Na D

The largest numerical aperture for optics used in air is 1. Thus, the smallest F# is 0.5.

All optical systems suffer from aberrations, or imperfections in the image quality, in addition to diffraction which limits the system resolution as discussed in Sec. 9.33. The principal optical aberrations are listed in Table 9-7. Chromatic aberration, or imperfections which are color or wavelength dependent, arises from various wavelengths being bent by different amounts when they pass through a lens. Consequently, only systems with at least one refractive element suffer chromatic aberration because reflective surfaces treat all wavelengths the same. (This is not absolutely true since some surfaces will reflect visible light, for example, but not X-rays. However, when reflection does occur it is independent of wavelength to first order.)

TABLE 9-7. Principal Aberrations In Optical Systems. See Table 9-8 for which of these are mitigated in various optical systems.

Chromatic Aberration = dispersion of the light due to the refractive index of a lens being a function of the wavelength. Causes different colors to focus at different distances.

Spherical Aberration = dispersion In which light from the periphery of a spherical lens or mirror is focused nearer the element than light from the center. Can be eliminated by making the optical surface parabolic, rather than spherical.

Coma = dispersion of off-axis portions of the Image. (So named because in a telescope off-axis star images look like tear drops or the coma of a comet pointing toward the center of the image.)

Astigmatism = aberration in which the distorted image is asymmetric such as when light in a horizontal plane comes to a slightly different focus than light in a vertical plane. A common problem in human vision.

Distortion = when an otherwise sharp Image is distorted in shape, such as when straight Ones on the surface being viewed appear curved on the focal plane. A uncorrectable distortion occurs when trying to image the celestial sphere onto a fiat focal plane. (See Sec. 5.1.)

Curvature of Flelfl= when a sharp Image is formed on a focal surface which Isn't flat Can be corrected in film systems by using a slightly curved focal plane.

Figure 9-9 shows the three basic types of telescopes. In each of the three, there is a corresponding refractive and reflective instrument The aberrations which can be corrected in each type are shown in Table 9-8. The lens doublet is the classic refractive telescope lens. The doublet can be designed to eliminate spherical aberrations, coma, distention and chromatic aberrations (see Table 9-8). In tele-optic lens systems the distance between the optical element and the focal plane is shorter than the focal length. Tele-optic lenses can eliminate spherical aberrations, coma, astigmatism, and curvature of field effects. They can also overcome chromatic aberrations. The lens triplet is the simplest refractive (spherical) optical system that theoretically allows for correction of all distortion!;. The price we pay for this advantage is the very high sensitivity of each of the optical elements with respect to displacement or tilt. The ray traces in

Refractive

Reflective

(A) Lens Doublet

(A) Lens Doublet

(B)Tete-opUe

(B)Tete-opUe

(gill

(gill

(C) Lens Triplet

(C) Lens Triplet

Fig. 9-9. Basic Configurations for Refractive and Reflective Optical Systems. Each of the reflective systems on the right is analogous to the corresponding refractive system on the left TMA = Three-mirror anastigmatic.

TABLE 9-8. Aberrations that can be Corrected by the Three Basic Optical Systems.

Checks indicate errors that are fully correctable and parenthetical checks Indicate that corrections are possible only for dedicated design parameters. (See Table 9-7 for definitions).

TABLE 9-8. Aberrations that can be Corrected by the Three Basic Optical Systems.

Checks indicate errors that are fully correctable and parenthetical checks Indicate that corrections are possible only for dedicated design parameters. (See Table 9-7 for definitions).

Image Error

Doublet/Schmidt

TeleOptlc/Cassegraln

Trlplet/TMA

Lateral Chromatic Aberration

Length Chromatic Aberration

Spherical Aberration

Coma

Astigmatism

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