When Good Numbers Don’t Tell the Whole Story
Over the years, we have examined a number of primary mirrors manufactured by various well-known companies and accompanied by certificates that show excellent optical figures. In many cases, the owners contacted us for a simple reason: the actual performance of the telescope did not match the expectations created by the published test results.
Most often, these mirrors had been tested using the Foucault test with a Couder mask, with the measurements analyzed using FigureXP. This approach has been widely used by amateur telescope makers and commercial mirror manufacturers for decades and, when properly performed, provides valuable information about the correction of a mirror from a sphere to a paraboloid.
The problem is that many amateurs interpret the Strehl ratio, RMS error, and Peak-to-Valley (PV) values calculated by FigureXP as a complete description of the optical surface quality. In reality, these values are derived from a limited set of measurements taken along a single profile of the mirror. They primarily describe how closely the measured profile follows the desired paraboloidal shape and provide valuable information about the mirror’s rotationally symmetric correction. However, they do not represent a full two-dimensional analysis of the entire optical surface.
A number of optical defects can remain partially or completely hidden when using this type of measurement. These defects include astigmatism, localized zones, surface irregularities, and other errors that can significantly affect image quality while remaining poorly represented by the one-dimensional profile used in the analysis.
In this article, we present a real-world case involving a large telescope mirror submitted to us for independent evaluation. The mirror arrived with a certificate showing excellent numerical results. However, a full-aperture interferometric analysis revealed a significant discrepancy between the published figures and the actual optical performance. We will follow the mirror through the entire process, from the initial evaluation, through refiguring, to the final corrected surface, and discuss why different testing methods can produce dramatically different assessments of the same mirror.
The manufacturer is well known within the amateur telescope community. However, the purpose of this article is not to evaluate a specific company but to illustrate the differences between profile-based and full-aperture optical testing methods. For that reason, the manufacturer is not identified and we will not publish the original certificate. Instead, we will reproduce the results in the same format generated by FigureXP.
The manufacturer’s reported values were:
• Optical diameter: D = 598 mm
• Radius of curvature: ROC = 4732 mm
• Strehl ratio: 0.979
• RMS error: 6.4 nm
• Peak-to-Valley: 1/12 wave
( Note: The original FigureXP report expresses RMS error in nanometers, while the interferometric analysis presented later in this article expresses RMS in waves.Results are shown in the original units reported by each analysis method. )
These are excellent numbers. If one considers only the reported values, without taking into account how they were obtained, it would be reasonable to conclude that the mirror is of exceptionally high quality.
The owner of the mirror is a lunar and planetary imager who became increasingly dissatisfied with its real-world performance. The telescope consistently failed to produce results comparable to those obtained with his smaller instruments. He provided us with his own Foucault measurements, as well as a series of star tests, and asked for our opinion.
The star tests clearly indicated the presence of astigmatism. After rotating the mirror by 90 degrees in its cell and observing that the astigmatism rotated with it, the source was confirmed to be the primary mirror itself.
The owner then decided to send the mirror to us for a complete interferometric evaluation, with the understanding that refiguring would be performed if the test confirmed our concerns.
Initial Evaluation
After receiving the mirror, we measured both the optical diameter and the radius of curvature.
A preliminary Foucault examination revealed a slight turned edge. The effective optical diameter had been reduced to D = 591 mm by a very large bevel around the edge. The measured radius of curvature was ROC = 4700 mm, differing noticeably from the published value.
A complete interferometric analysis was then performed. The mirror was measured in eight rotational orientations, spaced 45 degrees apart. Sixteen interferograms were acquired at each orientation and the results averaged in order to minimize the influence of the support structure.
The measurements revealed a significant amount of astigmatism, approximately 0.316 waves, which dominated the optical error budget and severely degraded image quality.
Results:
• Strehl ratio: 0.305
• RMS wavefront error: 0.173 waves
• Peak-to-Valley: 1/1.6 waves
The discrepancy between the interferometric results and the original Foucault-derived values is immediately apparent.
This difference exists because interferometry analyzes the entire optical surface using hundreds of thousands of measurement points, whereas a traditional Foucault analysis derives its conclusions from a small number of zones sampled along a single profile.
An interesting observation is that the synthetic star test generated from the interferometric data closely matched the actual star test images obtained by the owner.
DFTFringe also allows the user to isolate individual aberration terms. By removing non-axisymmetric aberrations and retaining only the rotationally symmetric components of the surface, it is possible to approximately simulate the type of information provided by traditional Foucault analysis.
The result was striking:
Strehl ratio: 0.974
This value is remarkably close to the original reported Strehl ratio of 0.979. The agreement suggests that the original Foucault analysis accurately described the mirror’s rotationally symmetric correction, while failing to reveal the significant astigmatism that dominated the overall optical performance.
This demonstrates that the mirror was reasonably well corrected in terms of its rotationally symmetric figure, but suffered from significant astigmatism that was not reflected in the original reported figures.
Refiguring Process
Having confirmed through both star testing and interferometric analysis that the mirror suffered from significant optical defects, we proceeded with refiguring.
The first step was to polish the mirror back toward a sphere.
This serves two purposes:
1. To remove the existing correction and return the overall correction factor to zero.
2. To eliminate astigmatism and restore rotational symmetry to the surface.
Only after obtaining a rotationally symmetric surface can accurate paraboloidal correction begin.
After approximately six hours of polishing, the mirror had been returned to a reasonably spherical state.
The critical question, however, was what had happened to the astigmatism.
Interferometric testing revealed the answer.
The surface had become noticeably smoother. The astigmatism had rotated slightly but retained nearly the same magnitude.
Astigmatism reduction was performed with appropriate strokes. A further half-hour of corrective polishing was performed, followed by another interferometric measurement.
This process was repeated eight times. Each cycle consisted of selectively reducing astigmatism, smoothing the surface, and verifying the result interferometrically.
After the ninth session, the mirror had reached a condition suitable for final paraboloid generation.
Parabolization
The final figuring process was performed using CNC-controlled figuring.
Based on the current surface shape and the correction percentage in each zone, an appropriate figuring pattern was selected and applied.
After each figuring session, the mirror was measured interferometrically and the resulting surface analyzed.
This cycle was repeated many times until the mirror reached full correction.
Play the video below.
Final Result
The completed mirror achieved the following values:
• Strehl ratio: 0.979
• RMS wavefront error: 0.023 waves
• Peak-to-Valley: 1/12.5 waves
When comparing before-and-after wavefronts, it is important to remember that most software automatically scales color maps between the minimum and maximum values in each dataset.
As a result, two surfaces may appear visually similar even though the magnitude of their errors differs dramatically.
The following images show the original and corrected surfaces using the same scale.
Conclusion
The purpose of this article is not to question the usefulness of the Foucault test or software such as FigureXP. Both have played an important role in telescope mirror making for decades and remain valuable tools when their capabilities and limitations are properly understood.
What is important is recognizing what these methods actually measure. The Strehl, RMS, and PV values derived from traditional Foucault measurements primarily describe the accuracy of the mirror’s rotationally symmetric correction. They provide only limited information about non-axisymmetric errors such as astigmatism and therefore cannot fully characterize the entire optical surface.
Interferometric testing operates on a fundamentally different principle. By analyzing the full aperture, it can detect astigmatism, localized surface defects, and other aberrations that may significantly affect image quality but remain hidden in profile-based measurements.
The case presented here demonstrates how important it is to interpret optical test data correctly. Excellent numerical values alone do not guarantee excellent optical performance if the testing method cannot fully characterize the entire surface.
Ultimately, the final judge is the image formed under the night sky. To predict and reproduce that performance reliably, one must use a measurement technique capable of describing the entire optical surface rather than only a small portion of it.
Yordan Stoykov
Owner&CEO
AstroReflect Ltd