil and a needle, with a red LED as light source. Image is very dim.

16-Jun-2013 Again back to longish B strokes to clean up the image lines. RoC difference is now at 10mm, but lines are better defined. Found a hi bri white LED, which I will use for later testing.

23-Jun-2013 One 30 min sessions with extreme A strokes cranks up the difference to 14mm. This is also after some lap maintenance, roughing it up with a knife. Another 30 minutes with B strokes yields a RoC difference of 12mm and the following images:

long 23-6 short 23-6
long ronchi 23-6 short ronchi 23-6

As the images show, the outer zones of the short RoC diameter are low, i.e. they are lagging correction. The plan is to focus a bit more on this diameter with B type MoT stokes. The goal is to consolidate the short RoC and at the same time extend the curve to the mirror edge. The long RoC curve is quite good already, judging from the fairly well define vertical image line and the equally spaced Ronchi lines.
For scale it should be kept in mind that the image line length is only 0.5mm...

26-Jun-2013 Today an extended 60 min sessions with A and B strokes, focusing a little more on the MOT side:

long 26-6 short 26-6
long ronchi 26-6 short ronchi 26-6

The short focus is now better defined. Also, the differential RoC is on target, 15mm. The extended session probably has more effect because the best contact is only achieved after 15 minutes or so. This is the moment to gradually shorten strokes in order to start improving the curve, i.e. more of B in the first session and when the diff RoC holds even down to C.

29-Jun-2013 Today I decided to make at least the TOT strokes for the long RoC a bit wider, in an attempt to better blend in the short RoC curve. So the stroke length wa sbetween A and B, duration 60 minutes. Images:

long 29-6 short 29-6
long ronchi 29-6 short ronchi 29-6

The delta RoC is now 16mm, slightly overshooting the target. The foci need better definition though, so next was 30 minutes of A strokes. As can be expected the delta decreases, to 15mm.

30-Jun-2013 The short RoC direction reacts quicker, but also suffers from the largest deviations of a spherical profile. The hypothesis at this moment is that the short RoC should be consolidated with 1/3 strokes, while the long RoC is stretched to meet the delta requirement. This should give fairly good curves and still sufficient buildup of RoC difference.
Unfortunately I started along the wrong orientation, i.e. short ROC with TOT. The strokes were corrected as planned (45min session), but the differential RoC was down to 13.5mm. The images showed fairly well defined short focus though...
One more 30 min session of long TOT and short MOT brought teh difference back to 14.5mm, still with fairly well defined lines. The idea is to do this another hour or so, overshooting the target, and then slowly go back with short TOT in both orientations (aka stroke C).

3-Jul-2013 The technique applied today targets at keeping the RoC difference at par by long 2/3 D TOT strokes in the long RoC orientation. At the same time, the short RoC direction is consolidated with 1/3 D strokes. During the L-TOT session now also the sohort RoC is included with a few 1/3 D strokes, in order to get a better surface profile. Two such sessions were done, 70min and 60 min, resulting in maintained delta RoC of 15mm and improved line defineition and Ronchi test.
The low edge zones are quite narrow now, so I presume that a more balanced 1/3 MOT and 1/3 TOT in both directions would improve the figure.

5-Jul-2013 Today I had to rechannel the lap, since the center grooves had fully closed-up. It made a lot of difference, much more even drag.
The session was 45 min of TOT B strokes, a little over 1/3 D in length, and MOT C strokes, about 1/3 D in length. In the TOT phase, the short RoC direction was also done with less and shorter than 1/3 D strokes.

long 5-7 short 5-7
long ronchi 5-7 short ronchi 5-7

The delta is still at 15mm and at the same time the images show a much improved figure. The short RoC line image has almost the same quality as the long RoC one. The Ronchi bands (although quite hard to capture) look more straight. The short RoC direction probably can do with some more and maybe also longer TOT strokes to get the outer zones in better shape. Although it is hard to see, I think that the TDE in this direction is quite small.
Regarding the Ronchi image I think I need a different grating period; the best band frequency suffers from destructive interference between the three visible Ronchi images. Also the pinhole needs to be smaller for more accuracy. I guess that another source of inaccuracy is caused by the light source being located about 60-80mm up to the right from the image. This induces additional astigmatism, and requires some attention next time.

31-Jul-2013 Return from holiday and pick up polishing. The lap appears to have suffered significantly from the summer weather that finally came: the pitch has oozed over the edges of the lap foundation causing a horrible non-matching figure. Also the channels have filled up. Next time keep the lap in the fridge during hot weather!
So, again rechanneled the lap and applied a looong pressing. Still the outer regions don't really touch the mirror surface, but I decided to start polishing anyway. Two sessions further the delta RoC has gone up to 18mm and back to 16mm. I now alternate TOT and MOT for both orientations, which results in much better Ronchi and a light residual TDE in the short RoC direction. This is exactly what should happen: improving figure and at the same time reducing the overshot delta.

ellipse test

So now it is time to move to ellipsoid testing at conjugate foci. For this purpose I updateded the test rig with a horizontal beam, carrying pinhole lightsource and testing device with a 520 mm separation (4520mm and 4505mm RoC). This test should yield results as if in the CoC of a sphere.
The formula for focus separation can be rewritten to have the delta RoC as a function of the focus separation s:
   δR = s2 / 4*RS

ellipse test

It is a parabola, where it can be seen that the base RoC does not influence it very much. Also, the cross test for measuring the delta RoC (which is done with the eyepiece just aside pinhole (35mm)) does not add much offset to the delta. Target separation/delta indicated in circle.


The test rig is based on my XYZ stage, but now there's an aluminium beam that separates the pinhole source and the tester location. The sepparation distance is set at 500mm, but can be increased slightly with shims. The eyepiece mounted next to the pinhole is used for the cross-test. The focuser tube on the far end can hold a Ronchi grating or an eyepiece.

testrig testrig

4-Aug-2013 Mixed up a new bottle of polishing compound, using the pure white Opaline I still had. This turned out to be quite disastrous; although it cuts very fast is is not very suitable for final figuring. The drag is enormous and in the end it destroyed the smooth surface of the glass. Now the figure is rough and needs to be repaired.

long 4-8 short 4-8

The above Ronchi images (outside RoC) show the bad figure, although the edge seems to be somewhat better now. These images are taken at conjugate focus of the toroid, at 50cm separation from the pinhole, where a KE test should give a null.
Now I have mixed the polishing compound 50/50 with pink Cerium-oxide and it polishes much more controllable. The lap is also regrooved again.

6-Aug-2013 A half hour session further, alternating MOT and TOT, in an attempt to get rid of the roughness, below Ronchigrams (inside RoC) result:

long 6-8 short 6-8

As can be seen, the figure is still quite rough but improved. Figure is a bit oblate.
One more session, concentrating on TOT and making the strokes longer to address the outer zones more and get rid of the oblateness.

long 6-8 short 6-8

Short diameter is vertical, so the short edges seem to be oblate and turned down, while the edges of the long diameter seem to be OK. Next retouching session must be targeted at bringing down the 80-90% zone of the short diameter.

7-Aug-2013 Did a little TDE retouching, by TOT accentuated pressure of tool edge over 90% zone, short strokes.

long 7-8 short 7-8

Not much happened, maybe better follow Tex' advice (fig 42-7) and apply accented pressure with tool overhanging the defective edge.

10/11-Aug-2013 Three 30' sessions of long (1/2 D) MoT strokes, alternated with 1/3 D ToT, to treat the oblate sphere. The ToT are used with accentuated pressure on the trailing half of the tool, which presumably has the same effect as Tex 42-7.

long 11-8 short 11-8

The oblate edge becomes less acute and starts to blend into the general curve. Measuring with the knife edge reveals a 6mm difference of RoC between outer regions and center of the mirror. Toroid differential RoC is still slightly more than 15mm. Plan is to just continue this treatment until high edge is gone.
A couple of sessions later, the following results:

long 11-8 short 11-8

The high edge RoC is 3mm shorter on the short diameter, and 4-5mm on the long diameter. Also, it can be seen that the RoC difference is still too high, the long RoC is relatively too long. Best to concentrate mor on MoT in long RoC orientation to get the edge down and to shorten the RoC. It is a long shot (probably several hours) but I don't know any faster way. The short RoC edges (vertical) tend to turn down, so the ToT will be shortened to max 1/3 D. Maybe best to apply this to the long orientation too.

14-Aug-2013 A couple of sessions later:

long 14-8 short 14-8

Ronchi lines become more straight, high edge is getting down: just continue this.

17-Aug-2013 Two more sessions done, re-channeled the lap.
Ronchi slowly improving, oblateness (high edge) slowly disappearing. Measurement of differential RoC yields 18mm, which is way too much. Recalculation of the optical model changes the angles a bit and optimizes on a differential RoC of 14mm (i.e. 4506 and 4520). So the coming sessions should be targeted at pushing the difference down, by long TOT on the short R orientation and long MOT on the long R orientation. The point is to find the sweet spot between quick correction but without ruining the current figure...
The lateral separation of the Toroid conjugate foci should then be 502mm.

31-Aug-2013 After retouching for several sessions, the RoC are now 4464mm and 4478mm respectively. The difference is on target, however the common base has shortened a few cm. This means that I have to recalculate the optical system again...

long 31-8 short 31-8

The Ronchigrams show a better sphere now on ellipsoid focus (at about 502mm). The image of the pinhole shows the pinhole details: it is apparently larger than 10μm (probably a few 10s of μm) and also not really round... The photo does not really do justice, but visually the image is a lot sharper and also shows the diffraction rings.

focus 31-8

So, right now the overall curve seems better and needs to be smoothed on the edges, especially the 45° orientations are oblate. These can probably be treated with 45° strokes, while keeping the mutual orientation of mirror and tool straight. Keep stroke length down at about 1/3 diameter.

long 31-8 short 31-8
long 31-8 short 31-8

Above set of images is after some edge treatment (Texereau fig 42-7) to cancel oblateness. This has been done in S and L orientations but also stronking in the 45° angles in between. Still the S edges are slightly oblate. Probably one more session, and the work can be considered is done...

2-Sep-2013 I made some more retouching, especially longish MOT on short RoC orientation to get rid of the high edge and at the same time shorten the RoC a bit (delta decreased to 13.3mm). I also made a better pinhole, smaller and round. The S edge appears to be hard to treat effectively!

long 2-9 short 2-9

Since the pinhole is a lot smaller, also less light is available for Ronchigrams: above images already took 1sec shutter. Nevertheless, the lines are quite good, and also the pinhole image is nice and round with diffraction rings around it. The short RoC direction (vertical) is still a bit oblate, but this is hard to treat well and hasn't changed a lot. Since it is not much, it will probably drown in the residual system abberations.

I may call it done, current parameters are RS = 4465 ± 3 mm and the RoC difference is 13.9 ± 0.1 mm. Just need to adapt the final system design now and do some startesting.

Coring the secondary

4-Sep-2013 So now it is time to get out the secondary. This is a bit tricky, since the front surface is polished and figured and care must be taken not to damage it. For this reason a spacer is made, and also the outer ring is carried by felt sliders.

coring coring

A duct-tape retaining dam is stuck to the mirror to keep the fluids in, and the drilling is started. It is very important to stop immediately when a change in sound or friction occurs, it means that the glass is gone. If you push through, the front surface will be damaged...

mirror set done

Above the mirror set, ready for the vacuum chamber.


26-Jan-2014 The secondary has been aluminized, so the primary can be startested in the target system. Collimation is not obvious, since the field of view is quite narrow, finding a suitable star with the uncoated primary is not an easy task.
In parallel, startesting on the stand is redone with a good quality commercial 10μ pinhole. The pinhole is used in combination with a laser module, of which the lens is re-adjusted to obtain a focal point at a few cm distance (i.e. on the pinhole...).

pinhole setup pinhole setup pinhole setup

The image of the pinhole in the toroidal focus, seen through a 10mm pinhole at 450x, now looks fairly good:

pinhole image ronchi lateral ronchi vertical

The intra-focus Ronchi images show a bit of oblateness though, which ideally need to be corrected. However, the tool has been decomissioned and would have been too old anyway. A new tool requires some sessions to break it in, which would most likely destroy the current figure. Maybe it is best still to put some aluminium on it and focus my efforts at practising the proper alignment in the scope.