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Full Article | PDF Article**Journal of the Optical Society of America**- Vol. 13,
- Issue 3,
- pp. 245-266
- (1926)
- •doi: 10.1364/JOSA.13.000245

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- When the refraction of the eye is measured from the center of the entrance-pupil, the image equations are:m2U′=U+mF,my′U′=yU,where U′ denotes the reciprocal of the “reduced” distance of the retina from the center of the exit-pupil, F denotes the refracting power of the optical system, and m and y′/y are the values of the magnification ratios with respect to the center of the entrance-pupil and the focus point, respectively. In the case of the unaided eye the value of m is very nearly constant for all focusings of the eye and equal to about +0.9. When the eye is reinforced by a spectacle glass, the magnitudes U and U′ must be measured from the pupils of the compound optical system, and F denotes the refracting power of the compound system.

- See English trans. of Helmholtz’sPhysiological Optics, I, p. 429.

- See also A. Gullstrand, Einführung in die Methoden der Dioptrik des Auges des Menschen (Leipzig, 1911), which is a work that should be carefully consulted by all ophthalmologists and by oculists and optometrists who are really scientific refractionists. Incidentally, this treatise contains a thorough description of the author’s methods of both subjective and objective stigmatoscopy, besides a critical survey of the various optometrical methods of refraction.

See also A. Gullstrand, Einführung in die Methoden der Dioptrik des Auges des Menschen (Leipzig, 1911), which is a work that should be carefully consulted by all ophthalmologists and by oculists and optometrists who are really scientific refractionists. Incidentally, this treatise contains a thorough description of the author’s methods of both subjective and objective stigmatoscopy, besides a critical survey of the various optometrical methods of refraction.

See English trans. of Helmholtz’sPhysiological Optics, I, p. 429.

When the refraction of the eye is measured from the center of the entrance-pupil, the image equations are:m2U′=U+mF,my′U′=yU,where U′ denotes the reciprocal of the “reduced” distance of the retina from the center of the exit-pupil, F denotes the refracting power of the optical system, and m and y′/y are the values of the magnification ratios with respect to the center of the entrance-pupil and the focus point, respectively. In the case of the unaided eye the value of m is very nearly constant for all focusings of the eye and equal to about +0.9. When the eye is reinforced by a spectacle glass, the magnitudes U and U′ must be measured from the pupils of the compound optical system, and F denotes the refracting power of the compound system.

See English trans. of Helmholtz’sPhysiological Optics, I, p. 429.

See also A. Gullstrand, Einführung in die Methoden der Dioptrik des Auges des Menschen (Leipzig, 1911), which is a work that should be carefully consulted by all ophthalmologists and by oculists and optometrists who are really scientific refractionists. Incidentally, this treatise contains a thorough description of the author’s methods of both subjective and objective stigmatoscopy, besides a critical survey of the various optometrical methods of refraction.

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Emmetropia, observed at a distance of one meter.

Hypermetropia, + 2 dptr, observed at a distance of one meter.

Myopia, −2.5 dptr, observed at a distance of one meter.

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$$\frac{1}{\text{LM}}=\frac{1}{\text{LX}}+F.$$

$$\begin{array}{ll}\text{LM}=-\frac{1+cU}{U},\hfill & \text{LR}=-\frac{1+cV}{V};\hfill \end{array}$$

$$V=\frac{U+(1+cU)F}{1-c(1+cU)F},$$

$$\frac{\text{GF}-\text{AE}}{\text{MA}}=\frac{{\text{S}}_{1}\text{S}+\text{AE}}{\text{AO}};$$

$$\text{GF}=p\frac{n+1+(1+\u220a)zU}{(1+\u220a)zU}.$$

$$\frac{\text{KJ}}{\text{GF}}=\frac{\text{AC}}{\text{MC}},$$

$$r=C\xb7\text{GF},$$

$$C=\frac{zU}{1+zU}.$$

$$r=p\frac{n+1+(1+\u220a)zU}{(1+\u220a)(1+zU)}.$$

$$r=\frac{(7+4zU)p}{4(1+zU)}.$$

$$\frac{7}{4}p$$

$$\frac{11}{8}p$$

$$\frac{5}{4}p$$

$$\frac{19}{16}p$$

$$\frac{9}{8}p$$

$$\frac{47}{44}p$$

$$\frac{73}{76}p$$

$$\frac{11}{12}p$$

$$\frac{17}{20}p$$

$$\frac{5}{8}p$$

$$\frac{1}{2}p$$

$$\frac{1}{4}p$$

$$-\frac{1}{2}p$$

$$\frac{5}{2}p$$

$$\text{A K}=C\xb7\text{MG};$$

$$\text{MG}=\frac{\text{MA}}{\text{OA}}\text{OS},$$

$$\text{A K}=C\frac{\text{MA}}{\text{OA}}\text{OS}.$$

$$\text{A K}=-\frac{y}{(1-\u220a)(1+zU)}.$$

$${\text{OS}}_{2}=-p\{1+(1+\u220a)(1+2zU)\};$$

$$\text{CN}=-2p(1+zU).$$

$$\begin{array}{ll}\frac{\text{OS}}{\text{PA}}=\frac{\text{CO}}{\text{AC}},\hfill & \frac{\text{KA}}{\text{OS}}=\frac{\text{MA}}{\text{MC}}\xb7\frac{\text{AC}}{\text{AO}};\hfill \end{array}$$

$$\begin{array}{l}\frac{\text{KA}}{\text{PA}}=\frac{\text{CO}}{\text{AO}}\xb7\frac{\text{MA}}{\text{MC}}.\hfill \end{array}$$

$$\frac{\text{CO}}{\text{AO}}=\frac{\u220a}{1+\u220a},$$

$$\alpha =\frac{\u220a}{1+\u220a}v,$$

$$S=\alpha \frac{\text{MA}}{\text{MC}};$$

$$S=\frac{\alpha}{1+zU}.$$

$$\text{AM}=\frac{1+\u220a}{1+2\u220a}\text{AC}.$$

$$\mathrm{\Delta}A=-\frac{{(A+F)}^{2}}{A+F+1000{n}^{\prime}/e},$$

$$\begin{array}{ll}{m}^{2}{U}^{\prime}=U+\text{m}F,\hfill & \text{m}{y}^{\prime}{U}^{\prime}=yU,\hfill \end{array}$$

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