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6.3. Aberrations and object type   ▐    6.4. Diffraction pattern and aberrations

6.3.2. Effect of telescope aberrations on the extended object image

Turning to extended objects, there is again the main distinction between faint and bright, on one hand, and contrasty and low-contrast objects on the other, with all intermediate scenarios possible. In general, most faint extended objects (nebulae, galaxies) are also of low contrast, while bright extended objects are either of high, or low contrast.

The Sun and the Moon are two well known bright contrasty extended objects. The Sun is in the category of its own, with every square arc second on its surface being nearly as bright as -11 magnitude star; even through D5 filter (w/glass optical density cutting light transmission down by a factor of 1/105), each square arc second of its surface is still brighter than a 2nd magnitude star. The Moon, without filter, comes to little fainter than a 3rd magnitude star per each square arc second of its surface. Thus, both of these objects are, diffraction-wise, at the level of bright stellar objects, with one important exception: most of the details on their surfaces are of lower, or much lower contrast than those of bright stars against sky background (with the average sky background being ~24 magnitudes dark, the difference in intensity vs. bright stars is over 20 magnitudes, or over 100 million times). Hence, it is to expect that the minimum angular size required by the eye to start recognizing a detail as extended (vs. point-like) is somewhat larger here. Assuming arbitrarily that it is roughly two times as large as for bright stars, leads to a minimum magnification that will start showing the effect of aberrations/diffraction at roughly double that for bright stars.

Another difference is that with further magnification increase, image quality will deteriorate at a faster pace. Main reason for this is that higher magnifications will expose the greater damage done by aberrations to the smaller detail substructure, making the image as a whole less well defined. It can be illustrated with simulations of the effect of the changes in PSF caused by optical aberrations on image quality in general, and resolution of low contrast detail in particular.

Low-contrast extended objects are the category most resistant to the negative effect of aberrations. They are just to faint to allow the eye to detect contrast changes nearly as efficient as with bright details. While nominally contrast does change just as much as in bright details, it is not likely to be seen. For instance, even relatively bright object as Orion nebula (M42), with integrated magnitude of 3.7, has an average brightness per square arc second of nearly 10th magnitude - not a subject to much of a change in appearance due to the effect of aberrations in most amateur telescopes, regardless of magnification. What has more of an effect is the background brightness in a telescope; hence dark skies, good baffling and low surface scatter are more of a factor for this kind of observing than the effect of aberrations - up to a certain level.

Finally, telescopic images of bright low-contrast objects, most notable being planetary surfaces, are also affected differently by optical aberrations. Their surfaces are not as bright - Jupiter, for instance, shines as if having a 6th magnitude star in each square arc second of its surface - which lowers their aberration sensitivity. However, it is more than offset with their other feature: low detail contrast. While it also has a good side, which is the larger minimum angular size required for the eye to start recognizing extended shapes and, therefore, higher magnification needed to begin noticing the effect of aberrations than with stellar and bright contrasty extended objects, that is where the benefit ends. Once the low contrast details are visible to the eye, so is the effect of aberrations, and it is greater than for bright contrasty extended details. Main reason for it is that low-contrast details have, as their very name implies, less of a contrast left. Consequently, with any given relative contrast loss due to the aberrations, the low contrast detail is being shifted closer to the resolution/detection threshold - or below it.

This can be illustrated with eye CSF (contrast sensitivity function) graph (FIG. 93). It implies that the eye is,

FIGURE 93: Limit to resolution of MTF-like line pattern on the retina is determined by eye contrast sensitivity. The level of sensitivity is highest in photopic mode (approximate average shown in yellow), somewhat lower in mesopic mode (green) and the lowest in scotopic mode (pink). The average planetary vision mode is within mesopic, as opposed to lunar vision mode, which is at a higher, scotopic level. At the same time, average planetary detail contrast level is lower than that of the average lunar detail. The contrast sensitivity graph also shows an additional factor of resolution limit, related to the angular size of a detail on the retina. In the scotopic vision mode, maximum contrast sensitivity is for ~8 cycles per degree (~7.5 arc minutes width of line pair). In the average mesopic mode it is ~5 cycles per degree (~12 arc minutes), and in the average scotopic mode between 2 and 1 cycles per degree (~0.5 to 1 degree). Differences in contrast sensitivity for mid-to-large detail sizes are relatively small within photopic and mesopic mode - contrast sensitivity, up to 3%-4% (they plummet as detail size goes below 20 cycles per degree, i.e. 3 arc minutes), and larger in the scotopic mode, ~10%. Note that contrast sensitivity levels shown, achieved under laboratory conditions, are higher than those practically achievable in field conditions. However, the main proportions remain in place.

under optimum conditions, capable of detecting an astoundingly low level of contrast difference. For contrasty, bright lines, it is nearly as low as 0.5%. In other words, as little of contrast differential is sufficient do detect the lines of the optimum size. It would imply that as little as 1% change in the absolute contrast level could noticeably - although still very slightly - affect image quality, as perceived by the eye. That would be comparable to the level of aberration indicated by ~0.99 Strehl, 1% reduction in aperture size, or the effect of D/15 linear central obstruction. In field conditions, this small changes in contrast cannot be detected at the eyepiece. For instance, nominal contrast difference between the two maximas and the minima between two stars at the Dawes' limit is still as high as ~4%. There are several factor that could be causing this discrepancy.

One is the ever present seeing error. Even if it is as small as 1/30 wave RMS, on the average - and only the smallest apertures in a very good seeing have that privilege - it already lowers the average contrast by ~4%, with constant fluctuations around the mean value. Contrast difference as small as 0.5%, already at the very limit of detection, is likely to be lost in such conditions. Also, contrast difference resulting in the loss of this threshold resolution may not be, and probably is not, apparent to the eye as a contrast level change per se. In addition, there are very few details that would be found, or lost - even if this level of change in contrast could be detected. Lastly, it is likely that eye strain resulting from peering into the eyepiece significantly worsens eye sensitivity thresholds in general.

It is generally accepted that the loss of contrast smaller than ~5% (~0.95 Strehl, or higher) is either insignificant, or undetectable in field conditions. Due to the generally lower magnitude of seeing error, small apertures are generally somewhat more sensitive to their optics error than large apertures, so this figure should be sort of informal average.

To some, generally limited extent, the effect of aberrations on image quality can be illustrated with simulations based on the aberrated PSF. Below are shown such simulations for a few different extended object types: planetary surfaces, generally considered bright of low contrast, lunar and solar surface, bright oh high contrast, and a nebula, generally a dim, low contrast object (simulations generated by Aberrator, Cor Berrevoets). Attempt was made to have the apparent image sizes correspond, at least roughly, to their usual apparent size in the actual observing (if observed from 15-inch distance, Jupiter appears as in a telescope magnifying about 300 times - when it is at its average angular size - and so do Mars and Saturn; the lunar crater in a telescope magnifying about 450 times, solar spots, depending on their actual size, anywhere between 100 and 600 times, and the nebula nearly 100 times magnification).

The top row shows object itself, or its perfect image, without aberrations and the effect of diffraction. Below is aberration-free image of that object with the effect of diffraction alone. Since it does smear a point image into diffraction pattern, it does act just like an aberration, softening definition and lowering contrast and resolution. The next row shows images with the effect of λ/4 wave P-V of spherical aberration added. The effect is generally small, but noticeable, further lowering the contrast and causing some details close to resolution threshold to become undetectable. That is, expectedly, more pronounced when the aberration level is increased to 0.35λ P-V That is also comparable to adding the equivalent of λ/4 of seeing error to λ/4 of spherical aberrations, with the two, being unrelated form-wise adding up as a square root of their squared numerical values.

The simulations indicate that these levels of aberrations noticeably lower the definition for all object types, even the dim low contrast ones. The latter is one of the limitations of such simulations, which does not take into account the eye, and the change in its performance level with - in this case - significant change in object brightness. Due to the shift toward scotopic mode, and rods dominance when observing dim objects like nebulae in most amateur size apertures, resolution threshold deteriorates significantly. Adding it to the simulation would entirely take out the smallest structures, and make the image less sensitive to the effect of aberrations.

Also, the screen image, due to the relatively large size of the pixel, may be coarse in comparison to the actual image, with the finest details already lost, making the effect of aberrations, especially small aberrations, less noticeable. On the other hand, simulation also cannot reproduce the contrast level between dark spot on a very bright surface - such as the case with sun spots - and may show more of the contrast/resolution loss than in the actual observing. There are also other limitations to the accuracy of simulations.

Follows more details on how various wavefront aberrations affect diffraction pattern.

6.3. Aberrations and object type   ▐    6.4. Diffraction pattern and aberrations

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