Zoom lens, and imaging system comprising the same

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is illustrative in section of Example 1 of the zoom lens according to the invention at the wide-angle end (a), in an intermediate state (b) and at the telephoto end (c) upon focusing on an object point at infinity.

FIG. 2 is illustrative, as in FIG. 1, of Example 2 of the zoom lens according to the invention.

FIG. 3 is illustrative, as in FIG. 1, of Example 3 of the zoom lens according to the invention.

FIG. 4 is illustrative, as in FIG. 1, of Example 4 of the zoom lens according to the invention.

FIG. 5 is illustrative, as in FIG. 1, of Example 5 of the zoom lens according to the invention.

FIG. 6 is illustrative, as in FIG. 1, of Example 6 of the zoom lens according to the invention.

FIG. 7 is illustrative, as in FIG. 1, of Example 7 of the zoom lens according to the invention.

FIG. 8 is illustrative, as in FIG. 1, of Example 8 of the zoom lens according to the invention.

FIG. 9 is illustrative, as in FIG. 1, of Example 9 of the zoom lens according to the invention.

FIG. 10 is illustrative, as in FIG. 1, of Example 10 of the zoom lens according to the invention.

FIG. 11 is illustrative, as in FIG. 1, of Example 11 of the zoom lens according to the invention.

FIG. 12 is illustrative, as in FIG. 1, of Example 12 of the zoom lens according to the invention.

FIG. 13 is illustrative, as in FIG. 1, of Example 13 of the zoom lens according to the invention.

FIG. 14 is illustrative, as in FIG. 1, of Example 14 of the zoom lens according to the invention.

FIG. 15 is illustrative, as in FIG. 1, of Example 15 of the zoom lens according to the invention.

FIG. 16 is indicative of aberration diagrams for Example 1 upon focusing on an object point at infinity.

FIG. 17 is indicative of aberration diagrams for Example 2 upon focusing on an object point at infinity.

FIG. 18 is indicative of aberration diagrams for Example 3 upon focusing on an object point at infinity.

FIG. 19 is indicative of aberration diagrams for Example 4 upon focusing on an object point at infinity.

FIG. 20 is indicative of aberration diagrams for Example 5 upon focusing on an object point at infinity.

FIG. 21 is indicative of aberration diagrams for Example 6 upon focusing on an object point at infinity.

FIG. 22 is indicative of aberration diagrams for Example 7 upon focusing on an object point at infinity.

FIG. 23 is indicative of aberration diagrams for Example 8 upon focusing on an object point at infinity.

FIG. 24 is indicative of aberration diagrams for Example 9 upon focusing on an object point at infinity.

FIG. 25 is indicative of aberration diagrams for Example 10 upon focusing on an object point at infinity.

FIG. 26 is indicative of aberration diagrams for Example 11 upon focusing on an object point at infinity.

FIG. 27 is indicative of aberration diagrams for Example 12 upon focusing on an object point at infinity.

FIG. 28 is indicative of aberration diagrams for Example 13 upon focusing on an object point at infinity.

FIG. 29 is indicative of aberration diagrams for Example 14 upon focusing on an object point at infinity.

FIG. 30 is indicative of aberration diagrams for Example 15 upon focusing on an object point at infinity.

FIG. 31 is illustrative of the basic concept for digital correction of image distortion.

FIG. 32 is a front perspective schematic illustrative of the outside shape of the inventive digital camera.

FIG. 33 is a rear perspective schematic of the digital camera of FIG. 32.

FIG. 34 is a sectional view of the digital camera of FIG. 32.

FIG. 35 is a component block diagram for an internal circuit in part of the digital camera of FIG. 32.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Examples 1 to 15 of the zoom lens according to the invention are now explained. FIGS. 1-15 are illustrative in section of Examples 1-15 in the wide-angle end (a), in an intermediate state (b) and at the telephoto end (c) upon focusing on an object point at infinity. In FIGS. 1-15, G1 represents a first lens group, S an aperture stop, G2 a second lens group, G3 a third lens group, G4 a fourth lens group, capital F an optical low-pass filter applied with an infrared cut coating, capital C a cover glass for an electronic imaging device (CCD or CMOS), and capital I an image plane (the receptor plane of the electronic imaging device). It is noted that in addition to the infrared cut coating, there may be an infrared cut absorption filter provide, and instead of the infrared cut coating, the cover glass C may additionally be provided on its surface with a wavelength limiting multilayer film. In FIGS. 1 to 15, the axial marginal light rays and the most off-axis chief ray at the wide-angle end, in the intermediate state and at the telephoto end are also indicated.

Example 1 is directed to a zoom lens made up of, in order from its object side, the first lens group G1 of negative refracting power, the second lens group G2 of positive refracting power, the third lens group G3 of positive refracting power and the fourth lens group G4 of positive refracting power, as shown in FIG. 1, with the aperture stop S located on the object side of, and integrally with, the second lens group G2. From zooming from the wide-angle end to the telephoto end, the first lens group G1 moves toward the image side in a convex orbit, and is positioned nearer to the image side at the telephoto end than at the wide-angle end. The second lens group G2 moves together with the aperture stop S monotonously toward the object side while the space between it and the first lens group G1 becomes narrow. The third lens group G3 moves toward the image side while the space between it and the second lens group G2 becomes wide. The fourth lens group G4 remains fixed.

In order from the object side, the first lens group G1 is made up of a double-concave negative lens and a double-convex positive lens; the second lens group G2 is made up of a double-convex positive lens and a cemented lens consisting of a positive meniscus lens convex on the object side and a negative meniscus lens convex on the object side; the third lens group G3 is made up of one double-convex positive lens; and the fourth lens group G4 is made up of one positive meniscus lens convex on the object side.

Six aspheric surfaces are used: two at both surfaces of the double-concave negative lens in the first lens group G1, two at both surfaces of the double-convex positive lens in the second lens group G2, one at the image side surface of the double-convex positive lens in the third lens group G3, and one at the object side surface of the positive meniscus lens in the fourth lens group G4.

Example 2 is directed to a zoom lens made up of, in order from its object side, the first lens group G1 of negative refracting power, the second lens group G2 of positive refracting power and the third lens group G3 of positive refracting power, as shown in FIG. 1, with the aperture stop S located on the object side of, and integrally with, the second lens group G2. From zooming from the wide-angle end to the telephoto end, the first lens group G1 moves toward the image side in a convex orbit, and is positioned nearer to the image side at the telephoto end than at the wide-angle end. The second lens group G2 moves together with the aperture stop S monotonously toward the object side while the space between it and the first lens group G1 becomes narrow. The third lens group G3 moves toward the image side while the space between it and the second lens group G2 becomes wide.

In order from the object side, the first lens group G1 is made up of a double-concave negative lens and a double-convex positive lens; the second lens group G2 is made up of a double-convex positive lens and a cemented lens consisting of a positive meniscus lens convex on the object side and a negative meniscus lens convex on the object side; and the third lens group G3 is made up of one double-convex positive lens.

Five aspheric surfaces are used: two at both surfaces of the double-concave negative lens in the first lens group G1, two at both surfaces of the double-convex positive lens in the second lens group G2, and one at the image side surface of the double-convex positive lens in the third lens group G3.

Example 3 is directed to a zoom lens made up of, in order from its object side, the first lens group G1 of negative refracting power, the second lens group G2 of positive refracting power, the third lens group G3 of positive refracting power and the fourth lens group G4 of positive refracting power, as shown in FIG. 3, with the aperture stop S located on the object side of, and integrally with, the second lens group G2. From zooming from the wide-angle end to the telephoto end, the first lens group G1 moves toward the image side in a convex orbit, and is positioned nearer to the image side at the telephoto end than at the wide-angle end. The second lens group G2 moves together with the aperture stop S monotonously toward the object side while the space between it and the first lens group G1 becomes narrow. The third lens group G3 moves toward the object side in a convex orbit while the space between it and the second lens group G2 becomes wide, and is positioned nearer to the image side at the telephoto end than at the wide-angle end.

In order from the object side, the first lens group G1 is made up of a double-concave negative lens and a double-convex positive lens; the second lens group G2 is made up of a double-convex positive lens and a cemented lens consisting of a double-convex positive lens and a double-concave negative lens; the third lens group G3 is made up of one double-convex positive lens; and the fourth lens group G4 is made up of one plano-convex positive lens convex on the object side.

Six aspheric surfaces are used: two at both surfaces of the double-concave negative lens in the first lens group G1, two at both surfaces of the single double-convex positive lens in the second lens group G2, one at the image side surface of the double-convex positive lens in the third lens group G3, and one at the object side surface of the plano-convex positive lens in the fourth lens group G4.

Example 4 is directed to a zoom lens made up of, in order from its object side, the first lens group G1 of negative refracting power, the second lens group G2 of positive refracting power, the third lens group G3 of positive refracting power and the fourth lens group G4 of positive refracting power, as shown in FIG. 4, with the aperture stop S located on the object side of, and integrally with, the second lens group G2. From zooming from the wide-angle end to the telephoto end, the first lens group G1 moves toward the image side in a convex orbit, and is positioned nearer to the image side at the telephoto end than at the wide-angle end. The second lens group G2 moves together with the aperture stop S monotonously toward the object side while the space between it and the first lens group G1 becomes narrow. The third lens group G3 moves toward the object side in a convex orbit while the space between it and the second lens group G2 becomes wide, and is positioned nearer to the image side at the telephoto end than at the wide-angle end. The fourth lens group G4 moves toward the image side while the space between it and the third lens group G3 becomes wide from the wide-angle end to the intermediate state and then becomes narrows from the intermediate state to the telephoto end.

In order from the object side, the first lens group G1 is made up of a double-concave negative lens and a positive meniscus lens convex on the object side; the second lens group G2 is made up of a double-convex positive lens and a cemented lens consisting of a double-convex positive lens and a double-concave negative lens; the third lens group G3 is made up of one double-convex positive lens; and the fourth lens group G4 is made up of one positive meniscus lnes convex on the image side.

Example 5 is directed to a zoom lens made up of, in order from its object side, the first lens group G1 of negative refracting power, the second lens group G2 of positive refracting power, the third lens group G3 of positive refracting power and the fourth lens group G4 of negative refracting power, as shown in FIG. 5, with the aperture stop S located integrally in the second lens group G2. From zooming from the wide-angle end to the telephoto end, the first lens group G1 moves toward the image side in a convex orbit, and is positioned nearer to the image side at the telephoto end than at the wide-angle end. The second lens group G2 moves together with the aperture stop S monotonously toward the object side while the space between it and the first lens group G1 becomes narrow. The third lens group G3 moves toward the object side while the space between it and the second lens group G2 becomes slightly narrow from the wide-angle end to the intermediate state and then becomes wide from the intermediate state to the telephoto end. The fourth lens group G4 moves toward the object side in a convex orbit while the space between it and the third lens group G3 becomes wide, and is positioned nearer to the image side at the telephoto end than at the wide-angle end.

In order from the object side, the first lens group G1 is made up of a cemented lens consisting of a double-concave negative lens and a positive meniscus lens convex on the object side; the second lens group G2 is made up of a positive meniscus lens convex on the object side, the aperture stop S and a cemented lens consisting of a negative meniscus lens convex on the object side and a double-convex positive lens; the third lens group G3 is made up of one positive meniscus lens convex on the object side; and the fourth lens group G4 is made up of one negative meniscus lens convex on the image side.

Six aspheric surfaces are used: one at the surface nearest to the object side of the cemented lens in the first lens group G1, two at both surfaces of the single positive meniscus lens in the second lens group G2, two at both surfaces of the positive meniscus lens in the third lens group G3, and one at the image side surface of the negative meniscus lens in the fourth lens group G4.

Example 6 is directed to a zoom lens made up of, in order from its object side, the first lens group G1 of negative refracting power, the second lens group G2 of positive refracting power, the third lens group G3 of positive refracting power and the fourth lens group G4 of negative refracting power, as shown in FIG. 6, with the aperture stop S located on the image side of, and integrally with, the second lens group G2. From zooming from the wide-angle end to the telephoto end, the first lens group G1 moves toward the image side in a convex orbit, and is positioned nearer to the image side at the telephoto end than at the wide-angle end. The second lens group G2 moves together with the aperture stop S monotonously toward the object side while the space between it and the first lens group G1 becomes narrow. The third lens group G3 moves toward the object side while the space between it and the second lens group G2 becomes slightly narrow from the wide-angle end to the intermediate state and then becomes wide from the intermediate state to the telephoto end. The fourth lens group G4 moves toward the object side in a convex orbit while the space between it and the third lens group G3 becomes wide, and is positioned nearer to the image side at the telephoto end than at the wide-angle end.

In order from the object side, the first lens group G1 is made up of a cemented lens consisting of a double-concave negative lens and a positive meniscus lens convex on the object side; the second lens group G2 is made up of a triplet consisting of a positive meniscus lens convex on the object side, a negative meniscus lens convex on the object side and a double-convex positive lens; the third lens group G3 is made up of one positive meniscus lens convex on the object side; and the fourth lens group G4 is made up of one negative meniscus lens convex on the image side.

Five aspheric surfaces are used: one at the surface nearest to the object side of the cemented lens in the first lens group G1, one at the surface nearest to the object side of the triplet in the second lens group G2, two at both surfaces of the positive meniscus lens in the third lens group G3, and one at the image side surface of the negative meniscus lens in the fourth lens group G4.

Example 7 is directed to a zoom lens made up of, in order from its object side, the first lens group G1 of negative refracting power, the second lens group G2 of positive refracting power, the third lens group G3 of positive refracting power and the fourth lens group G4 of negative refracting power, as shown in FIG. 7, with the aperture stop S located integrally in the second lens group G2. From zooming from the wide-angle end to the telephoto end, the first lens group G1 moves toward the image side in a convex orbit, and is positioned nearer to the image side at the telephoto end than at the wide-angle end. The second lens group G2 moves together with the aperture stop S monotonously toward the object side while the space between it and the first lens group G1 becomes narrow. The third lens group G3 moves toward the object side while the space between it and the second lens group G2 becomes wide. The fourth lens group G4 remains fixed.

In order from the object side, the first lens group G1 is made up of a cemented lens consisting of a double-concave negative lens and a positive meniscus lens convex on the object side; the second lens group G2 is made up of a double-convex positive lens, the aperture stop S and a cemented lens consisting of a positive meniscus lens convex on the object side and a negative meniscus lens convex on the object side; the third lens group G3 is made up of one positive meniscus lens convex on the object side; and the fourth lens group G4 is made up of one negative meniscus lens convex on the image side.

Seven aspheric surfaces are used: two at the surfaces nearest to the object and image sides of the cemented lens in the first lens group G1, two at both surfaces of the single double-convex positive lens in the second lens group G2, two at both surfaces of the positive meniscus lens in the third lens group G3, and one at the object side surface of the negative meniscus lens in the fourth lens group G4.

Example 8 is directed to a zoom lens made up of, in order from its object side, the first lens group G1 of negative refracting power, the second lens group G2 of positive refracting power, the third lens group G3 of positive refracting power and the fourth lens group G4 of positive refracting power, as shown in FIG. 8, with the aperture stop S located on the object side of, and integrally with, the second lens group G2. From zooming from the wide-angle end to the telephoto end, the first lens group G1 moves toward the image side in a convex orbit, and is positioned nearer to the image side at the telephoto end than at the wide-angle end. The second lens group G2 moves together with the aperture stop S monotonously toward the object side while the space between it and the first lens group G1 becomes narrow. The third lens group G3 moves toward the object side in a convex orbit while the space between it and the second lens group G2 becomes wide, and is positioned nearer to the image side at the telephoto end than at the wide-angle end. The fourth lens group G4 moves toward the image side while the space between it and the third lens group G3 becomes wide from the wide-angle end to the intermediate state and then becomes slightly narrow from the intermediate state to the telephoto end.

In order from the object side, the first lens group G1 is made up of a cemented lens consisting of a double-concave negative lens and a positive meniscus lens convex on the object side; the second lens group G2 is made up of a double-convex positive lens and a cemented lens consisting of a positive meniscus lens convex on the object side and a negative meniscus lens convex on the object side; the third lens group G3 is made up of one double-convex positive lens; and the fourth lens group G4 is made up of one negative meniscus lens convex on the image side.

Six aspheric surfaces are used: two at the surfaces nearest to the object and image sides of the cemented lens in the first lens group G1, two at both surfaces of the single double-convex positive lens in the second lens group G2, one at the image side surface of the double-convex positive lens in the third lens group G3, and one at the object side surface of the positive meniscus lens in the fourth lens group G4.

Example 9 is directed to a zoom lens made up of, in order from its object side, the first lens group G1 of negative refracting power, the second lens group G2 of positive refracting power, the third lens group G3 of positive refracting power and the fourth lens group G4 of positive refracting power, as shown in FIG. 9, with the aperture stop S located on the image side of, and integrally with, the second lens group G2. From zooming from the wide-angle end to the telephoto end, the first lens group G1 moves toward the image side in a convex orbit, and is positioned nearer to the image side at the telephoto end than at the wide-angle end. The second lens group G2 moves together with the aperture stop S monotonously toward the object side while the space between it and the first lens group G1 becomes narrow. The third lens group G3 moves toward the object side while the space between it and the second lens group G2 becomes wide. The fourth lens group G4 remains fixed.

In order from the object side, the first lens group G1 is made up of a cemented lens consisting of a double-concave negative lens and a positive meniscus lens convex on the object side; the second lens group G2 is made up of a double-convex positive lens and a cemented lens consisting of a double-convex positive lens and a double-concave negative lens; the third lens group G3 is made up of one positive meniscus lens convex on the object side; and the fourth lens group G4 is made up of one double-convex positive lens.

Seven aspheric surfaces are used: two at the surfaces nearest to the object and image sides of the cemented lens in the first lens group G1, two at both surfaces of the single double-convex positive lens in the second lens group G2, two at both surfaces of the positive meniscus lens in the third lens group G3, and one at the object side surface of the double-convex positive lens in the fourth lens group G4.

Example 10 is directed to a zoom lens made up of, in order from its object side, the first lens group G6 of negative refracting power, the second lens group G2 of positive refracting power, the third lens group G3 of positive refracting power and the fourth lens group G4 of negative refracting power, as shown in FIG. 10, with the aperture stop S located on the object side of, and integrally with, the second lens group G2. From zooming from the wide-angle end to the telephoto end, the first lens group G1 moves toward the image side in a convex orbit, and is positioned nearer to the image side at the telephoto end than at the wide-angle end. The second lens group G2 moves together with the aperture stop S monotonously toward the object side while the space between it and the first lens group G1 becomes narrow. The third lens group G3 moves toward the object side while the space between it and the second lens group G2 becomes wide. The fourth lens group G4 moves slightly toward the image side while the space between it and the third lens group G3 becomes wide.

In order from the object side, the first lens group G1 is made up of a cemented lens consisting of a double-concave negative lens and a positive meniscus lens convex on the object side; the second lens group G2 is made up of a double-convex positive lens and a cemented lens consisting of a positive meniscus lens convex on the object side and a negative meniscus lens convex on the object side; the third lens group G3 is made up of one positive meniscus lens convex on the object side; and the fourth lens group G4 is made up of one plano-convex positive lens.

Seven aspheric surfaces are used: two at the surfaces nearest to the object and image sides of the cemented lens in the first lens group G1, two at both surfaces of the single double-convex positive lens in the second lens group G2, two at both surfaces of the positive meniscus lens in the third lens group G3, and one at the object side surface of the double-convex positive lens in the fourth lens group G4.

Example 11 is directed to a zoom lens made up of, in order from its object side, the first lens group G1 of negative refracting power, the second lens group G2 of positive refracting power, the third lens group G3 of positive refracting power and the fourth lens group G4 of positive refracting power, as shown in FIG. 11, with the aperture stop S located integrally in the second lens group G2. From zooming from the wide-angle end to the telephoto end, the first lens group G1 moves toward the image side. The second lens group G2 moves together with the aperture stop S monotonously toward the object side while the space between it and the first lens group G1 becomes narrow. The third lens group G3 moves toward the object side while the space between it and the second lens group G2 becomes wide. The fourth lens group G4 moves toward the image side.

In order from the object side, the first lens group G1 is made up of a cemented lens consisting of a double-concave negative lens and a positive meniscus lens convex on the object side; the second lens group G2 is made up of a double-convex positive lens, the aperture stop S and a cemented lens consisting of a positive meniscus lens convex on the object side and a negative meniscus lens convex on the object side; the third lens group G3 is made up of one positive meniscus lens convex on the object side; and the fourth lens group G4 is made up of one double-convex positive lens.

Eight aspheric surfaces are used: two at the surfaces nearest to the object and image sides of the cemented lens in the first lens group G1, two at both surfaces of the single double-convex positive lens in the second lens group G2, one at the surface nearest to the object side of the cemented lens in the second lens group G2, two at both surfaces of the positive meniscus lens in the third lens group G3, and one at the object side surface of the double-convex positive lens in the fourth lens group G4.

Example 12 is directed to a zoom lens made up of, in order from its object side, the first lens group G1 of negative refracting power, the second lens group G2 of positive refracting power, the third lens group G3 of positive refracting power and the fourth lens group G4 of positive refracting power, as shown in FIG. 12, with the aperture stop S located on the image side of, and integrally with, the second lens group G2. From zooming from the wide-angle end to the telephoto end, the first lens group G1 moves toward the image side in a convex orbit, and is positioned somewhat nearer to the object side at the telephoto end than at the wide-angle end. The second lens group G2 moves together with the aperture stop S monotonously toward the object side while the space between it and the first lens group G1 becomes narrow. The third lens group G3 moves toward the object side while the space between it and the second lens group G2 becomes wide. The fourth lens group G4 moves toward the image side.

In order from the object side, the first lens group G1 is made up of a cemented lens consisting of a double-concave negative lens and a positive meniscus lens convex on the object side; the second lens group G2 is made up of a double-convex positive lens and a cemented lens consisting of a positive meniscus lens convex on the object side and a negative meniscus lens convex on the object side; the third lens group G3 is made up of a negative meniscus lens convex on the image side and a double-convex positive lens; and the fourth lens group G4 is made up of one positive meniscus lens convex on the image side.

Nine aspheric surfaces are used: two at the surfaces nearest to the object and image sides of the cemented lens in the first lens group G1, two at both surfaces of the single double-convex positive lens in the second lens group G2, one at the surface nearest to the object side of the cemented lens, two at both surfaces of the double-convex positive lens in the third lens group G3, and two at both surface of the positive meniscus lens in the fourth lens group G4.

Example 13 is directed to a zoom lens made up of, in order from its object side, the first lens group G1 of negative refracting power, the second lens group G2 of positive refracting power, the third lens group G3 of positive refracting power and the fourth lens group G4 of negative refracting power, as shown in FIG. 13, with the aperture stop S located integrally in the second lens group G2. From zooming from the wide-angle end to the telephoto end, the first lens group G1 moves toward the image side. The second lens group G2 moves together with the aperture stop S monotonously toward the object side while the space between it and the first lens group G1 becomes narrow. The third lens group G3 moves toward the object side while the space between it and the second lens group G2 becomes somewhat narrow from the wide-angle end to the intermediate state and then becomes wide from the intermediate state to the telephoto end. The fourth lens group G4 moves in a convex orbit toward the image side while the space between it and the third lens group G3 becomes wide, and is positioned nearer to the image side at the telephoto end than at the wide-angle end.

In order from the object side, the first lens group G1 is made up of one double-concave negative lens; the second lens group G2 is made up of a double-convex positive lens, the aperture stop S and a cemented lens consisting of a positive meniscus lens convex on the object side and a negative meniscus lens convex on the object side; the third lens group G3 is made up of one positive meniscus lens convex on the object side; and the fourth lens group G4 is made up of one negative meniscus lens convex on the image side.

Seven aspheric surfaces are used: two at both surfaces of the double-concave negative lens in the first lens group G1, two at both surfaces of the single double-convex positive lens in the second lens group G2, two at both surfaces of the positive meniscus lens in the third lens group G3, and one at the image side surface of the negative meniscus lens in the fourth lens group G4.

Example 14 is directed to a zoom lens made up of, in order from its object side, the first lens group G1 of negative refracting power, the second lens group G2 of positive refracting power, the third lens group G3 of positive refracting power and the fourth lens group G4 of positive refracting power, as shown in FIG. 14, with the aperture stop S located on the image side of, and integrally with, the second lens group G2. From zooming from the wide-angle end to the telephoto end, the first lens group G1 moves toward the image side in a convex orbit, and is positioned somewhat nearer to the image side at the telephoto end than at the wide-angle end. The second lens group G2 moves together with the aperture stop S monotonously toward the object side while the space between it and the first lens group G1 becomes narrow. The third lens group G3 moves toward the object side while the space between it and the second lens group G2 becomes slightly narrow from the wide-angle end to the intermediate state and then becomes wide from the intermediate state to the telephoto end. The fourth lens group G4 moves toward the image side.

In order from the object side, the first lens group G1 is made up of one double-concave negative lens; the second lens group G2 is made up of a positive meniscus lens convex on the object side and a cemented lens consisting of a positive meniscus lens convex on the object side and a negative meniscus lens convex on the object side; the third lens group G3 is made up of a negative meniscus lens convex on the image side and a double-convex positive lens; and the fourth lens group G4 is made up of one positive meniscus lens convex on the image side.

Nine aspheric surfaces are used: two at both surfaces of the double-concave negative lens in the first lens group G1, two at both surfaces of the single double-convex positive lens in the second lens group G2, one at the surface nearest to the image side of the cemented lens in the second lens group G2, two at both surfaces of the double-convex positive lens in the third lens group G3, and two at both surfaces of the positive meniscus lens in the fourth lens group G4.

Example 15 is directed to a zoom lens made up of, in order from its object side, the first lens group G1 of negative refracting power, the second lens group G2 of positive refracting power, the third lens group G3 of positive refracting power and the fourth lens group G4 of positive refracting power, as shown in FIG. 15, with the aperture stop S located on the image side of, and integrally with, the second lens group G2. From zooming from the wide-angle end to the telephoto end, the first lens group G1 moves toward the image side in a convex orbit, and is positioned somewhat nearer to the image side at the telephoto end than at the wide-angle end. The second lens group G2 moves together with the aperture stop S monotonously toward the object side while the space between it and the first lens group G1 becomes narrow. The third lens group G3 moves toward the object side in a convex orbit while the space between it and the second lens group G2 becomes wide, and is positioned nearer to the object side at the telephoto end than at the wide-angle end. The fourth lens group G4 moves toward the image side while the space between it and the third lens group G3 becomes wide from the wide-angle end to the telephoto end and then becomes somewhat narrow from the intermediate state to the telephoto end.

In order from the object side, the first lens group G1 is made up of one double-concave negative lens; the second lens group G2 is made up of a double-convex positive lens and a cemented lens consisting of a positive meniscus lens convex on the object side and a negative meniscus lens convex on the object side; the third lens group G3 is made up of a negative meniscus lens convex on the image side and a double-convex positive lens; and the fourth lens group G4 is made up of one positive meniscus lens convex on the image side.

Nine aspheric surfaces are used: two at both surfaces of the double-concave negative lens in the first lens group G1, two at both surfaces of the single double-convex positive lens in the second lens group G2, one at the surface nearest to the object side of the cemented lens in the second lens group G2, two at both surfaces of the double-convex positive lens in the third lens group G3, and two at both surfaces of the positive meniscus lens in the fourth lens group G4.

The numerical data on each of the aforesaid examples are set out below. The symbols used hereinafter but not hereinbefore have the following meanings: f is the focal length of the whole zoom lens system, F_NOis an F-number, 2ω is an angle of view, WE is the wide-angle end, ST is the intermediate state, TE is the telephoto end, r₁, r2, . . . is the radius of curvature of each lens surface, d₁, d₂, . . . is the spacing between lens surfaces, n_d1, n_d2, . . . is the d-line refractive index of each lens, and ν_d1, ν_d2, . . . is the Abbe number of each lens. Here let x be an optical axis provided that the direction of travel of light is positive and y be a direction orthogonal to the optical axis. Then, aspheric surface shape is given by

x=(y²/r)/[1+{1−(K+1)(y/r)²}^1/2]+A₄y⁴+A₆y₆+A₈y⁸+A₁₀y¹⁰+A₁₂y¹²+A₁₄y¹⁴

Here r is a paraxial radius of curvature, K is a conical coefficient, and A₄, A₆, A₈, A₁₀, A₁₂and A₁₄are the 4^th, 6^th, 8^th, 10^th, 12^thand 14^th-order aspheric coefficients, respectively.
EXAMPLE 1

r₁= −20.591 (Aspheric)
d₁= 0.85
n_d1= 1.74320
ν_d1= 49.34

r₂= 11.203 (Aspheric)
d₂= 1.99

r₃= 22.665
d₃= 2.40
n_d2= 2.00330
ν_d2= 28.27

r₄= −1878.730
d₄=

(Variable)

r₅= ∞ (Stop)
d₅= 0.00

r₆= 8.370 (Aspheric)
d₆= 2.80
n_d3= 1.59201
ν_d3= 67.02

r₇= −38.980 (Aspheric)
d₇= 0.10

r₈= 9.076
d₈= 2.40
n_d4= 1.88300
ν_d4= 40.76

r₉= 159.652
d₉= 0.50
n_{d5 = 1.76182}
ν_d5= 26.52

r₁₀= 4.770
d₁₀=

(Variable)

r₁₁= 163.107
d₁₁= 2.30
n_d6= 1.52542
ν_d6= 55.78

r₁₂= −13.302 (Aspheric)
d₁₂=

(Variable)

r₁₃= 47.335 (Aspheric)
d₁₃= 0.80
n_d7= 1.52542
ν_d7= 55.78

r₁₄= 157.532
d₁₄= 0.50

r₁₅= ∞
d₁₅= 0.74
n_d8= 1.54771
ν_d8= 62.84

r₁₆= ∞
d₁₆= 0.50

r₁₇= ∞
d₁₇= 0.50
n_d9= 1.51633
ν_d9= 64.14

r₁₈= ∞
d₁₈= 1.00

r₁₉= ∞ (Imaging plane)

Aspherical Coefficients

1st surface

K = −4.857

A₄= 1.91170 × 10⁻⁵

A₆= −7.93990 × 10⁻⁷

A₈= 1.25291 × 10⁻⁸

A₁₀= 0

2nd surface

K = −0.331

A₄= −4.83010 × 10⁻⁵

A₆= −1.87391 × 10⁻⁶

A₈= 9.14916 × 10⁻⁸

A₁₀= −2.06253 × 10⁻⁹

A₁₂= 1.96883 × 10⁻¹¹

6th surface

K = −0.325

A₄= −1.08286 × 10⁻⁴

A₆= 5.17066 × 10⁻⁷

A₈= −7.59167 × 10⁻⁸

A₁₀= 3.18869 × 10⁻⁹

7th surface

K = −18.058

A₄= 7.08103 × 10⁻⁵

A₆= 5.33584 × 10⁻⁷

A₈= −6.05038 × 10⁻⁸

A₁₀= 3.22384 × 10⁻⁹

12th surface

K = 0.000

A₄= 2.25205 × 10⁻⁴

A₆= 1.09111 × 10⁻⁵

A₈= −1.45088 × 10⁻⁶

A₁₀= 2.99941 × 10⁻⁸

13th surface

K = 0.000

A₄= −3.95988 × 10⁻⁴

A₆= 5.73474 × 10⁻⁵

A₈= −4.14057 × 10⁻⁶

A₁₀= 6.74351 × 10⁻⁸

Zooming Data (∞)

WE
ST
TE

f (mm)
7.98
12.38
22.98

F_NO
1.84
2.30
3.45

2ω (°)
62.01
39.12
21.14

d₄
17.81
9.15
1.30

d₁₀
6.49
11.36
21.21

d₁₂
2.51
1.87
1.55

EXAMPLE 2

r₁= −24.369 (Aspheric)
d₁= 0.85
n_d1= 1.74320
ν_d1= 49.34

r₂= 9.860 (Aspheric)
d₂= 2.17

r₃= 23.496
d₃= 2.40
n_d2= 2.00330
ν_d2= 28.27

r₄= −235.853
d₄=

(Variable)

r₅= ∞ (Stop)
d₅= 0.00

r₆= 7.700 (Aspheric)
d₆= 2.80
n_d3= 1.59201
ν_d3= 67.02

r₇= −37.265 (Aspheric)
d₇= 0.10

r₈= 9.047
d₈= 2.40
n_d4= 1.88300
ν_d4= 40.76

r₉= 52.604
d₉=0.50
n_d5= 1.78472
ν_d5= 25.68

r₁₀= 4.574
d₁₀=

(Variable)

r₁₁= 171.626
d₁₁= 2.30
n_d6= 1.52542
ν_d6= 55.78

r₁₂= −11.651 (Aspheric)
d₁₂=

(Variable)

r₁₃= ∞
d₁₃= 0.74
n_d7= 1.54771
ν_d7= 62.84

r₁₄= ∞
d₁₄= 0.50

r₁₅= ∞
d₁₅= 0.50
n_d8= 1.51633
ν_d8= 64.14

r₁₆= ∞
d₁₆= 1.00

r₁₇= ∞ (Imaging plane)

Aspherical Coefficients

1st surface

K = −1.139

A₄= 2.02421 × 10⁻⁵

A₆= −9.60379 × 10⁻⁷

A₈= 1.58142 × 10⁻⁸

A₁₀= 0

2nd surface

K = −0.491

A₄= −1.25226 × 10⁻⁴

A₆= −2.13739 × 10⁻⁶

A₈= 7.45918 × 10⁻⁸

A₁₀= −1.10786 × 10⁻⁹

A₁₂= 9.55589 × 10⁻¹²

6th surface

K = −0.367

A₄= −1.10084 × 10⁻⁴

A₆= −2.26216 × 10⁻⁶

A₈= 7.28014 × 10⁻⁸

A₁₀= −4.77178 × 10⁻¹⁰

7th surface

K = −9.634

A₄= 9.98274 × 10⁻⁵

A₆= −2.11753 × 10⁻⁶

A₈= 9.22826 × 10⁻⁸

A₁₀= −7.79379 × 10⁻¹⁰

12th surface

K = −1.098

A₄= 6.82670 × 10⁻⁴

A₆= −3.32068 × 10⁻⁵

A₈= 1.32590 × 10⁻⁶

A₁₀= −2.29769 × 10⁻⁸

Zooming Data (∞)

WE
ST
TE

f (mm)
7.89
12.63
22.74

F_NO
1.84
2.36
3.54

2ω (°)
61.68
38.23
21.61

d₄
17.52
8.34
1.30

d₁₀
6.12
11.18
20.44

d₁₂
3.22
2.52
1.44

EXAMPLE 3

r₁= −32.805 (Aspheric)
d₁= 0.85
n_d1= 1.74320
ν_d1= 49.34

r₂= 8.821 (Aspheric)
d₂= 2.37

r₃= 21.367
d₃= 2.40
n _d2= 2.00330
ν_d2= 28.27

r₄= −990.027
d₄=

(Variable)

r₅= ∞ (Stop)
d₅= 0.00

r₆= 8.138 (Aspheric)
d₆= 2.80
n_d3= 1.59201
ν_d3= 67.02

r₇= −49.623 (Aspheric)
d₇= 0.10

r₈= 9.644
d₈= 2.40
n_d4= 1.88300
ν_d4= 40.76

r₉= −398.189
d₉= 0.50
n_d5= 1.76182
ν_d5= 26.52

r₁₀= 4.845
d₁₀=

(Variable)

r₁₁= 23.104
d₁₁= 2.30
n_d6= 1.52542
ν_d6= 55.78

r₁₂= −25.555 (Aspheric)
d₁₂=

(Variable)

r₁₃= 37.552 (Aspheric)
d₁₃= 0.80
n_d7= 1.52542
ν_d7= 55.78

r₁₄= ∞
d₁₄= 0.50

r₁₅= ∞
d₁₅= 0.74
n_d8= 1.54771
ν_{d8 = 62.84}

r₁₆= ∞
d₁₆= 0.50

r₁₇= ∞
d₁₇= 0.50
n_d9= 1.51633
ν_d9= 64.14

r₁₈= ∞
d₁₈= 0.93

r₁₉= ∞ (Imaging plane)

Aspherical Coefficients

1st surface

K = 0.000

A₄= −7.23340 × 10⁻⁵

A₆= 7.82522 × 10⁻⁷

A₈= 1.74057 × 10⁻⁸

A₁₀= −2.80490 × 10⁻¹⁰

2nd surface

K = −0.680

A₄= −2.17245 × 10⁻⁴

A₆= 9.78691 × 10⁻⁷

A₈= 2.15020 × 10⁻⁸

A₁₀= −7.54735 × 10⁻¹²

A₁₂= −6.96482 × 10⁻¹²

6th surface

K = −0.211

A₄= −1.08462 × 10⁻⁴

A₆= −6.11103 × 10⁻⁷

A₈= −4.74554 × 10⁻⁸

A₁₀= 2.70946 × 10⁻⁹

7th surface

K = 0.000

A₄= 1.17441 × 10⁻⁴

A₆= −1.80136 × 10⁻⁷

A₈= −2.26721 × 10⁻⁸

A₁₀= 2.61135 × 10⁻⁹

12th surface

K = 0.000

A₄= −4.78766 × 10⁻⁵

A₆= 3.82653 × 10⁻⁶

A₈= −1.68282 × 10⁻⁷

A₁₀= 2.74886 × 10⁻⁹

13th surface

K = 0.000

A₄= −5.40034 × 10⁻⁴

A₆= 1.23392 × 10⁻⁵

A₈= −2.71717 × 10⁻⁷

A₁₀= 3.52095 × 10⁻⁹

Zooming Data (∞)

WE
ST
TE

f (mm)
8.01
13.61
23.18

F_NO
1.84
2.41
3.45

2ω (°)
60.98
36.09
21.26

d₄
18.24
6.57
1.23

d₁₀
7.26
12.17
23.55

d₁₂
2.58
3.38
1.71

EXAMPLE 4

r₁= −32.705 (Aspheric)
d₁= 0.85
n_d1= 1.74320
ν_d1= 49.34

r₂= 8.879 (Aspheric)
d₂= 2.38

r₃= 21.569
d₃= 2.30
n_d2= 2.00330
ν_d2= 28.27

r₄= 202364.298
d₄=

(Variable)

r₅= ∞ (Stop)
d₅= 0.00

r₆= 8.220 (Aspheric)
d₆= 2.80
n_d3= 1.59201
ν_d3= 67.02

r₇= −47.063 (Aspheric)
d₇= 0.10

r₈= 9.799
d₈= 2.40
n_d4= 1.88300
ν_d4= 40.76

r₉= −111.185
d₉= 0.53
n_d5= 1.76182
ν_d5= 26.52

r₁₀= 4.926
d₁₀=

(Variable)

r₁₁= 25.699
d₁₁= 2.30
n_d6= 1.52542
ν_d6= 55.78

r₁₂= −22.867 (Aspheric)
d₁₂=

(Variable)

r₁₃= −34.483 (Aspheric)
d₁₃= 0.80
n_d7= 1.52542
ν_d7= 55.78

r₁₄= −21.613
d₁₄=

(Variable)

r₁₅= ∞
d₁₅= 0.74
n_d8= 1.54771
ν_d8= 62.84

r₁₆= ∞
d₁₆= 0.20

r₁₇= ∞
d₁₇= 0.50
n_d9= 1.51633
ν_d9= 64.14

r₁₈= ∞
d₁₈= 1.00

r₁₉= ∞ (Imaging plane)

Aspherical Coefficients

1st surface

K = 0.000

A₄= −3.37307 × 10⁻⁵

A₆= −9.72817 × 10⁻⁷

A₈= 4.31496 × 10⁻⁸

A₁₀= −4.11460 × 10⁻¹⁰

2nd surface

K = −0.674

A₄= −1.76528 × 10⁻⁴

A₆= −1.06503 × 10⁻⁶

A₈= 4.02343 × 10⁻⁸

A₁₀= 2.29184 × 10⁻¹⁰

A₁₂= −1.01966 × 10⁻¹¹

6th surface

K = −0.210

A₄= −1.21130 × 10⁻⁴

A₆= −8.55663 × 10⁻⁷

A₈= −3.16534 × 10⁻⁸

A₁₀= 1.27827 × 10⁻⁹

7th surface

K = 0.000

A₄= 1.09439 × 10⁻⁴

A₆= −8.89418 × 10⁻⁷

A₈= 7.17937 × 10⁻⁹

A₁₀= 8.91942 × 10⁻¹⁰

12th surface

K = 0.000

A₄= −8.69778 × 10⁻⁵

A₆= 8.22798 × 10⁻⁶

A₈= −3.15609 × 10⁻⁷

A₁₀= 4.70020 × 10⁻⁹

13th surface

K = 0.000

A₄= −7.46044 × 10⁻⁴

A₆= 2.71091 × 10⁻⁵

A₈= −7.30692 × 10⁻⁷

A₁₀= 9.34974 × 10⁻⁹

Zooming Data (∞)

WE
ST
TE

f (mm)
8.01
13.55
23.21

F_NO
1.84
2.41
3.45

2ω (°)
60.75
36.12
21.27

d₄
18.51
7.09
1.60

d₁₀
7.22
12.00
23.05

d₁₂
1.35
3.07
2.29

d₁₄
2.03
1.09
0.52

EXAMPLE 5

r₁= −145.383 (Aspheric)
d₁= 0.90
n_d1= 1.69350
ν_d1= 53.21

r₂= 8.650
d₂= 2.00
n_d2= 2.00069
ν_d2= 25.46

r₃= 10.651
d₃=

(Variable)

r₄= 12.185 (Aspheric)
d₄= 2.26
n_d3= 1.74320
ν_d3= 49.34

r₅= 81.448 (Aspheric)
d₅= 0.80

r₆= ∞ (Stop)
d₆= 0.20

r₇= 111.218
d₇= 0.55
n_d4= 1.84666
ν_d4= 23.78

r₈= 8.992
d₈= 2.50
n_d5= 1.88300
ν_d5= 40.76

r₉= −45.340
d₉=

(Variable)

r₁₀= 11.124 (Aspheric)
d₁₀= 2.00
n_d6= 1.69350
ν_d6= 53.21

r₁₁= 21.087 (Aspheric)
d₁₁=

(Variable)

r₁₂= −13.435
d₁₂= 1.00
n_d7= 1.68893
ν_d7= 31.07

r₁₃= −21.718 (Aspheric)
d₁₃=

(Variable)

r₁₄= ∞
d₁₄= 0.74
n_d8= 1.54771
ν_d8= 62.84

r₁₅= ∞
d₁₅= 0.50

r₁₆= ∞
d₁₆= 0.50
n_d9= 1.51633
ν_d9= 64.14

r₁₇= ∞
d₁₇= 0.50

r₁₈= ∞ (Imaging plane)

Aspherical Coefficients

1st surface

K = 0.000

A₄= 1.25228 × 10⁻⁵

A₆= −1.68857 × 10⁻⁷

A₈= 5.23426 × 10⁻⁹

A₁₀= −1.91214 × 10⁻¹¹

A₁₂= −2.14972 × 10⁻¹²

A₁₄= 2.50471 × 10⁻¹⁴

4th surface

K = −2.274

A₄= −1.31273 × 10⁻⁴

A₆= −6.67025 × 10⁻⁶

A₈= 3.40034 × 10⁻⁸

A₁₀= −7.37366 × 10⁻⁹

5th surface

K = 0.000

A₄= −2.71343 × 10⁻⁴

A₆= −3.88226 × 10⁻⁶

A₈= −1.41496 × 10⁻⁷

A₁₀= −1.80000 × 10⁻⁹

10th surface

K = −2.888

A₄= −3.04589 × 10⁻⁴

A₆= −1.11767 × 10⁻⁵

A₈= −5.04355 × 10⁻⁷

A₁₀= 0

11th surface

K = 0.000

A₄= −7.15384 × 10⁻⁴

A₆= −1.94625 × 10⁻⁵

A₈= 0

A₁₀= 0

13th surface

K = 0.000

A₄= 8.96159 × 10⁻⁴

A₆= 5.87184 × 10⁻⁶

A₈= −2.49866 × 10⁻⁷

A₁₀= 0

Zooming Data (∞)

WE
ST
TE

f (mm)
7.99
12.35
22.99

F_NO
1.86
2.14
2.84

2ω (°)
62.43
39.90
21.32

d₃
16.93
8.07
1.10

d₉
6.36
6.18
14.52

d₁₁
1.95
3.61
8.43

d₁₃
2.95
4.14
1.79

EXAMPLE 6

r₁= −78.142 (Aspheric)
d₁= 0.90
n_d1= 1.74320
ν_d1= 49.34

r₂= 8.767
d₂= 2.00
n_d2= 2.00170
ν_d2= 20.64

r₃= 12.214
d₃=

(Variable)

r₄= 11.533 (Aspheric)
d_{4 = 2.27}
n_d3= 1.74320
ν_d3= 49.34

r₅= 40.855
d₅= 0.55
n_d4= 1.84666
ν_d4= 23.78

r₆= 7.068
d₆= 3.30
n_d5= 1.88300
ν_d5= 40.76

r₇= −115.072
d₇= 0.00

r₈= ∞ (Stop)
d₈=

(Variable)

r₉= 12.459 (Aspheric)
d₉= 2.00
n_d6= 1.69350
ν_d6= 53.21

r₁₀= 30.922 (Aspheric)
d₁₀=

(Variable)

r₁₁= −14.299
d₁₁= 1.00
n_d7= 1.68893
ν_d7= 31.07

r₁₂= −18.793 (Aspheric)
d₁₂=

(Variable)

r₁₃= ∞
d₁₃= 0.74
n_d8= 1.54771
ν_d8= 62.84

r₁₄= ∞
d₁₄= 0.50

r₁₅= ∞
d₁₅= 0.50
n_d9= 1.51633
ν_d9= 64.14

r₁₆= ∞
d₁₆= 0.50

r₁₇= ∞ (Imaging plane)

Aspherical Coefficients

1st surface

K = 0.000

A₄= 1.56906 × 10⁻⁵

A₆= −1.29413 × 10⁻⁶

A₈= 8.45917 × 10⁻⁸

A₁₀= −2.66460 × 10⁻⁹

A₁₂= 3.93437 × 10⁻¹¹

A₁₄= −2.22233 × 10⁻¹³

4th surface

K = 1.054

A₄= −1.58746 × 10⁻⁴

A₆= −3.45221 × 10⁻⁶

A₈= 8.56173 × 10⁻⁸

A₁₀= −1.87648 × 10⁻⁹

9th surface

K = −1.904

A_{4 = −4.66723 × 10}⁻⁴

A_{6 = −1.21485 × 10}⁻⁵

A_{8 = −5.97308 × 10}⁻⁷

A_{10 = 0}

10th surface

K = 0.000

A₄= −7.04701 × 10⁻⁴

A₆= −2.17479 × 10⁻⁵

A₈= 0

A₁₀= 0

12th surface

K = 0.000

A₄= 9.63721 × 10⁻⁴

A₆= −3.46884 × 10⁻⁶

A₈= 2.58483 × 10⁻⁸

A₁₀= 0

Zooming Data (∞)

WE
ST
TE

f (mm)
8.06
12.46
22.88

F_NO
1.86
2.17
2.99

2ω (°)
62.14
39.39
21.48

d₃
16.66
7.71
1.10

d₈
7.78
7.73
15.29

d₁₀
1.87
4.02
9.10

d₁₂
2.27
3.11
1.55

EXAMPLE 7

r₁= −29.732 (Aspheric)
d₁= 0.90
n_d1= 1.69350
ν_d1= 53.21

r₂= 14.601
d₂= 1.80
n_d2= 1.83918
ν_d2= 23.85

r₃= 27.894 (Aspheric)
d₃=

(Variable)

r₄= 12.843 (Aspheric)
d₄= 2.20
n_d3= 1.74320
ν_d3= 49.34

r₅= −99.138 (Aspheric)
d₅= 0.80

r₆= ∞ (Stop)
d₆= 0.20

r₇= 7.183
d₇= 2.15
n_d4= 1.88300
ν_d4= 40.76

r₈= 29.767
d₈= 0.50
n_d5= 1.80810
ν_d5= 22.76

r₉= 5.037
d₉=

(Variable)

r₁₀= 10.779 (Aspheric)
d₁₀= 2.57
n_d6= 1.69350
ν_d6= 53.21

r₁₁= 42.476 (Aspheric)
d₁₁=

(Variable)

r₁₂= 40.000 (Aspheric)
d₁₂= 1.00
n_d7= 1.52542
ν_d7= 55.78

r₁₃= 30.242
d₁₃= 1.00

r₁₄= ∞
d₁₄= 0.74
n_d8= 1.54771
ν_d8= 62.84

r₁₅= ∞
d₁₅= 0.50

r₁₆= ∞
d₁₆= 0.50
n_d9= 1.51633
ν_d9= 64.14

r₁₇= ∞
d₁₇= 0.41

r₁₈= ∞ (Imaging plane)

Aspherical Coefficients

1st surface

K = 0.000

A₄= 1.70392 × 10⁻⁴

A₆= −2.36418 × 10⁻⁶

A₈= 1.14962 × 10⁻⁸

A₁₀= 3.13033 × 10⁻¹⁰

A₁₂= −5.19506 × 10⁻¹²

A₁₄= 2.48049 × 10⁻¹⁴

3rd surface

K = 0.000

A₄= 1.33513 × 10⁻⁴

A₆= −1.87741 × 10⁻⁶

A₈= −1.49663 × 10⁻⁸

A₁₀= 3.63709 × 10⁻¹¹

4th surface

K = 0.597

A₄= −1.74298 × 10⁻⁴

A₆= −1.34175 × 10⁻⁶

A₈= −8.12069 × 10⁻⁸

A₁₀= −2.96234 × 10⁻⁹

5th surface

K = 0.000

A₄= −7.76740 × 10⁻⁵

A₆= −8.18520 × 10⁻⁷

A₈= −1.51793 × 10⁻⁷

A₁₀= −4.25649 × 10⁻¹⁰

10th surface

K = 0.000

A₄= −3.34112 × 10⁻⁴

A₆= 1.72489 × 10⁻⁶

A₈= −1.12625 × 10⁻⁷

A₁₀= 0

11th surface

K = 0.000

A₄= −6.82941 × 10⁻⁴

A₆= 3.40824 × 10⁻⁶

A₈= −5.60943 × 10⁻⁸

A₁₀= 0

12th surface

K = 0.000

A₄= −1.84764 × 10⁻³

A₆= 5.24923 × 10⁻⁵

A₈= −3.73324 × 10⁻⁶

A₁₀= 1.00779 × 10⁻⁷

Zooming Data (∞)

WE
ST
TE

f (mm)
7.86
12.38
22.52

F_NO
1.86
2.18
3.04

2ω (°)
63.24
39.99
22.67

d₃
21.80
9.68
1.69

d₉
6.30
7.92
17.36

d₁₁
1.64
3.31
4.99

EXAMPLE 8

r₁= −20.204 (Aspheric)
d₁= 0.90
n_{d1 = 1.49700}
ν_d1= 81.54

r₂= 17.545
d₂= 1.80
n_d2= 1.84666
ν_d2= 23.78

r₃= 23.794 (Aspheric)
d₃=

(Variable)

r₄= ∞ (Stop)
d₄= 0.10

r₅= 18.034 (Aspheric)
d₅= 2.20
n_d3= 1.69350
ν_d3= 53.21

r₆= −27.012 (Aspheric)
d₆= 0.10

r₇= 6.333
d₇= 2.60
n_d4= 1.88300
ν_d4= 40.76

r₈= 12.298
d₈= 0.60
n_d5= 1.92286
ν_d5= 20.88

r₉= 4.561
d₉=

(Variable)

r₁₀= 53.796
d_{10 = 2.80}
n_d6= 1.74320
ν_d6= 49.34

r₁₁= −14.000 (Aspheric)
d₁₁=

(Variable)

r₁₂= −24.948 (Aspheric)
d₁₂= 1.00
n_d7= 1.52542
ν_d7= 55.78

r₁₃= −14.904
d₁₃=

(Variable)

r₁₄= ∞
d₁₄= 0.74
n_d8= 1.54771
ν_d8= 62.84

r₁₅= ∞
d₁₅= 0.50

r₁₆= ∞
d₁₆= 0.50
n_d9= 1.51633
ν_d9= 64.14

r₁₇= ∞
d₁₇= 0.63

r₁₈= ∞ (Imaging plane)

Aspherical Coefficients

1st surface

K = 0.000

A₄= 4.98101 × 10⁻⁵

A₆= 2.62991 × 10⁻⁷

A₈= −1.54568 × 10⁻⁸

A₁₀= 5.46523 × 10⁻¹⁰

A₁₂= −8.17649 × 10⁻¹²

A₁₄= 3.64148 × 10⁻¹⁴

3rd surface

K = 0.000

A₄= −1.34508 × 10⁻⁵

A₆= 8.32834 × 10⁻⁸

A₈= 2.05078 × 10⁻⁸

A₁₀= −3.59245 × 10⁻¹⁰

5th surface

K = −2.484

A₄= −4.56019 × 10⁻⁵

A₆= 1.56225 × 10⁻⁷

A₈= −5.92118 × 10⁻⁸

A₁₀= −5.94787 × 10⁻¹¹

6th surface

K = −1.006

A₄= −7.09011 × 10⁻⁷

A₆= −5.19547 × 10⁻⁷

A₈= −3.21483 × 10⁻⁸

A₁₀= −3.47781 × 10⁻¹⁰

11th surface

K = −3.068

A₄= −1.15031 × 10⁻⁴

A₆= −1.41621 × 10⁻⁶

A₈= 2.96767 × 10⁻⁸

A₁₀= 0

12th surface

K = 0.000

A₄= −1.17795 × 10⁻³

A₆= 1.48055 × 10⁻⁵

A₈= −1.81960 × 10⁻⁸

A₁₀= 0

Zooming Data (∞)

WE
ST
TE

f (mm)
8.17
12.51
23.49

F_NO
1.86
2.25
3.35

2ω (°)
61.31
38.70
20.79

d₃
18.23
9.18
2.05

d₉
5.72
9.27
19.64

d₁₁
1.47
2.41
2.19

d₁₃
1.20
0.54
0.30

EXAMPLE 9

r₁= −28.866 (Aspheric)
d₁0.90
n_d1= 1.58313
ν_d1= 59.38

r₂= 12.613
d₂= 1.80
n_d2= 1.83918
ν_d2= 23.85

r₃= 17.351 (Aspheric)
d₃=

(Variable)

r₄= 10.328 (Aspheric)
d₄= 2.14
n_d3= 1.69350
ν_d3= 53.21

r₅= −125.640 (Aspheric)
d₅= 0.20

r₆= 7.249
d₆= 2.60
n_d4= 1.88300
ν_d4= 40.76

r₇= −63.997
d₇= 0.40
n_d5= 1.78472
ν_d5= 25.68

r₈= 4.607
d₈= 1.50

r₉= ∞ (Stop)
d₉=

(Variable)

r₁₀= 10.095 (Aspheric)
d₁₀= 2.20
n_d6= 1.74320
ν_d6= 49.34

r₁₁= 18.794 (Aspheric)
d₁₁=

(Variable)

r₁₂= 33.259 (Aspheric)
d₁₂= 1.00
n_d7= 1.52542
ν_d7= 55.78

r₁₃= −645.512
d₁₃= 1.14

r₁₄= ∞
d₁₄= 0.74
n_d8= 1.54771
ν_d8= 62.84

r₁₅= ∞
d₁₅= 0.50

r₁₆= ∞
d₁₆= 0.50
n_d9= 1.51633
ν_d9= 64.14

r₁₇= ∞
d₁₇= 0.46

r₁₈= ∞ (Imaging plane)

Aspherical Coefficients

1st surface

K = 0.000

A₄= 6.38764 × 10⁻⁵

A₆= −1.09687 × 10⁻⁶

A₈= 2.22426 × 10⁻⁸

A₁₀= 1.99264 × 10⁻¹¹

A₁₂= −2.98978 × 10⁻¹²

A₁₄= −1.81600 × 10⁻¹⁴

3rd surface

K = 0.000

A₄= 2.14506 × 10⁻⁵

A₆= −4.03380 × 10⁻⁷

A₈= 2.18349 × 10⁻⁸

A¹⁰= −5.77518 × 10⁻¹²

4th surface

K = −0.161

A₄= −1.43882 × 10⁻⁴

A₆= −1.09831 × 10⁻⁷

A₈= −8.65978 × 10⁻⁹

A₁₀= −3.29195 × 10⁻¹⁰

5th surface

K = 0.000

A₄= −2.18434 × 10⁻⁵

A₆= 2.23702 × 10⁻⁷

A₈= −9.89591 × 10⁻⁹

A₁₀= −1.54656 × ⁻¹⁰

10th surface

K = 0.000

A₄= −5.79354 × 10⁻⁴

A₆= 1.20789 × 10⁻⁵

A₈= −2.73123 × 10⁻⁷

A₁₀= 0

11th surface

K = 0.000

A₄= −1.07181 × 10⁻³

A₆= 2.06212 × 10⁻⁵

A₈= −3.85314 × 10⁻⁷

A₁₀= 0

12th surface

K = 0.000

A₄= −1.57377 × 10⁻³

A₆= 0

A₈= 0

A₁₀= 0

Zooming Data (∞)

WE
ST
TE

f (mm)
7.99
12.24
22.75

F _NO
1.86
2.29
3.46

2ω (°)
62.67
40.39
22.11

d₃
17.00
8.17
1.43

d₉
3.90
5.09
13.29

d₁₁
1.51
3.27
5.31

EXAMPLE 10

r₁= −45.206 (Aspheric)
d₁= 0.90
n_d1= 1.69350
ν_d1= 53.21

r₂= 11.291
d₂= 1.80
n_d2= 1.84666
ν_d2= 23.78

r₃= 17.553 (Aspheric)
d₃= (Variable)

r₄= ∞ (Stop)
d₄= 0.10

r₅= 9.783 (Aspheric)
d₅= 2.26
n_d3= 1.74320
ν_d3= 49.34

r₆= −107.620 (Aspheric)
d₆= 0.10

r₇= 6.333
d₇= 2.00
n_d4= 1.72916
ν_d4= 54.68

r₈= 9.228
d₈= 0.60
n_d5= 2.00170
ν_d5= 20.64

r₉= 4.744
d₉= (Variable)

r₁₀= 14.018 (Aspheric)
d₁₀= 2.72
n_d6= 1.69350
ν_d6= 53.21

r₁₁= 260.132 (Aspheric)
d₁₁=

(Variable)

r₁₂= 130.344 (Aspheric)
d₁₂= 1.00
n_d7= 1.52542
ν_d7= 55.78

r₁₃= ∞
d₁₃=

(Variable)

r₁₄= ∞
d₁₄= 0.74
n_d8= 1.54771
ν_d8= 62.84

r₁₅= ∞
d₁₅= 0.50

r₁₆= ∞
d₁₆= 0.50
n_d9= 1.51633
ν_d9= 64.14

r₁₇= ∞
d₁₇= 0.90

r₁₈= ∞ (Imaging plane)

Aspherical Coefficients

1st surface

K = 0.000

A₄= 1.90374 × 10⁻⁶

A₆= −3.84263 × 10⁻⁷

A₈= 8.63693 × 10⁻⁹

A₁₀= 6.67354 × 10⁻¹²

A₁₂= −1.53332 × 10⁻¹²

A₁₄= 1.13376 × 10⁻¹⁴

3rd surface

K = 0.000

A₄= −2.63248 × 10⁻⁵

A₆= 2.90936 × 10⁻⁷

A₈= −1.20811 × 10⁻⁸

A₁₀= 1.85370 × 10⁻¹⁰

5th surface

K = −0.263

A₄= −5.86359 × 10⁻⁵

A₆= 2.39004 × 10⁻⁷

A₈= 2.34845 × 10⁻⁸

A₁₀= 5.34915 × 10⁻¹⁰

6th surface

K = −234.189

A₄= 2.88968 × 10⁻⁵

A₆= 1.01712 × 10⁻⁶

A₈= 9.63087 × 10⁻⁹

A₁₀= 7.64550 × 10⁻¹⁰

10th surface

K = −6.835

A₄= 1.00639 × 10⁻⁶

A₆= −4.88584 × 10⁻⁶

A₈= 0

A₁₀= 0

11th surface

K = 0.000

A₄= −4.99152 × 10⁻⁴

A₆= −9.09044 × 10⁻⁷

A₈= 0

A₁₀= 0

12th surface

K = 0.000

A₄= −1.55873 × 10⁻³

A₆= 5.84821 × 10⁻⁶

A₈= 0

A₁₀= 0

Zooming Data (∞)

WE
ST
TE

f (mm)
7.87
12.54
22.67

F_NO
1.86
2.14
2.93

2 ω (°)
63.07
38.84
21.80

d₃
19.50
8.63
1.90

d₉
5.74
6.07
14.93

d₁₁
2.05
4.80
8.03

d₁₃
0.48
0.41
0.29

EXAMPLE 11

r₁= −13.852 (Aspheric)
d₁= 0.90
n_d1= 1.49700
ν_d1= 81.54

r₂= 24.684
d₂1.59
n_d2= 1.83918
ν_d2= 23.85

r₃= 43.897 (Aspheric)
d₃= (Variable)

r₄= 10.521 (Aspheric)
d₄= 1.82
n_d3= 1.69350
ν_d3= 53.21

r₅= −77.251 (Aspheric)
d₅= 0.80

r₆= ∞ (Stop)
d₆= 0.00

r₇= 6.907
d₇= 2.53
n_d4= 1.88300
ν_d4= 40.76

r₈= 87.359
d₈= 0.59
n_d5= 1.83918
ν_d5= 23.85

r₉= 4.354 (Aspheric)
d₉= (Variable)

r₁₀= −30.574 (Aspheric)
d₁₀= 1.99
n_d6= 1.80610
ν_d6= 40.92

r₁₁= −12.104 (Aspheric)
d₁₁=

(Variable)

r₁₂= 40.000 (Aspheric)
d₁₂= 0.80
n_d7= 1.52542
ν_d7= 55.78

r₁₃= −73.398
d₁₃=

(Variable)

r₁₄= ∞
d₁₄= 0.74
n_d8= 1.54771
ν_d8= 62.84

r₁₅= ∞
d₁₅= 0.50

r₁₆= ∞
d₁₆= 0.50
n_d9= 1.51633
ν_d9= 64.14

r₁₇= ∞
d₁₇= 0.51

r₁₈= ∞ (Imaging plane)

Aspherical Coefficients

1st surface

K = 0.000

A₄= 4.06059 × 10⁻⁴

A₆= −6.07979 × 10⁻⁶

A₈= 5.43296 × 10⁻⁸

A₁₀= 3.25528 × 10⁻¹¹

A₁₂= −2.48489 × 10⁻¹²

A₁₄= −2.01707 × 10⁻¹⁵

3rd surface

K = 0.000

A₄= 1.68867 × 10⁻⁴

A₆= −1.12760 × 10⁻⁶

A₈= −1.24654 × 10⁻⁷

A₁₀= 4.77759 × 10⁻⁹

A₁₂= −6.82004 × 10⁻¹¹

A₁₄= 3.36755 × 10⁻¹³

4th surface

K = 0.172

A₄= −1.43531 × 10⁻⁴

A₆= 2.42963 × 10⁻⁷

A₈= −8.81758 × 10⁻⁸

A₁₀= 2.81587 × 10⁻⁹

5th surface

K = 0.000

A₄= −2.60495 × 10⁻⁵

A₆= 7.62112 × 10⁻⁷

A₈= −2.59097 × 10⁻⁹

A₁₀= 1.04283 × 10⁻⁹

9th surface

K = 0.000

A₄= 2.21869 × 10⁻⁴

A₆= −5.83726 × 10⁻⁶

A₈= 2.76274 × 10⁻⁷

A₁₀= −1.82983 × 10⁻⁸

10th surface

K = 0.000

A₄= −5.33927 × 10⁻⁴

A₆= 1.39916 × 10⁻⁵

A₈= −1.37267 × 10⁻⁷

A₁₀= 4.11809 × 10⁻⁹

11th surface

K = 0.000

A₄= −5.20824 × 10⁻⁴

A₆= 1.11823 × 10⁻⁵

A₈= −1.36807 × 10⁻⁷

A₁₀= 3.68016 × 10⁻⁹

12th surface

K = 0.000

A₄= −1.22480 × 10⁻³

A₆= 4.02065 × 10⁻⁵

A₈= −1.24733 × 10⁻⁶

A₁₀= 1.99247 × 10⁻⁸

Zooming Data (∞)

WE
ST
TE

f (mm)
8.10
10.89
23.55

F_NO
1.86
2.11
3.21

2ω (°)
61.86
44.92
21.09

d₃
19.16
11.95
0.50

d₉
3.97
4.97
12.74

d₁₁
2.16
4.03
6.90

d₁₃
1.80
0.81
0.19

EXAMPLE 12

r₁= −18.164 (Aspheric)
d₁= 0.90
n_d1= 1.51633
ν_{d1 = 64.14}

r₂= 13.285
d₂= 1.80
n_d2= 1.83918
ν_d2= 23.85

r₃= 17.066 (Aspheric)
d₃= (Variable)

r₄= 13.962 (Aspheric)
d₄= 2.20
n_d3= 1.74320
ν_d3= 49.34

r₅= −25.345 (Aspheric)
d₅= 0.10

r₆= 6.022 (Aspheric)
d₆= 2.90
n_d4= 1.80610
ν_d4= 40.92

r₇= 119.085
d₇= 0.50
n_d5= 2.00069
ν_d5= 25.46

r₈= 4.353
d₈= 1.72

r₉= ∞ (Stop)
d₉= (Variable)

r₁₀= −8.900
d₁₀= 2.20
n_d6= 1.92286
ν_d6= 18.90

r₁₁= −12.685
d₁₁= 2.20

r₁₂= 64.569 (Aspheric)
d₁₂= 2.20
n_d7= 1.80610
ν_d7= 40.92

r₁₃= −13.461 (Aspheric)
d₁₃=

(Variable)

r₁₄= −11.384 (Aspheric)
d₁₄= 1.00
n_d8= 1.52542
ν_d8= 55.78

r₁₅= −6.418 (Aspheric)
d₁₅=

(Variable)

r₁₆= ∞
d₁₆= 0.74
n_d9= 1.54771
ν_d9= 62.84

r₁₇= ∞
d₁₇= 0.50

r₁₈= ∞
d₁₈= 0.50
n_d10= 1.51633
ν_d10= 64.14

r₁₉= ∞
d₁₉= 0.46

r₂₀= ∞ (Imaging plane)

Aspherical Coefficients

1st surface

K = −0.690

A₄= 1.00171 × 10⁻⁴

A₆= −1.63342 × 10⁻⁷

A₈= 0.000

A₁₀= 2.47553 × 10⁻¹²

3rd surface

K = −2.051

A₄= 8.63337 × 10⁻⁵

A₆= −3.14892 × 10⁻⁸

A₈= 7.47008 × 10⁻⁹

A₁₀= 0.000

4th surface

K = −0.478

A₄= −1.21096 × 10⁻⁴

A₆= 2.15656 × 10⁻⁶

A₈= −1.23897 × 10⁻⁷

A₁₀= 1.80977 × 10⁻⁹

5th surface

K = −8.737

A₄= −3.31436 × 10⁻⁵

A₆= −1.24138 × 10⁻⁶

A₈= −6.21293 × 10⁻⁹

A₁₀= 5.65326 × 10⁻¹⁰

6th surface

K = 0.224

A₄= −2.71845 × 10⁻⁵

A₆= −6.16672 × 10⁻⁶

A₈= 1.14404 × 10⁻⁷

A₁₀= −6.55772 × 10⁻⁹

12th surface

K = −511.997

A₄= −1.35640 × 10⁻⁴

A₆= −9.45635 × 10⁻⁶

A₈= −1.55393 × 10⁻⁷

A₁₀= 0

13th surface

K = 0.910

A₄= −1.71590 × 10⁻⁴

A₆= −7.55572 × 10⁻⁶

A₈= −1.11729 × 10⁻⁸

A₁₀= −1.29134 × 10⁻⁹

14th surface

K = −0.773

A₄= −1.36202 × 10⁻³

A₆= 7.62379 × 10⁻⁵

A₈= 0

A₁₀= 0

15th surface

K = 0.000

A₄= 0.000

A₆= 7.95903 × 10⁻⁵

A₈= 1.49209 × 10⁻⁷

A₁₀= 0

Zooming Data (∞)

WE
ST
TE

f (mm)
7.33
12.42
21.06

F_NO
1.86
2.57
3.86

2ω (°)
66.51
38.99
23.65

d₃
19.41
10.28
5.74

d₉
2.74
5.59
14.38

d₁₃
1.12
4.30
5.22

d₁₅
2.44
1.20
0.49

EXAMPLE 13

r₁= −24.536 (Aspheric)
d₁= 0.90
n_d1= 1.43875
ν_d1= 94.93

r₂= 19.004 (Aspheric)
d₂= (Variable)

r₃= 10.959 (Aspheric)
d₃= 2.40
n_d2= 1.69350
ν_d2= 53.21

r₄= −86.829 (Aspheric)
d₄= 0.80

r₅= ∞ (Stop)
d₅= 0.20

r₆= 7.563
d₆= 2.00
n_d3= 1.81600
ν_d3= 46.62

r₇= 11.746
d₇= 0.55
n_d4= 1.92286
ν_d4= 20.88

r₈= 5.783
d₈= (Variable)

r₉= 8.932 (Aspheric)
d₉= 2.20
n_d5= 1.59201
ν_d5= 67.02

r₁₀= 28.850 (Aspheric)
d₁₀=

(Variable)

r₁₁= −16.006
d₁₁= 1.00
n_d6= 1.68893
ν_d6= 31.07

r₁₂= −19.735 (Aspheric)
d₁₂=

(Variable)

r₁₃= ∞
d₁₃= 0.74
n_d7= 1.54771
ν_d7= 62.84

r₁₄= ∞
d₁₄= 0.50

r₁₅= ∞
d₁₅= 0.50
n_d8= 1.51633
ν_d8= 64.14

r₁₆= ∞
d₁₆= 0.50

r₁₇= ∞ (Imaging plane)

Aspherical Coefficients

1st surface

K = 0.000

A₄= 3.31292 × 10⁻⁴

A₆= −1.13962 × 10⁻⁵

A₈= 2.47541 × 10⁻⁷

A₁₀= −3.22394 × 10⁻⁹

A₁₂= 2.47078 × 10⁻¹¹

A₁₄= −8.24959 × 10⁻¹⁴

2nd surface

K = 0.936

A₄= 2.51032 × 10⁻⁴

A₆= −7.12570 × 10⁻⁶

A₈= 7.42959 × 10⁻⁸

A₁₀= 0

3rd surface

K = −0.469

A₄= −8.90377 × 10⁻⁵

A₆= −2.70516 × 10⁻⁶

A₈= 1.34920 × 10⁻⁷

A₁₀= −6.48691 × 10⁻⁹

4th surface

K = 0.000

A₄= −4.79022 × 10⁻⁵

A₆= −2.20902 × 10⁻⁶

A₈= 5.88068 × 10⁻⁸

A₁₀= −4.52956 × 10⁻⁹

9th surface

K = −0.354

A₄= −1.20596 × 10⁻⁴

A₆= −4.73292 × 10⁻⁶

A₈= −2.19357 × 10⁻⁷

A₁₀= 0

10th surface

K = 0.000

A₄= −2.02080 × 10⁻⁴

A₆= −1.42932 × 10⁻⁵

A₈= 0

A₁₀= 0

12th surface

K = 0.000

A₄= 1.30109 × 10⁻³

A₆= −2.61566 × 10⁻⁵

A₈= 1.01606 × 10⁻⁶

A₁₀= 0

Zooming Data (∞)

WE
ST
TE

f (mm)
8.04
11.69
22.91

F_NO
1.79
1.99
2.75

2ω (°)
62.15
41.58
21.63

d₂
23.22
11.29
0.40

d₈
5.20
4.91
12.25

d₁₀
1.71
2.91
6.99

d₁₂
1.58
2.27
0.76

EXAMPLE 14

r₁= −28.621 (Aspheric)
d₁= 0.90
n_d1= 1.43875
ν_d1= 94.93

r₂= 13.270 (Aspheric)
d₂= (Variable)

r₃= 18.910 (Aspheric)
d₃= 1.83
n_d2= 1.76802
ν_d2= 49.24

r₄= −52.548 (Aspheric)
d₄= 0.10

r₅= 7.084
d₅= 2.90
n_d3= 1.88300
ν_d3= 40.76

r₆= 27.980
d₆= 0.55
n_d4= 1.83918
ν_d4= 23.85

r₇= 5.338 (Aspheric)
d₇= 1.72

r₈= ∞ (Stop)
d₈= (Variable)

r₉= −7.790
d₉= 0.80
n_d5= 1.92286
ν_d5= 18.90

r₁₀= −11.396
d₁₀= 0.15

r₁₁= 60.657 (Aspheric)
d₁₁= 2.34
n_d6= 1.76802
ν_d6= 49.24

r₁₂= −11.972 (Aspheric)
d₁₂=

(Variable)

r₁₃= −26.874 (Aspheric)
d₁₃= 1.00
n_d7= 1.69350
ν_d7= 53.20

r₁₄= −17.612 (Aspheric)
d₁₄=

(Variable)

r₁₅= ∞
d₁₅= 0.74
n_d8= 1.54771
ν_d8= 62.84

r₁₆= ∞
d₁₆= 0.50

r₁₇= ∞
d₁₇= 0.50
n_d9= 1.51633
ν_d9= 64.14

r₁₈= ∞
d₁₈= 0.30

r₁₉= ∞ (Imaging plane)

Aspherical Coefficients

1st surface

K = −0.134

A₄= 2.47196 × 10⁻⁷

A₆= 2.34297 × 10⁻⁷

A₈= 0.000

A₁₀= 0.000

2nd surface

K = −1.454

A₄= 1.35646 × 10⁻⁵

A₆= −1.44746 × 10⁻⁷

A₈= 6.88829 × 10⁻⁹

A₁₀= 0.000

3rd surface

K = −0.093

A₄= 3.65504 × 10⁻⁵

A₆= −1.10311 × 10⁻⁷

A₈= −4.25458 × 10⁻⁸

A₁₀= 2.18338 × 10⁻¹⁰

4th surface

K = −18.402

A₄= 3.23935 × 10⁻⁵

A₆= −6.55955 × 10⁻⁷

A₈= −3.93067 × 10⁻⁸

A₁₀= 4.20213 × 10⁻¹⁰

7th surface

K = 0.004

A₄= 1.46877 × 10⁻⁴

A₆= 8.79444 × 10⁻⁶

A₈= 1.86813 × 10⁻⁷

A₁₀= 8.06203 × 10⁻⁹

11th surface

K = −12.098

A₄= −1.37660 × 10⁻⁴

A₆= 1.15212 × 10⁻⁶

A₈= −2.15963 × 10⁻⁷

A₁₀= 0

12th surface

K = −0.296

A₄= −5.40491 × 10⁻⁵

A₆= −2.16122 × 10⁻⁶

A₈= −3.79109 × 10⁻⁸

A₁₀= −2.42168 × 10⁻⁹

13th surface

K = −5.302

A₄= −3.55522 × 10⁻⁴

A₆= 2.30162 × 10⁻⁵

A₈= 0

A₁₀= 0

14th surface

K = 0.000

A₄= 0.000

A₆= 2.63358 × 10⁻⁵

A₈= 1.38995 × 10⁻⁸

A₁₀= 0

Zooming Data (∞)

WE
ST
TE

f (mm)
8.14
14.00
23.45

F_NO
1.86
2.31
3.68

2ω (°)
60.86
35.29
21.39

d₂
20.49
6.87
5.23

d₈
4.12
3.63
17.92

d₁₂
1.11
7.40
5.08

d₁₄
3.67
1.80
0.28

EXAMPLE 15

r₁= −22.016 (Aspheric)
d₁= 0.90
n_d1= 1.43875
ν_d1= 94.93

r₂= 15.461 (Aspheric)
d₂= (Variable)

r₃= 14.701 (Aspheric)
d₃= 2.06
n_d2= 1.74320
ν_d2= 49.34

r₄= −32.999 (Aspheric)
d₄= 0.10

r₅= 6.405 (Aspheric)
d₅= 2.90
n_d3= 1.80610
ν_d3= 40.92

r₆= 33.244
d₆= 0.50
n_d4= 2.00069
ν_d4= 25.46

r₇= 4.856
d₇= 1.72

r₈= ∞ (Stop)
d₈= (Variable)

r₉= −8.940
d₉= 0.80
n_d5= 1.92286
ν_d5= 18.90

r₁₀= −16.611
d₁₀= 0.18

r₁₁= 45.839 (Aspheric)
d₁₁= 2.55
n_d6= 1.80610
ν_d6= 40.92

r₁₂= −11.009 (Aspheric)
d₁₂=

(Variable)

r₁₃= −10.879 (Aspheric)
d₁₃= 1.00
n_d7= 1.52542
ν_d7= 55.78

r₁₄= −7.731 (Aspheric)
d₁₄=

(Variable)

r₁₅= ∞
d₁₅= 0.74
n_d8= 1.54771
ν_d8= 62.84

r₁₆= ∞
d₁₆= 0.50

r₁₇= ∞
d₁₇= 0.50
n_d9= 1.51633
ν_d9= 64.14

r₁₈= ∞
d₁₈= 0.30

r₁₉= ∞ (Imaging plane)

Aspherical Coefficients

1st surface

K = −0.519

A₄= 3.69695 × 10⁻⁵

A₆= 5.65774 × 10⁻⁸

A₈= 0.000

A₁₀= 3.73887 × 10⁻¹²

2nd surface

K = −2.161

A₄= 4.21993 × 10⁻⁵

A₆= −1.75597 × 10⁻⁷

A₈= 8.97310 × 10⁻⁹

A₁₀= 0.000

3rd surface

K = −0.175

A₄= −9.06679 × 10⁻⁶

A₆= −3.53110 × 10⁻⁷

A₈= −2.44657 × 10⁻⁸

A₁₀= 2.47234 × 10⁻¹⁰

4th surface

K = −17.775

A₄= −2.80828 × 10⁻⁵

A₆= −1.49749 × 10⁻⁷

A₈= −1.08247 × 10⁻⁸

A₁₀= 1.49523 × 10⁻¹⁰

5th surface

K = 0.037

A₄= −3.97693 × 10⁻⁵

A₆= −1.02246 × 10⁻⁶

A₈= −1.04292 × 10⁻⁹

A₁₀= −2.35540 × 10⁻¹³

11th surface

K = −11.838

A₄= −1.64575 × 10⁻⁴

A₆= −3.82233 × 10⁻⁶

A₈= −2.40636 × 10⁻⁷

A₁₀= 0

12th surface

K = −0.837

A₄= −6.41167 × 10⁻⁵

A₆= −6.74867 × 10⁻⁶

A₈= −4.23546 × 10⁻⁸

A₁₀= −2.74519 × 10⁻⁹

13th surface

K = −2.908

A₄= −1.08544 × 10⁻³

A₆= 4.99868 × 10⁻⁵

A₈= 0

A₁₀= 0

14th surface

K = 0.000

A₄= 0.000

A₆= 4.25126 × 10⁻⁵

A₈= 1.52833 × 10⁻⁷

A₁₀= 0

Zooming Data (∞)

WE
ST
TE

f (mm)
8.14
13.82
23.46

F_NO
1.85
2.47
3.85

2ω (°)
60.81
35.74
21.43

d₂
20.70
9.76
6.47

d₈
3.54
6.20
17.38

d₁₂
1.23
5.56
4.71

d₁₄
3.38
1.41
0.16

Aberration diagrams for Examples 1-15 upon focusing on an object point at infinity are given in FIGS. 16-30 wherein (a), (b) and (c) stand for spherical aberrations (SA), astigmatism (AS), distortion (DT) and chromatic aberrations (CC) at the wide-angle end (a), in the intermediate state (b) and at the telephoto end (c), respectively, with “ω” being indicative of a half angle of view (°).

The values of conditions (1) to (14) in the respective examples are set out just below.

Example

1
2
3
4
5
6
7
8

Condition(1)
20.38
20.10
21.46
21.11
19.84
19.81
21.31
18.72

Condition(2)
20.38
20.10
21.46
21.11
19.84
19.81
21.31
18.72

Condition(3)
0.35
0.36
0.35
0.36
0.26
0.26
0.28
0.27

Condition(4)
2.05
1.71
2.09
1.81
1.53
1.49
1.54
1.72

Condition(5)
1.76
1.75
1.88
1.86
1.61
1.61
1.83
1.69

Condition(6)
1.40
1.43
1.44
1.40
1.11
1.10
1.55
1.62

Condition(7)
0.34
0.35
0.32
0.34
0.34
0.34
0.30
0.28

Condition(8)
0.48
0.48
0.47
0.48
0.47
0.48
0.46
0.48

Condition(9)
1.07
1.06
1.07
1.11
0.97
0.98
0.94
0.86

Condition(10)
0.81
0.78
0.91
0.90
0.79
0.97
0.80
0.70

Condition(11)
0.68
0.68
0.70
0.70
0.81
0.86
0.66
0.64

Condition(12)
2.88
2.88
2.89
2.90
2.88
2.84
2.87
2.88

Condition(13)
62.01
61.68
60.98
60.75
62.43
62.14
63.24
61.31

Condition(14)
2.74
2.86
2.51
2.56
2.66
2.14
3.46
3.21

Example

9
10
11
12
13
14
15

Condition(1)
17.91
19.79
18.48
21.63
19.60
19.97
19.85

Condition(2)
17.91
19.79
18.48
21.69
19.60
19.97
19.85

Condition(3)
0.27
0.27
0.28
0.28
0.28
0.27
0.27

Condition(4)
1.41
1.70
1.36
1.76
1.25
1.30
1.35

Condition(5)
1.58
1.70
1.60
1.71
1.80
1.69
1.68

Condition(6)
1.38
1.36
1.60
1.36
1.68
1.36
1.36

Condition(7)
0.32
0.32
0.31
0.33
0.31
0.32
0.33

Condition(8)
0.47
0.47
0.48
0.43
0.49
0.48
0.48

Condition(9)
0.89
0.95
0.89
0.91
0.99
0.98
0.99

Condition(10)
0.68
0.73
0.49
0.61
0.65
0.72
0.65

Condition(11)
0.59
0.72
0.64
0.42
0.75
0.48
0.44

Condition(12)
2.85
2.88
2.91
2.87
2.85
2.88
2.88

Condition(13)
62.67
63.07
61.86
66.51
62.15
60.86
60.81

Condition(14)
3.15
3.41
4.83
4.34
4.47
3.50
3.94

In these examples, there are zoom lenses achievable, which, albeit having a zoom ratio of as high as about 3 and an angle of view of about 60° at the wide-angle end, has an F-number value of as small as about 1.8 at the wide-angle end, exhibit fairly good optical performance all over the zoom range and object distance, and can be received compactly in an associated lens mount.

In the respective examples, the focusing on the farthest distance is tantamount to focusing on an object at infinity. Except Example 12, the full length of the zoom lens grows longest at the time of focusing on an infinite object at the wide-angle end. Note here that focusing on a near distance may be implemented by the third lens group G3 and/or the fourth lens group G4.

In each one of the examples, the aperture stop S may have a variable aperture size for brightness control. Alternatively, with the aperture size of the stop remaining fixed, the quantity of light may be controlled by inserting or de-inserting a light quantity control filter in or from other site.

In each one of the examples, the aperture stop S assumes on a circular form about the optical axis on full aperture, with the radius of that aperture given below.

Example
Aperture Radius (mm)

1
4.67

2
4.63

3
4.67

4
4.85

5
4.33

6
3.97

7
4.00

8
3.85

9
2.49

10
4.22

11
3.78

12
2.25

13
4.17

14
2.82

15
2.61

By the way, an antireflection coating is generally applied to the air contact surface of a lens for the purpose of preventing ghosts and flares.

At the cementing surface of a cemented lens, on the other hand, the refractive index of the adhesive material is much higher than that of air; in most cases, the cementing surface has a reflectivity that is on a par with or lower than that of a single layer coating, so that there is little need of applying the antireflection coating. However, if the antireflection coating is intentionally applied to the cementing surface too, there are then further reductions achievable in ghosts and flares, which could in turn make sure images of better quality.

Especially in recent years, vitreous materials having high refractive indices have grown popularity, and they have often been used with camera optical systems for the reasons of their enhanced effect on correction of aberrations. When a high-refractive-index vitreous material is used as a cemented lens, reflection at the cementing surface would also be not negligible. In such a case, it would be particularly effective to have an antireflection coat applied on the cementing surface.

Effective use of cementing surface coating is disclosed in JP-A's 2-27301, 2001-324676 and 2005-92115 and U.S. Pat. No. 7,116,482, etc. In those publications, there is the particular mention of the cementing lens surface coating in the first lens group of the zoom lens. In the examples of the invention, too, it goes without saying that the cementing surface coating on the basis of the same idea takes effect.

Depending on the refractive index of the lens involved and the refractive index of the adhesive material used, use may be made of coating materials of relatively high refractive index such as Ta₂O₅, TiO₂, Nb₂O₅, ZrO₂, HfO₂, CeO₂, SnO₂, In₂O₃, ZnO, and Y₂O₃as well as coating materials of relatively low refractive index such as MgF₂, SiO₂, and Al₂O₃. These coating materials may then have a suitable thickness selected in such a way as to meet phase conditions.

As a matter of course, the cementing surface coating may just as well be multi-coating as is the case with the coating to the air contact surface of the lens. By optional combinations of two- or multi-layer coating materials with thicknesses, it is possible to achieve a further lowering of reflectivity, and control the spectral and angle properties of reflectivity, etc.

And now, with the zoom lens of the invention, image distortion may be corrected in an electrically digital way. The basic concept of how image distortion is digitally corrected is now explained.

As shown typically in FIG. 31, there is a magnification fixed on the circumference (image height) of a circle of radius R inscribed in the long side of an effective imaging plane with the point of intersection of an optical axis with the imaging plane as a center, and that circumference is used as the reference for correction. And then, points on the circumference of other arbitrary circle of radius r(ω) are moved in substantially radial directions; they are concentrically moved to a radius ‘r’ (ω) for correction. In FIG. 31 as an example, a point P₁on the circumference of an arbitrary circle of radius r₁(ω) positioned inside the circle of radius R is moved to a point P₂on the circumference of an arbitrary circle of radius r₂to be corrected in a direction toward the center of the circle. On the other hand, a point Q₁on the circumference of an arbitrary circle of radius r₂(ω) positioned outside the circle of radius R is moved to a point Q₂on the circumference of a circle of radius r₂′ (ω) to be corrected in a direction away from the center of the circle. Here, r′(ω) is represented by

r′(ω)=αf tan ω(0≦α≦1)

where ω is a subject half angle of view, and f is the focal length of an imaging optical system (the zoom lens in the invention).

Here let Y be an ideal image height corresponding to on the aforesaid circle of radius R. Then,

α=R/Y=R/f tan ω

The optical system here is ideally rotationally symmetric about the optical axis; distortion occurs rotationally symmetrically about the optical axis, too. Therefore, when optically produced distortion is electrically corrected as described above, it would be favorable in view of the quantities of data and computation to implement correction by fixing, on a reproduced image, a magnification on the circumference (image height) of the circle of radius R inscribed in the long side of an effective imaging plane with the point of intersection of an optical axis with the imaging plane as a center, and moving points on the circumference (image height) of other arbitrary circle of radius r(ω) moved in substantially radial directions to move them concentrically to radius r′(ω).

However, an optical image stops being a continuous quantity (for sampling) at the time of being imaged at an electronic imaging device. Strictly speaking, therefore, the aforesaid circle of radius R drawn on the optical image, too, stops being an accurate circle unless pixels on the electronic imaging device are lined up in a radial way. It follows that when it comes to the shape correction of image data represented per discrete coordinate point, there is none of the circle capable of fixing the aforesaid circle. It is therefore preferable to make use of a method that determines coordinates (X_i′, Y_j′) for where the points are to be moved to per each pixel (X_i, Y_j). Note that when two or more points (X_i, Y_j) are moved to the coordinates (X_i′, Y_j′), there is the average of the values the respective pixels have taken, and when there are no incoming points, interpolation may be implemented using the values of the coordinates (X_i′, Y_j′) for some neighboring pixels.

Such a method is effective for especially when the aforesaid circle of radius R drawn on the aforesaid optical image becomes badly distorted and asymmetric with respect to the optical axis for the reason of fabrication errors of the optical system and electronic imaging device of an electronic imaging system the zoom lens has. That method is also effective for correction of geometric distortion or the like occurring at the time of reproduction of signals as an image at the imaging device or various output devices.

With the electronic imaging system of the invention, r(ω), i.e., the relation between the half angle of view and the image height or the relation between the real image height r and the ideal image height r′/α may have been recorded in a recording medium built in it for the purpose of figuring out r′(ω)−r(ω).

It is here noted that to prevent the image after the correction of distortion from running extremely short of light quantity at both ends in the short side direction, it is preferable for the aforesaid radius R to satisfy the following condition:

0≦R≦0.6L_s

where L_sis the length of the short side of the effective imaging plane.

For the aforesaid radius R it is more preferable to satisfy the following condition.

0.3L_s≦R≦0.6L_s

Most preferably, the aforesaid radius R should be much the same as that of a circle inscribed in the effective imaging plane in the short side direction. Note here that the correction with the magnification fixed at or near the radius R=0, viz., at or near the optical axis is somewhat disadvantageous in terms of the substantial number of images; even in a wide-angle arrangement, however, there is the advantage of compactness still ensured.

It is noted that the focal length interval for which correction is in need is divided into several focal zones. And then, correction may be implemented in the same quantity as there is the result of correction obtained which satisfies substantially r′(ω)=αf tan ω at or near the telephoto end within the divided focal zones. In that case, however, there is some barrel distortion remaining at the wide-angle end within the divided focal zones. Too many divided zones are not that preferable because of the need of storing too much intrinsic data necessary for correction in the recording medium. Therefore, one or few coefficients in association with the focal lengths in the divided focal zones have been figured out in advance. Such coefficients may have been determined on the basis of simulations or measuring devices. And then, there is the quantity of correction worked out corresponding to the result of correction that satisfies substantially r′(ω)=αf tan ω at or near the telephoto end within the divided focal zones, and that amount of correction may be evenly multiplied by the aforesaid coefficients per focal length to obtain the final quantity of correction.

By the way, when there is no distortion in the image obtained by imaging an infinite object,

f=y/tan ω

Here y is the height (image height) of an image point from the optical axis, f is the focal length of an imaging system (the zoom lens in the invention), and ω is the angle (subject half angle of view) with the optical axis of an object point direction corresponding to an image point formed from the center on the imaging plane to the position of y.

When there is barrel distortion in the imaging system,

f>y/tan ω

It follows that with both the focal length f of the imaging system and the image height y kept constant, the value of ω grows large.

FIGS. 32, 33 and 34 are illustrative in conception of the construction of a digital camera according to the invention, in which the inventive zoom lens is built in its taking optical system 41. Specifically, FIG. 32 is a front perspective view of the appearance of a digital camera 40, FIG. 33 is a rear front view of the digital camera 40, and FIG. 34 is a sectional schematic view of the construction of the digital camera 40. Note here that FIGS. 32 and 34 show that the taking optical system 41 is housed in a camera body. In this embodiment, the digital camera 40 comprises a taking optical system 41 positioned on a taking optical path 42, a finder optical system 43 positioned on a finder optical path 44, a shutter button 45, a flash 46, a liquid crystal display monitor 47, a focal length change button 61, a mode select switch 62 and so on. When the taking optical system 41 is housed in the camera body, a cover 60 is slid over the taking optical system 41, the finder optical system 43 and the flash 46. As the cover 60 is slid open to place the camera 40 in a taking mode, the taking optical system 41 is put out of the camera body, as shown in FIG. 34. Then, as the shutter button 45 mounted on the upper side of the camera 40 is pressed down, it causes taking to be implemented through the taking optical system 41, for instance, the zoom lens of Example 1. An object image formed through the taking optical system 41 is formed on the imaging plane (photoelectric conversion plane) of CCD 49 via a low-pass filter LF with a wavelength range limiting coating applied on it and a cover glass CG. The object image received at CCD 49 is displayed as an electronic image on the liquid crystal display monitor 47 mounted on the back surface of the camera via processing means 51. Note here that the processing means 51 could be connected with recording means 52 for recording the taken electronic image in it. Also note that the recording means 52 could be provided separately from the processing means 51 or, alternatively, it could be designed such that images are electronically recorded and written on a floppy disk, a memory card, an MO or the like. Further, a silver-halide film could be used in place of CCD 49 to set up a silver-halide camera.

Further, a finder objective optical system 53 is located on the finder optical path 44. The finder objective optical system 53 comprises a zoom optical system that is made up of a plurality of lens groups (three groups in the embodiment of FIGS. 32-34) and an erecting prism system 55 comprising erecting prisms 55a, 55b and 55c with its focal length variable in operable association with the zoom lens that is the taking optical system 41. An object image formed through the finder objective optical system 53 is formed on a field frame 57 of the erection prism system 55 that is an image-erecting member. In the rear of the erection prism system 55, there is an eyepiece optical system 59 located for guiding an erected image into the eyeball E of the viewer. Note here that a cover member 50 is located on the exit side of the eyepiece optical system 59.

FIG. 35 is a component block diagram illustrative of the internal circuit of a main part of the aforesaid digital camera 40. In the following description, the aforesaid processing means 51, for instance, comprises a CDS/ADC portion 24, a temporary storage memory 17, an image processing portion 18 and so on, and the storage means 52, for instance, comprises a memory medium portion 19 and so on.

As shown in FIG. 35, the digital camera 40 comprises an operation portion 12, a control portion 13 connected to the operation portion 12, an imaging drive circuit 16 connected to the control signal output port of the control portion 13 via buses 14 and 15, a temporary storage memory 17, an image processing portion 18, a storage medium portion 19, a display portion 20 and a mode information storage memory portion 21.

The aforesaid temporary storage memory 17, image processing portion 18, storage medium portion 19, display portion 20 and mode information storage memory portion 20 are set up such that data can be mutually entered or outputted, and the imaging drive circuit 17 is connected with CCD 49 and CDS/ADC portion 24.

The operation portion 12 comprises various input buttons, switches and so on, and provides a circuit for notifying of the control portion event information entered from outside (a camera operator) via those input buttons or switches. The control portion 13, for instance, is a central processing unit made up of a CPU and so on, and has a built-in program memory (not shown). Pursuant to the program stored in that program memory, that circuit controls the whole digital camera 40 in response to a command entered by the camera operator via the control portion 12.

CCD 49 receives an object image formed through the inventive taking optical system 41. CCD 49 is an imaging device that is driven and controlled by the imaging drive circuit 17 so that the quantity of light of that object image per pixel is converted into electrical signals to enter them in the CDS/ADC portion 24.

The CDS/ADC portion 24 is a circuit adapted to amplify the electrical signals entered from CCD 49 and subject them to digital transformation, entering into the temporary storage memory 17 image raw data (VEYOR data or RAW data) subjected to amplification and digital transformation alone.

The temporary storage memory 17 is a buffer comprising SDRAM as an example and so on, and a memory device adapted to provide a temporal storage of the aforesaid RAW data produced out of the CDS/ADC portion 24. The image processing portion 18 is a circuit adapted to read the RAW data stored in the temporal storage memory 17 or RAW data stored in the storage medium portion 19, thereby implementing various image processing inclusive of distortion correction on the basis of an image quality parameter designated from the control portion 13.

The recording medium portion 19 is a control circuit for the device wherein a card or stick type storage medium comprising a flash memory as an example is attached or detached to record and store the RAW data transferred from the temporary storage memory 17 or the image data processed at the image processing portion 18 in the card or stick type flash memory.

The display memory 20 is a circuit comprising a liquid crystal display monitor 47 and adapted to display images, operating menus and so on that liquid crystal display monitor 47. The mode information storage memory portion 21 comprises a ROM section with various image quality parameters loaded in it and a RAM section adapted to store the image quality parameter selected by input operation of the operation portion 12 out of the image quality parameters read out of that ROM section. The mode information storage memory portion 21 is a circuit adapted to control inputs to and outputs from those memories.

The thus constructed digital camera 40 is much improved in terms of performance, size and wide-angle capabilities, because albeit having plenty of wide-angle area and compact size, the taking optical system 41 of the invention has a higher zoom ratio and very stable imaging capabilities all over the zooming range. Further, faster focusing operation is ensured at the wide-angle and telephoto sides.

The present invention is applicable not only to the so-called compact digital cameras designed to take images of such general subjects as described above but also to surveillance cameras requiring wide angles of view and cameras of the lens interchangeable type.

Zoom lens, and imaging system comprising the same

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