Jump to content

  •  

CNers have asked about a donation box for Cloudy Nights over the years, so here you go. Donation is not required by any means, so please enjoy your stay.

Photo

Unmasked Foucault testing and related topics

  • Please log in to reply
61 replies to this topic

#51 brucesdad13

brucesdad13

    Apollo

  • *****
  • Posts: 1034
  • Joined: 25 Jan 2015
  • Loc: Rutland, MA

Posted 26 September 2016 - 03:39 PM

Got it :D Is he generating the FigureXP screenshot for inclusion in the spreadsheet realtime with some macros or was that sort of pasted in later. I don't know if FigureXP takes commandline input... that would be sort of neat. :D


Edited by brucesdad13, 26 September 2016 - 03:39 PM.


#52 mark cowan

mark cowan

    Vendor (Veritas Optics)

  • *****
  • Vendors
  • topic starter
  • Posts: 8195
  • Joined: 03 Jun 2005
  • Loc: salem, OR

Posted 26 September 2016 - 04:21 PM

There's no realtime, just done the same way as outlined in this thread.  SixTests takes a simple txt file for input, sorts it for you if needed, with no limit on the number of "zones".   But it doesn't have the visualization tools of FigXP.


  • brucesdad13 likes this

#53 ckh

ckh

    Apollo

  • -----
  • Posts: 1177
  • Joined: 21 Feb 2015
  • Loc: Arizona

Posted 27 September 2016 - 01:51 PM

This stuff is not extremely hard to do yourself, if you're an experienced programmer.  I'm experimenting with this. My program finds the brightness of the null by sampling along a vertical line through the center of the mirror.  Then the program finds where that null brightness occurs on the mirror overall. This method should reveal left/right asymmetries in the null, which the flip/diff method cannot. 

 

Here is an example for one of the shots in that Dutch paper. 

 

gallery_240847_5047_10609.png

 

 

 

gallery_240847_5047_1782.png

 

The top/bottom asymmetry is probably due to (vertical?) separation of the source and KE rather than astig in the mirror.  Some of the wiggles might be turbulence.

 

I'm not making any claims about this method yet. It's just an experiment at this stage.  I'm attempting to get more information by removing the left/right symmetry forced by the flip/diff method.  All along that dark line you can calculate the slope of the mirror surface along the x-direction. By rotating the mirror 90 degrees you can get the slopes along the y-direction. If you do this for say 50 zones, you should be able to integrate thousands of x,y slopes to produce a full surface contour. It would similar to what is done in processing results from the Hartmann test, except that the sampling is finer (perhaps diffraction effects are reduced as well).


  • brucesdad13 likes this

#54 mark cowan

mark cowan

    Vendor (Veritas Optics)

  • *****
  • Vendors
  • topic starter
  • Posts: 8195
  • Joined: 03 Jun 2005
  • Loc: salem, OR

Posted 27 September 2016 - 03:20 PM

The center null is not really related to the zonal nulls, necessarily, and the zonal nulls are not areas along a line of constant intensity - they are areas along a line where the left and right pixels are the same value.  Any small error of a pixel or more in nailing the radii makes the test far less accurate.  But all approaches are of course welcome so long as they converge on the same output.   :waytogo:

 

Soon I'll be comparing the unmasked results to what I get with a couple of different Bath interferometers - although the latter won't have nearly the same precision, it will determine if the overall curves the unmasked Foucault generates are basically sound to a tenth-wave or so.  It might also help figure out how to turn the Foucault into a full mirror test, whereas currently what it shows is based on an assumption of rotational symmetry.  What it shows is an average of the left and right sides of the mirror, not the individual sides.  

 

The Hartmann test (in various forms) measures the tilt of the return beam from the mirror by isolating small areas at one (or two) specific longitudinals and then measuring displacements directly across the mirror, one way or another.  Foucault can't return that information because it cuts across the caustic to locate matching zones at different longitudinals and can't distinguish the zones other than that.

Re. that particular image, it has diffraction artifacts due to the use of a too-small source, and dust motes in the imaging train as well.  There are no obvious air currents.

 

Here's a rotate-and-diff of that image, standard procedure:

 

dutch image rotate and diff.jpg

 

And here's the difference betweeen that and the other analysis - there's significant variation...

 

rot-and-diff flip difference difference.jpg

 

 

 

 

 

 

 


  • jdupton likes this

#55 brucesdad13

brucesdad13

    Apollo

  • *****
  • Posts: 1034
  • Joined: 25 Jan 2015
  • Loc: Rutland, MA

Posted 27 September 2016 - 03:43 PM

I never got that far with image processing algorithms. What libraries are you using?



#56 ckh

ckh

    Apollo

  • -----
  • Posts: 1177
  • Joined: 21 Feb 2015
  • Loc: Arizona

Posted 27 September 2016 - 11:49 PM

Charlie, I'm using C# with .NET libraries, no special image processing programs. Just the functions provided by the Bitmap and Math classes. The programs finds the brightness of the central area and then locates other areas on the mirror that have the same brightness. The dark places in the processed image all have the same brightness and therefore x-direction slope relative to the KE. By measuring their distance from the center you can compute the actual slope of each dark spot relative to the plane of the mirror.

 

Mark, The difference is that rotate and diff creates a left/right symmetry that doesn't actually exist on the mirror. In this other method you pick some place along the center area of the mirror as a basis for brightness (the amount of light from that area that misses the KE). That brightness reflects the x-direction slope of that central area relative to the KE. Any place on the mirror that has the same brightness has the same slope relative to the KE as that central area.

 

Even though you don't know exactly what that center area slope is, you know that the x-direction slopes of all other points with the same brightness have the same slope (relative to KE).  With multiple images taken at closely spaced positions along the optical axis, you can integrate a contour along every horizontal line that reflects the actual slopes even if they are different on the left and right sides. All of those contour lines will all be tilted by the same amount as the tilt of the central area you choose as a basis (if the KE moves along the mirror axis). This tilt is unimportant and is easily removed. So one series of images gives you the x-direction slopes for the whole surface. A second set of images taken with the mirror rotated 90 degress gives you the y-direction slopes. From those you can form a 2D contour map of the mirror.  The methods for doing this 2D integration of slopes accurately are varied and the best ones are somewhat complicated. I'm trying to learn about them.

 

Carl


  • brucesdad13 likes this

#57 mark cowan

mark cowan

    Vendor (Veritas Optics)

  • *****
  • Vendors
  • topic starter
  • Posts: 8195
  • Joined: 03 Jun 2005
  • Loc: salem, OR

Posted 28 September 2016 - 01:37 AM

As has been discussed before (and elsewhere) there's no difference in the analysis provided through "flip-and-diff" or "rotate-and-diff" since you're only looking at the horizontal axis of the mirror.   Lack of symmetry only shows itself in the "rotate-and-diff" operation because of test stand astigmatism (primary contributor); displacement of the source and KE (not a problem in most setups where they are within a cm or so, ideally half a cm; and lastly actual astigmatism on the mirror itself (which Foucault is completely blind to).

 

So it's not even an academic question, the method described in this thread ("unmasked Foucault") is about extracting fine grained readings across the horizontal axis of the mirror, and secondly doing some local averaging to pin down those diameters to subpixel accuracy (necessary for the process to represent the mirror axis faithfully).  Local averaging would be done across slightly tilted diameters of the original data (in essence accomplishing the "rotate-and-diff" directly).  Over small angles the symmetry of the mirror is more than sufficient (actual tests of actual mirrors) to support either method.  

 

This thread is not really about producing full surface mappings, as that is not what Foucault lends itself to or can be applied to, IMHO.  For that you really want to explore alternative techniques, Hartmann testing, Shack-Hartmann imaging, and IF, all of which measure the mirror surface contours either directly (IF through OPD differences, Hartmann variants through measurement of surface tilt).  Foucault measures slope.

 

Since we've been discussing this via PM for some time now I have some idea of what you're trying to do, but if it's going to become long and complex I would really like you do it some other thread, one devoted to the method you're trying to propose here.  This thread is devoted solely to unmasked Foucault testing as described above and in the introduction, and I've got enough experience with it now to appreciate the immense value of an assumption free, ancillary optic free, and most particularly bias free method of very accurately acquiring slope data for mirrors.

 

Just to be completely clear - Foucault only measures the radii of zones across the mirror which null at the same longitudinal position along the caustic curve.  That's ALL it does.  The information may look like it can be processed independently without regard to the nulls on both sides, and you're more than welcome to pursue that idea, but I request specifically that you do that in some other thread as I consider it off topic here.

 

I concede it is remotely possible that Foucault testing has been used for 150 years with nobody ever realizing that it contained a hidden method to extract accurate full surface mapping comparable to, say, IF - and that of course would be a welcome discovery.  I don't think that's very likely though - and with respect I don't think you've discovered it just by working over a few Foucaultgrams - and it doesn't stop me from considering it in detail, certainly, as there may be new life in the old test yet. :shrug:

 

Now, to get to what I hope will be the end of  this discussion here- Foucault has, necessarily, different sensitivity at different portions of the caustic.  The closer you get to the paraxial focus (of the center) the less the sensitivity becomes, until ultimately you have none at all (contains test stand astig and in-process roughness) at the paraxial focus itself:

 

0000%20rotate%20and%20diff.jpg

 

There is no necessary condition of the center line of the mirror that can return data on a null that's accurate enough to use to determine the radii of either side independently of the diameter you're actually measuring.   Just take a stab at this rotate-and-diff image of a 55% complete 18" f/3.58 mirror, showing some test stand astig under the rotate-and-diff (not in the mirror to be sure):

 

a0425.jpg

rotate-and-diff.%20425.jpg

 

If you measure from the left null to the center line, and from the center line to the right null, you get different numbers.  But if you measure from the left null to the left edge of the mirror, and from the right null to the right edge of the mirror (all here well centered) you get the same numbers.   This demonstrates clearly that the nulls are where they should be on a mirror with good figure of revolution, but that the center line is ill-defined.  The center line HAS to be there, somewhere, in this test method, as somewher between the left side and the right side there is indeed an area with the same values under rotate-and-diff (because the curve across the face graduates from light to dark to light to dark as it should) but the information in that graduation is only useful where the change is steepest, as illustrated below in a composite picture showing the actual overlay:

 

rotate-and-diff%20darkest%200425.jpg

 

Note that the nulls on the outside lie clearly on the crest of the waves, as it were.  But the outer crests are clearly delineated, as they are actually crossing the axis , where the KE always is, at this particular longitudinal (4.25 mm from paraxial focus).    The center OTOH has no such delineation - it is very far from any focus at all, and as such it is at the mercy of minor diffraction defects in the image, small variations in illumination, sensor response, and the like.  This is a critical point, because the sensitivity of the Foucault test depends strongly on this delineation.  Where you don't have that critical zonal crossing you just don't have good data, and you absolutely need good data to get to subpixel accuracy in running this particular test, or you will get garbage out.

 

It occurs to me you might want to look at producing an automated version of the traditional Caustic test, where the zones are nulled at their actual foci along the caustic horn, and separated, not joined along the center longitudinal line.  That test relies on measuring the actual separation of the two separate focal points at given longitudinals, and so could directly tell you about the two sides of the mirror.  It can be done with a wire and an unmasked mirror, but it will require automation in x and z to a very high precision, and orthogonality,  to yield useful data.  Unmasked Foucault currently appears to achieve the same sort of precision (1/100th wave or so) without elaborate mechanisms, but sacrifices knowledge of the full surface in order to produce an average of the particular axis measured.


  • jdupton and brucesdad13 like this

#58 ckh

ckh

    Apollo

  • -----
  • Posts: 1177
  • Joined: 21 Feb 2015
  • Loc: Arizona

Posted 28 September 2016 - 01:00 PM

You misunderstand the method suggested. It does not involve measuring the distance of the outer (circular) null to the center null.  All that is taken from the center is a brightness level.  That brightness level reflects the (unknown) x-slope of that small central region. Other parts of the mirror with the same brightness level have the same x-slope (with respect to the KE) as the central region. When you take multiple images at different longitudinal KE positions, the slope of the central part chosen is the same in each. In each image you find areas with the same x-slope (relative to the KE) as that central region and then you can calculate the actual slopes (with a fixed overall tilt). There is no forced symmetry, so you can get actual left/right slopes rather than artificially symmetric slopes.  

 

At least it seems plausible, but certainly it needs a lot more thought and experimentation.  

 

The image above has substantial tilt, probably due to horizontal KE/source separation. If I sample the central brightness, I get:

 

gallery_240847_5047_60946.png

 

 

If I move the central sample to the left 29 pixels, the tilt of the outer slopes is just about removed, but the slight left/right asymmetries in the outer slopes are apparent:

 

gallery_240847_5047_2837.png

 

(Obviously my method of narrowing the areas of matching brightness is not as good as yours and needs work.)

 

The point of this method is to explore the possibility of producing full surface contours with the Foucault test setup.

 

I won't go on since this thread is specifically about the rotate/diff method for the "standard" method of Foucault-gram analysis. I just wanted to respond to the incorrect understanding of the suggested method. I apologize for the diversion.

 

I agree the rotate/diff method may provide very accurate, standard Foucault measurements along the equator of the mirror. It certainly has the potential to be a vast improvement over eyeballing shadows with a couder mask or pins!  :waytogo:

 

Carl



#59 sixela

sixela

    Hubble

  • *****
  • Posts: 15149
  • Joined: 23 Dec 2004
  • Loc: Boechout, Belgium

Posted 29 September 2016 - 06:19 AM

Another one creeping out of the woodwork, for anyone who wants to brush up on his° French:

http://diaxen.free.f...ucault_auto.pdf

[I can translate if necessary]

--
°used as gender-neutral pronoun

Edited by sixela, 29 September 2016 - 06:19 AM.


#60 Pierre Lemay

Pierre Lemay

    Apollo

  • *****
  • Posts: 1065
  • Joined: 30 Jan 2008
  • Loc: Montréal, Canada

Posted 29 September 2016 - 12:15 PM

Another one creeping out of the woodwork, for anyone who wants to brush up on his° French:

http://diaxen.free.f...ucault_auto.pdf

[I can translate if necessary]

--
°used as gender-neutral pronoun

That article basicaly describes the construction and use of a RoboFoucault tester. It's a good, well written article but it's not quite the same thing as Mark is describing in this thread. However I believe the RoboFoucault tester described could be used to generate the images to do the analysis the way Mark intends them to be made rather than just comparing "greyness" of shadows with a digital camera, like classic RoboFoucault testers do.



#61 sixela

sixela

    Hubble

  • *****
  • Posts: 15149
  • Joined: 23 Dec 2004
  • Loc: Boechout, Belgium

Posted 01 October 2016 - 02:47 PM

6.3 does talk about the exact same method as Mark describes.

#62 ckh

ckh

    Apollo

  • -----
  • Posts: 1177
  • Joined: 21 Feb 2015
  • Loc: Arizona

Posted 01 October 2016 - 05:25 PM

Filtering helps on the image above. Here the brightness is averaged in small windows around each pixel. Then pixels within a narrow range of the central brightness are selected. This eliminates some noise and sharpens the null.

 

 

gallery_240847_5047_22330.png


  • brucesdad13 likes this


CNers have asked about a donation box for Cloudy Nights over the years, so here you go. Donation is not required by any means, so please enjoy your stay.







Cloudy Nights LLC
Cloudy Nights Sponsor: Astronomics