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The optical performance of a telescope depends, of course, on the quality of its optical components. This webpage describes the different measures of optical quality, and how the optical quality of a telescope design can be calculated from the known quality of the individual components.

Now, the quality of the design and components does not tell the whole story. The ACTUAL overall quality will be degraded by any errors in manufacture or use (such as alignment errors, excessive play in moving parts, as well as user-errors such as incorrect collimation or focusing).

But the design calculation is still very useful, as it can establish a MAXIMUM quality for any given telescope design. For example, we shall learn how the typical 34% central obstuction of Schmidt-Cassegarin telescopes prevents their achieving the normally-accepted minimum standard of 1/4λ P-V (Strehl 0.82).


The optical performance of a telescope depends, of course, on the quality of its optical components. So, the more carefully and accurately a telescope's primary lens or mirror is made, the better will be the telescope's resolution (sharpness of images).

The illustration at right shows the (much magnified) image of a star, as would be seen in an imaginary "perfect" telescope. Due to the wave nature of light, even if our mirror/lens is perfect, and all the light is brought to a single focus point, the light will actually form a small disk surrounded by ever fainter rings (diffraction rings). This is the Airy disk and rings. The diffraction is caused by interference of light at the aperture of the telescope. In a perfect telescope (ie a telescope having no aberrations, and no central obstuction), 84% of the starlight goes to the central Airy disk and 16% to the rings. By the laws of light, it is impossible for more light to go into the central disk. The airy disk is perfect. So we set this as our 100% maximum. Our perfect telescope produces a perfect diffraction pattern of Airy disk and rings, is said to have a Strehl ratio = 1.


The ability of even a perfect telescope to split close double-stars (its resolution) will obviously be effected by diffraction. The effect of diffraction on telescope resolution was discovered in 1878. Lord Rayleigh calculated that the effect of diffraction puts a limit on the smallest detail (angular resolution) that we can see in any (unobstructed) telescope , however perfect. He calculated the limit at 138/D arc seconds, where D is aperture of telescope in mm. This is called the "Rayleigh Limit".

The formal Rayleigh Limit is close to the empirical resolution limit found earlier by the English astronomer W. R. Dawes who tested human observers on close binary stars of equal brightness.

No telescope can have resolution better than the Rayleigh/Dawes limit, so this has been used as a criterion for the optical quality of telescopes.


Now we have seen that our perfect telescope produces a perfect diffraction pattern with 84% of the starlight going to the central Airy disk and 16% to the rings. We would expect a less-than-perfect telescope to have aberrations which would disperse more light to the rings, and reduce the light going to the central Airy disk. So we would expect a less-than-perfect telescope to have poorer resolution than a perfect one.

Fortunately, this is not the case! A telescope does NOT have to be completely perfect in order to perform to the Rayleigh Limit. You do not need a perfect telescope (strehl=1). In fact, a telescope will perform to the Rayleigh limit, so long as its Strehl ratio is equal to, or greater than, 0.82. [In other words, light to the Airy disk is 82% of maximum possible].

So the minimum standard for high-quality optical performance can be stated in three, equivalent, ways.
"Rayleigh Limit", "diffraction limit", and "Strehl=0.82", all refer to this same level of optical performance. Please note that by "diffraction limit" we refer to the diffraction for a telescope without central obstruction.


While the most useful benchmark scale for optical quality is the Strehl Ratio, other optical benchmarks are in use. The most common of these is the Wavefront Error (de-formation error in the wavefront of light) measured as Peak-to-Valley (P-V) or Root-Mean-Square. The relationship between these benchmarks is set out in the table below.

Reading across the table below, you will see that the Rayleigh Limit (Strehl 0.82) is equivalent to a wavefront error of 1/4 wave Peak-to-valley (λ/4 P-V), 0.071 RMS. This is the standard of optical excellence that we require of our telescopes.

However, the matter is not without controversy, and more recently it has been suggested that at a strehl ratio of 0.87 (1/5 wave P-V), an optical system becomes "just noticeably" sharper (to experienced observers) than an optical system with a Strehl ratio of 0.80 or less.

Wavefront Relationships

RMS Strehl Comments
1/2 0.50 0.143 0.447  
1/3 0.33 0.095 0.699  
1/4 0.25 0.071 0.818 Rayleigh Limit (Diffraction Limit) Minimum standard for high Quality Optical Performance
1/5 0.20 0.057 0.879 Few commercial telescopes achieve this score
1/6 0.17 0.048 0.914
1/7 0.14 0.041 0.936
1/8 0.12 0.036 0.951
1/9 0.11 0.032 0.961
1/10 0.10 0.029 0.968
1/12 0.083 0.024 0.978  
1/14 0.071 0.020 0.984  
1/16 0.063 0.018 0.987  
1/18 0.056 0.016 0.990  
1/20 0.05 0.014 0.992  


The Strehl Ratio is a very useful measure of optical quality, because it enables the SR for the whole telescope system to be calculated from the SR of the individual components. You simply multiply together the Strehl ratios for the individual components.

Why do we need to do this? There is generally very little information available on the optical quality of telescopes. "Diffraction Limited", "1/8 wave optics" are typical terms used, but these invariably refer to the quality of the optics used in the manufacture, not to the performance of the telescope as a complete system. These are two different things - the overall optical quality of a telescope (assessed as a system) will always be less than the optical quality of its individual optical elements. The term "diffraction limited" is also used in a inconsistent way, making it difficult for the intending purchaser to compare different types of telescope.

The Strehl calculation will throw light on these difficulties and help to proper comparisons to be made.


Here, we take the example of a very high quality 200mm aperture F6 Newtonian mirror, made to 1/9 wave standards, strehl 0.96. The makers claim that with this mirror you can "enjoy image quality equal to apochromatic refractors".

But this statement overlooks the fact that a primary mirror is not the only element in a Newtonian telescope system. There are in fact three elements: the primary mirror, the secondary mirror, and the central obstruction of the secondary mirror holder. The strehl ratio calculation will show what is the true optical quality of the telescope AS A SYSTEM.

We have to take account of the central obstruction because it causes additional diffraction patterns, and thereby degrades the images somewhat. So that we can compare different telescope designs consistently, we won't re-define diffraction limit, because we want to make a valid comparision with the quality of unobstructed scopes (=rayleigh limit=strehl 0.82). We will therefore treat the central obstruction as an element within the optical design, with its own strehl ratio.

In our example Newtonian, the central obstruction is 50mm diameter, that's 25% of the aperture. We see from the table below that its strehl ratio is 0.90. That is to say, the central obstruction has the same effect on overall quality, as if we had introduced an additional optical element whose strehl=0.9.`

Strehl Factors for Central Obstructions

(as % of dia)
(as decimal)
0% 0.10 1.00
10% 0.10 0.98
15% 0.15 0.96
20% 0.20 0.93
25% 0.25 0.90
30% 0.30 0.85
33% 0.33 0.82
34% 0.34 0.81
35% 0.35 0.80
For Central obstructions, Strehl Number=1-(σ2/0.6), where σ is central obstruction as decimal of diameter
derived from

The Strehl Ratio (SR) of the whole system, ie both mirrors and central obstruction is then:-

SR(telescope system) = SR(main mirror) x SR(secondary mirror) x SR(central obstruction)

= 0.96 x 0.96 x 0.90

= 0.83

Thus, the telescope system just meets the diffraction limit (strehl 0.82, or 1/4 wave P-V).

So, although we used 1/9 wave optics (Strehl 0.96 - as assessed individually), we end up with a telescope (assessed as a system) which has just 1/4 wave P-V accuracy (Strehl 0.82). But, no real harm done, the telescope still delivers diffraction limited performance overall.


Here, we take the example of a 200mm aperture F10 SCT, with a 30% central obstruction, and 1/8 wave P-V optics.

Now there are four elements in the SCT telescope system: the front corrector plate, the primary mirror, the secondary mirror, and the central obstruction of the secondary mirror. From the table, the strehl ratio for 1/8 wave P-V optics is 0.951.

We see from the table above that the 30% central obstruction is equivalent to a strehl ratio of 0.85.
The Strehl Ratio (SR) of the whole system, ie corrector, both mirrors and central obstruction is then:-

SR(telescope system) = SR (corrector) x SR(main mirror) x SR(secondary mirror) x SR(central obstruction)

= 0.951 x 0.951 x 0.951 x 0.85

= 0.73

Thus, the telescope system has a strehl of just 0.73 when assessed as a whole system. The Wavefront table above show this is 1/3 wave P-V error, so less than the diffraction limit (0.82).

To actually achieve a Strehl ratio of 0.82, with a 30% central obstruction, we would have to start with 1/16 wave P-V optics (strehl 0.987): system strehl calculation becomes -

Strehl Ratio = 0.987 x 0.987 x 0.987 x 0.85

= 0.82

So, with a 30% central obstruction, the quality of the components would have to be very high indeed, with no errors of manufacture, to ensure the diffraction limit could be achieved.

This is also the conclusion of Rutten and van Venrooig in "Telescope Optics", who point out that -

"A 30% obstruction is as bad for image quality as a 1/4 wave error in the optical system .... This means that centrally obstuctive systems must be considerably more accurate than unobstructed systems to attain the same net performance. Rayleigh's 1/4 wave criterion, while perhaps adequate for an unobstructed system, is insufficient for telescopes with a central obstruction".


The latest commercial SCTs have typical 34% central obstructions. (The table above shows Strehl Ratio = 0.81 for 34% obstruction). If we assume that the quality of the optics is very high indeed, at 1/16 wave P-V (0.987 strehl), the system strehl becomes -

Strehl Ratio = 0.987 x 0.987 x 0.987 x 0.81

= 0.78

Just below the diffraction limit (0.82), but not significantly so. But the calculation does show that, in order for modern Schmidt-Cassegrain telescopes (34% central obstruction) to be Diffraction Limited overall, their individual optical components must be of exceptional, premium quality.


We have seen above that the large central obstruction in SCTs causes a reduction in the resolution (Strehl Ratio). We could say that the central obstruction reduces the resolution down to that of a smaller telescope without obstruction (a refractor, say). In fact, ignoring other factors, it has been shown that the reduction in resolution is proportional to the percentage linear obstruction. Thus an 9" SCT with a 33% obstruction by diameter, will have roughly the same resolution as a 6" refractor. That is not so bad. A good 6" refractor is a very expensive item, compared with a 9" SCT. But the comparison is a best case scenario - it assumes that the SCT optics are of the highest quality, as is the quality of manufacture.

Also, we must also bear in mind the light loss in an SCT, in comparison with a refractor. The central obstruction obstructs light, and in addition the SCT has two reflecting surfaces. Even with the best modern coatings, light is lost on reflection, and transmission through SCT's is about 85% at very best. These two factors reduce light transmission of the SCT by about 1/3 in aperture terms. Thus, you could say that a 9" SCT behaves, in terms both of resolution, and of light gathering, the same as a 6" refractor. But, I repeat, this is a best case scenario. The SCT is a complex optical system with various elements, moving parts, etc, and so has potential problems not experienced in the simpler design of the refractor.


The calculation of Strehl for a refractor is very simple. There is only one element, so provided it's aligned accurately, its strehl is the same as the system strehl.

Long focus achromatic strehl can be 0.97 Short focus as low as 0.67


First of all, (apart from long focus achromatic and apochromatic refractors) very few modern commercial telescopes achieve the higher limit of 1/5 wave (0.88 Strehl), when assessed as a full system. This may seem very surprising, given that you often see telescope mirrors described as 1/8 wave "surface accuracy" (0.95 strehl).


So, what lessons do we learn from all this? When looking at telescope specs, be aware that the Strehl ratio for the Telescope System will always be less than the strehl ratio of the main mirror or lens. When you see a telescope advertised as "diffraction limited optics", its important to know whether the system as a whole is diffraction limited, or just the main optic on its own. Too often, advertisers quote the quality of the main optic only, as if that were the whole story.

Another example of misleading advertising is when you see a Newtonian telescope adverised as "1/8 wave surface accuracy". Most people would think that description is better than "1/4 wave wavefront accuracy", but in fact the two descriptions are just the same. Moreover, the term "1/8 wave surface accuracy" obviously refers to the main mirror only. As we have seen, the whole telescope system accuracy will be much lower.

Another "trick" used by some advertisers is to quote the wavefront accuracy in Root-Mean-Square (RMS) terms, rather than Peak-to-Valley (P-V). 1/4 wave P-V is exactly the same as 1/14 wave RMS. To the unknowing, the RMS value seems better and so can be misleading.

And finally, it is very common now for manufacturers of SCTs to quote the Rayleigh/Dawes limit (unobstructed telescopes) in the Specification for their SCTs, thereby ignoring the effects of the central obstruction on image quality. Please also note that manufacturers' Ray Tracing Spot Diagrams do not normally take account of the effects of diffraction caused by the central obstruction.


By this we mean the build quality of the telescopes and its optical components. For example, how precisely has the main mirror or objective been figured, and how accurately the optical components are aligned, positioned, and how free from mechanical deformation. These qualities can only be known by testing (or reading test reports).


However, there are inherent optical errors (aberrations) which are inherent in any optical element, lens, mirror, etc. Knowledge of these aberrations can help assess the optical quality of a system, even if the optical quality measures (eg strehl ratios) are unknown. These aberrations; Chromatic Aberration, Spherical Aberration, and Coma are described here.

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