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IMAGE QUALITY IN REFLECTING TELESCOPES
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Is it true that visually perfect diffraction limited images are formed by an optical system when all light rays entering
the system converge at the focal plane with a phase error of 0.250 wavelength of light or less? The popular astronomy
literature of today almost always states optical quality by one number, the peak-to-valley (PV) wavefront error. Can this
one number accurately describe the imaging potential of an optical system? According to the professional testing guide
book "Optical Shop Testing" the answer is no. The literature states, "The PV error must be regarded with some
skepticism because it is calculated from the worst two interferometric data points out of possible thousands, it might make
the system under test appear worse than it really is."
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What does this statement mean? A good example is: A 20" f 5.0 optic is analyzed via interferometry and the PV
wavefront error is determined to be 0.320. The Rayleigh Criterion states that diffraction limited optical performance
requires an optic to have a wavefront error of no more than 0.250. Accordingly, our test optic could not possibly
provide excellent image quality. However, when the test optic is placed in a telescope it passes all the imaging tests
including the star test with ease. How can this be? The areas of larger error on the optics' surface are very small and do
not degrade the over-all image quality.
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How then should optics be evaluated? To quote Optical Shop Testing again, "The RMS error is a statistic that is
calculated from all of the measured data and gives a better indication of the overall system performance..."
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To obtain the RMS wavefront error value, interferometric data points numbering in the thousands are measured
uniformly over the entire area of the wavefront, the errors are squared and averaged, then the square root is extracted.
In the example most of the wavefront deviates less than 0.320 and the RMS wavefront error is much smaller.
This is true in most cases. If the optic in the test example above had large and numerous errors the RMS and the PV
values will be similar and the optics performance in the telescope will be poor.
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Correlating PV and RMS is relatively straight forward. Generally, the RMS value is 4 to 6 times smaller in magnitude
than the PV value when the surface of the optic is smooth and suffers only from pure spherical aberration or very small
localized aberrations. This rule breaks down when zones and aberrations are large. Accordingly, an optic with a
wavefront error much worse than 0.250 PV can still be better than diffraction limited when quality is stated with the
more even-handed RMS value. The 20.0 f 5.0 optic in the example above is an excellent example of this having a RMS
wavefront value of 0.052. The literature states and physical tests prove that an optic with a RMS wavefront value of
0.076 or less is fully diffraction limited.
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