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telescopeѲptics.net .......................................................................................... CONTENTS
6.5. MTF 3: Aberration compounding, MTF limitationsExpressing the combined effect of two or more aberrations through the MTF can be done, similarly as for the wavefront aberrations, either precisely, through a complex calculation, or as a single number extracted from statistically averaged probability (approximation). As the above graphs show, difference in the effect on performance of various aberrations with a similar RMS wavefront error level becomes more significant as the nominal error increases. For two or more aberrations combined, the effect is, on average, greater than either single aberration components alone. However, they do not add up arithmetically. For relatively small, unrelated or random wavefront errors, the combined effect is given by the square root of the individual errors squared, or ωc= (Sωi2)1/2 (57) with ωi being the individual RMS wavefront error. Similarly, the combined effect on peak intensity of the PSF (Strehl) and, thus, average MTF contrast loss can be, for mostly unrelated smaller aberrations, closely approximated as the product of individual Strehl ratios for any number i of different aberrations, Strehl being, in fact, an MTF (contrast) degradation factor: Sc= S1S2 ... Si (58) The product Sc is a combined Strehl (the peak diffraction intensity ratio) for the errors included; it also expresses the average MTF contrast level in units of the average contrast level of a perfect aperture. The conventional minimum acceptable level of optical quality - so called diffraction-limited standard - is 1/4 wave P-V wavefront error of spherical aberration or, in more universal form, the associated 1/13.4 wave RMS (0.80 Strehl). That corresponds to 0.42 wave P-V of coma, 0.37 wave P-V of astigmatism, and so on. This criterion is not strict - it is a somewhat lose dividing line between good and bad optics. In fact, since it is, in the commercial environment, habitually applied to the quality level inherent to optical surfaces alone, it is safe to assume that the actual quality minimum is lower, perhaps significantly. In addition to induced aberrations considered earlier, as well as chromatism, one of the factors lowering optical quality in addition to that determined by the wavefront aberration level alone is the effect of central obstruction. Finally, a word about limitations of the standardized MTF in projecting its results to the actual observing. One comes from the standardized MTF being strictly exact only for the object used: parallel, contrasty, brightly illuminated dark and bright lines. For different types of objects, both contrast transfer and cutoff frequency (limiting resolution) will deviate. Also, the MTF assumes continuous spread of energy; in other words, every line interacts with all the energy reaching it from both, left and right. Actual observing objects are finite, and the absence of continuous spread results in the outer areas being subjected to less of overlapping energy that the MTF assumes. It is particularly pronounced with small, or narrow objects (FIG. 47).
FIGURE 47: LEFT: Typical continuous MTF pattern exposes every single point to all the energy from all surrounding points that extends to it (gray circles). All lines between A and B will contribute energy spread out by diffraction and aberrations to the mid point marked by the cross. RIGHT: Relatively small ( with respect to the width of diffraction/aberrated pattern) object image can have significant portion of the energy lost to the Airy disc spread out of the its area (C), with comparatively less of the scattered energy affecting points within the image. It would result in less of an effect for given aberration level. The consequence is better contrast transfer and resolution than what the MTF (thus, also PSF and the Strehl) would indicate, even for an object identical to the standardized MTF pattern. Specifics of this effect vary with the object type, as well as type and level of present aberrations.
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6.5. Effects of aberrations: MTF 2
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7. OBSTRUCTION EFFECTS
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