13. THE TELESCOPIC EYE
The light passing through the telescope objective and eyepiece is focused onto retina by the optics of the eye, after which it is neurally processed into the visual image. Hence it is the optical media of the eye - cornea, crystalline lens, and aqueous fluid filling the eye - that determine the final shape of the wavefront reaching retinal photoreceptors. Being bio-engineered, eye optics is far from high standards of a quality telescope. However, due to its small aperture and low magnification, significant aberrations generated by it generally do not have much of an effect on the perceived image quality. The two exceptions are eye defocus error - which is effectively corrected by appropriately defocusing the eyepiece, thus inconsequential for the telescope user - and, to a smaller extent, eye astigmatism.
Placing eye at the eyepiece end of a telescope changes its optical parameters. This change is significant enough to justify establishing a specific term for this particular mode of operation: the telescopic eye. The most important change is that its aperture stop is now the eyepiece exit pupil, not the iris. This not only directly determines the level of eye aberrations due to its effective aperture, but also may induce additional aberrations resulting from displaced stop. In addition, unlike the "unarmed" eye, which observes objects directly, the telescopic eye observes diffracted image of these objects. In general, the consequences of it are not significant, but should be addressed nevertheless.
Neural response and processing of light signals in the eye varies significantly with their intensity and wavelength, making it an important subject for the telescope user.
In evaluating the properties of telescopic eye, the starting point is, unavoidably, optical properties of the eye alone.
13.1. The human eye: Physical properties, transmittance and acuity
The entire purpose of a visual telescope is to gather light from distant objects and to enlarge the incoming light angles, so that these objects appear brighter, larger and more detailed to the eye. Added benefit of the larger aperture of a telescope is lessening limitations to image quality imposed by diffraction. Since the light passes through both, telescope system and the eye, optical properties of the latter can affect the final image created by the brain.
Being an optical element itself, the eye is, just as the telescope objective, subjected to the effects of diffraction of light and wavefront aberrations. Physical and optical properties of human eye vary individually, often significantly; those presented here are based on experimentally determined averages (FIG. 216).
Retinal arc extends ~32mm through the central meridian. Outer retinal area of relatively low sensitivity to daylight surrounds the yellowish oval spot of ~4mm (nearly 15°) in diameter, centered at ~3.4mm (nearly 12°) from the optical axis of the eye, called macula, which converges toward fovea, the highest daylight sensitivity area. From the outskirts of macula outwards, roughly 20° wide, extends the ring-shaped area of the highest sensitivity to low-intensity light.
Eye light transmittance is relatively high in the 500nm-700nm range (and beyond, into infrared), but falling off quickly toward the blue/violet end of the spectrum (FIG. 217).
217: (A) Range of eye spectral transmittance, based on several
small-scale studies. The results indicate wide individual
differences, although it could also result from small sample sizes (four
to nine individuals in four separate studies) and/or differences in
procedures. It is unclear whether eye transmittance - specifically
its preference for mid- and longer wavelengths within the visual
spectrum - has been factored out from the eye spectral response (sensitivity)
curve. If not,
it would superficially lower
sensitivity of the eye in the blue/violet relative to that in the green and red for
both, cones and rods. Since the relative change in transmittance
over the range of wavelengths doesn't seem to vary significantly
with the transmission level, it shouldn't affect individual
perception of chromatism. Variations in eye transmittance would mainly
affect perceived brightness, with the difference between high and low
transmission level being close to one magnitude, roughly evenly across
the visible spectrum (possible exception is that some individuals
may have the ability to sense wavelengths well below 400nm, and some not).
Eye photoreceptors cells, cones and rods, form the light-sensing lining of the retina. We need them to sense light, just as we need nerve endings in the skin to sense touch. They range in size from ~2μ to over 10μ, in general becoming larger toward the outer area of the retina, the cones more so than the rods. Dominant retinal photoreceptors at medium-to-small pupil sizes (daylight and indoor light conditions) are the cones, while at large pupil sizes (in low-light conditions) the dominant photoreceptors are the rods. The two differ significantly in, among other properties, their respective resolution limits. Eye resolution level is termed acuity. It varies over the retina, depending on the receptor type and size. It is also a function of the illumination level (FIG. 218).
The area of highest cone acuity coincides with the area of their highest density and smallest individual size - foveola. Area of the highest rode acuity is just outside the macula, in the ring roughly centered at the fovea, some 10° to 15° in radius.
Highest acuity level doesn't coincide with the highest image quality, in terms of contrast level. For the naked eye, retinal images are of the highest quality at a pupil diameter of ~2mm (which means in bright-light conditions with the cones dominant), when the combined effect of aberrations and diffraction is at its lowest. In regard to point-image resolution, it is better at ~4mm pupil size (in dim light conditions), with the cones still sufficiently active, diffraction disc is half the size of the disc at 2mm pupil, and the aberration level of ~0.15 wave RMS still doesn't significantly affect the size of central diffraction disc, thus neither resolution of near-equal intensity point sources. However, for most other detail forms, resolution is inferior to that at 2mm pupil size.
Retinal resolution shown at left applies to the naked eye, which forms its own point-source diffraction image. For the telescopic eye, there is no point sources, since it images (through the eyepiece) the Airy disc formed by the objective. Hence, given aberration level of the objective, it is the level of eye aberrations that determines image quality which, in general, favors smaller eyepiece exit pupil (this, in turn, favors smaller apertures, with smaller exit pupil for given nominal magnification). However, this effect is, after a certain level, outweighed by the negative effects of higher magnifications.
13.2. EYE AT THE TELESCOPE END
At the telescope end, eye plays a dual role; it is an optical element and a photo-detector. Eye optics preceding retinal photoreceptors determines quality of the image formed at the receptors, while size and photo-sensitivity of the receptors, combined with the modes of neural processing of their input, determine perceived quality of his image.
Optical part of the eye, consisting of the cornea, eye lens and aqueous fluid, is a simple 2-element system. Expectedly, it generates significant aberrations, on- and off-axis. Eye off-axis aberrations are generally irrelevant, since fixation onto selected object by eye movements brings that object onto the visual axis, with its image falling onto fovea. Image quality in the outer field quickly decreases, but it is inconsequential since the field of high acuity is narrow, and both increasing size and pooled circuitry of the outer retinal receptors farther from central retina - as opposed to individual circuitry of foveal receptors - actually set acuity limit for the outer field, rather than its inherent aberration level.
On-axis eye aberration, on the other hand, have disproportionally small effect on perceived image quality. That is mainly the consequence of low effective magnification (i.e. small size of the Airy disc on retina) of the image formed by eye. However, the magnitude of eye aberrations - in particular, defocus and (central) astigmatism - is commonly large enough to noticeably degrade image quality in daily life. Luckily, telescope users are given two important breaks: eye defocus error is effectively corrected by the offsetting error in focusing the eyepiece, and effective eye pupil (determined by the exit pupil of eyepiece) at higher magnifications is small, exponentially lowering eye aberration level.
Placed behind telescope eyepiece, eye is looking at the image formed by objective that is magnified by the eyepiece. The corresponding optical scheme is different than for the eye looking at an object directly (FIG. 219).
Since the image formed by the objective is subjected to its diffraction, any point in it is replaced by diffraction pattern formed by the objective. For 0.55μ wavelength, angular size of the Airy disc formed by the objective is 4.6/D in arc minutes, for aperture diameter D in mm. The same relation applies to the eye, if D is replaced by the effective eye aperture E. If eye is looking at the image of the objective directly, E is much smaller than D, and diffraction disc formed by the objective is always effectively a point-source for the eye. Through the eyepiece, effective aperture of the eye equals the exit pupil of the eyepiece, or E=fEP/F, where F is the telescope focal ratio. The corresponding angular Airy disc size is 4.6F/fEP. This is larger than Airy disc of the objective 4.6/D by a factor of f/fEP, where f is the telescope focal length. Since this is the ratio defining telescope magnification, the magnified angular diffraction pattern of the objective, subtended at infinity in the eyepiece, equals angular diffraction pattern of the telescopic eye.
As illustrated on the FIG. 219 B, bottom, this
implies that every point of the diffraction pattern imaged by the eye is
replaced by eye's own diffraction pattern of identical angular size. In
practice, any single point of the imaged diffraction pattern in the
eyepiece is too weak to produce a perceptible central maxima on the
retina. As is generally the case with extended objects, only a cluster
of point sources, with their diffraction patterns overlapping, generates
sufficient energy to form a smallest detectable patch of the image. The
peculiarity of the telescopic eye is that it forms an image of a
diffraction image, created by objective and magnified by the eyepiece.
With the angular size of diffraction pattern in this diffraction image
equal to that of the telescopic eye, the latter forms its retinal image
based on the smallest object emitting entities somewhat larger than what
strict point-source definition is. The effect on its image is, as