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KENNETH N. OGLE, "The Correction of Aniseikonia with Ophthalmic Lenses," J. Opt. Soc. Am. 26, 323337 (1936)
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Cf. Bibliography.

Under the shape category, aniseikonia also includes declination errors. Such errors can usually be interpreted in terms of a meridional magnification of the dioptric image at some oblique axis.

Zero verging power magnification lenses.

The term "retinal image" as used here, describes that section of the bundle of image forming rays in the vitreous humor of the eye which falls upon the retina, and to which the retinal elements respond.

The sign system used is as follows: light is incident from the left; distances are measured from surfaces; distances to left are negative; distances to right are positive. All separations for purposes of development are taken negative. A reduced distance is an actual distance in an optical medium divided by the index of refraction of that medium.

Surface powers are defined by D=(n1)/r, where r is the radius of the curve in meters and n is the index of refraction.

Cf. T. Smith, "The Primordial Coefficients of Asymmetrical Lenses," Trans. Opt. Soc. 29, 170 (1928). M. Herzberger, Strahlenoptik, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Bd. 35, 61 (1931). They may be determined by other methods, e.g., cf. C. Pendlebury, Lenses and Systems of Lenses (London, 1884). J. G. Leatham, Symmetrical Optical Instrument (Cambridge, 1908).

If such a lens corrects an ametropic eye, for a given object distance, V is the reciprocal of the distance measured from the ocular surface of the lens to the plane that is conjugate to the retina of the ametropic eye.

Though this division of the magnification into factors for the eye and correcting lens is the most straightforward from the point of view of geometrical optics, it is not the only one, as will be shown later.

Here t, c, h and u are taken positive.

This factor is designated the "effectivity factor," by T. Smith. Cf. Trans. Opt. Soc. 26, 31 (1924).

These relations, easily found by applying the Gauss theory to the object and image distances referred to a second pair of conjugate points, are identical with the vergence equations of A. Gullstrand. Cf. Helmholtz, Physiological Optics, Eng. Trans., Vol. I, p. 277ff.

The entrance pupil of the eye is the image of the real pupil formed by that part of the dioptric system which lies between the real pupil and the object. The distance of the entrance pupil from the pole of the cornea can be measured by means of a corneal microscope. The exit pupil will be the image of the real pupil formed by that part of the dioptric system lying between the true pupil and the retina.

This is essentially correct as concerns the human eye—see unpublished work, Determination of the Effective Entrance Pupil, by K. N. Ogle, October, 1933.

This may not be strictly true in cases of large spherical aberration. It must be borne in mind that this discussion pertains to centered systems. Actually the pupil is decentered and the dioptric system of the eye is both decentered and tipped relative to visual axis.

This relation differs from that of Eq. (19) in that h_{e} here is measured from the entrance pupil instead of the cornea. In the schematic eye the entrance pupil lies about 3.2 mm behind the cornea. Becausc this expression is best adapted for either blurred or sharp imagery it is perhaps the best to use empirically.

If V_{0}=0, D_{1}=0, L_{0}=angular magnification of plane parallel of thickness t mm.

Comparing the ocular images in any other manner explicitly involves the absolute magnitude of one of the k's. The ratio permits one to compare the sizes in percentages.

As would be the case in the testing instrument.

The Gauss coefficients for a four surface system are [equation]

Cf. T. Smith, "Back Vertex Powers," Trans. Opt. Soc., 26, 35 (1924), for case when U=0, i.e., parallel incident light.

Taking c, h and u as positive here.

In general R differs from unity by a few percent, and it has been convenient to express R as R=1+e, and refer to the percent eikonic difference, viz., 1OOe.

Referred to the points before the eyes at which the vergence powers of the trial case lenses were specified.

These relations follow since the positions of the images formed by the spectacle lenses must be the same as were the positions of the images formed by the corresponding trial case lenses.

This additive property is found in most of the trial case sets manufactured today.

The L factor is unity for distant vision and hence does not enter into the cylindrical excess magnification. If cylindrical lenses are included before both eyes in the test, even though one is of zero power, the L factor drops out of the eikonic trial case lens ratio.

One means for doing this is to design the shape of the cylindrical lens for distant vision so that its shape factor S_{01} just offsets the T factor, i.e., S_{01}T=1. A different set of cylinders would be required for near vision unless cylindrical lenses are always placed before both eyes (though one may be of zero power).

In terms of the surface powers and thickness of the lens the vertex power (cf. Eq. (19)) can be written V_{0}=D_{1}+D_{2}+e, where e is an allowance factor equal to S_{0}D_{1}2_{c}(=D_{1}2_{c}, approximately) that can be found from prepared tables.

Dr. E. D. Tillyer first pointed out this simplification.

These lenses have excellent field properties with negligible distortion.

This follows from the series expansion of log_{e} M, i.e., log_{e}M=(M1)½(M1)^{2} ⅓(M1)^{3}.... When ½(M1)^{2} is below precision of measurements, (100) log_{e}M is identical with percent magnification.
Gullstrand, A.

These relations, easily found by applying the Gauss theory to the object and image distances referred to a second pair of conjugate points, are identical with the vergence equations of A. Gullstrand. Cf. Helmholtz, Physiological Optics, Eng. Trans., Vol. I, p. 277ff.
Helmholtz, Cf.

These relations, easily found by applying the Gauss theory to the object and image distances referred to a second pair of conjugate points, are identical with the vergence equations of A. Gullstrand. Cf. Helmholtz, Physiological Optics, Eng. Trans., Vol. I, p. 277ff.
Ogle, K. N.

This is essentially correct as concerns the human eye—see unpublished work, Determination of the Effective Entrance Pupil, by K. N. Ogle, October, 1933.
Smith, Cf. T.

Cf. T. Smith, "Back Vertex Powers," Trans. Opt. Soc., 26, 35 (1924), for case when U=0, i.e., parallel incident light.
Smith, T.

This factor is designated the "effectivity factor," by T. Smith. Cf. Trans. Opt. Soc. 26, 31 (1924).
Tillyer, E. D.

Dr. E. D. Tillyer first pointed out this simplification.
Trans. Opt. Soc.

This factor is designated the "effectivity factor," by T. Smith. Cf. Trans. Opt. Soc. 26, 31 (1924).

Cf. T. Smith, "Back Vertex Powers," Trans. Opt. Soc., 26, 35 (1924), for case when U=0, i.e., parallel incident light.
Other

Taking c, h and u as positive here.

In general R differs from unity by a few percent, and it has been convenient to express R as R=1+e, and refer to the percent eikonic difference, viz., 1OOe.

Referred to the points before the eyes at which the vergence powers of the trial case lenses were specified.

These relations follow since the positions of the images formed by the spectacle lenses must be the same as were the positions of the images formed by the corresponding trial case lenses.

This additive property is found in most of the trial case sets manufactured today.

The L factor is unity for distant vision and hence does not enter into the cylindrical excess magnification. If cylindrical lenses are included before both eyes in the test, even though one is of zero power, the L factor drops out of the eikonic trial case lens ratio.

One means for doing this is to design the shape of the cylindrical lens for distant vision so that its shape factor S_{01} just offsets the T factor, i.e., S_{01}T=1. A different set of cylinders would be required for near vision unless cylindrical lenses are always placed before both eyes (though one may be of zero power).

In terms of the surface powers and thickness of the lens the vertex power (cf. Eq. (19)) can be written V_{0}=D_{1}+D_{2}+e, where e is an allowance factor equal to S_{0}D_{1}2_{c}(=D_{1}2_{c}, approximately) that can be found from prepared tables.

Dr. E. D. Tillyer first pointed out this simplification.

These lenses have excellent field properties with negligible distortion.

This follows from the series expansion of log_{e} M, i.e., log_{e}M=(M1)½(M1)^{2} ⅓(M1)^{3}.... When ½(M1)^{2} is below precision of measurements, (100) log_{e}M is identical with percent magnification.

These relations, easily found by applying the Gauss theory to the object and image distances referred to a second pair of conjugate points, are identical with the vergence equations of A. Gullstrand. Cf. Helmholtz, Physiological Optics, Eng. Trans., Vol. I, p. 277ff.

The entrance pupil of the eye is the image of the real pupil formed by that part of the dioptric system which lies between the real pupil and the object. The distance of the entrance pupil from the pole of the cornea can be measured by means of a corneal microscope. The exit pupil will be the image of the real pupil formed by that part of the dioptric system lying between the true pupil and the retina.

This is essentially correct as concerns the human eye—see unpublished work, Determination of the Effective Entrance Pupil, by K. N. Ogle, October, 1933.

This may not be strictly true in cases of large spherical aberration. It must be borne in mind that this discussion pertains to centered systems. Actually the pupil is decentered and the dioptric system of the eye is both decentered and tipped relative to visual axis.

This relation differs from that of Eq. (19) in that h_{e} here is measured from the entrance pupil instead of the cornea. In the schematic eye the entrance pupil lies about 3.2 mm behind the cornea. Becausc this expression is best adapted for either blurred or sharp imagery it is perhaps the best to use empirically.

If V_{0}=0, D_{1}=0, L_{0}=angular magnification of plane parallel of thickness t mm.

Comparing the ocular images in any other manner explicitly involves the absolute magnitude of one of the k's. The ratio permits one to compare the sizes in percentages.

As would be the case in the testing instrument.

The Gauss coefficients for a four surface system are [equation]

Cf. Bibliography.

Under the shape category, aniseikonia also includes declination errors. Such errors can usually be interpreted in terms of a meridional magnification of the dioptric image at some oblique axis.

Zero verging power magnification lenses.

The term "retinal image" as used here, describes that section of the bundle of image forming rays in the vitreous humor of the eye which falls upon the retina, and to which the retinal elements respond.

The sign system used is as follows: light is incident from the left; distances are measured from surfaces; distances to left are negative; distances to right are positive. All separations for purposes of development are taken negative. A reduced distance is an actual distance in an optical medium divided by the index of refraction of that medium.

Surface powers are defined by D=(n1)/r, where r is the radius of the curve in meters and n is the index of refraction.

Cf. T. Smith, "The Primordial Coefficients of Asymmetrical Lenses," Trans. Opt. Soc. 29, 170 (1928). M. Herzberger, Strahlenoptik, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Bd. 35, 61 (1931). They may be determined by other methods, e.g., cf. C. Pendlebury, Lenses and Systems of Lenses (London, 1884). J. G. Leatham, Symmetrical Optical Instrument (Cambridge, 1908).

If such a lens corrects an ametropic eye, for a given object distance, V is the reciprocal of the distance measured from the ocular surface of the lens to the plane that is conjugate to the retina of the ametropic eye.

Though this division of the magnification into factors for the eye and correcting lens is the most straightforward from the point of view of geometrical optics, it is not the only one, as will be shown later.

Here t, c, h and u are taken positive.
1924, Smith, Trans. Opt. Soc.

This factor is designated the "effectivity factor," by T. Smith. Cf. Trans. Opt. Soc. 26, 31 (1924).
1924, Smith, Trans. Opt. Soc.

Cf. T. Smith, "Back Vertex Powers," Trans. Opt. Soc., 26, 35 (1924), for case when U=0, i.e., parallel incident light.
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