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Influence of various roughness scales on Strehl?

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#1 Lucullus

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Posted 15 September 2019 - 05:00 AM

The telescope-optics.net chapter about fabrication  shows some good graphs for the dimensions of various roughness terms. Also it says the following:

 

Large-scale roughness is not a usual term, and here will partly overlap with figure error. We'll define it as a pattern of random surface deviations with the dominant structure averaging, approximately, D/10 to D/5 in diameter. It is not a frequent form of optical surface roughness - although isolated local surface errors of that size are rather common - but it is certainly possible with poor fabrication methods.

 

Medium-scale roughness (also dog biscuit, or primary ripple) is usually a random pattern  resulting from the existence of empty interspaces on the polishing tool. Its dominant structure average is between D/10 and D/20 in diameter.

 

And small-scale roughness, or microripple (also, secondary ripple), is caused by the abrasive action of polishing material. Average size of surface irregularity here is approximately 1mm in diameter. For special applications, such as laser optics, significantly smaller structures can be important, but for general amateur astronomy their effect is entirely negligible.

If you had some monetary budget left what specific roughness scale would you want your telescope mirror maker try to improve to get a better final Strehl ratio and less overall light scattering?

 

What longterm influence do subsurface cracks have?



#2 mark cowan

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Posted 15 September 2019 - 09:42 AM

All of the above. ;)


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#3 MKV

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Posted 15 September 2019 - 10:22 AM

If you had some monetary budget left what specific roughness scale would you want your telescope mirror maker try to improve to get a better final Strehl ratio and less overall light scattering?

You may wish to read more on this here https://zambutomirro...oopticalce.html

 

The key is the medium-scale roughness or primary ripple whcih is responsible for light scatter and loss of contrast. Unfortunately, as the above link shows, interferometric assessment of optics doesn't take that into account.

 

Medium-scale surface roughness is not uncommon in automated machine mirror production process, and requires an optician to remove it. Thus, a high Strehl score alone is not a guarantee that the surface roughness is sufficiently reduced to result in a top-performing optic.



#4 BGRE

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Posted 15 September 2019 - 05:56 PM

Nonsense, all it actually shows is the transfer function of the interferometer used (an early Zygo or similar?) is inadequate for the task. Using a higher resolution image sensor and not projecting the interferogram onto a ground glass screen (as in some early interferometers ) will help immensely. Using an interferometer with a virtual reference can also help improve its transfer function.


Edited by BGRE, 16 September 2019 - 08:57 AM.


#5 Mark Harry

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Posted 15 September 2019 - 06:03 PM

I agree 200% with Mr. Cowan's comment. I don't want -ANY- type of roughness.


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#6 Pinbout

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Posted 15 September 2019 - 07:03 PM

 

If you had some monetary budget left what specific roughness scale would you want your telescope mirror maker try to improve to get a better final Strehl ratio and less overall light scattering?

I would expect my mirror maker to make the mirror smooth enough that no roughness can be seen with the knife edge.

if they don’t, they ain’t worth the money.


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#7 luxo II

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Posted 16 September 2019 - 07:20 AM

Strehl correlates very strongly with RMS wavefront error - for the simple reason that both are calculated from the same measurements - ie both are essentially measurements of smoothness, and effectively equivalent..

 

The correlation between Strehl and P-V wavefront error isn't so perfect, however. The graph below is from scope test results for SCT and mak scopes 7" or more aperture, published on the Russian lab website I found a while back. I've discarded the worst of the scopes (below strehl 0.75). The curves are just least squares fits to the data using Excel, not based on the theory, and that they don't intercept at 0 is most likely due to limitations in the test equipment, more than anything else.

 

When looking at the test results its possible for example to have optics showing a bad turned edge that normally would be rejected (bad P-V measurement) yet is smooth and has a good strehl value. Conversely systems can have a poor smoothness (low strehl under 0.85) and yet have an acceptable P-V wavefront error under 0.3.

 

In this respect both P-V and RMS (or strehl) values are relevant.

 

Nirvana is theoretically possible - you could be lucky enough to acquire a scope with P-V under 0.1 wave and strehl above 0.985... in 20 years I have seen only two examples that good and neither were SCTs.

Attached Thumbnails

  • Wavefront error vs Strehl.jpg

Edited by luxo II, 16 September 2019 - 07:34 AM.


#8 MKV

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Posted 16 September 2019 - 12:00 PM

This can be very misleading. The Strehl ratio alone applies only to systems capable of forming Airy discs  -- in other words, to a high contrast point source object. It really doesn't tell you too much about performance on extended objects. 



#9 luxo II

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Posted 16 September 2019 - 03:34 PM

Correct. It’s really only of academic interest imho.

Edited by luxo II, 16 September 2019 - 04:56 PM.


#10 Vla

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Posted 16 September 2019 - 08:21 PM

Mladen, that doesn't add up. How is the Strehl relevant for point source image, and not for extended image, made of point source images? In fact, MTF integral implies that the Strehl figure represents contrast transfer averaged over MTF frequencies. That is important piece of information, even if it does not tell what is the contrast transfer at specific frequencies.

 

One thing that shouldn't be generalized is that there is a tight correlation between Strehl and RMS wavefront error. That is valid only for low level of aberrations, in general below 0.15 waves RMS. The more it goes beyond it, the looser correlation, even for rotationally symmetrical aberrations like spherical. That's because the real Strehl is calculated from the RMS phase error, which is a different animal. For instance, a trench-like zone 1/2 wave deep, 20% radius wide, centered at the 70% zone, will produce corresponding wavefront deformation 1 wave deep; it will be reflected in the RMS wavefront error (0.45 waves, according to Suiter's "Aperture"), but will not affect the RMS phase error, i.e. Strehl. Or, a 5-wave 95% turned edge will have a whooping 0.634 waves RMS wavefront error, but better than "diffraction limited" central intensity of 0..834, "corresponding" to 0.067 RMS wavefront error.


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#11 BGRE

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Posted 16 September 2019 - 08:38 PM

phase error of what exactly?



#12 MKV

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Posted 16 September 2019 - 09:33 PM

Vla,

I was trying to avoid going off on a tangent (aka "hijacking the thread"). The Strehl ratio by itself doesn't give you an indea how well a telescope will perform on extended objects.

 

The Strehl ratio is defined by an object with 0 spatial spread, i.e. "point source," in terms of how much energy is in the central maxima of the Airy disc compared to a "perfect lens." The amount of energy is proportional to how bright the center of the Airy disc will be. The rest of the light is in the diffraction rings of which only the first and most intense is seen..

 

The illustration below it shows the intensity bar at about 0.8 for an unobstructed and otherwise optically perfect  6-inch f/8 sphere. The Strehl is ≈ 0.8 (or 80% of light intensity in the Aity disc maxima compared to a perfect lens). and corresponds to 1/14 wave rms or 1/4 wave pv w.  

 

6 in f8 sphere Strehl.jpg

 

But while this is so, it is also misleading because there are other factors that come into play (scratches, central obstruction, TDE, etc.). I think that should be addressed in a separate thread. 

 

A Strehl ratio taking in to account only spherical aberration can be calculated using  S ≈ 1 - (2πw)2, where π is the Pi or 3.141592654..., and w is the wavefront spherical rms error. In this case it will be ≈ 0.07 waves or λ/14.

 

Of course, MTF provides contrast information, but it's not just the Strehl ratio. It's more than that. But the "straight" Strehl ratio is defined by the central Airy disc energy intensity. 

 

Mladen


Edited by MKV, 16 September 2019 - 09:34 PM.


#13 Vla

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Posted 16 September 2019 - 10:46 PM

Mladen, Strehl ratio is a measure of wavefront quality. Of course that obstructions of any kind should be taken into account if they are present (Strehl does cover any wavefront deformation, including TE and microripple), but it also boils down to the point-source image. It is the building block of any extended image. The Strehl is not misleading, it tells you what it is supposed to tell you about the wavefront, i.e. point-source image quality it produces, and directly implies - in general terms - the extended objects image quality, as far as the wavefront is concerned. Including the effect of obstructions and/or pupil transmission modifications, if present, only completes the picture.



#14 Starman1

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Posted 17 September 2019 - 11:46 AM

Strehl correlates very strongly with RMS wavefront error - for the simple reason that both are calculated from the same measurements - ie both are essentially measurements of smoothness, and effectively equivalent..

 

The correlation between Strehl and P-V wavefront error isn't so perfect, however. The graph below is from scope test results for SCT and mak scopes 7" or more aperture, published on the Russian lab website I found a while back. I've discarded the worst of the scopes (below strehl 0.75). The curves are just least squares fits to the data using Excel, not based on the theory, and that they don't intercept at 0 is most likely due to limitations in the test equipment, more than anything else.

 

When looking at the test results its possible for example to have optics showing a bad turned edge that normally would be rejected (bad P-V measurement) yet is smooth and has a good strehl value. Conversely systems can have a poor smoothness (low strehl under 0.85) and yet have an acceptable P-V wavefront error under 0.3.

 

In this respect both P-V and RMS (or strehl) values are relevant.

 

Nirvana is theoretically possible - you could be lucky enough to acquire a scope with P-V under 0.1 wave and strehl above 0.985... in 20 years I have seen only two examples that good and neither were SCTs.

Exactly.

If the surface of a mirror were a plowed field an acre wide, it could be smooth or rough on several scales:

--from edge to edge (which we call wedge normally, but we'll call "figure" in this example)

--height variations from side to side in the form of small hills (which we call zones)

--piles of dirt in rows (which we call micro-ripple)

--rocks and clods of dirt (which we call surface roughness)

 

The question is, which level of smoothness has the greatest impact?

Well, just about everyone would say figure is the most important.

But what is critical beyond that?

That's where you get into a grey area.  Zones certainly throw light in different places, but micro ripple can scatter light all over the place.

 

When you see two mirrors of 1/8 wave P-V on the wavefront, which mirror would you rather have, the one with a perfectly smooth surface but

one 1/16 wave deep pit, or a mirror with a coarse, rough surface that never exceeds +/- 1/16 wave from the ideal surface.

Both have he same P-V, but the 2nd mirror will be obviously poorer in the field than the first one.

 

And that is where RMS comes in because it describes a weighted average for the surface.  In this case, the first mirror would have a higher RMS than the second,

which would calculate out to a higher Strehl ratio, too.

 

Yet, there isn't a mirror exactly like the first, that is perfect except for one tiny flaw in one spot.  The 2nd example is far more likely to be the case in practice.

So what we care about is P-V and RMS and smoothness on the micro level as well.  CZ is right that smoothness on all levels is important.

A mirror maker that makes a mirror with a low P-V error, and a smooth surface on both the larger and smaller scales is one I want to do business with.


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