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Old 31-08-2019, 11:30 AM
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Strehl ratio

Hi fellow IIS-ers.

Recent comments about Strehl ratio for one wavelength got me thinking that perhaps I got it wrong. Several much more experienced astronomers used PV value only in estimating Strehl, ignoring the rms wavefront error or even stating that rms wavefront error is meaningless in determining Strehl. This has challenged my understanding, which can be summarised that it is exactly the rms wavefront error that should be used in estimating Strehl, and that PV can be ignored as long as it is within a good standard. I found this article confirming my line of thinking, but is it a credible source of information?

Here is the relevant part from the article:

However, it is not the peak-to-valley nominal aberration, which only specifies the peak of deviation, and tells nothing about its extent over the wavefront area. It is the root-mean-square, or RMS wavefront error, which expresses the deviation averaged over the entire wavefront. This average wavefront deviation determines the peak intensity of diffraction pattern and, hence, numerical value of the Strehl ratio (note that the RMS error itself is accurately representing the magnitude of wavefront deviation only when it is affecting relatively large wavefront area, which is generally the case with the conic surface aberrations).
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Old 31-08-2019, 11:53 AM
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Your thinking is correct.

I lifted this quote (of a quote) by Roland Christien.

The "Bible" of optical shop testing, Malacara states:

"The P-V error must be regarded with some
skepticism, particularly when it is derived from a large number of
measured data points, as is the case with phase shifting
interferometry. Even relatively large wavefront errors often have
little effect on the optical performance if the error involves only a
very small part of the aperture
.

Because the P-V error is calculated from just two data points out of possibly thousands,
it might make the system under test appear worse than it actually is.
The RMS error is a statistic that is calculated from all of the measured data, and it gives a better indication of the overall system performance


The corollary being, if the PV error is over an extended area, bad things happen. A turned edge would be a case in point. I once sent an RCOS mirror back to the manufacturer for that very reason....most of the mirror had a great figure...but the turned edge proved fatal.
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Old 31-08-2019, 12:54 PM
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Interesting posts. Makes sense it would have to represent the surface as a whole.

Ideally under various wavelengths as well as that is what you want from an APO - no false colour.

Not sure how a turned down edge applies to a triplet in a lens cell there the lens looks to go into the cell at least 5mm.

I had an RCOS 12.5mm and it had a slight turned down edge and I simply made a mask for the outer edge. I can't say it made a huge difference but every bit counts. So there must be worse turned down edges than others.

Greg.
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Old 31-08-2019, 12:56 PM
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https://www.telescope-optics.net/Strehl.htm
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Old 31-08-2019, 03:24 PM
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Thanks for that Ken.

Greg.
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Old 31-08-2019, 06:37 PM
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Thank you all for your posts.

It looks like then that the rms wavefront error gives a much more accurate and realistic indication of the optical quality that PV. I found a few academic articles about Strehl, and all used rms wavefront error for Strehl calculation.

To conclude, I will quote Peter Ceravolo: In the past, I, like most amateur astronomers, only considered the PV wave value when assessing a telescope's optical quality. But after observing with a 1/2 wave PV MaksutovNewtonian telescope that passed the star test and yielded excellent images of Saturn and double stars, I felt compelled to reconsider how I evaluated optical quality.
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Old 31-08-2019, 07:57 PM
Ukastronomer (Jeremy)
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As a photographer I live in the real world, I have never ever looked at DxO camera marks, or any Pv etc.

My Edh=ge Hd Celestron is 1/4 Pv I know that, I asked Celestron, I had a 1/18th Pv in the past, as a person I never saw and will never see any difference.

My D4s, D810 bought new with quality Nikkor lenses do what I want when I want, my scopes are the same, I could not justify a Tak, I don't want a Tak, I don't want a 30" Dob.

As I say, I live in the real world, I buy my gear for me not Strehl ratio or wavelengths.

I often shoot at sports events, www.jrs-photography.co.uk and see people obsessed with gear. Never posted my site before.

Buy, enjoy and use it
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Old 31-08-2019, 10:40 PM
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Quote:
Originally Posted by Slawomir View Post

To conclude, I will quote Peter Ceravolo: In the past, I, like most amateur astronomers, only considered the PV wave value when assessing a telescope's optical quality. But after observing with a 1/2 wave PV MaksutovNewtonian telescope that passed the star test and yielded excellent images of Saturn and double stars, I felt compelled to reconsider how I evaluated optical quality.
FYI Peter and I are friends.

I've been with Ceravolo when he's been totally legless
and caution he is not the Messiah, and is often just a very naughty boy.
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Old 31-08-2019, 11:25 PM
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Quote:
Originally Posted by Peter Ward View Post
FYI Peter and I are friends.

I've been with Ceravolo when he's been totally legless
and caution he is not the Messiah, and is often just a very naughty boy.

LOL


Ya, but he's usually really funny at the same time, good memories.



Another Ottawa boy...
EB
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Old 01-09-2019, 05:39 PM
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Fair observation, however there is a reasonable data set to test the idea - the Russian lab data I found a while back provides data for 128 scopes using the same setup. Sure there's some scatter in the plot of strehl vs P-V but the correlation is useful. RMS is as expected since the Strehl is calculated off the same data set.

That the lines don't cross the strehl axis at 1.0 suggests limitations on their equipments accuracy with small errors.
Attached Thumbnails
Click for full-size image (PV and RMS vs Strehl.jpg)
151.0 KB28 views

Last edited by Wavytone; 01-09-2019 at 07:29 PM.
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Old 01-09-2019, 05:50 PM
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Hi Nick,

On the PV v Strehl graph issue you mentioned earlier of both graphs not intersecting / passing through (1,0) a higher order curve fit may have cured that as it seemed, at least on the previous version of the graph, that the "line" was a little hockey stick down as the Strehl ratio approached 1. On this version of the graph it is not quite as obvious. Not that any of that negates the conclusion of a very strong correlation.

Best
JA
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Old 01-09-2019, 06:21 PM
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Interesting graph - thank you Nick. Am I reading it correctly - the best scopes in this sample of 128 scopes that were approaching 1 Strehl had a PV of 1/8 wavelength?
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Old 01-09-2019, 06:59 PM
Ukastronomer (Jeremy)
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It still isn't real life though is it

ten years ago I had an argument with camera club members who swore blind that different cameras/pixels, dxo marks, lenses made so much difference I set a challenge

As many people as you like take their cameras out together on to Bodmin Moore, we all set up same place, same iso, same f ratio, same shutter speed, and I will print the same images to A3+

NO ONE could tell any difference between a Canon?Nikon/Pentax, zoom or prime

I 100% ignore Strehl and any other, because unless you are compatring a £1k scope with a £100 scope etc, etc no one will "see" any difference between scopes of similar size/type/cost

Real world, I don't live in a lab
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Old 01-09-2019, 07:16 PM
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Quote:
Originally Posted by Ukastronomer View Post
It still isn't real life though is it

ten years ago I had an argument with camera club members who swore blind that different cameras/pixels, dxo marks, lenses made so much difference I set a challenge

As many people as you like take their cameras out together on to Bodmin Moore, we all set up same place, same iso, same f ratio, same shutter speed, and I will print the same images to A3+

NO ONE could tell any difference between a Canon?Nikon/Pentax, zoom or prime

I 100% ignore Strehl and any other, because unless you are compatring a £1k scope with a £100 scope etc, etc no one will "see" any difference between scopes of similar size/type/cost

Real world, I don't live in a lab
A lot of it comes down to whether or not you're pushing any system towards its limits, that's when the differences start to become noticeable. A perfect example of this can be when comparing two CFF reflectors which are of the same quality and price; a 400mm F/20 Classical Cassegrain and a 400mm F/8 RC. The focal ratios themselves don't make any difference per se but when viewing planets there will be a significant difference in fine contrast due to the secondary mirror size differences and this will show up in the Strehl of the two systems.

The larger secondary (usually around 50%) on the RC drops the Strehl as it takes a lot of energy from the centroid and deposits it in the airy disk. Someone who is better familiar with the terminology can correct me but I think I got the terms correct

Another example would be with a 150mm F/5 achro, it could have a Strehl of .98 in green due to having a very smooth optical surface which would be confirmable with a green filter on planetary contrast BUT such a refractor would have a polychromatic Strehl of .5 making it terrible for planetary viewing without any kind of filter.
If you wanted to do some comparisons with the same size, focal ratio and kinda same price, compare this against a 150mm F/5 newtonian. It could have a Strehl of .92 (polychromatic or otherwise) and there is no way you cannot tell me that you wouldn't see a difference between those two
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Old 01-09-2019, 07:30 PM
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UPDATE: updated graph - see below. I've coaxed Excel into doing a quadratic least-squares fit instead of linear, and zoomed in on the region of most interest. FWIW the curves are automatic in Excel, not of my doing.

I was interested because previously from the Russian examples I had guessed a few rough approximations, as follows:

PV 0.30 (⅓ wavelength) ~ Strehl 0.90
PV 0.25 (ľ wavelength) ~ Strehl 0.94
PV 0.16 (1/6 wavelength) ~ Strehl 0.95
PV 0.12 (1/8 wavelength) ~ Strehl 0.98

Though it's only a rough correlation as pointed out before, eg a turned edge vs a central hump.

Last edited by Wavytone; 01-09-2019 at 08:06 PM.
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Old 02-09-2019, 05:51 AM
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Interesting Nick. It is clear to me that RMS gives a far more accurate indication of Strehl than PV, therefore any manufacturer that states PV yet ignores RMS should be perhaps avoided.

Thank you for your comments Jeremy but my question was specifically about RMS and PV in estimating Strehl - I did not ask about personal opinions about whether Strehl is useful or not, albeit your point of view is interesting
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Old 02-09-2019, 11:26 AM
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I've owned and used many 'scopes over the years: C8's, C9.25", C11, Questar 3.5, Questar 7, Meade 10SCT, Takahashi FSQ106, Takahashi FSQ85, AP130, AP130GTX, AP155EDF, AP 305RHA, AP92, GSO RC8, GSO RC10, William Optics 132, William Optics 80mm, William Optics 90mm, RCOS12.5, RCOS14, Alluna RC16 and Alluna RC20.

While it has only been in more recent times that I have been privy to the test data of these instruments....I can say without doubt the higher the Strehl value, the better the results I've seen or managed to achieve.

However, there is more to an imaging system than just the optical quality. Those optics need to be mechanically and thermally stable, and I've found without a rigid focus mechanism you are always chasing your tail, particularly with larger sensors, keeping the entire field in focus.

Strehl counts for naught if the mechanicals won't hold stable focus! Then there is the mount....(won't go there just now)

The good news is manufacturers than actually take the time to actually certify their optics (though some manufacturers, who will remain nameless, have proved to have zero cred, their certificates should have been issued on toilet paper) also tend to spend time making the other mechanical elements of an optical tube assembly worthy of their optics.

I have read with interest heroic accounts on IIS where users have literally re-built OTA's replacing all but the optics, yet still have residual problems, despite the optics likely having an acceptable Strehl.

So it is not all about the optics, but all things being equal there and getting back to the point at hand...does a high Strehl produce better images?

I think unequivocally yes. (taken to it's absurd conclusion, comparing 0.2 Strehl and 0.99 Strehl system, the results are black and white....it would be reasonable to assume there are shades of grey in between )

If a system is marginal and say has a Strehl of 0.8, then ANY seeing disturbance will drop the system below "diffraction limited" . A high quality system with say a Strehl of 0.98, can absorb significantly higher disturbances from seeing before it hits the diffraction limited stop.
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Old 02-09-2019, 04:07 PM
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Quote:
Originally Posted by Peter Ward View Post
I've owned and used many 'scopes over the years: C8's, C9.25", C11, Questar 3.5, Questar 7, Meade 10SCT, Takahashi FSQ106, Takahashi FSQ85, AP130, AP130GTX, AP155EDF, AP 305RHA, AP92, GSO RC8, GSO RC10, William Optics 132, William Optics 80mm, William Optics 90mm, RCOS12.5, RCOS14, Alluna RC16 and Alluna RC20.

While it has only been in more recent times that I have been privy to the test data of these instruments....I can say without doubt the higher the Strehl value, the better the results I've seen or managed to achieve.

However, there is more to an imaging system than just the optical quality. Those optics need to be mechanically and thermally stable, and I've found without a rigid focus mechanism you are always chasing your tail, particularly with larger sensors, keeping the entire field in focus.

Strehl counts for naught if the mechanicals won't hold stable focus! Then there is the mount....(won't go there just now)

The good news is manufacturers than actually take the time to actually certify their optics (though some manufacturers, who will remain nameless, have proved to have zero cred, their certificates should have been issued on toilet paper) also tend to spend time making the other mechanical elements of an optical tube assembly worthy of their optics.

I have read with interest heroic accounts on IIS where users have literally re-built OTA's replacing all but the optics, yet still have residual problems, despite the optics likely having an acceptable Strehl.

So it is not all about the optics, but all things being equal there and getting back to the point at hand...does a high Strehl produce better images?

I think unequivocally yes. (taken to it's absurd conclusion, comparing 0.2 Strehl and 0.99 Strehl system, the results are black and white....it would be reasonable to assume there are shades of grey in between )

If a system is marginal and say has a Strehl of 0.8, then ANY seeing disturbance will drop the system below "diffraction limited" . A high quality system with say a Strehl of 0.98, can absorb significantly higher disturbances from seeing before it hits the diffraction limited stop.

Spot on Peter.

Visual specialists for sure can tell the subtle differences between optics and splitting double stars etc, different shades and details on Saturn and Jupiter. Warm colours, neutral colours, false colour on the edges of the moon.

Imagers though are far more tough on optics. A highly precise and well designed optic stands out. It punches above its size in clarity and detail.
Stars are smaller and tighter, sharp details are able to be coaxed out. There are no spurious colours and rings around stars.

Visually a high end optic gives a wow factor at the eyepiece.

The most obvious difference with high end optics is whether the stars are round in the corners or not, whether there is false colour around the brighter stars and how sharp is the detail in the image.

I also totally agree with the need for high end mechanicals. This is where some earlier FSQ EDX models fell over. There were too many having issues with the focuser who used large heavy cameras, filter wheels and guiding gear. Luckily the ones I had were good.

A good Feathertouch focuser or AP focuser is the closest you can get to a guarantee you won't have these issues. Typically the cheaper scopes tend to have this as a weak spot although it seems to have improved a lot over the last several years as Chinese made scopes have improved and improved. Nice FPL 53 triplet optics have come down in price dramatically in the last several years. Also there is a supply of Canon Optron FPL53 triplets that make there way into several brands as well.



Greg.
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Old 03-09-2019, 05:00 AM
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Quote:
Originally Posted by Wavytone View Post
UPDATE: updated graph - see below. I've coaxed Excel into doing a quadratic least-squares fit instead of linear, and zoomed in on the region of most interest. FWIW the curves are automatic in Excel, not of my doing.

I was interested because previously from the Russian examples I had guessed a few rough approximations, as follows:

PV 0.30 (⅓ wavelength) ~ Strehl 0.90
PV 0.25 (ľ wavelength) ~ Strehl 0.94
PV 0.16 (1/6 wavelength) ~ Strehl 0.95
PV 0.12 (1/8 wavelength) ~ Strehl 0.98

Though it's only a rough correlation as pointed out before, eg a turned edge vs a central hump.
Nick, try using the commonly used approximation formula for Strehl, instead of doing linear fits or quadratic least-squares :

Strehl = 1 / (e^(2pi rms)^2

I donít think there is a simple equation for calculating Strehl from PV, but it will be similar to the one above when PV approaches RMS wavefront error.

Again, PV IMO should not be used in evaluating the quality of optics.

Example: two optical surfaces, one with PV 1/7 lambda, one with PV 1/10 lambda. Many would jump into a conclusion that the one with PV 1/10 must be better.

Your graph suggests that optical surface with PV 1/7 can have Strehl of 0.97, and perhaps even higher if the surface was perfectly smooth.

If the supposedly superior optical surface with PV 1/10 had a rougher polish and RMS wavefront = PV, then it could at the most reach Strehl of 0.67, if we utilise the commonly used formula above.

It does make perfect sense to me, since rougher polish will scatter light more (plus will cause more small scale interference and diffraction patterns).

To me it is clear, RMS wavefront gives a much more accurate indication of the quality of the optical surface, while PV alone can be misused by manufacturers who might be trying to hide rough polish.
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