Optical Performance of The Refractor

The concept of Strehl ratio as a measure of optical excellence

John D Timmins FRAS

For years the measure of the surface accuracy of a lens or mirror has been rather haphazard - 1/10 wave, peak to valley, RMS, Rayleigh Limit, Diffraction Limited ............... the list goes on.

It would appear that some manufactureres have hidden behind this confusion in an attempt to overstate the quality of their products and as ever, caveat emptor is the rule. More often than not, however, there is no intention to deceive, the problems being the misunderstanding of the metrology and misinterpretation of results.

Fortunately, there is a way of determining the relative optical performance of a lens or mirror but, as we shall see, there are always problems associated with absolute measurement, not only due to the variation in test equipment and procedural parameters but also the interpretation of results.

Several UK manufactureres address the issue of optical measurement in detail on their websites. In addition, some distributors and retailers, particularly in the US, discuss the relative merits of surface accuracy and the type of optical system - reflector vs refractor vs SCT, etc. These are well worth reading.

There are also discussions on these and related topics in a variety of publicationsand on many websites - more on this later.

One article that sums up the problem succinctly is " A Better Method of Measuring Optical Performance" by R.F.Royce, who is a well respected American optician renowned for very high quality optical design and manufacturing of mirrors and components for demanding military and industrial applications as well as astronomical use ( www.rfroyce.com/standards.htm ).

The subtitle of the paper is "Move over P-V and make way for Strehl". For those unfamiliar with the Strehl measurement, Royce summarises as follows:

"The significant advantage of the Strehl ratio is that it is a measure of optical excellence in terms of theoretical performance results, rather than an expression of the physical surface or the shape of the wavefront. It is a complete statement, in terms of a single number, that describes probably the most significant measure of an optic's performance. In very simple terms, the Strehl ratio is an expression of the amount of light contained within the Airy disk as a percentage of the theoretical maximum that would be contained within the disk with a perfect optical system. More correctly stated, it is the measure of the fractional drop in the peak of the Airy disk as a function of wavefront error. Strehl performance is usually expressed as a range of numbers from 1 to 0, more rarely from 100% to 0%. A perfect system is 1, a completely imperfect system is 0, and acceptable standards occur somewhere in between. So, if someone says you have a mirror that has a Strehl of .95 you understand that 95 percent of the theoretical maximum amount of light is going where it should go. And 5 percent of that light is going into the surrounding rings (mostly and most noticeably into the first order ring) and contributing to a reduction in contrast. It's as simple as that. This is a concept that can be easily understood by anyone once appropriate parameters have been set and is a completely honest and accurate representation of optical performance."

The "appropriate parameters" are significant. The Peak to Valley (P-V) criterion is flawed as it looks at only two points and ignores anything in between, and takes no account of surface roughness. The Root Mean Square (RMS) gives a statistical evaluation of many points over an optical surface. (Please refer to Royce's paper in full for a detailed explanation).

The resulting table will clarify these points:

Commonly Encountered Wavefront Relationships
P-V Fraction	P-V Decimal	Marechal RMS^*	Strehl Ratio	Comments
1/3	.333	.094	.71
1/4	.250	.071	.82	Rayleigh Limit
1/5	.200	.057	.88
1/6	.167	.047	.92	Good
1/7	.143	.041	.94	Very Good
1/8	.125	.036	.95	Excellent
1/9	.111	.032	.96	Excellent
1/10	.100	.028	.969	Excellent
1/11	.091	.026	.974
1/12	.083	.024	.978

* Derived from 1/4 wave, P-V of spherical aberration, wavefront equaling an RMS of 1/14.05 or .071

Measurement parameters

As previously stated, the actual methodology of measurement, variation in type of interferometer and calibration may produce a degree of variability in results such that a variation in Strehl figures may be obtained by different laboratories or practitioners. This problem is not unique to optical testing and is often a bugbear of researchers - I know this personally as a former industrial chemist involved in refined analytical techniques.

Indeed, John Nicholl of Nicholl Optical (a respected UK mirror maker) rightly reminded me that the tollerance of any measurement is critical - in other words the statement that a mirror has a Strehl measurement of 0.99 is meaningless if there is a ±0.02 tollerance as the optic may fall into a range of 0.97 to 1.01, the latter figure obviously not possible.

However, as Royce points out, "The Airy disk of an unobstructed objective will contain a maximum of 83.8% of the energy from that star entering the objective. The first order ring will contain 7.2% of the light, the second order ring 2.8%, and so on, diminishing monotonically with each successive ring. Usually only the first ring is clearly visible on a steady night. Basically, what it's all about is getting as much of the light into the Airy disk as is possible. Arguments arise about whether additional light in the first order ring aids in the separating of double stars, but for all practical purposes the more light in the Airy disk, the better off you are."

In other words, the higher the Strehl ratio, the better the optical performance. Unfortunately very few manufactureres give specific, rathere than generic, test data and even fewer offer interferometer test reports as standard. And that's not where the story ends, because various other factors affect the optical performance.

System Strehl

So, now we have a system of comparative measurement it is necessarry to look at other factors which come into play such as:

- Telescope design : central obstruction - secondary mirror(s), spiders

- Collimation : how many variables in the system

- Eyepices : correction, number of elements

And of course, atmospheric conditions and the visual acuity of the observer also play a very significant part. Do you need excellent optics, given the UK's weather quality? Most certainly yes.The eye/brain system is superb for picking out subtle detail during fleeting, often sub-second, moments of optimum seeing. By comparison, digital imaging employs averaging/stacking of images to create a composite so clearly optical quality is important.

Telescope design

Basically, you cannot beat the laws of physics. There are websites that claim the central obstruction in an SCT (or other reflecting system with large secondary) have little or no effect on image quality. Various sources show computer simulated images with varying percentages of central obstruction, some of which show superior images with fairly large obstructions.

However, a definitive analysis appears on the Telescope-Optics.net site (www.telescope-optics.net/obstruction.htm) . This looks at the effect of central obstruction on the Modular Transfer Function (MTF), the most widely used scientific method of describing optical performance. It is, as the name suggests, a measure of the transfer of modulation (or contrast) from the subject to the image. In other words, it measures how faithfully the optic reproduces (or transfers) detail from the object to the image produced by the lens or miror. The following table is derived :

OPTICS STREHL			1	0.95	0.90	0.85	0.80
MAX. C.OBSTRUCTION (ο) FOR PRESERVING 0.80 STREHL IN ABERRATION-FREE APERTURE	mid-to-low MTF frequencies	unadjusted	0.32	0.28	0.24	0.17	0
	mid-to-low MTF frequencies	adjusted	0.35	0.31	0.26	0.19	0
	entire range of MTF frequencies		0.45	0.40	0.33	0.24	0

This indicates that, for a 0.90 Strehl mirror, a 33% cental obstruction will reduce the system Strehl to 0.8 for the entire range of MTF frequencies.

It is also important to understand that the Strehl figure for each component needs to be taken into account, as the effects are cumulative. So, for example, a 0.9 Strehl primary mirror and 0.9 Strehl secondary results in a compound 0.81 Strehl system. Taking the cental obstruction into account, the system Strehl may be further reduced to, say, 0.71 - way below the Raleigh Limit and not diffraction limited.

This next table summarises the cumulative effect:

A comparison of the size of central obstruction found in different designs is revealing (secondary holders and spiders add to the problem and may introduce a smearing of the image):

Ritchey Cretian, Dall Kirkham, Schmidt Cassegrain, Schmidt Newtonian 30 - 45%

Newtonian 15 - 30%

Maksutov 14 - 30%

Refractors, Off -axis designs ( Herschellian, Schiefspiegeler, Yolo, etc) zero

This is why so many observers are disappointed when viewing high definition/fine detail objects such as planets, the Moon, double stars and small deep sky objects with fast Newtonians and SCTs and are amazed at the superb planetary images seen in refractors of modest aperture - many of the cheaper, mass produced Chinese achromats give Strehl ratios of 0.85 to 0.9 and and therefore comfortably outperform the off the shelf SCT system. The original Celestron 8, the Meade version and subsequent larger apertures and variants are all compromise systems which stray from the original Schmidt concept. Very good, portable and affordable telescopes they are but they are not optimised for high definition, critical observation whereas well made refractors are.

It is also obvious that slow Newtonians ( F8 to F10) and the Maksutov-Newtonians have very small central obstructions in the order of 14 to 20 % and provide very good image detail. Many reference articles state that a central obstruction of 15% or below is undiscernible and will give apochromat quality images. Indeed, it is argueable that a small obstruction may enhance the ability to separate close doubles and fine detail but small is the key here. JB Sidgewick recorded in his seminal treatise 'Amateur Astronomer's Handbook' that an aperture stop of one fifth to one sixth (20-16% approx.) may improve separation of close doubles, which is quite possible for point sources. Some websites use predictive programs to 'prove' the benefit of a central obstruction, but the size is the key - above 20%, the central obstruction wil always adversely affect resolution. An interesting and informative article appeared in 'Telescope Technology Today' volume 7 issue 6: Nov-Dec 2013, where it is demonstrated that 150-180mm apochromats gave comparable resolution to fast Newtonians of up to 750mm aperture when observing bar test targets. It should be noted that this article is not based on scientifically rigorous laboratory evaluation, also that resolution of extended objects (lines) is better than for point sources for all optics, but the comparison of telescope systems is basically valid.

(Note : reference to off-axis designs is for completeness - these are specialist designs with critical optical figuring and mechanical requirements.)

Just to refer back to measurement of Strehl for a moment, there are programmes that enable the user to measure optical performance by reference to star images taken through the telescope.An example is the Roddier Test and one site has compared a 9.25 inch SCT to Maksutovs and refractors for image quality, reporting the SCT as being "1/19th wave RMS and 0.90 Strehl". This effectively means that the mirror in this telescope has a Strehl of 1.0, improbable to say the least. As with all things, interpretation and rigorous technique is essential otherwise results are misleading.

Collimation

This is, of course, a critical element in all optical systems and the ability of a particuler design to maintain optimum alignment is a function of the optcal quality, mechanical tollerances and materials used in construction. Nearly every Newtonian I have used has exhibited some movement of the optics at varying tube orientation, and on transporting or set-up. Compounds also exhibit collimation problems.

It is true that even the budget manufacturers are starting to produce well designed OTAs but in many cases the engineering tollerances are slack - it is an unfortunate fact that even some of the so-called "hand made" telescopes produced in the UK and abroad fall in to this category.

It is also surprising that observers will spend a vast amount of money on a superbly stable and accurate mount to facilitate imaging and yet fail to appreciate the need for engineering competence in the OTA.

Despite the relative simplicity of design, refractors will exhibit flaws induced by inadequate materials and engineering. A well designed refractor will have a tube of substantial wall thickness to minimise flexure, particularly when long focal lengths and/or heavy triplet objectives are involved. It is reasonable to expect no flexure, irrespective of tube orientation, and provided that the objective lens is precision made with zero wedge (edge thickness variation) then in reality it is not even necessary to have a collimating cell. For example, axial run-out of 0.003 inches on a 6 inch lens amounts to 0.03 degrees of tilt, insignificant for an aplanatic lens. What is required is a precision machined cell and a completely squared tube end.

Eyepieces

This is a complex topic and I have yet to find two observers who totally agree on the merits of various types and brands. However, one criticism of refractors is often that the absorption due to the 2, 3 or more objective elements is severely detrimental to image brightness when compared to mirror systems - yet many of the premium oculars have 6 or more elements.

I think the choice of eyepice(s) is one of the more subjective areas of astronomy, but it is true that longer focal length achromats require less well corrected eyepieces and therefore fewer lens elements.

Another overlooked factor is that eyepieces will, of course, have a measurable Strehl ratio and further affect the tabulated figures above, but as far as the writer is aware no Strehl measurements for accessories are available.

Refractors - a summary

The optical performance of a well-made achromatic refractor may offer the best performance of any telescope type on many grounds. To summarise the above and related issues:

1. The lack of central obstruction yields the highest contrast possible and resolution of fine detail.

2. The closed tube of a refractor minimises temperature changes and resulting tube currents.

3. The relatively thin optical elements cool down faster than thick correctors or apochromatic triplets.

4. Once the objective has been squared-on to the optical axis, either in a fixed cell or a high quality push-pull cell, collimation is maintained and rarely - if ever - needs attention, even if the telescope is roughly handled during transport, etc.

5. The traditional achromat uses well established, stable glasses that are less susceptible to degradation over time than may be some of the more exotic glasses used in certain types of apochromat. This is evidenced by the large numbers of vintage and even antique refractors still in use, where the objective lenses have rarely been dissembled.

6. Longer focus achromats - over F10 - also have greater depth of focus, and are therefore less affected by wavefront changes caused by atmospheric turbulence.

7. An unobstructed system will outperform a compound system of significantly greater aperture - see the Choice of Aperture page.

8. Long focus Newtonians with small obstructions, preferably down to 15%, may yield equivalent performance to an unobstructed system but will still suffer from multiple light path passes through any tube currents and ,generally, collimation issues.

Of course, the main perceived drawback of the achromatic refractor is colour correction, but this is very much overstated. The rash of 6 inch short focus, bulk manufactured Chinese telescopes (F8 or shorter) do exhibit a certain amount of false colour, particularly on bright objects such as Venus or the Moon, and have given achromats bad press. However, when focal length is F10 or above and with the benefit of the latest optical design, materials and coatings, the effect is minimised. Indeed, Istar's unique R30 and R35 offer doublet designs with 30 and 35% reduction in chromatic aberration and image spot size.

The Strehl figure comes in here too - any colour separation will fall into diffraction rings surrounding the Airy disc, so the higher the Strehl then the better the colour correction.

In addition, field correctors offer certain advantages, particularly at shorter focal ratios - in essence, the corrector may be considered as part of a multi-element apochromatic design. An interesting example of this is the TAL 125 Apolar which has sub-diameter correctors, another is the Vixen NA140 SSF Neo Achromat with Petzval-type 4 element design.

For photographic or imaging purposes, it is highly desirable to have as short a focal ratio as possible, and this is where the apochromat comes in to it's own. It is no coincidence that the 80 to 120mm short-focus apochromat is the telescope of choice for many imagers.

Many observers will question the material presented here, but the proof of the system performance is clear when you talk to observers who have had the opportunity of using a refractor of even moderately good figure. I have discussedd the subject with many visual observers, including professional astronomers. The views of the late David Sinden, former Grubb Parsons optician, are appropriate. David told me that the cleanest, most detailed and highest contrast images he had ever seen were through two optical systems that satisfy the above system criteria - an Astro-Physics 7 inch Starfire triplet refractor and a Maksutov of his own design and construction with a 14% central obstruction. David had, of course, made and used some of the world's largest telescopes at the time and in later years had supplied commercial SCTs and Newtonians as well as his own products to amateurs. And Sir Patrick Moore on many occasions stated "Give me a refractor every time".

In addition, it is relevant to question the thinking behind the construction of large refractors in the late 19th century, such as the Yerkes 40inch (1897), when larger aperture modern style reflectors were technically possible (Ealing 60 inch - 1889, Mount Wilson 60 inch - 1908). The reflectors were, of course, designed to push the limits of the observable universe whereas refractors were preferred for detailed planetary work. To this day, the compound telescope suffers from the effects of secondary obstruction and the Hale 200 inch, Hubble and Isaac Newton 100 inch telescopes do not achieve system Strehls of 0.82 and are not therefore diffraction limited.

See here for more information about OPD diagrams.