How to enter lambda in Matlab variables

Cutter with a komatically deformed main mirror

What's that about? Quite simply, this is the consequence of the discussions and practices from the threads:…CHIVE=true&TOPIC_ID=61343…ID=63920&SearchTerms=Zwei

Because of the size of the above threads, I allow myself the following brief explanation.
The system according to the title is a Schiefspiegler after Kutter in anastigmatic arrangement in which the remaining coma error is compensated by comatic deformation of the HS. I have no idea whether this has been demonstrated in practice before. I am of course familiar with the anastigmatic system. Anyway, I've had something like that for a few days and it works! (The working name is KoKu. Other suggestions for names are very welcome).

<b>KoKu enstand aus ToKu, dem Kutter mit torisch deformiertem HS </b>
The first picture shows a 152mm f / 25 ToKu on the provisional fork mount (for more details with detailed measurement results for this version, see the threads above).

<b>Bild 1</b>

First, the mechanical deformation device was removed from the HS, which made the HS fully spherical again in a flash. Next, the boom with the FS on the base plate had to be moved in the HS direction so that the tilt angle of the FS is 5.9 °. This corresponds to the anastigmatic system. It was practical to drill 8 new holes for the fastening elements of the boom. Including the subsequent collimation, this cost less than 2 hours of work.

I left the calculation of the correct 5.9 ° angle to "Winspot". For comparison, the corresponding Winspot results:

<b>Bild 2</b>

Obviously, the anastigmatic system is more slender. Toku has a maximum width of 630mm, whereas the anastigmatic system is only 440 mm. Of course, this has practical advantages.

<b>Bild 3</b>

The black circles correspond to the diameter of the Airy disc. With the ToKu version, all spot diagrams are obviously considerably smaller than the diameter of the Airy disc (black circles). In contrast, it looks less friendly with the anastigmatic system. Unfortunately, "Winspot" is not set up for the design with comatic deformation of the HS.

Fortunately, the sky was clear enough that evening to test the anastigmatic system in the sky. The seeing was rather modest, but in the star test you could clearly see the coma. When observing the moon at approx. 200x magnification. (5 days before full moon), however, showed no opt. Error.

<b>Wellenfrontanalyse mit „openFringe“ nach Interferogrammen </b>
a) Laboratory test of the entire system

The telescope was set up in AC in front of my Michelson interferometer.

<b>Bild 4</b>

The actual cutter system consists only of the main mirror with the secondary mirror. Laser, expansion lens, converging lens, beam splitter and reference sphere form the interferometer based on Michelson's basic principle. The plane mirror is required for testing in autocollimation. For the vis. Observation of the interference stripes or the star test image, the gray filter with approx. ND2 is required. The eyepiece is only used for viewing or photography (eyepiece projection, i.e. camera without lens) of the star test image. The interference fringes are photographed with a suitable camera lens.

The focal image of the converging lens can be used as an artificial star for the laboratory star test. The bundle of rays of the reference sphere is covered. This has the advantage that you can switch from interferometry to star test without changing the interferometer setting. This star test also makes the collimation of the cutter system much easier. As an alternative, a red laser diode without optics can be used as an artificial star instead of the converging lens. However, because the coherence length is too short, this is not suitable for interferometer operation.

With the small aperture ratios typical of cutter systems, the spherical aberration introduced by the splitter cube is negligibly small. This error is automatically compensated for in interferometer operation because the same error is impressed on the reference beam.

A Bath interferometer can of course also be used here. However, this does not allow the o. comfortable star test.

For the actual wavefront analysis one needs of course interferograms with which one z. B. must feed "openFringe". Here's one of them.

<b>Bild 5</b>

In order to suppress the interference caused by artifacts in the interferogram and air streaks in the beam path, it makes sense to evaluate several similar ones and to average the "Zernikes" obtained for further processing. The position of the stripes is completely uncritical for "openFringe". However, it is not wrong to vary these from recording to recording. If you z. B. selects 4 interferograms for an evaluation, then a rotation of the stripe position by approx. 90 ° is recommended. A synthetic one can also be created from 4 interferograms. This only serves as a template for simulating the wavefront analysis, synthetic star test, etc.

<b>Bild 6</b>

With an error-free telescope, the interference fringes would be pin straight and exactly the same distance apart. The s-shaped curvature of the lines is an unmistakable sign of coma. Instead of philosophizing about it, you can of course ask “openFringe” what it thinks of it. The wavefront with the associated Strehl number then looks like this:

<b>Bild 7</b>

All Zernikes were activated here. The deformation typical of first-order coma can be seen. The PtV value 0.53 lambda was taken from the corresponding "contour plot" (this also applies to all subsequent representations of this type). If you only activate the Koma Zernikes, the PtV value is slightly lower at 0.46 lambda. In any case, first-order coma remains by far dominant.

My idea was to polish the spherical HS in such a way that the coma in the above wavefront ideally disappears. To do this, you only have to remove the areas that appear red to yellow by approx. 1/2 lambda wavefront = 1/4 lambda surface.

But first let's look again at the calculated deformation of the wavefront at ToKu.

<b>Bild 8</b>

Here the wavefront of the HS has to be torically deformed by more than 5 wavelengths in order to neutralize the Asti as a result of the coma-free system. That is more than 10 times as much as the comatic deformation with an anastigmatic system according to Figure 7!

<b>Wie poliert man eine „Komasphäre“?</b>
Admittedly, I only really became aware of the above facts a few weeks ago. On my pertinent, unsuspecting question to the Schiefpieglereperts, see
I have not yet received a usable answer. There can be several reasons for this, e.g .:

a) It doesn't work in principle.
b) It works, but only with disproportionate effort.
c) Nobody has tried it yet.
d) Someone tried it but didn't publish it.
e) It's as clear as daylight to everyone, only Kurt hasn't noticed it yet.

Assuming case e) applies, thank you very much for your consideration, dear experts.

Anyway, I wanted to know more and went to work. If Jolo experts manage to deform their secondary mirrors in the order of magnitude of 5 lambda surface and rather more successfully by polishing (or also by force?), Then the ¼ lambda should not pose a particular problem in a comatose way.

A ring tool Da = 150, Di = 120 seemed to be suitable as a tool.

<b>Bild 9</b>

<b>Bild 10</b>

The tool was guided in such a way that edge pressure could be applied to areas A and B, respectively. The red parts of the surface should be removed more than the rest. For the first session, I thought 6 minutes of polishing time was appropriate. And this is what the first result looked like:

<b>Bild 11</b>

At first glance this actually corresponds to a comatic deformation, unfortunately far too much of it. In addition, the detailed wavefront analysis showed considerable proportions of asti, triangular deformation and higher-order coma. 3 minutes of polishing time would have been right. After all, the attempt shows that it went in the right direction straight away. Suggestions for improvement are very welcome.

<b>Messung am separaten Hauptspiegels </b>
The HS was placed in front of the interferometer in the ROC. R is here 4656 mm. At this length, despite the relatively small test, you have to reckon with considerable interference from air streaks. Therefore, the interferometer measuring section was set up in the completely cooled hobby room (approx. 10 ° C room temperature). A thermally insulating housing for the beam path would be ideal but complex.

The mirror, which is only 20 mm thick, needed more than 3 hours on the test stand after polishing at 21 ° C until the temperature difference to its surroundings could no longer be determined. An inexpensive radiation thermometer is ideal for this type of temperature measurement. A Borofloat disk, which was permanently placed in the immediate vicinity of the mirror holder, served as the reference measuring surface.

This time my Bath interferometer was used because the Michelson with mirrored reference sphere can only be adapted to the reflectivity of the non-mirrored test object by using damping glasses in the reference branch. Of course, several interferograms were also evaluated here in order to minimize the random errors. Here is a typical interferogram from this series of measurements:

<b>Bild 12</b>

Please note: it was won in CoC mode.

In principle, the non-mirrored HS could also be built into the telescope and the entire system could be measured interferometrically in AC. Unfortunately, one has the problem that the light has to pass the non-reflective test object twice, which would lead to an intensity reduction to less than 2 per thousand. Then, because of the intensity of the almost inevitable artifacts and system-related scattered light, only miserably contaminated, low-contrast interference fringes are found.

Back to the actual task: how do you make a HS sphere specifically comatic? The deformation shown in Figure 11 had to be reduced. This was done with a full tool and in the normal way of polishing within approx. 1 hour of polishing time with a few intermediate measurements and the resulting small corrections to the tool. The latest state of the correction cannot yet be described as near perfect.

<b>Bild 13</b>

The detailed wavefront analysis brought 0.35 lambda PtV to the desired coma correction. In addition, portions of undesired spherical aberration are found distributed over 6 orders, i.e. H. Zone errors, but luckily with significantly lower PtV values. If you enter these errors with the already achieved coma correction in the Zernike calculation under "openFringe", then a considerable improvement in the wavefront of the overall system compared to the anastigmatic system without coma correction can be expected. To support this consideration, I silvered the HS again, built it into the telescope and measured the entire system after collimation in the laboratory star test again in AC mode:

<b>Das vorläufige Endergerbnis</b>

<b>Bild 14</b>

Strehl = 0.93 compared to 0.76 previously (Fig. 7) undoubtedly means a noticeable improvement in optics. Quality. The detailed analysis shows that coma is still the dominant residual defect.

To simulate the evaluation according to Figure 14 and the following illustration, there is the appropriate synthetic I-gram, averaged from 3 individual I-grams:

<b>Bild 15</b>

If the coma were completely compensated without correcting the remaining residual errors, the result would be Strehl = 0.96.

The final evaluation is the MTF curves with star tests.

<b>Bild 16</b>

The gain in contrast transfer (difference between green and red curve) is more than clear. The distance between the green curve and the ideal curve (black) is no longer too great. That means that much increase in contrast through further improvement of the correction is no longer to be expected. It looks a little different with the quality of the focal constellation. A clear asymmetry of the brightness distribution in the 1st diffraction ring is still disturbing here. On visual inspection in the AC laboratory star test, however, the first diffraction ring was at least closed all round. You can also see this in the synthetic star test. Since a red laser diode was used as an artificial star for the AC laboratory star test images, I also colored the synthetic images red.

Before I decide on a possible further correction of the HS, I want to wait several nights of observation to see how the coma error will present itself in the live star test. Yesterday I took the first opportunity to do so. Result: because the seeing was far below average, no diffraction rings could be made out.

For people who believe a nice kab apo of the 4-6 “class (corresponding to 2 - 7 k €) would have no problems with the focal star image, I found something" nice ":

<b>Bild 17</b>

Only number 10 is really good without complaints). In my opinion, you have to search pretty carefully before you find such quality.

Greetings Kurt