telescopeѲptics.net .......................................................................................... CONTENTS


◄ 11.14. Houghton-Cassegrain comparison   ▐    12.2. Eyepiece aberrations I ►
 

                                          12. TELESCOPE EYEPIECE: Functions and aberrations

12.1. Eyepiece functions

The image formed by the telescope objective is real, and can be observed directly. However, as explained in
1.4. Main functions of a telescope, its magnification is limited to ƒ/250, ƒ being the objective focal length. Also, since an average eye can't focus properly looking at objects closer than ~25cm, it can grasp only a fraction of light coming from the image formed by the objective (Fig. 5). It is telescope eyepiece that solves both of these problems. It increases telescope magnification by a 250/ƒe factor (ƒe being the eyepiece f.l. in mm), and brings all the light emitted by the object-image to the eye pupil (Fig. 6).

Telescope eyepiece is a complex positive lens system placed between the eye and the image formed by the objective. If the object image formed by the objective is located at the ocular's front focal plane, the eyepiece images every image point at infinity - in other words, it transforms (desirably) spherical wavefronts emerging from the object image's points into flat wavefronts merging at the location of the eyepiece exit pupil (FIG. 118). These wavefronts enter the eye, which transforms them into near-spherical and have them focus onto the retina, creating the final magnified apparent image.


FIGURE 118: Eyepiece with the object-image I formed by the objective at its front focal plane re-images every point source of the object-image at infinity. Image of the objective formed by the eyepiece (dotted lines) is the exit pupil ExP, where the pencils of collimated light merge, making possible for the eye - with the eye lens placed at the exit pupil - to receive all the light emitted by the object image. With the objective image magnification given by the image distance ƒƒe/(ƒ-ƒe) to the object distance ƒ+ƒe ratio, the exit pupil diameter is ExP=Dƒƒe/(ƒ2-ƒe2) or, practically, ExP=Dƒe/ƒ=ƒe/F~D/M, M being the telescope magnification, and F the telescope F#. Telescope magnification M=tanε/tanα, ε being the apparent eyepiece image angle, and α the apparent object angle. The distance ER between the eye lens and the exit pupil is called eye relief. For full field edge illumination, the front lens needs to be somewhat larger than object-image in the focal plane (specific value varies with the eyepiece type - i.e. stop to field lens separation - and telescope ƒ-ratio).

Limit to the eyepiece apparent field is set by field stop, an axially centered opening in front of the field lens, which for focused eyepiece coincides with the objective's image plane. Angular size of the field stop as seen from the center of the entrance pupil (α,  FIG. 118) is called true field of view (TFOV), and its angular size as seen through the eyepiece (ε,  FIG. 118) is apparent field of view (AFOV) of a telescope. The AFOV/TFOV ratio approximates telescope magnification; however, its approximate accuracy varies with the degree of eyepiece image distortion. Since magnification is defined as apparent image size vs. apparent object size, it is given by the ratio of tangents, or M=tan(AFOV/2)/tan(TFOV/2). With the TFOV being always a small angle, image distortion is negligible, and the actual image angle is practically given by tan(TFOV/2)=T/2ƒ, T being the diameter of eyepiece field stop (being a small angle, it is also closely approximated in degrees by TFOV~180T/2ƒπ).

However, the eyepiece field of view, much larger angularly, suffers from significant distortion. In telescope eyepieces, it is usually positive distortion, which means that image magnification increases with the image point height. In effect, the outer image portion is stretched out and seen at a magnification higher than that for the inner image portions (this may and may not be accompanied with spherical aberration of exit pupil). In effect, AFOV inflated by distortion implies the field stop - and true field - larger by a factor of distortion than what it actually is. That is relatively insignificant with small AFOV eyepieces (~5% average in a conventional ~45° eyepiece), but since distortion increases with the third power of the angle, it can be a factor in the wide-field varieties. For instance, a zero-distortion 10mm 60° AFOV eyepiece would have 11.5mm field stop diameter, while one with 15% distortion would have it ~9.8mm.

Details seen in the eyepiece as extended are of ~3 arc minutes angular size, or larger. For the average eye, details smaller than that don't have recognizable shape, even when they don't appear point-like. Airy disc diameter in the eyepiece is 4.6F/ƒe arc minutes, for the 550nm wavelength, with F being the telescope focal ratio number. This sets the minimum eyepiece focal length needed to begin recognizing it as a spot at ƒe~1.5F (assuming sufficiently bright star). This, of course, can and does vary individually.

◄ 11.14. Houghton-Cassegrain comparison   ▐    12.2. Eyepiece aberrations I ►

Home  |  Comments