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▪ CONTENTS
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13.6. Eye chromatism
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13.8. Eye intensity
response
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13.7. COMBINED EYE
ABERRATIONS, DIFFRACTION
In any optical system, the effect of wavefront aberrations -
either those induced by the eye itself, by the optical train of a
telescope, or externally - is adding
to the effect of diffraction in
further spreading out the energy making up the point-image. Eye is not
an exception. At small pupil sizes, eye diffraction is the main
determinant of image quality; at large pupil sizes, that role belongs to
eye aberrations, and at intermediate pupil sizes, both diffraction and
aberrations are significant factors.
Not surprisingly, studies give different indications of the maximum
average pupil size at which the eye is still diffraction-limited (0.80
Strehl, or better). The range spans from 1.22mm diameter, or as low as
0.76mm when tilt is excluded (Thibos et al. 2002), to 2.8mm (Howland and
Howland, 1977). Prevailing view is that the average eye remains
diffraction limited up to about 2mm pupil diameter, after which its
exponentially increasing aberrations cause the Strehl to plummet (FIG.
236A). However, the perceived image quality is much less affected
than the average nominal Strehl, primarily due to the low effective
magnification of the eye (in other words, angular size of either
dominant diffraction pattern, or dominant aberrated pattern, remain
below detection threshold of the eye).
Size of the geometric aberrated blur (i.e. ray spot size) also varies
with the eye model used.
There is a number of optical models of the
eye, from the simplest one by Emsley (1946), with a single
refracting surface on a water-like
medium (1.333 refractive index), to a complex system proposed by Liou and Brennan in 1997,
incorporating aspheric surfaces and varying refractive indici (the
latter is most closely resembling biological eye, and reproducing its
aberrations). The plot is based on eye model with physical dimensions of
the average eye, constructed to produce its type and level of foveal
aberrations. Specs given in table below (surrounding medium for the
cornea and lens is water; their dispersive properties are obtained by
scaling up those for water approximately corresponding to the change in
e-line refractive index). CORNEA LENS R1/aspheric Thickness/n/V R2/aspheric R1/aspheric
Thickness/n/V R2/aspheric Tilt Decenter 7.8mm 0.5mm 6.5mm 10.2mm 3.6mm -6mm 2° 0.2mm R=radius of
curvature; n=F/e/C refractive index; V=F/e/C
Abbe number; *conic;
**toric curvature
As presented previously, both monochromatic and chromatic foveal
aberrations are nominally significant at medium to large eye pupils.
Their combined and separate effects are best illustrated on MTF graph (FIG.
236B). Same goes for monochromatic aberrations - which are usually
the primary concern - and their dependence on the pupil size (FIG.
166C,D). The actual size of diffraction pattern, either nearly
aberration-free (at small pupil sizes) or heavily aberrated (at large
pupil sizes), does not change much going from small to large pupil sizes
- certainly much less than the nominal Strehl, or the RMS wavefront
error value (FIG. 236E).
FIGURE 236: (A) Generalized
scheme of the respective magnitudes of aberration-free
(diffraction-limited) and average real (i.e. aberrated) eye, on axis.
Geometric blur size and RMS wavefront error have nearly identical rate
of change, thus both scales apply to the same plot. With all eye
aberrations included, diffraction dominates for pupil diameters smaller than ~2mm, and for
larger pupils eye aberrations. Geometric size of point-image blur - as
aberrated ray spot blur, or diffraction blur conventionally represented
by the Airy disc - is smallest at ~2mm pupil diameter. For larger
pupils, it is enlarged due to eye aberrations, and for smaller pupils
due to diffraction. With defocus corrected, which applies to the
telescopic eye, eye is diffraction limited for pupils diameters smaller
than ~3.5mm. Relative magnitude of higher-order aberrations increases
with the pupil size, becoming comparable to the defocus-corrected eye
(i.e. plagued only by primary astigmatism) at about 7mm pupil diameter.
Eye aberrations lower object-to-image
contrast transfer, hence the perceived image quality and resolution
limit. Actual effect on image quality, however, depends not only on the
wavefront error, but also on the retinal image size (magnification). An
aberrated image has to be large enough, angularly, to allow the eye to
detect the aberration. Average eye begins to recognize image shape, as its
size exceeds ~3 arc minutes. Any detail below that size appears
point-like to the eye. Consequently, in order for the eye to discern the
effect of wavefront aberrations in the retinal image - whether an
extended detail or a point-object image - has to be larger than ~3 arc
minutes.
That is why the edge-field coma in an ƒ/6 paraboloid is so
inconspicuous; at 15mm off-axis, with the coma wavefront error at 2.5
waves P-V (0.45 wave RMS), the sagittal blur size produced by a 25mm
eyepiece is still only 3.6 arc minutes on the retina. It takes the blur
size of ~5 arc minutes in diameter for the average eye to clearly
recognize that it is not point-like; in this case, it would take ~ƒ/5 paraboloid.
Considering that the astigmatism of standard eyepieces usually adds
significantly to the blur size that far off axis, 5 arc minutes blur
size is probably still borderline between inconspicuous and obvious
level of aberrations for the average observer.
The required minimum spot size for shape
recognition is greater for less contrasty details, as well as for those
that fall in the low-sensitivity range of eye photoreceptor cells, cones
and rods.
A glance at FIG. 236E reveals that despite its very high nominal
aberrations, the aberrated diffraction blur of the average eye is still
significantly smaller than 5 arc minutes for pupils smaller than about
5mm in diameter, thus with relatively small effect on the perceived
image quality. The exception is eye defocus error (assumed corrected in
the patterns shown), which is typically by far the largest eye
aberration. It often very noticeably degrades quality of the visual
image; fortunately, it does not affect the telescope user.
In addition to eye aberrations, other important factors determining
properties of the image formed by the eye are its spectral response, intensity response, and contrast sensitivity.
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13.6. Eye chromatism
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13.8. Eye intensity response
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