this Web page last updated Nov 7 2006.
This is a work in progress during 2005 and 2006, on an 8-inch f/5.5 mirror cut from a sheet of Pyrex. To see what I did from that flat blank to grinding and polishing, see my "myglass" Web page describing those details. My work to get the mirror from polish to in and out of sphere is on this "zones" Web page. On this page I'll discuss figuring the mirror BACK to a sphere AGAIN, and then figuring the parabola by Gordon Waite's and Michael Lindner's work plus my own.
The desired parabola
my "myglass" Web page to get the mirror ground, polished, figured;
polishing and figuring in and out of sphere and parabola;
August 21st: working zones from the previous ATM session
Sept 11th: more working zones
Sept 25th: back to the sphere again again, and done!
Oct 23th: ..or is it done? Cool off!
Pitch laps: to sphere or parabola? zones?
Change of figure with uneven cooling
The mirror is an 8in, zones radaii 1.789, 2.530, 3.098, 3.578, 4.0.
The desired deltas for a ROC R=89.19, on measuring the zones (in mills) are:
-- 22 18 18 18 delta 76.
The ROC shrank to 89 inches, so the "22" became and "20" delta and the total became +74
Aug 21st 2006:
Details of this session and previous sessions are in my "zones" document, about polishing and figuring in and out of sphere and parabola.
By the end of the Aug 21st session, my 12:30AM:resulting Foucaultgram and Ronchigram are as shown. Numbers for this session were:
206 - 208 +02 235 +27 249 +14 265 +16 delta +59 min to max +59
Results: deltas between zones 5 and 4 and 3 are increasing, delta for 3&2 dropping, both good directions. Seems reasonable to repeat this pattern and monitor results. Then, work on getting zones 1 & 2 down.
The strategy: ZOnes 3, 4, 5 are now reasonable. But Zone 2 is down too far, by 3/2ths; and zone 1 is FLAT. How about working down zones 3, 4, 5 uniformly, by COD across these zones only? Try two or three minutes of that strategy as follows. Starting with the mirror center over the tool center, move it out to the edge between zone 2 and 3; then back to center?
I did a 6 minute warm press after scrubbing with brash brush, 8 min no weights. Room temperature 70-71 degrees F. Two minutes of above stroke, 5 strokes then turn mirror, one walkaround the stand. then 1.5 minutes 4 strokes then turn, one walk around. Results at 8PM?
8:10PM: Resulting Foucaultgram and Ronchigram are shown. Numbers for this session were:
417 - 425 +08 451 +26 462 +11 478 +16 delta +61 min to max +61
Problem: I did a 2.2-inch stroke - TOO FAR IN! Should have done 1.5" stroke! Worked the wrong zone!
9PM: 10 min warm press after scrub, cold mirror, then no weight for 6 min. Did the "proper" 2.2" stroke for 5 minutes, 4 strokes then turn, around the stand four times.
9:30PM: Resulting Foucaultgram and Ronchigram are shown. Numbers for this session were:
459 - 469 +10 492 +23 507 +15 518 +11 delta +59 min to max +59
Comments from Gordon: "Starting to lose the diffraction ring. Probably went back too far on stroke, overworked Zone 4. Therefore try a stoke 1/2" shorter and DON"T OVERSHOOT the center." So I warm pressed after scrub for 10 minutes, cool for 3 minutes no weight. Did 5 minutes of the shorter stroke, 4 strokes then turn, four times around the stand.
11:30PM: Resulting Foucaultgram and Ronchigram are shown. Numbers for this session were:
427 - 434 +07 461 +27 475 +14 485 +10 delta +58 min to max +58
Gordon reviewed my work and suggested a spherizing stoke, the 1/3 COC stroke, to smooth the mirror and "resolve the 'cliff' you have." MIchael suggested just taking it back to a sphere, in effect more time on the spherizing stroke. Michael, Gordon and I discussed whether the pitch lap was at issue. Was it too hard? What did that mean for correcting zones versus spherizing or parabolizing? See my notes below for that discussion.
In the discussion, the three of us decided to take it back to the sphere next time; and from my prior work it might take 20 minutes of sessions to do so.
8pm: From last session, I planned to do 20 minutes of a 1/3 COC stroke to respherize. This would smooth the surface as well, get rid of the "cliff" and so on. Discussion suggested waiting at the 10-minute point for the mirror to cool down. I did a scrub and warm press as usual; 5 minutes with weights, several without weights to cool. The session at 8PM was 5 minutes COC; add CerOx; 5 minutes COC; 5 minutes cool including 10 lbs weight for 3.5 minutes. Then 5 minutes COC, add CerOx, 5 minutes COC. Part of my COC stoke was a "slight W" maybe 1/2" either side of center - a mistake as the numbers told me below.
8:45PM: Resulting Foucaultgram and Ronchigram are shown. Numbers for this session were:
247 - 246 -01 254 +08 265 +09 280 +15 delta +33 min to max +34
Gordon reviewed the results. When I noted my "W" action, he reminded me that such a stroke amounts to doing offset strokes (mirror left or right of center) and "working the edge". That explained why the last delta was HIGHER (from +15 previously to +10) while all the other zones were LOWER. The only good thing about this result was that I "got" the explanation immediately! Gordon also reminded me that for a smoother surface, I needed more pressure, by stroking with my whole upper body with arms extended; not by stroking with bent arms and standing still. During this session, however, I was handicapped by a very very cramped workspace.
9:45PM:Scrub and press as usual with 20 lbs for 5 minutes; no weight cool for 12 minutes. Did two 5-minute sessions, pressed for 6 minutes, two 5-minute sessions.
11 PM: Resulting Foucaultgram and Ronchigram are shown. Numbers for this session were:
247 - 233 -14 234 +01 249 +15 259 +10 delta +12 min to max +26
The photos show a zony mirror with a belly-button, and a need to get it smooth with long strokes. Also it was clear I needed to revise my polishing methods.
12 PM: First, my hands need to be such that the fingertips curl just over the leading edge of the mirror, with the HEEL of my hands over the centerline and providing pressure. But don't put fingers too close to the working edge, the heat will distort the edge. Also, my pace around the stand should be to make steps of about 1/8th circumference, while turning the mirror 1/8 in the other direction; and, after a time, reverse both directions while giving the mirror an extra large turn. Also the length of the stroke needs to be just right; Gordon marked the 1/3 length on the mirror with bits of tape.
Gordon monitored my next 20 minutes of work over four sessions, coaching me to change rotations and my stride accordingly.
12 PM and later: Resulting Foucaultgram is shown. Numbers for this session were:
223 - 199 -24 190 -09 202 +12 209 +07 delta -14 min to max +33
The mirror did not look good. (What's wrong with this picture! It was zony. I had a cross-hatch problem, from following the bits of tape too closely. And, the mirror was rough. Gordon was determined to fix this once and for all.
First, Gordon suggested I used too much pressure and the locations of my strokes were too short, and too regular - I was following the tape marks. Also, he said "the tool is not acting right". So Gordon physically "hacked" my lap in two ways. First, he slashed across the squares with a razor blade, a method he recommended once before to facet the lap squares. Second, he trimmed the squares along the tool edge ("Don't let the squares get too round along the edge.") and also where they started to close together. Also, Gordon was not too fond of my workstand. And my Cerox mix was way too thick. "Look at yours, Herb"; it was thick white and a few teaspoon's worth per 8 ounces. "...and now look at mine"; Gordon's was noticably paler, watery.
After cleaning up the pitch tool, Gordon set up his stand with my tool and wet the tool with his Cerox. He pressed the hacked mirror with FORTY pounds of weight for five minutes. Then Gordon directed Michael and I and himself to work on the mirror, with strokes of his selection. I did 5 minutes of work, then Michael, then Gordon who wrapped up his efforts with about a minute of figure-eight strokes left and right, although he said while in process that "the lap is too hard and thin". A later photo of the pitch lap shows how short the facets have become.
Resulting Foucaultgram and Ronchigram are shown. Numbers for this session were:
068 - 045 -23 036 -09 039 +03 055 +16 delta -13 min to max +32
1AM: The above numbers were better but still oblate. Two more sessions of similar work as directed by Gordon. Resulting Ronchigram is shown. Numbers produced by 1:35AM:
**hot** **1 min** **4 min** time on tester 151 - 140 -- -- -- 186 +35 179 +39 -- +32 211 +25 202 +23 -- +23 230 +19 219 +17 -- 238 +08 219 +09 -- +23 (from Zone 3) min to max +87 +88 +90
1:35AM: This aggressive work produced a turned-UP edge "but we can fix that" said Gordon. I worked as directed and got these results as below. Plus, we remeasured the ROC and established new "perfect" numbers for a 89.0 ROC. Resulting Foucaultgram and Ronchigram are shown from 2AM. The numbers:
**hot** **4 min** **7 min* **perfect** 114 - 097 -- 087 -- --- 124 +10 119 +22 110 +23 +20 148 +28 146 +27 132 +22 +18 167 +19 167 +21 154 +22 +18 188 +21 186 +19 173 +19 +18 min to max +74 +89 1/3.57 wave +86 +77
2:35AM: Gordon said "this mirror has a good surface" and by the numbers it's already a 1/3.57 wave. At 2AM Gordon prescribed that I do 1/3 COC; followed by working the 80% zone with a 1-1/4" offset, with my thumb over that zone. Resulting Foucaultgram and Ronchigram are shown from 2:39 and 2:57AM. The numbers:
**+7 mins* **12 min** **longer* **perfect** 123 - 121 -- 118 -- --- 145 +22 143 +22 142 +24 +20 164 +19 159 +16 160 +18 +18 179 +15 178 +19 174 +14 +18 193 +14 192 +14 192 +18 +18 min to max +70 +71 +73 +74 1/8.9 wave 1/12.35 wave
Gordon announced it "a really good mirror", but with some "slight central issues". But we called it a night anyway.
Herb Johnson
Oct 23rd, Nov 7th:On Oct 23rd I brought the mirror back to Gordon's to check it again. It sat in the shop most of the evening before testing, so it was temperature-stablized. Let's look at the numbers and images:
Resulting Foucaultgram and Ronchigram are shown. Numbers for this session were:
074 - "average" 095 +21 108 +13 122 +14 133 +11 min to max +59, 1/3.71 wave
Is this a reading error? I tried again on Nov 6th Resulting Foucaultgram and Ronchigram are shown. Numbers for this session by myself (Herb) and by Gordon were:
Herb Gordon gordon 294 - 289 -- 293 -- 308 +14 309 +20 311 +18 320 +12 322 +13 322 +11 338 +18 339 +17 337 +15 348 +10 349 +10 348 +11 +54 1/4.57 wave +60 +55 avr of three: 1/4.61, Strehl .861
(The "average" value for zone 1 is due to the uneven condition around the center and the first zone.) The mirror has some roughness and microripple, says Gordon. The mirror also has some "zonyness". It's not readily apparent in the Foucaultgram, but the Ronchigrams show uneven thickness of the bars from the center to about three inches out, a slight zone just outside of the center area. Also, look at the ends of the bars: thick and bent, a "rolled up" edge says Gordon, not quite a turned-up edge. The numbers above, especially for the 5th zone, confirm the outer zone is a little "high" as the last delta is relatively low.
What accounts for this slight but noticable change in figure from September's readings? In brief, uneven cooling. A COOLING mirror will have cooler zones which will appear LOWER than adjacent warmer zones. Generally the center is warmest of all, so it will be HIGHER; the edge will be cooler and appear relatively LOWER. So the edge will seem lower while COOLING; but HIGHER after the whole mirror has cooled uniformly. To see the reasoning behind this, check my footnote.
So, what to do, what to do? In the short term, I've decided to put the mirror aside. Two reasons. First, the pitch tool is almost worn out. The other is based on my secret plans. One of my goals as of 2006 was to make MULTIPLE mirrors from this glass, of different qualities of figure. One was to be "ordinary" or "commercial", that is 1/4 wave; one to be much better, perhaps 1/10 wave; and one worse. Telescopes of otherwise identical mirrors of identical focal lengths and diameter would be a test of both optics and sky quality. So, I can either improve this mirror later; or use it as the "commercial" telescope.
Herb Johnson
Other notes appear on my Web pages on roughing the mirror and and figuring the mirror.
My work of Sept 11th left me with a zony parabola, and prompted the usual discussion: fix the parabola or go back to the sphere? Michael, Gordon and I discussed whether the pitch lap was at issue. Was it too hard? What did that mean for correcting zones versus spherizing or parabolizing?
Gordon reviewed my work and noted: "The problem with just 'working zones' is that most zones [on small mirrors] are too narrow - they are too hard to control. Also, short strokes are too short and so they make the surface rough and 'zony'. So a spherizing stoke, the 1/3 COC stroke, will not only smooth the mirror, it will resolve the 'cliff' you have."
Michael's take on it was "Why not spend 30 minutes on a 1/3 COC stroke and respherize the mirror? It smooths it too. THEN you can parabolize." Gordon added that some problems of surface may be due to a harder lap. Polishing with a harder pitch lap back to a sphere is no problem, the lap does not have to conform to a paraboloid; the parabola requires a more conforming (that is, softer) lap.
So how does Gordon make his laps, mine being one of them? He mixes 55 and 64 Goltz at about 50-50 for use at 68 degrees. He figures pure 64 Goltz for use at 80-83 degrees F. But "in reality", he reuses pitch and addes either 55 grade or 64 grade as needed. Only for a "figuring lap" will he use fresh pitch.
And how long would a re-spherizing session be? Gordon says he can do it for these mirrors in 15 minutes, and 15 more to parabolize to a perfect delta of 72. He suggested I do 30 minutes for each. I said that would just be more time to get into trouble! My last time from sphere to parabola - a delta change from +10 to +43 or +49, was done (badly) in about TEN minutes. Gordon, always the calculator, says "so do 72/33 as long, 33 being the ten-minute change. That's about 20 minutes."
In Sept 2006, I measured my finished mirror SEVEN minutes after figuring and cleaning, versus after HOURS of sitting dry in the shop a month later. Numbers for the cooling mirror and the stable mirror were:
* 7 mins * * hours * 123 -- 074 - 145 +22 095 +21 164 +19 108 +13 179 +15 122 +14 193 +14 133 +11 delta 70, delta 59 1/8.9 wave 1/3.71 wave
What accounts for this slight change in figure from September's readings? In brief, uneven cooling. In September, the mirror was measured a few to tens of minutes after figuring. Figuring work generates heat, the mirror gets warm; sometimes it's even warm to the touch after a lot of work! Now, follow this reasoning carefully; Gordon called out the problem as a "higher edge after cooling"; the reasoning is mine.
After working, the first part of the mirror to cool is the EDGE; it has the top and bottom plus the edge area to dissipate heat, so it cools first. Cooler material contracts; warmer material is expanded. Consequently, a COOLING mirror will show an edge which is LOWER, or a longer ROC, or less delta, than the warmer interior. The center is warmest of all, so it will be HIGHER, by the same reasoning.
So in effect, a COOLING mirror will have a "taper" imposed on the figure, higher in the center and lowest at the cooler edge, and depending on radius (the volume of glass) the temperature distribution (the surface area of glass). A mirror at UNIFORM temperature will not have this taper.
And in fact, the measurements of the "cooling" mirror at various times, and versus the "stabilized" mirror show something of this behavior, somewhat masked by the error in measurement. Discounting the first delta as Zone 1 as hard to measure; the stablized mirror has deltas in the low teens; the UNstable mirror shows several mills of variation over several minutes for the other three deltas.
For a plate glass mirror, the variation is greater because plate glass has a higher temperature coefficient; Pyrex by design is much lower. "My glass" is not branded, but it's behavior under these conditions is more Pyrex-like than plate-like.
Herb Johnson
Contact information:
Copyright © 2006 Herb Johnson
