Tilt dependent astigmatism


Franz
 
Edited

Hey folks,
for some time now I had the impression, that more fringes (or more tilt) result in more astigmatism in the wavefront.
So I made a small experiment.
The mirror is an unfinished 6 inch f 2.8.
I made some interferograms with different amounts of tilt, without touching the mirror in between.
I got this result:
x Tilt      y Tilt     Astig (polar)
12.7         11           0.055
21.9         19           0.143 
23.2        22.3         0.143
29.0        29.0         0.21

It seems like astigmatism is proportional to tilt. And it is substantial.

Does anyone know if this is normal?
It makes measuring astig really hard because it only cancels out for equal tilts.
My beam separation is 6.5 mm. DCX diverger with 9 mm focal lenght.

Cheers,
Franz


Michael Peck
 

On 5/26/2021 7:47 AM, franz.hagemann@... wrote:

It seems like astigmatism is proportional to tilt. And it is substantial.

Does anyone know if this is normal?
It makes measuring astig really hard because it only cancels out for equal tilts.
My beam separation is 6.5 mm. DCX diverger with 9 mm focal lenght.

Cheers,
Franz

Tilt dependent astigmatism isn't exactly normal but it has been observed and discussed here a number of times. It's likely due to coma in the collimating lens of your laser, which in turn is likely due to decentering.

-- 
Michael Peck
http://wildlife-pix.com
mlpeck54 -at- earthlink.net


Franz
 

Thanks Michael!
That seems very likely as my laser beam moves in a circle when I turn the fucusing element.
I will try to improve the laser and report back.


Franz
 

I bought  a new Laser module and did the same experiment. I got a very similar result.
In these first two experiments the laser was focused on the mirror. I then did a third experiment with the laser beam collimated / parallel (and only Y tilt). Again a very similar result.
To me it seems unlikely that both laser modules have the same coma, but it is possible.
Any thoughts?
Below is a copy of my spreadsheet with the results.

Roithner Laser:   focused on mirror      
           
x Tilt y Tilt Tilt Astig    
12,7 11 16,80 0,055    
21,9 19 28,99 0,143    
23,2 22,3 32,18 0,143    
29 29,05 41,05 0,21    
           
Picotronic Laser:   focused on mirror      
           
x Tilt y Tilt Tilt X Astig Y Astig Astig
9,8 5,8 11,39 0,025 0,09 0,09
14,4 10,2 17,65 0,017 0,088 0,09
23,3 15,3 27,87 0 0,138 0,14
36,6 21,7 42,55 0,097 0,18 0,20
           
Picotronic Laser:   parallel beam      
           
x Tilt y Tilt Tilt X Astig Y Astig Astig
0 12,7 12,7 0,02 0,078 0,08
0 17 17 0,01 0,147 0,15
0 25,5 25,5 0,029 0,132 0,14
0 37,1 37,1 0,068 0,189 0,20
0 45,4 45,4 0,064 0,231 0,24


 

If I remember correctly, the astig-tilt relationship is caused by the fact that the Bath is not *exactly* a common path interferometer, because depending on the amount of tilt the beam returning from the mirror will not go through exactly the same spot on the small lens as it went in opposite direction (going from Bath to mirror). Depening on characteristics of the actual lens this may cause astigmatism, or cancel it (partly) out. Therefore it is adviced to make - in each rotational position used - igrams with different amounts of tilt to average this astigmatism out as much as possible. 

Jan.


Op 1-6-2021 om 17:33 schreef franz.hagemann@...:

I bought  a new Laser module and did the same experiment. I got a very similar result.
In these first two experiments the laser was focused on the mirror. I then did a third experiment with the laser beam collimated / parallel (and only Y tilt). Again a very similar result.
To me it seems unlikely that both laser modules have the same coma, but it is possible.
Any thoughts?
Below is a copy of my spreadsheet with the results.

Roithner Laser:   focused on mirror      
           
x Tilt y Tilt Tilt Astig    
12,7 11 16,80 0,055    
21,9 19 28,99 0,143    
23,2 22,3 32,18 0,143    
29 29,05 41,05 0,21    
           
Picotronic Laser:   focused on mirror      
           
x Tilt y Tilt Tilt X Astig Y Astig Astig
9,8 5,8 11,39 0,025 0,09 0,09
14,4 10,2 17,65 0,017 0,088 0,09
23,3 15,3 27,87 0 0,138 0,14
36,6 21,7 42,55 0,097 0,18 0,20
           
Picotronic Laser:   parallel beam      
           
x Tilt y Tilt Tilt X Astig Y Astig Astig
0 12,7 12,7 0,02 0,078 0,08
0 17 17 0,01 0,147 0,15
0 25,5 25,5 0,029 0,132 0,14
0 37,1 37,1 0,068 0,189 0,20
0 45,4 45,4 0,064 0,231 0,24
_._,_._,_



Bruce Griffiths
 

The test surface also has field astigmatism which is tilt dependent.

However this is usually insignificant except when  testing large test surfaces.

The field astigmatism of the test surface can easily be calculated from the beam separation (at the interferometer head), the test surface diameter and RoC. 

Similarly the field coma and astigmatism of the diverger lens can be found by raytracing.

Bruce

On 02 June 2021 at 03:58 janvangastel <jhm.vangastel@...> wrote:

If I remember correctly, the astig-tilt relationship is caused by the fact that the Bath is not *exactly* a common path interferometer, because depending on the amount of tilt the beam returning from the mirror will not go through exactly the same spot on the small lens as it went in opposite direction (going from Bath to mirror). Depening on characteristics of the actual lens this may cause astigmatism, or cancel it (partly) out. Therefore it is adviced to make - in each rotational position used - igrams with different amounts of tilt to average this astigmatism out as much as possible. 

Jan.


Op 1-6-2021 om 17:33 schreef franz.hagemann@...:
I bought  a new Laser module and did the same experiment. I got a very similar result.
In these first two experiments the laser was focused on the mirror. I then did a third experiment with the laser beam collimated / parallel (and only Y tilt). Again a very similar result.
To me it seems unlikely that both laser modules have the same coma, but it is possible.
Any thoughts?
Below is a copy of my spreadsheet with the results.

Roithner Laser: focused on mirror   
      
x Tilty TiltTiltAstig  
12,71116,800,055  
21,91928,990,143  
23,222,332,180,143  
2929,0541,050,21  
      
Picotronic Laser: focused on mirror   
      
x Tilty TiltTiltX AstigY AstigAstig
9,85,811,390,0250,090,09
14,410,217,650,0170,0880,09
23,315,327,8700,1380,14
36,621,742,550,0970,180,20
      
Picotronic Laser: parallel beam   
      
x Tilty TiltTiltX AstigY AstigAstig
012,712,70,020,0780,08
017170,010,1470,15
025,525,50,0290,1320,14
037,137,10,0680,1890,20
045,445,40,0640,2310,24


 


Franz
 

Thanks Jan and Bruce!


Bruce Griffiths
 
Edited

C4 (amplitude of Z4) due to finite beam separation is 49.3 nm (use the laser wavelength to convert this to waves).

The separation of the return test and reference focal spots may be as large as 0.15mm (for a 650nm laser wavelength).

This can be estimated from C2, C3

s= N*lambda^(R/D) where N is the number of tilt fringes across the diameter of the test surface,

The corresponding difference in field astigmatism contributions for a BK7 equibiconvex dierger lens with a focal length of 9mm is significant for such a separation however this varies as the square of the field angle. If the test and reference beams field angles at the diverger are equal and opposite the field astigmatism contribution of the diverger lens cancels for an equibiconvex diverger.

The stand could alos contribute some astigmatism that is invariant with tilt.

Its more likely that there is significant coma common to both test and reference beams.

Ideally the aberrations of the laser module output beam should be measured as well as the aberrations of the test beam produced by the diverger lens. Using a point diffraction interferometer together with an auxiliary lens is the best way of measuring the aberrations of these beams. A method of measuring the aberrations of the auxiliary lens is also required (a point diffraction pinhole laser source should suffice).

Bruce

On 02 June 2021 at 10:04 franz.hagemann@... wrote:

Thanks Jan and Bruce!


Michael Peck
 

Just for reference here are previous posts that discussed possible mechanisms for producing tilt dependent astigmatism. This isn't an exhaustive list -- I just entered the terms "tilt astigmatism coma" in the search box at the top of the messages area in the web interface. Links go to the original message. I'll list the author and maybe a note. Some of these posts were part of longer threads and those might be worth browsing through in some cases.

29735 (Bruce - 17/07/2020) - repeats a previously made assertion.
28782 (Bruce - 09/12/2019) - camera lens distortion as a source of instrumental aberrations (but not tilt dependent astigmatism).
28677 (Bruce - 01/12/2019) - same topic as above
27821 (Bruce - 09/09/2019) - one of many mentions of tilt dependent coma and astigmatism arising from source aberrations
26004 (Bruce - 23/02/2019) - notes that Bath's original design suffers from tilt dependent astigmatism. Maybe this is relevant here??
24843 (Bruce - 10/11/2018) - again a reference to Bath's original design
24640 (Bruce - 22/10/2018) - more of the same
23410 (Bruce - 14/04/2018) - mentions effect of tilting the beamsplitter cube and again references Bath's original geometry
21333 (Bruce - 09/07/2017) - an early claim about the effects of uncorrected camera lens distortion
14968 (Dave Schaack - 10/01/2015) - Was Bruce aware of this discussion? The document mentioned is likely lost since this was on the old Yahoo group.
6641 (Dave Schaack - 28/08/2009) - An earlier discussion of the effect of source aberrations, and in particular the effect of centration error when using aspherical collimating lenses.
5251 (Dave Schaack - 04/06/2008) - getting closer to the original discussions of this topic.

There were earlier discussions and some empirical data, but I think Dave Schaack's analysis in message 5251 was the first to clearly pin down this particular mechanism for instrumental aberrations. Again, this is far from an exhaustive list.

Mike



George Roberts (Boston)
 

Franz you only show positive X and Y tilt in your examples.
1) Are these values from DFTFringe Zernicke terms column?  I'm assuming so.
2) Is there a quick summary of how to reduce the error?  For example (A) do equal amount of waves of +Xtilt and -Xtilt?  Or (B) equal amounts of +Xtilt and +Ytilt?


I'm looking for a "rule of thumb" here for when taking measurements to help cancel out tilt induced astig.  I know a lot of people here like to do equal tilt in 4 directions centered and symmetrical around "center".  For example I think some people do above/below/left/right of center.  Others do diagonals.  And they get equal quantity of igrams in each of the 4 positions.  when I'm doing it quick I tend to do one left and one right but maybe those don't cancel out the astig?

Or maybe just stick with one position (e.g. always do 30 waves +Xtilt) and then rotate the mirror 90 degrees and averge igrams from the 2 rotations to cancel out induced asig.  This should work.


Franz
 
Edited

Thanks for all the answers guys!

Bruce, I appreciate your instructions, but I am not familiar with raytracing and stuff like that. I am interested in the cause of the tilt dependent astig too and I might pursue what you propose in the future. For now my main goal is to find a way to cancel out tilt dependent astig reliably without taking about 100 igrams. Also, I think that if I have to measure the aberrations of the test beam and the aberrations of the source (the laser), to be able to calculate the tilt dependent astig, I would have to do these measurments every time I clean the optics and every time I focus the laser on a different mirror (because the alignment and / or source aberrations will change a bit). To me, that seems to be too labor intensive.
But let me ask you this: How is C4 (defocus, right?) related to beam separation? I thought that I simply set defocus by adjusting the distance from the mirror. So to me they seem to be unrelated.

Michael, thanks for all the links! I also found this thread and read most of it. It was very informative.

George, 1) yes, those are values from DFTFringe Zernicke terms column! The tilts were actually all positive, but I dropped some minuses on the X astig values. 2) I don't have established a scheme to reduce the error yet.
I used to take igrams for 4 mirror positions and did one or two different tilts for each position. I recorded 6 igrams for each mirror position and tilt. I tried to keep the tilt equal by looking on the camera display. This procedure proved to be insufficient.

I also had in mind to do what you describe in your last proposal. Exactly the same tilt for two or four mirror positions. I will try to mount my micrometer dial gauge to my xyz-stage somehow to do repeatable tilt settings. I will do that tomorrow.


George Roberts (Boston)
 

I don't recommend micrometer when you can just count the fringes.  The micrometer reading will get smaller and smaller the farther you are from focus (back to this in a sec).  If XTilt is 20 you will have about 40 fringes (exactly 40 if your mirror is a sphere and you are right at focus).  So I'd just count the fringes (or even just count them roughly - within 30% accuracy may be enough).

It's good to be near focus - the point where left/right movement reverses - when taking your igrams.  You can see the defocus value in dftfringe in the zernicke terms.  Withing 2 waves of focus (-2 to +2) is so close to zero that I consider that zero.  "at focus" is basically (because it's parabolic mirror it's more complicated) the position where you have the least amount of fringes (when there is zero tilt). Positive values of defocus means you are outside of focus (farther from mirror).

The errors you saw may be dependent on tilt and also defocus zernicke values.

A good way to find focus - is the same technique with Foucault.  Center tilt so you get a "bulls eye" pattern.  Then push the bath gently to the left (or right).  If the bulls eye moves in the same direction I call this "same".  Otherwise call it "opposite".

If you move the bath closer or farther from your mirror, one direction will reduce the number of fringes.  That moves you towards focus.  As you pass through focus "same" will change to "opposite" (or opposite to same).

I can even tell if you are inside or outside of focus using this rule:
Some Bath's have the camera facing the mirror under test and the laser mounted 90 degrees from the mirror under test.  Some Bath's have the camera mounted pointed 90 degrees from the mirror under test and the laser initially aimed directly at the mirror under test.
For camera facing mirror and looking at camera display, SAME IMPLIES INSIDE FOCUS.  If you dim the laser a LOT and look with your eye instead of the camera it's the same as looking through the camera.  If you project the igram onto paper it will be opposite (smae implies outside focus).
If your camera is aimed 90 degrees from your mirror under test then this is reversed (SAME IMPLIES OUTSIDE FOCUS).

By the way, "focus" is probably the wrong word here but you know what I mean.


Bruce Griffiths
 

If the astigmatism is a linear function of tilt a straight line can be fitted to the plot of astigmatism (C4, C5) versus tilt (C1, C2) and the zero tilt intercept found. This is useful when exactly equal and opposite tilts cannot be achieved.

Bruce

On 03 June 2021 at 08:01 "George Roberts (Boston)" <bb@...> wrote:

I don't recommend micrometer when you can just count the fringes.  The micrometer reading will get smaller and smaller the farther you are from focus (back to this in a sec).  If XTilt is 20 you will have about 40 fringes (exactly 40 if your mirror is a sphere and you are right at focus).  So I'd just count the fringes (or even just count them roughly - within 30% accuracy may be enough).

It's good to be near focus - the point where left/right movement reverses - when taking your igrams.  You can see the defocus value in dftfringe in the zernicke terms.  Withing 2 waves of focus (-2 to +2) is so close to zero that I consider that zero.  "at focus" is basically (because it's parabolic mirror it's more complicated) the position where you have the least amount of fringes (when there is zero tilt). Positive values of defocus means you are outside of focus (farther from mirror).

The errors you saw may be dependent on tilt and also defocus zernicke values.

A good way to find focus - is the same technique with Foucault.  Center tilt so you get a "bulls eye" pattern.  Then push the bath gently to the left (or right).  If the bulls eye moves in the same direction I call this "same".  Otherwise call it "opposite".

If you move the bath closer or farther from your mirror, one direction will reduce the number of fringes.  That moves you towards focus.  As you pass through focus "same" will change to "opposite" (or opposite to same).

I can even tell if you are inside or outside of focus using this rule:
Some Bath's have the camera facing the mirror under test and the laser mounted 90 degrees from the mirror under test.  Some Bath's have the camera mounted pointed 90 degrees from the mirror under test and the laser initially aimed directly at the mirror under test.
For camera facing mirror and looking at camera display, SAME IMPLIES INSIDE FOCUS.  If you dim the laser a LOT and look with your eye instead of the camera it's the same as looking through the camera.  If you project the igram onto paper it will be opposite (smae implies outside focus).
If your camera is aimed 90 degrees from your mirror under test then this is reversed (SAME IMPLIES OUTSIDE FOCUS).

By the way, "focus" is probably the wrong word here but you know what I mean.


Bruce Griffiths
 

Franz

DFTFringe uses the Wyant scheme for labelling Zernike polynomials:

C0 is Zernike piston term (Z0) amplitude

C1 is Zernike defocus term (Z1) amplitude

C2 is Zernike x tilt  term (Z2) amplitude

C3 is Zernike y tilt term (Z3) amplitude

C4 is Zernike x astigmatism (Z4) amplitude

C5 is Zernike y astigmatism (Z5) amplitude

are you using a different Zernike polynomial labelling scheme than that used by DFTFringe?

Other Zernike polynomial labelling schemes are also used such as the Noll scheme which is popular in Europe.

Bruce

On 03 June 2021 at 07:08 franz.hagemann@... wrote:

[Edited Message Follows]

Thanks for all the answers guys!

Bruce, I appreciate your instructions, but I am not familiar with raytracing and stuff like that. I am interested in the cause of the tilt dependent astig too and I might pursue what you propose in the future. For now my main goal is to find a way to cancel out tilt dependent astig reliably without taking about 100 igrams. Also, I think that if I have to measure the aberrations of the test beam and the aberrations of the source (the laser), to be able to calculate the tilt dependent astig, I would have to do these measurments every time I clean the optics and every time I focus the laser on a different mirror (because the alignment and / or source aberrations will change a bit). To me, that seems to be too labor intensive.
But let me ask you this: How is C4 (defocus, right?) related to beam separation? I thought that I simply set defocus by adjusting the distance from the mirror. So to me they seem to be unrelated.

Michael, thanks for all the links! I also found this thread and read most of it. It was very informative.

George, 1) yes, those are values from DFTFringe Zernicke terms column! The tilts were actually all positive, but I dropped some minuses on the X astig values. 2) I don't have established a scheme to reduce the error yet.
I used to take igrams for 4 mirror positions and did one or two different tilts for each position. I recorded 6 igrams for each mirror position and tilt. I tried to keep the tilt equal by looking on the camera display. This procedure proved to be insufficient.

I also had in mind to do what you describe in your last proposal. Exactly the same tilt for two or four mirror positions. I will try to mount my micrometer dial gauge to my xyz-stage somehow to do repeatable tilt settings. I will do that tomorrow.


Dale Eason
 

I just want to point out that not every one sees any tilt dependent astig to the magnitude that you find.  I have tried several times to discover any and have never found any larger than the background noise of .01 - .02.   I have done so with several different Bath and mirror's.   

Make sure that both your beams are more or less parallel to within a few degrees.  I once saw system induced astig when I had the beams at an angle of more than 10 deg.

To remove any you don't need 100's of igrams.   Just a few with at lest + and - tilt values of similar magnitude.   I look through my camera's view finder to see the fringe count.  Then adjust the stage first one way and take igrams then back the opposite direction till the fringe count is about the same in the opposite direction.   You do of course want to take or at least average the same number at each tilt magnitude.

Dale


George Roberts (Boston)
 

Also note that astig is the most annoying thing with the Bath interferometer because it sees the astig so easily (most other tests, astig is very hard to see).  And it can be caused by air currents or air stratification.  Just walking towards the mirror and back again can cause all kinds of changes in astig temporarily.  I find if I have 3 degrees of temp difference between ceiling and floor then I get pretty serious amounts of astig (usually fixed by running a fan for 20 minutes).


Franz
 
Edited

Bruce, thanks for pointing out that there is the Noll scheme and others. I only looked in the first column in the wikipedia article and there it said index 4 for Defocus. But that was not the Wyant column.
I agree that it would be helpful if astig is a linear function of tilt, an I think it is. That means it is correct to average some igrams with different tilts to get a certain tilt, and hence astig for futher averaging.

Dale, my beams are parallel and I payed a lot of attention to go through the center of the diverging lens. My beam separation of 6.5mm should be ok.
Maybe I see so much tilt dependent astig because my mirror is small and very fast?

George, I know I could count fringes, but for this mirror I need about 50 fringes or preferably more, when it is fully parabolized. Counting 50 fringes in the viewfinder or on the display is hard (at least to me). That is why I prefer the micrometer gauge. I mounted it yesterday and for a tilt of 30 I needed a displacement of 0.125mm which is easily measurable and can be set quickly with a bull's eye pattern as starting point for each new set of igrams.
But first I made some measurements to see if tilt dependent astig is related to defocus, because you mentioned this possibility. I am glad that there at least seems to be no strong correlation.
Each data point is an average of 4 igrams, so it is a bit noisy. Unfortunately I didn't do larger positive defocus velues.
I subtracted my Bath astig (0.074) from the X astig, to get only the tilt dependent astig. I aslo divided the tilt dependent astig by the X tilt, to see the ratio and to see if Astig is a linear function of tilt.
I assumed that my bath astig is positive. My test beam is on the right, reference beam left. Is that correct?
Here is my data:
large negative Defocus                
Defocus x Tilt y Tilt Tilt X Astig Y Astig Astig tilt dep. Astig (tilt dep. Astig /
X Tilt)*1000
-8,22 -45,6 5,6 45,94 -0,132 0,061 0,15 -0,206 4,52
                 
medium negative Defocus                
Defocus x Tilt y Tilt Tilt X Astig Y Astig Astig tilt dep. Astig (tilt dep. Astig /
X Tilt)*1000
-5,2 -60,7 3,4 60,80 -0,213 -0,037 0,22 -0,287 4,73
-5 -36,4 1,3 36,42 -0,082 0,005 0,08 -0,156 4,29
-4,9 -30,5 1,3 30,53 0,018 0,058 0,06 -0,056 1,84
                 
small negative Defocus                
Defocus x Tilt y Tilt Tilt X Astig Y Astig Astig tilt dep. Astig (tilt dep. Astig /
X Tilt)*1000
-3,8 -54,4 4 54,55 -0,215 -0,027 0,22 -0,289 5,31
-3,63 -50 5 50,25 -0,191 0,042 0,20 -0,265 5,30
-3,49 -42,7 3,2 42,82 -0,127 -0,02 0,13 -0,201 4,71
-3,5 -35,6 2 35,66 -0,091 -0,027 0,09 -0,165 4,63
-3,6 -24,3 1,36 24,34 -0,052 -0,005 0,05 -0,126 5,19
-3,39 -24 2,8 24,16 -0,058 0,009 0,06 -0,132 5,50
                 
small positive Defocus                
Defocus x Tilt y Tilt Tilt X Astig Y Astig Astig tilt dep. Astig (tilt dep. Astig /
X Tilt)*1000
2,36 -53,9 3 53,98 -0,146 -0,113 0,18 -0,22 4,08
2,5 -34,2 2,7 34,31 -0,125 -0,049 0,13 -0,199 5,82
2,6 -22,8 0,74 22,81 -0,025 -0,055 0,06 -0,099 4,34
2,7 -10,8 1,13 10,86 -0,019 -0,031 0,04 -0,093 8,61


So the last two colums are the most interesting I think.


Bruce Griffiths
 

Franz

1) Are you using the right angle form of the Bath interferometer or the original Bath?

2) What is the size of the beamsplitter cube?

Can you post some pictures of your Bath interferometer?

With sufficient information I can attempt to raytrace your test setup.


Bruce

On 04 June 2021 at 21:20 franz.hagemann@... wrote:

[Edited Message Follows]

Bruce, thanks for pointing out that there is the Noll scheme and others. I only looked in the first column in the wikipedia article and there it said index 4 for Defocus. But that was not the Wyant column.
I agree that it would be helpful if astig is a linear function of tilt, an I think it is. That means it is correct to average some igrams with different tilts to get a certain tilt, and hence astig for futher averaging.

Dale, my beams are parallel and I payed a lot of attention to go through the center of the diverging lens. My beam separation of 6.5mm should be ok.
Maybe I see so much tilt dependent astig because my mirror is small and very fast?

George, I know I could count fringes, but for this mirror I need about 50 fringes or preferably more, when it is fully parabolized. Counting 50 fringes in the viewfinder or on the display is hard (at least to me). That is why I prefer the micrometer gauge. I mounted it yesterday and for a tilt of 30 I needed a displacement of 0.125mm which is easily measurable and can be set quickly with a bull's eye pattern as starting point for each new set of igrams.
But first I made some measurements to see if tilt dependent astig is related to defocus, because you mentioned this possibility. I am glad that there at least seems to be no strong correlation.
Each data point is an average of 4 igrams, so it is a bit noisy. Unfortunately I didn't do larger positive defocus velues.
I subtracted my Bath astig (0.074) from the X astig, to get only the tilt dependent astig. I aslo divided the tilt dependent astig by the X tilt, to see the ratio and to see if Astig is a linear function of tilt.
I assumed that my bath astig is positive. My test beam is on the right, reference beam left. Is that correct?
Here is my data:
large negative Defocus        
Defocusx Tilty TiltTiltX AstigY AstigAstigtilt dep. Astig(tilt dep. Astig /
X Tilt)*1000
-8,22-45,65,645,94-0,1320,0610,15-0,2064,52
         
medium negative Defocus        
Defocusx Tilty TiltTiltX AstigY AstigAstigtilt dep. Astig(tilt dep. Astig /
X Tilt)*1000
-5,2-60,73,460,80-0,213-0,0370,22-0,2874,73
-5-36,41,336,42-0,0820,0050,08-0,1564,29
-4,9-30,51,330,530,0180,0580,06-0,0561,84
         
small negative Defocus        
Defocusx Tilty TiltTiltX AstigY AstigAstigtilt dep. Astig(tilt dep. Astig /
X Tilt)*1000
-3,8-54,4454,55-0,215-0,0270,22-0,2895,31
-3,63-50550,25-0,1910,0420,20-0,2655,30
-3,49-42,73,242,82-0,127-0,020,13-0,2014,71
-3,5-35,6235,66-0,091-0,0270,09-0,1654,63
-3,6-24,31,3624,34-0,052-0,0050,05-0,1265,19
-3,39-242,824,16-0,0580,0090,06-0,1325,50
         
small positive Defocus        
Defocusx Tilty TiltTiltX AstigY AstigAstigtilt dep. Astig(tilt dep. Astig /
X Tilt)*1000
2,36-53,9353,98-0,146-0,1130,18-0,224,08
2,5-34,22,734,31-0,125-0,0490,13-0,1995,82
2,6-22,80,7422,81-0,025-0,0550,06-0,0994,34
2,7-10,81,1310,86-0,019-0,0310,04-0,0938,61


So the last two colums are the most interesting I think.


Franz
 

Bruce, here you wrote, that the tilt of the beamsplitter leads to coma in the beams and hence to tilt dependent astig. I know you were referring to the 45° variant. My beamsplitter is tilted by about 3° to get rid of the reflection from the beamsplitter face. Do you think that this could be the source of the large tilt dep. astig?


Franz
 

Yes, I will make a picture. I am using the right angle form.
My beamsplitter size is 10mm. My diverger lens is this one.