Optical Quality - What does it really mean?

As a mirror maker I'm often asked just what the differences are between common, low cost mirrors and a premium optical surface. There is certainly a large price difference. Add to that the confusing array terms and methods used to claim accuracy and you have a very thick soup indeed. The purpose of this article is to try and clarify just what defines a premium optical surface, why they cost as much as they do and why, in the final analysis, they are worth having.

A Little Theory

The goal of any telescope is to produce an image at the focal plan with the highest possible contrast and resolution. Contrast and resolution, while related, are really two separate qualities. Resolution is set by optical theory and is limited by the size of the aperture. Contrast is a measure of how well the optical system preserves the tonal qualities of the actual object being imaged or observed.

One common term that's seen again and again is "diffraction limited". This is a term that's often used to describe optical performance. while the term doesn't really have a solid scientific definition it is most commonly used to describe an optical system that's accurate enough to meet the Rayleigh Criterion, or a wavefront at the focus the deviates from the ideal by no more 1/4 wavelength. If you're imaging a star and the seeing is perfect this will result in the smallest possible airy disk at focus. No matter how much better you make the optics the diffraction pattern will not get any smaller. This fact could lead you to believe that 1/4 wave optics are really as good as anyone needs. After all, why go beyond that when you're already at the diffraction limit?

Contrast

While the relationship of the geometric qualities of the diffraction pattern are easy to understand in terms of gross resolution, the effect of contrast, while important, isn't as obvious. The best way to think about contrast is to imagine the optical system as a filter that reduces contrast from what would be seen if there was nothing between you and the object of interest. It's sort of like looking through a dirty window. The better the optical system is (the cleaner the window) the lower the contrast losses are from reality. We are all familiar with the contrast loss caused by secondary obstructions. This is obvious to anyone who's compared images between a refractor and a reflector of the same apature. Contrast loss through surface defects on the optics have the same result. In 1/4 wave optical systems these effects do not change the gross geometry of the diffraction pattern but they do effect the ratio of light that goes into the central airy disk verses the diffraction rings. As optics get better the airy disk doesn't shrink but the amount of light in the surrounding diffraction ring system decreases while the amount of light going into the airy disk increases. This is demonstrated in the synthetic diffraction pattern images below. The pattern on the left is from a prefect system with a 20% obstruction. The pattern on the right is from a 20% obstructed system with a 1/4 wavefront error. The difference in the brightness of the first diffraction ring is obvious. Also note that this is with an otherwise perfect surface with no edge defects or surface roughness, something we'll touch on later.

Since the image of any extended object is made up of an infinite number of overlapping diffraction patterns, the net effect of changing the ratio of the light going into the airy disk verses the rings is to change the overall contrast of the image. If the overall contrast of a system is low, low contrast detail will be lost to view even if the system is diffraction limited. In other words, putting the light in the right place does no good if there's not enough contrast to define the detail of interest. Once you reach the diffraction limited plateau it's contrast that drives visibility of detail.

A Sea of Numbers

There are many ways that the accuracy of an optical surface can be defined. The most commonly seen are surface ratings in fractions of a wavelength expressed as RMS or PV along with Strehl ratios. These are useful values but it's important to understand what they really define and more importantly, what they don't. Important point number one is that RMS and PV are completely different calculations resulting in very different numbers. RMS stands for root mean square and is a statistical measure of the departure of the surface from the ideal shape. PV stands for peak to valley and is simply the distance in wavelengths from the lowest point of the surface to the highest. Because these are calculated differently they result in very different rating numbers. For example, a mirror that's 1/10 wave PV would be 1/35 wave if expressed as RMS. Just to make things even more confusing you have be clear if the rating is being given for the surface or for the wavefront. Because we're dealing with reflective optics the light rays have to traverse the surface errors twice. This doubles the requirement for the surface to reach any given wavefront rating. In other words, to deliver a 1/4 wavefront the mirror's surface must be accurate to 1/8 wave.

Another thing to be wary of regarding P/V measurements is that it's only valid for a smooth surface. As an example, imagine a 12" mirror that has a perfect surface except for a 1/4" diam. hole that's 1/4 wave deep. Because P/V doesn't take into account the extent of the defect it will give a wave rating for this surface of 1/2 on the wavefront even though the mirror is nearly perfect!

Because of this confusion strehl ratio has become a popular way to rate mirrors. Rather then describing he accuracy of the surface the Strehl ratio simply describes the result in terms of the amount of light going into the airy disk verses that going into the rings. This follows very close to what we've just discussed regarding contrast so it's a very easy to understand number. A mirror with a strehl ratio of 95 obviously will deliver a higher contrast image then one with a ratio of 86.

Another useful number that just starting to see a lot of use is RTA or Relative Transverse Error. This is a ray tracing result and as such it ignores diffraction effects. Simply put it's the size of the focus spot relative to the airy disk that the mirror would produce if diffraction did not exist. As such it's a very useful measure of the accuracy of the surface.

To give you a starting point with which to compare numbers a reasonably smooth 1/4 wavefront mirror has a PV rating of 1/8 wave, an RMS rating of 1/14 wave and a strehl ratio of 0.82

The Great Unknowns

While the numbers discussed above give you a feel for the overall quality of a surface they don't tell the whole story. There are two important qualities that a mirror must have for the above ratings to be truly valid and that's edge condition and surface smoothness. It's possible to test a mirror and get a high strehl and PV rating but if the edge is bad and the surface has a lot of small scale roughness it will not perform nearly as well as the numbers suggest.

Edge problems are almost universal in the professional optics industry and is probably the most common optical defect one will find. It is formed when the curve on the glass suddenly turns up or down from the ideal right at the edge of the surface, most commonly down. The effect tends to be narrow so it often escapes popular test methods yet it is very damaging to overall performance. Here's the effect on the diffraction pattern of a perfect 20% obstructed mirror with an 5mm wide edge that's turned down a total of 1 wave, not an unusual condition.

As the pattern on the right shows, the effect on the diffraction pattern is disastrous. The only choice if you have a mirror with this defect is to reduce the aperture by masking the bad edge. The reason bad edges are so common is that they often are created by standard mirror making techniques and require extra time and care to eliminate before figuring can begin. If it appears during figuring then the optician usually has to go back to the start to correct it. Both options require time and care to execute which is why it is so often left undone. If you ever see a mirror with a very wide bevel on the edge, it was probably put there as an easy way to cure a bad edge.

Surface roughness is less obvious in it's effects. When talking about surface roughness I'm describing medium and small scale roughness which is often described as "orange peel", "dog biscuit" or "micro ripple". Unless this is extreme it won't totally kill the performance of a mirror in the way that a bad turned edge can. What it will do is prevent a mirror from reaching the performance level that the rating numbers suggest. Its main effect, like so many defects is on contrast. All the little slope errors are throwing light where it shouldn't go. Taken together it can make a significant impact in the final image. Also of importance is the smoothness of the surface on very small scales. This micro-roughness can be impossible to see with standard testing methods but can also have an impact in overall image contrast. It takes a lot of extra polishing time to create a smooth microsurface with a very low pit count.

One other defect to watch for that isn't covered by the standard ratings is astigmatism. This is more commonly found in thin mirrors that are not properly supported but it can also be a defect that's on the surface. Instead of being a true figure of revolution the surface has different focal lengths along different diameters. Think of the surface of a potato chip and you'll have a gross idea of what the defect is. Like turned edge this can also be a killer defect if present in significant amounts. The following graphics shows the effect of 1/4 wave of astigmatism on an otherwise perfect 20% obstructed aperture.

It All Adds Up

In the real world of optical surfaces we usually don't see isolated defects but rather combinations of many defects of varying degree. In the next example we compare a perfect 20% obstructed system with an low cost 6" F/8 commercial mirror that was recently tested in our shop. The test example had approximately 10% worth of zonal correction error with a narrow turned edge and a rather rough surface.

Surprisingly, if you look at the zonal test data alone which ignores the edge and surface roughness you would think you had a 1/15 wavefront mirror. Obviously that's not the case here when all errors are taken into account. This points up the importance of proper application of test data. An experienced optician using the Ronchi test or looking at the full surface under the knife edge would know at a glance that although the zonal test numbers are within limits, the overall surface is far from acceptable. This mirror might be diffraction limited (just) but would deliver very low contrast images. The slightest seeing distortion would drop the resolution drastically as the central disk merges with the very bright first ring.

All this brings up the concept of headroom. I'm often asked why anyone would need a mirror corrected to say 1/20 on the wavefront when 1/8th is clearly good enough. The answer is of course that the primary doesn't exist in a vacuum but is part of a system that includes not only other surfaces and mechanical issues but the atmosphere as well. In the Newtonian, the secondary mirror, support vanes and other optical elements such as barlows, oculars, and filters all have an impact on the final wavefront, usually negative. In addition there are issues of structure and support. Anyone who has laid out a complex primary mount in Plop knows how important proper support is. However, to even come close to the predicted results the mount needs to be fabricated to a precision that few ATMs actually meet and plop doesn't address edge support issues at all.

Then there are thermal issues. Even with a fully cooled mirror there's always a boundary layer of air that is slightly warmer then ambient that also effects the wavefront. Of course, the biggest thermal issue of all is the seeing. The brighter the first diffraction ring is the faster it will merge with the airy disk in conditions of poor seeing. In short, systems that can deliver a highly corrected wavefront to the focal plan are much more resilient to bad seeing and deliver much better images under average conditions when compared to lower strehl ratio systems.

Lastly there is testing error. There is a zone of uncertainty with any optical test and different tests can give different results. When you take all of the above together, it's easy to see why highly corrected primary mirrors really are necessary. In order to assure good system performance the primary mirror must be considerably better then one might think.