All interferometric results are obtained on a Michelson interferometer in which the reflected light from a high-precision reference optic interferes with the light of the test piece. Thus deviations from the ideal shape of the specimen can be measured.
The final evaluation of each finished optics consists of an interferometric measurement series. I document this in detail, store it and enclose a CD with the delivered optics. Everybody, even people without extensive prior experience can track my measurements.
What makes a measurement consistent and reliable? Is there ever a measurement result, which is absolutely flawless? I would like to answer these questions best possible at least for my measurements and their evaluations with the following article.
Error analysis
In measurement technology, it is standard to describe random and systematic measurement errors, so this also belongs to each interferometric analysis. An absolute measurement value, if possible with many decimal places, might be much more pleasant for the customer and the result appears to have a particularly high precision. In reality, however, every measurement contains errors, whether the measurement of the length of your kitchen table, the determination of the weight of an apple using scales, and even the experimental determination of the speed of light.
Some sources of errors of optical measurements, especially random measurement errors due to seeing influences or deflection of the measuring set-up at large thin mirrors, are hardly to quantify accurately. Nevertheless, it is always desirable to minimize these measurement errors which are never completely avoidable in the final analysis. This requires experience, a well-engineered measurement set-up (and measurement execution), and if possible further cross-checks with different measuring devices.
Experience
Over the years and after viewing thousands of interferograms, a sense for failures is nurtured which helps to identify and weed out incorrect interferograms. Repeatedly, a series of interferograms might show outliers, mostly caused by exceptionally strong, short-term air turbulence between specimen and interferometer. Or entire series must be repeated, since, for example, the mirror support was minimal unfavorable in test set-up. Both, the correct use of the analysis and the interpretation of the results depend on experience.
Measurement set-up and execution
The larger and thinner the optics, the more important is a reliable test set-up for reproducible individual measurements, which allows a complete description of all errors. Particularly regarding the evaluation of the mirror's astigmatism a correctly equipped and precisely constructed test set-up decides whether incidental bends allow or obscure the representation of an existing astigmatism.
In the past there were two practices in use of how too strong and uncontrolled bending during a measurement in the later evaluation was treated: Either a poor result caused by external influences was accepted in the final evaluation, or, assuming the measured astigmatism was entirely due to external influences, the astigmatism was technically deactivated. But in both cases, the result of measurement is at least incomplete and at worst even grossly flawed. For this reason, the quality of the measurement hinges on well-engineered measurement techniques and conscientious implementation through which astigmatism caused by external influences can be effectively suppressed.
Today and with the technical advancements in recent years, well-engineered test set-ups can be realized to such an extent that even ambitious projects can be measured completely, including all possible surface defects. So measurement protocols made up with contemporary methods reveal a profound state of the mirror - astigmatism and other errors are no longer neglected in good measurement performances.
Random errors caused by air turbulence can be largely avoided by measurements in an insulated tunnel. The still remaining errors caused by turbulence can then be suppressed up to insignificance by averaging many interferograms. I use to average 25 to 35 interferograms even for the evaluation of smaller optics, to effectively suppress random errors due to seeing influences.
Other criteria, such as clean interferograms with as few distorting artifacts as possible or the elimination of the astigmatism caused by the test set-up by averaging many interferograms from several angles of rotation of the specimen, are of course also part of a good implementation.
I consider all above mentioned activities for an implementation of a convincing measure as the standard for many years and take them into account in any final evaluation. The result is a significant increase in certainty for the representation of the state of each optics.
Cross-check
Up to this point I went into random errors such as deflection of the measuring set-up or uncertainties emerging during observation. Besides these random errors, there are as well systematic errors – mistakes that occur in every measurement in the same amount. Examples for this kind of error are an incorrect determination of the focal length and of the diameter of the specimen. The “faster” the optics, the more precisely you have to determine both values.
The interferometer’s ever-present deviations from the ideal are among the systematic measurement errors as well. This may originate from an insufficiently accurate reference surface, to which the specimen is compared. Or the validator assumes an incorrect test wavelength for the interferometric evaluation. As well may the astigmatism of the measuring equipment itself count as systematic measurement error, if it is not measured exactly on the optical axis (as practiced with the Bath interferometer). Several other systematic errors are also conceivable.
I only succeed to prove or exclude these systematic measurement errors by using an independent cross-check of my test set-up. Although past cross-checks were carried out with a convincing agreement, a truly sound comparison was only accomplished with the commission of the Company Wellenform. Independently, Wellenform and I measured the same mirror with the greatest care. We wanted to compare the results of two measurement set-ups that were distinctly different.
As a result, the height of the Strehl value is of less importance. Rather noteworthy is that both measurement results are close together. My measurements yielded a Strehl of 0.97, Wellenform determined the Strehl value to 0.99.
You can download the complete certificate of Wellenform here.
And this is the result of my analysis:
Within the limits of unavoidable tolerances one can speak of a good matching of our surveys. Thus I was able to show that gross systematic measurement errors of my test set-up are improbable.
What does this mean for you as a customer?
I perform every final analysis of finished optics with high diligence. The years of experience in the production and analysis of optical systems are as indispensable as a well-engineered, reliable measuring set-up.
I seek transparency, so you may know where my results come from. This means that I carry out comparison measurements, which show that independent examiners with other test set-ups achieve matching results in the evaluation of my optics within the limits of tolerance. Finally, this includes that my measurement is provided together with the delivered optics, so that the customer can track my results. Every single measurement can be clearly assigned to the particular optics.