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MKV
Carpal Tunnel

Reged: 01/20/11

Re: Baker Reflector Corrector help [Re: Ajohn]
#5677550 - 02/13/13 11:57 AM

John, NVL are tri-dimentinal direction cosines. If you read Kingslake or Smith you'll know what they are and how they are used in raytracing calculations.

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MKV
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Reged: 01/20/11

Re: Baker Reflector Corrector help [Re: Mike I. Jones]

Mike, CODE-V has been used by professionals at least since the 1960.s. ATMs continued to use the old z = AY^2 + BY^4...ZY^n format. I am not sure the student freebie OSLO version can find the "pinch" point by REAY, but this can be "forced" by the choice of the vertex radius and subsequent optimization. And the vertex radius can be found in a variety of ways, algebraically, as well as by raytrace results (long. sph. abberation). This is how Wright calculated the "relative" strength of his corretcor (the term used by authors such as Rutten and van Venrooij, etc).

When you use a three-decimal slide rule or log tables, or freebie versions of raytrace programs, you have to devise ways of getting to the desired result in a roundabout way. Manual raytracce was a an absolute must in those days.

Thus, the way Wright looked at the solution was simply by knowing that his oblate spheroid had twice as much spherical aberration as an ordinary sphere of the same radius of curvature using the (1+e²) coefficient of SA, where e² is the positive oblate "conic" constant. His mirror was exactly the opposite figure of a paraboloid, so e² = +1. And knowing that, he could easily figure out the OPD-equivalent spherical mirror -- i.e. a spherical mirror of a given radius R that would produces the same amount of optical path difference as the oblate spheorid of raidus R'. And knowing that sp. aberration is a cubic function, he found R simply by diving the R' by the cube root of 2 or about 1.26, i.e. R = R'/(2^1/3). Another way of saying this is that for an f/4 Wright mirror you need to make a corrector as if making it for a spherical (Schmidt camera) mirror of f4, i.e. 4/1.26 or f/3.175 (~f/3.2).

This can easily be obtained also by the Schwartzchild expressions where the coeff. of sph. aberration G = b/8f³ or simply b/R³, where b is the cc and f is the focal lenght of the mirror. The OPD-equivalent mirror radius of curvature then is simply cube root(1/G).

And knowing that long. sph. aberr = G*f²*y², where y = aperture radius, you get the OPD-equivalent sphere of radius R and calcuate its correctcor from that, including the vertex radius which is ½A in the z = Ar^2 + Br^4... series.
It is the A coefficient in this case which takes into account the "pinch" point and will vary accordingly.

You're absolutely right about the 86.6% zones being overall better than the 70%. I believe the 70.71% was popular/preferred because it requires less glass removal and because its RMS/PV error is the smallest, even tough inconsequental.

Below are the results of three independent 200 mm f/3 Schmidt cameras. The first one has a vertex radius Rv = "0" (actually infinity), and the vertex curvature curvature Cv = 0), so the "neutral zone" (NZ) is at the center of the plate. The next one has the NZ at the 70.71% zone and the last at 86.6%.

Notice in the picture below ow this affects the deformation coefficients ever so slightly but significantly.

So, as far as John is concerned, the student version of OSLO works as long as you can apply the old fashioned manual raytracing and/or know the concepts involved. You get more sophisticated results in a roundabout way, which requires more than the basic entry level knowledge of optics.

And BTW, every new version of OSLO seems to have more restrictions. I still have a working copy of OSLO 5.4 LT (which was a freebie way back), and many of the functions that are now restricted in the EDU version are available in the 5.4 LT. The 5.4 LT can also handle up to 12 instead of 10 surfaces.

Cheers,

Edited by MKV (02/13/13 01:07 PM)

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Mike I. Jones
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Reged: 07/02/06

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Re: Baker Reflector Corrector help [Re: MKV]
#5677789 - 02/13/13 02:32 PM

Were you just using d,F,C wavelengths? Try really broadbanding it with the same scope, like 0.38µm, 0.58µm and 1.0µm, with different NZ's.

Also, the color spread at max field angle counts, too.
Mike

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Ajohn
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Reged: 12/03/07

Re: Baker Reflector Corrector help [Re: Mike I. Jones]
#5677910 - 02/13/13 03:56 PM

I'm nearly there with it Mike and as MKV and others say it's an amazing piece of software for free. The reason I used the term for a laugh is that I wouldn't expect a general purpose optimising routine to generate a perfect schmidt plate from a flat surface. There are several optimisation routines in oslo. Opic for instance seems to be very good for tidying things up. GENII can be directed to zones. :-) Or maybe it's the other way round. Then there are ray and aberration operands. It churns out Seidels etc. There is a lot there. My biggest problem with it is terminology such as what a specific term actually means on the glass. The macro language is rather basic C. Adequate and easy to learn. The commands it offers aren't so easy to learn though.

Basically I think it's a program largely aimed at keyboard use and probably flies when driven that way by some one who really does know what they are doing. I suspect their market share suffers because of that and it's appearance. Software is an area I really do know something about. Where it falls down in my opinion is certain aspects of convenience as software is supposed to help. I don't think that the documentation they provide with it is very good either but that is a common problem with technical software that is to be used by experts. That aspect can have a very distinct bearing on just how long it takes for some one to become an expert though. I'd guess that they sell with support. Common dodge to earn more money. I don't think that the examples they use cover the typical things that some one might want to do to a lens either as it's a bit like a design a schmidt on another site - "now set the sliders like this".

Baker used AY^2 ........ to 5 terms going on his papers that I have found so most probably worked the same way in the 1940's. I suspect the 70% zone relates to vacpans as it can't produce anything else. That's intuitive because it's hard to see how it could produce a neutral zone at a number of different positions and have a correct figure elsewhere.

The sag chart that I posted was chased down until oslo showed +/-5e-6 mm scale. The SA at that stage was S shaped and took up about 2/3 of the scale. Can't remember what the scale was before that one but it was very small and the change did improve all spots.

One thing for sure his reflector corrector is an amazing piece of work. I think I am beginning to get an idea how he balanced it all up - well at least a way that oslo can mostly cope with.

John
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wh48gs
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Re: Baker Reflector Corrector help [Re: Mike I. Jones]

Quote:

The "depth" of a figure-of-revolution surface like your aspheric plate varies only with radius.

The depth "z" of a curve can be expressed as

z = (cr²)/[1+SQR(1-(1+K)c²r²)] + Ar^4 + Br^6 + Cr^8 + Dr^10

The conic surface sagitta does not belong to the terms defining the Schmidt profile. The first term, which can be called the (corrector's vertex) radius term, is actually defocus term, which specifies how much of defocus is combined with spherical aberration at the paraxial focus. This goes to the very basics of the Schmidt profile, which is directly determined by the aberrated wavefront it is made to correct. It needs to produce a wavefront aberration that is identical in magnitude and shape but opposite in sign to the mirror aberration. Thus its shape is the shape of mirror aberration multiplied by the medium (light retardation) factor 1/(n'-n), n and n' being the refractive index of the incident and exit media.

Since the shape of wavefront deviation changes with the point of defocus, so does the Schmidt profile. Relative defocus L (from 0 at the paraxial to 2 at the marginal focus) is directly related to the relative height of the neutral zone N as L=2N^2. Best focus location for primary spherical is midway between the paraxial and marginal focus, thus with L=1 and N=(0.5)^0.5. Hence this is the Schmidt shape producing the smallest wavefront error in non-optimized wavelengths, thus lowest spherochromatism (it is also the easiest to make).

The complete profile is described as a sum of defocus term and as many spherical aberration terms as needed:

(2N^2*r^2*d^4)A4 + [(rd)^4]A4 + [(rd)^6]A6 + ....

where N is the neutral zone position, "r" the zonal height for semi-aperture normalized to 1, "d" the semi-aperture, A4=1/4(n'-1)R^3 the aberration parameter for primary spherical and A6=3/8(n'-n)R^5 the aberration term for secondary spherical, R being the mirror r.o.c.

Taking "d" as unit, and neglecting the A terms (which merely determine curve depth), Schmidt shape is proportional to the sum of

-2N^2*r^2 + r^4 + xr^6 +...

where the signs reflect the fact that the defocus error, as defined, is always opposite in sign to the spherical aberration error ("x" is the ratio in magnitudes secondary-to-primary spherical). This can be used to illustrate how these terms generate the final Schmidt profile. For the best Schmidt shape N=1, and the combined plot is proportional to (r^4-r^2). For the smallest blur, N=1.5 and the combined plot is proportional to (r^4-1.5r^2).

Note that the secondary spherical term is given for paraxial focus only, but it can also be used with its own defocus factor, which is generally preferable for fabrication (it also minimizes secondary spherochromatism, but that is negligible). All wavefront deviation shapes are exaggerated, and secondary spherical is exaggerated vs. primary.

All this said, in this particular design mirror has zero spherical aberration, and the corrector corrects spherical aberration of the field lens. Since this lens has weak curves, it is only its primary spherical that matters.

Vla

Edit: The primary s.a. aberration parameter A4 on the pic was incorrectly written as A6

Edit 2: the second plot from left (A4+a) was also mistakenly plotted as r^6, instead r^4. Sorry - just noticed that.

Edited by wh48gs (02/16/13 07:32 AM)

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Ajohn
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Re: Baker Reflector Corrector help [Re: Ajohn]
#5677928 - 02/13/13 04:07 PM

I'll tuck the meaning of that term away for future reference MKV. I'm not sure I want to know at the moment.

What I really do need to know is which of those figure relate to the position of the neutral zone and if at that point the corrector has zero power or a power generated by the base curve the figuring has been applied too.

I think I can see a way of establishing the correct base curve to keep the other refractive optics happy. If I then "schmidt it" I need to know if that power will still be there. He does point out that he makes use of the hump in the middle of a schmidt plate so it may have to be figured by hand anyway. He doesn't really give any other info apart from a list of sags.

Hope you can find time to answer for me.

John
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Mike I. Jones
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Re: Baker Reflector Corrector help [Re: Ajohn]
#5677940 - 02/13/13 04:14 PM

Simple question: Can't you adjust the NZ radius by the diameter of the support O-ring? If your O-ring is at the 70% diameter, then the vacuum will only have influence on the part of the plate within the 70% diameter. The larger the O-ring diameter, the more of the plate gets deformed by vacuum. That has to make sense. Now the question is, is the shape of the plate that springs back at 1 atmosphere after being ground and polished flat under vacuum anywhere near the right shape regardless of the O-ring diameter? Or does it only work when the O-ring is at or near the 70% diameter point?

Time to break out Roark's "Formulas for Stress and Strain" and wade through it, I guess. Just not enough hours in the day.

Mike

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MKV
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Reged: 01/20/11

Re: Baker Reflector Corrector help [Re: Mike I. Jones]

Quote:

Were you just using d,F,C wavelengths? Try really broadbanding it with the same scope, like 0.38µm, 0.58µm and 1.0µm, with different NZ's.

Also, the color spread at max field angle counts, too.
Mike

Mike I am not sure what the point is. My point was to show that 86.6% NZ corrector gives better correction, as you said, but the 70.71% may be easier to make.

Other than that, the camera performs well in the spectral range from 0.38 to 1.01 nm, optimized at 0.58, keeping in mind that Schmidt camera would require a field corrector/flattener that would be suitable for CCD imaging and that most of the surfaces in color were done using astronomical emulsion plates with specific filters and then combined.

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Ajohn
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Reged: 12/03/07

Re: Baker Reflector Corrector help [Re: Mike I. Jones]
#5678184 - 02/13/13 06:59 PM

I don't think so Mike. Depress the centre of a disc with a support in from the edge and the rim will be forced to turn upwards in a rather odd way due to tension in the circumference. I shudder to think about getting to grips with the math for that. Celestron and other do it by having a form tool and sucking all of the air out and then grinding the curve. It seems the chinese now do this to an accuracey that doesn't need figuring on the 2ndry mirror in a SCT anymore. When they started doing this though they stopped advertising 1/10 wave. With the new Edge they are back to figuring the 2ndry but those have a very high quality field.

As I understand it the plate is ground flat and then supported at the rim and sucked down to some depth at the centre. A tool has been prepared by grinding it to a calculated rad and that rad is then ground into the corrector. When it's released from the pan it springs back and has the correct form. Air under the blank isn't of much use it has to be an uncompressable liquid. There is a company in the UK who made a replacement SCT corrector for some one and I would have thought that they would be well aware of the methods of doing it. I cussed them because when they made the vacuum pan it was only for one rather large size of corrector. It could have been stepped in for other sizes.

I have hours in the day problem too. That prevents be going any more deeply into a subject than I need too. Age also makes new learning more difficult. In this case it's more of a question of just how best to get oslo edu to do the job and interpreting the output it gives.

One thought struck me on schmit plates. As Vla pointed out these are calculated on a unity basis in some respects. Given a "correct" plate it can be scaled. Unless some odd scaling is involved a "correct" plate could be scaled to a certain diameter on the basis of it's oslo parameters and the power could then be varied by multiplying the coefficients only by a constant. If the scaling which I do know works on them is as simple as that it's a viable method of sorting it out with the neutral zone anywhere. In fact it would appear that this could be done with a slider.

Once again though I need an answer to a very simple question - does oslo scale correctors that way.

The other question about the neutral zone concerns a possible method of using oslo to balance out the aberrations in the scope. I had a lot of trouble with the reduction in F ratio the design gives and a lot less trouble with one that hardly changes the F ratio of the mirror. If I am to go through it again properly I need that info.

John
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MKV
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Reged: 01/20/11

Re: Baker Reflector Corrector help [Re: Ajohn]
#5678254 - 02/13/13 07:55 PM

John, why not make a template out of aluminum the way Celestron makes the correctors? If I think there's much less of a chance for breakage and the blank is held over its entire surface rather than just at the edge. The sag would probably be no more than a couple of thousands deep. If I had to make a Schmidt corrector, I think I would go with that idea.

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Ajohn
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Re: Baker Reflector Corrector help [Re: MKV]
#5678762 - 02/14/13 04:28 AM

If you wanted to make a very precise form jig like that would you make it out of aluminium mkv? I don't know what Celestron use but I know what I would use and after I had made maybe a dozen corrector plates with it I suspect they could come out as accurately as needed. I could go out an buy a super precision cnc profiling machine I suppose which would reduce subsequent hand work they crop up on ebay all of the time.

John
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MKV
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Re: Baker Reflector Corrector help [Re: Ajohn]
#5678853 - 02/14/13 06:51 AM

Celestron developed the method way before the CNC machines. I imagine it could be made by the same way we grind optics, except using some sort of speculum (metal) material. Also, I don't think having a CNC shop generate one in a 220 mm size would be prohibitively costly.

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Ajohn
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Re: Baker Reflector Corrector help [Re: MKV]
#5678926 - 02/14/13 08:08 AM

I would look at using a rather large block of zerodor or something similar for production MKV. I believe there is one embryonic machining technique that might get to the sort of accuracy that is needed via an ion beam. As to profiling machines there have been a number of methods about for donkey's years that might meet long wave needs. Some ir optics are directly machined on super precision machines. I believe canon also produce a limited number of diffractive optics to the usual camera standard. It would be interesting to know how they do it. On the face of it apart from time and equipment it should be cheaper option but they tend to be rather expensive even if they are made in what might be nearly referred to as bulk quantities.

If suitable equipment is about it would be cheaper to get them to machine the corrector and a lot simpler. It might even work out at long IR.

John
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Ajohn
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Re: Baker Reflector Corrector help [Re: Ajohn]
#5680873 - 02/15/13 08:50 AM

Doh. It looks like schmidt's equation will scale due to the R^3 term based on the main mirror rad. This does have a finite set of solution in a way though so might prove useful. It could be used to establish a series of base curves where the neutral zone is where it's needed for interpolation. Oslo's constants don't seem to scale in any obvious way.

Problem though. In some respects it's not a schmidt plate as Vla pointed out. Worse still in some ways Baker seems to have put the "neutral zone" at 70% to minimise the amount of glass that has to be removed. In quotes as naughty me I assumed something. Mainly that it was desirable. The neutral zone in terms of the total sag zone doesn't seem to exist.

Looking at the figures more closely the aspheric depths from a rad don't have a neutral zone either other than if the power of the asphere overcomes the sphere. Might be possible with some other set of curves. At inch intervals they are
0.0,0.01,0.02,0.05,0.08,0.09,0.12,0.11,0.08,0.00
in thou's as they used to be called. The total sags show ever increasing depths indicating a sphere with a sag of 0.174 thou but he suggests starting from 0.2 so some of the form may project past the 0.174 sag rad. More likely margin for error on an analogue spherometer. These are for a 18in dia corrector. The scope has an 17in aperture corrector, 18in o/d. These needn't tie up as he expects the final figure to be put in by hand anyway. Basically it's a -ve asphere on a positive sphere. He also gives figures for a 40in corrector for an 100in FL mirror. The total sag does drop of near the outer rim of these figures from around a 15in zone height.

If the system is scaled for focal length first for a smaller faster mirror than he uses it's possible to finish up with a slight reduction in F ratio rather than an increase in speed. It's much easier to play with without getting severe astigmatism problems.

In days of old when knighst were bold and having plates coated was rather difficult it seems people put slight concaves on the none aspherised side of the corrector to avoid problems with reflections.

John
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Mike I. Jones
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Reged: 07/02/06

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Re: Baker Reflector Corrector help [Re: Ajohn]
#5681173 - 02/15/13 11:05 AM

Aspheric coefficient scaling is simple:

Let r = radius of the aspheric aperture
n = power,
Cn = nth order aspheric coefficient, and
S = the desired scale factor

A general aspheric deformation term is Cn (r^n). n can be both even and odd integers.

Scaling the system or particular aspheric surface by S scales the aspheric coefficient as

C'n = Cn * S^(1-n)

The scaling routine in OSLO should already do this properly. Have you tried using it?

Mike

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Ajohn
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Re: Baker Reflector Corrector help [Re: Mike I. Jones]
#5682861 - 02/16/13 05:57 AM

Thanks Mike. I did a quick check on what happens to the ^4 term and a scaling of 0.6 on the whole scope produced a 10:1 change. What I was getting at is the schmidt formulae is set be etc/4(n-1)R^3 so power can be changed by simply multiplying it by a factor as the R^3 term sets it. So if there is a spec of some shmidt corrector with the zone in the correct place it can be scaled to a power to suit other types and the zone will still be in correct place. A tedious way of getting round the edu problem as it could be used to narrow down the rad needed on the plate to get the neutral zone in the right place - assuming that the optimisation then does it's job correctly.

Scaling the ^4 powers etc would be even more tedious as olso wont scale the plates power on it's own. MKV has posted a plate design with the neutral zone in the correct place and in principle that could be scaled to suit any scope that needs one while keeping the neutral zone in the right place.

Mentioned as an aside really as I'm fairly sure the Baker doesn't use a schmidt type plate.

John
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wh48gs
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Re: Baker Reflector Corrector help [Re: MKV]
#5682896 - 02/16/13 07:28 AM

Quote:

My point was to show that 86.6% NZ corrector gives better correction, as you said, but the 70.71% may be easier to make.

The 0.707 zone is certainly easier to make, being less than half as deep as 0.866 zone profile. The profile dept is also directly proportional to the wavefront error of spherochromatism, so it also has less than half the spherochromatism. The only "advantage" of the 0.866 neutral zone is that it focuses at the smallest blur focus, thus produces the smallest geometric blur. Many sources (including Schroeder and Mahajan) state that it minimizes spherochromatism based on this criterion, but the criterion is flawed. We don't see the geometric blur, we see diffracted energy, and it is the wavefront error that determines its distribution.

It is easy to check: place neutral zone at either location and look at the wavefront error in the same unoptimized wavelength. The 0.866 zone will always have it more than twice larger.

Vla

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Mike I. Jones
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Re: Baker Reflector Corrector help [Re: wh48gs]
#5683014 - 02/16/13 09:17 AM

Vla, this is not consistent with (1) refereed, published articles and (2) my own analysis. I do respect your analytical abilities, though, so maybe this would be a good subject for a new thread, as this is sort of OT and buried too far down in this one.
Mike

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MKV
Carpal Tunnel

Reged: 01/20/11

Re: Baker Reflector Corrector help [Re: Mike I. Jones]

Quote:

Vla, this is not consistent with (1) refereed, published articles and (2) my own analysis. I do respect your analytical abilities, though, so maybe this would be a good subject for a new thread, as this is sort of OT and buried too far down in this one.

I posted comparative results three 200-mm f/3 Schmidt cameras and they show that the geometrical blur is the smallest with the NZ at 86.6%, but it also confirms Vla's assertion that the wavefront error and chromatic aberration will be the smallest at the 70.71% NZ location.

Is it significant (i.e. perceptible)? I think not, certainly not photographically or interferometrically. I think the PSFs make that perfectly clear. A thing to remember is that geometric raytrace analysis of the image blur (spot diagram) does not show accurate energy distribution because it neglects diffraction effects.

Edited by MKV (02/16/13 11:48 AM)

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Ajohn
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Re: Baker Reflector Corrector help [Re: MKV]
#5683510 - 02/16/13 01:13 PM

I take it those are axial MKV? If as Vla suggests the profiles are distinctly different they will have differing degrees of colour correction off axis.

I would guess that the 86.6% wins out in that respect.

John
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