Analytic function optical component

Claim 2

An analytic function optical component comprising at least one transparent element that is disposed along an optical axis, said element having on one side a first surface that has a predetermined shape which is at least a part of a surface of revolution and on the other side thereof a second aspheric surface that is nonrotationally symmetric and mathematically described by a preselected polynomial equation having a nonzero term of at least 4th order, said first and second surfaces of said element being structured so that said element can be displaced generally laterally relative to said optical axis by rotation of said element about an axis of revolution other than said optical axis such that said second surface of said element operates to continuously change certain optical properties of said component as said element moves relative to said optical axis while said first surface of said element remains optically invariant, not effecting any changes in any optical properties of said component, as said element moves relative to said optical axis.

Claim 3

The component of claim 1 wherein said first surface is planar.

Claim 4

The component of claim 1 wherein said axis of revolution is offset and parallel with respect to said optical axis.

Claim 5

The component of claim 1 wherein said polynomial equation describing said second surface is in Cartesian coordinates of the form: z=K.sub.1 (xy.sup.2 +1/3x.sup.3)-k.sub.2 x.sup.3 y+K.sub.3 xy.sup.3 where K 1 is assignable constants and ##EQU10##

Claim 6

The component of claim 1 wherein said polynomial equation describing said second surface is in Cartesian coordinates of the form: z=K.sub.1 (xy.sup.2 +1/3x.sup.3)-K.sub.2 x.sup.3 y+K.sub.3 xy.sup.3 +K.sub.4 x.sup.4 +K.sub.5 x.sup.2 y.sup.2 where K 1 -K 4 are assignable constants and K 5 =2K 4 plus residue conveniently set to zero.

Claim 7

An analytic function optical component comprising at least one pair of transparent elements that are disposed in tandem along an optical axis, said elements each having on one side a first surface that has a predetermined shape which is at least a part of a surface of revolution and on the other side thereof a second aspheric surface that is nonrotationally symmetric and mathematically described by a preselected polynomial equation having a nonzero term of at least 4th order, said first and second surfaces of said elements being structured so that said elements can be displaced generally laterally relative to one another by rotation of one or both of said elements about one or more axes of revolution, other than said optical axis, such that said second surfaces of said elements operate to continuously change certain optical properties of said component as said elements move relative to one another while said first surfaces of said elements remain optically invariant, not effecting any changes in any optical properties of said component, as said elements move relative to one another.

Claim 8

An analytic function optical component comprising at least one pair of transparent elements that are disposed in tandem along an optical axis, said elements each having on one side a first surface that has a predetermined shape which is at least a part of a surface of revolution and on the other side thereof a second aspheric surface that is nonrotationally symmetric and mathematically described by a preselected polynomial equation having a nonzero term of at least 4th order, said first and second surfaces of said elements being structured so that said elements can be displaced generally laterally relative to one another by rotation of one or both of said elements about one or more axes of revolution, other than said optical axis, such that said second surfaces of said elements operate to continuously change certain optical properties of said component as said elements move relative to one another while said first surfaces of said elements remain optically invariant, not effecting any changes in any optical properties of said component, as said elements move relative to one another.

Claim 9

The component of claim 6 wherein said first surface is planar.

Claim 10

The component of claim 6 wherein said axis or axes of revolution is offset and parallel with respect to said optical axis.

Claim 11

The component of claim 6 wherein said polynomial equation describing said second surface is in Cartesian coordinates of the form: z=K.sub.1 (xy.sup.2 +1/3x.sup.3)-K.sub.2 x.sup.3 y+K.sub.3 xy.sup.3 where K 1 is assignable constants and ##EQU11##

Claim 12

The component of claim 6 wherein said polynomial equation describing said second surface is in Cartesian coordinates of the form: z=K.sub.1 (xy.sup.2 +1/3x.sup.3)-K.sub.2 x.sup.3 y+K.sub.3 xy.sup.3 +K.sub.4 x.sup.4 +K.sub.5 x.sup.2 y.sup.2 where K 1 -K 4 are assignable constants and K 5 =2K 4 plus residue conveniently set to zero.

Claim 13

An analytic function optical component comprising a plurality of transparent elements that are disposed in tandem along an optical axis, the outwardly facing sides of the outer ones of said elements each having a surface that has a predetermined shape which is at least a part of a surface of revolution while the inwardly facing sides of said outer elements and each of the oppositely facing sides of the remaining ones of said elements have an aspheric surface that is nonrotationally symmetric and mathematically described by a preselected polynomial equation having a nonzero term of at least 4th order, said surfaces of said elements being structured so that said elements can be displaced generally laterally relative to one another by rotation of one or more of said elements about one or more axes of revolution, other than said optical axis, such that said nonrotationally symmetric aspheric surfaces of said elements operate to continuously change certain optical properties of said component as said elements move relative to one another while said outer surfaces of said outer elements remain optically invariant, not effecting any changes in any optical properties of said component, as said elements move relative to one another.

Claim 14

An analytic function optical component comprising a plurality of transparent elements that are disposed in tandem along an optical axis, the outwardly facing sides of the outer ones of said elements each having a surface that has a predetermined shape which is at least a part of a surface of revolution while the inwardly facing sides of said outer elements and each of the oppositely facing sides of the remaining ones of said elements have an aspheric surface that is nonrotationally symmetric and mathematically described by a preselected polynomial equation having a nonzero term of at least 4th order, said surfaces of said elements being structured so that said elements can be displaced generally laterally relative to one another by rotation of one or more of said elements about one or more axes of revolution, other than said optical axis, such that said nonrotationally symmetric aspheric surfaces of said elements operate to continuously change certain optical properties of said component as said elements move relative to one another while said outer surfaces of said outer elements remain optically invariant, not effecting any changes in any optical properties of said component, as said elements move relative to one another.

Claim 15

The component of claim 11 wherein said first surface is planar.

Claim 16

The component of claim 11 wherein said axis or axes of revolution is offset and parallel with respect to said optical axis.

Claim 17

The component of claim 11 wherein said polynomial equation describing said second surface is in Cartesian coordinates of the form: z=K.sub.1 (xy.sup.2 +1/3x.sup.3)-K.sub.2 x.sup.3 y+K.sub.3 xy.sup.3 where K 1 is assignable constants and ##EQU12##

Claim 18

The component of claim 11 wherein said polynomial equation describing said second surface is in Cartesian coordinates of the form: z=K.sub.1 (xy.sup.2 +1/3x.sup.3)-K.sub.2 x.sup.3 y+K.sub.3 xy.sup.3 +K.sub.4 x.sup.4 +K.sub.5 x.sup.2 y.sup.2 where K 1 -K 4 are assignable constants and K 5 =2K 4 plus residue conveniently set to zero.

Claim 19

An optical system comprising an analytic function optical component having at least one transparent element that is disposed along an optical axis, said element having on one side a first surface that has a predetermined shape which is at least a part of a surface of revolution and on the other side thereof a second aspheric surface that is nonrotationally symmetric and mathematically described by a preselected polynomial equation having a nonzero term of at least 4th order, said first and second surfaces of said element being structured so that said element can be displaced generally laterally relative to said optical axis by rotation of said element about an axis of revolution, other than said optical axis, such that said second surface of said element operates to continuously change certain optical properties of said optical system as said element moves relative to said optical axis while said first surface of said element remains optically invariant, not effecting any changes in any optical properties of said optical system, as said element moves relative to said optical axis.

Claim 20

An optical system comprising an analytic function optical component having at least one transparent element that is disposed along an optical axis, said element having on one side a first surface that has a predetermined shape which is at least a part of a surface of revolution and on the other side thereof a second aspheric surface that is nonrotationally symmetric and mathematically described by a preselected polynomial equation having a nonzero term of at least 4th order, said first and second surfaces of said element being structured so that said element can be displaced generally laterally relative to said optical axis by rotation of said element about an axis of revolution, other than said optical axis, such that said second surface of said element operates to continuously change certain optical properties of said optical system as said element moves relative to said optical axis while said first surface of said element remains optically invariant, not effecting any changes in any optical properties of said optical system, as said element moves relative to said optical axis.

Claim 21

The component of claim 16 wherein said first surface is planar.

Claim 22

The component of claim 16 wherein said axis of revolution is offset and parallel with respect to said optical axis.

Claim 23

The component of claim 16 wherein said polynomial equation describing said second surface is in Cartesian coordinates of the form: z=K.sub.1 (xy.sup.2 +1/3x.sup.3)-K.sub.2 x.sup.3 y+K.sub.3 xy.sup.3 where K 1 is assignable constants and ##EQU13##

Claim 24

The component of claim 16 wherein said polynomial equation describing said second surface is in Cartesian coordinates of the form: z=K.sub.1 (xy.sup.2 +1/3x.sup.3)-K.sub.2 x.sup.3 y+K.sub.3 xy.sup.3 +K.sub.4 x.sup.4 +K.sub.5 x.sup.2 y.sup.2 where K 1 -K 4 are assignable constants and K 5 =2K 4 plus residue conveniently set to zero.

Claim 25

An optical system comprising at least a pair of analytic function optical components arranged in tandem along an optical axis and each component having at least one transparent element that is disposed along said optical axis, said elements each having on one side a first surface that has a predetermined shape which is at least a part of a surface of revolution and on the other side thereof a second, aspheric surface that is nonrotationally symmetric and mathematically described by a preselected polynomial equation having a nonzero term of at least 4th order, said first and second surfaces of said elements being structured so that said elements can be displaced generally laterally relative to one another by rotation of one or both of said elements about one or more axes of revolution, other than said optical axis, such that said second surfaces of said elements operate to continuously change certain optical properties of said optical system as said elements move relative to one another while said first surfaces of said elements remain optically invariant, not effecting any changes in any optical properties of said optical system, as said elements move relative to one another.

Claim 26

An optical system comprising at least a pair of analytic function optical components arranged in tandem along an optical axis and each component having at least one transparent element that is disposed along said optical axis, said elements each having on one side a first surface that has a predetermined shape which is at least a part of a surface of revolution and on the other side thereof a second, aspheric surface that is nonrotationally symmetric and mathematically described by a preselected polynomial equation having a nonzero term of at least 4th order, said first and second surfaces of said elements being structured so that said elements can be displaced generally laterally relative to one another by rotation of one or both of said elements about one or more axes of revolution, other than said optical axis, such that said second surfaces of said elements operate to continuously change certain optical properties of said optical system as said elements move relative to one another while said first surfaces of said elements remain optically invariant, not effecting any changes in any optical properties of said optical system, as said elements move relative to one another.

Claim 27

The component of claim 21 wherein said first surface is planar.

Claim 28

The component of claim 21 wherein said axis or axes of revolution is offset and parallel with respect to said optical axis.

Claim 29

The component of claim 21 wherein said polynomial equation describing said second surface is in Cartesian coordinates of the form: z=K.sub.1 (xy.sup.2 +1/3x.sup.3)-K.sub.2 x.sup.3 y+K.sub.3 xy.sup.3 where K 1 is assignable constants and ##EQU14##

Claim 30

The component of claim 21 wherein said polynomial equation describing said second surface is in Cartesian coordinates of the form: z=K.sub.1 (xy.sup.2 +1/3x.sup.3)-K.sub.2 x.sup.3 y+K.sub.3 xy.sup.3 +K.sub.4 x.sup.4 +K.sub.5 x.sup.2 y.sup.2 where K 1 -K 4 are assignable constants and K 5 =2K 4 plus residue conveniently set to zero.

Claim 31

The system of claim 21 wherein said optical system includes at least one positive meniscus lens element located along said optical axis and forward of said pair of analytic function components.

Claim 32

The system of claim 21 wherein said optical system includes one positive glass meniscus lens element located along said optical axis and forward of said pair of analytic function components.

Claim 33

The system of claim 21 wherein all components thereof are comprised of a single material.

Claim 34

The system of claim 28 wherein said single material is an optical plastic.

Claim 35

An optical system comprising an analytic function optical component having a plurality of transparent elements that are disposed in tandem along an optical axis, the outwardly facing sides of the outer ones of said elements each having a surface that has a predetermined shape which is at least a part of a surface of revolution while the inwardly facing sides of said outer elements and each of the oppositely facing sides of the remaining ones of said elements have an aspheric surface that is nonrotationally symmetric and mathematically described by a preselected polynomial equation having a nonzero term of at least 4th order, said surfaces of said elements being structured so that said elements can be displaced generally laterally relative to one another by rotation of one or more of said elements about one or more axes of revolution, other than said optical axis, such that said nonrotationally symmetric aspheric surfaces of said elements operate to continuously change certain optical properties of said optical system as said elements move relative to one another while said outer surfaces of said outer elements remain optically invariant, not effecting any changes in any optical properties of said optical system as said elements move relative to one another.

Claim 36

An optical system comprising an analytic function optical component having a plurality of transparent elements that are disposed in tandem along an optical axis, the outwardly facing sides of the outer ones of said elements each having a surface that has a predetermined shape which is at least a part of a surface of revolution while the inwardly facing sides of said outer elements and each of the oppositely facing sides of the remaining ones of said elements have an aspheric surface that is nonrotationally symmetric and mathematically described by a preselected polynomial equation having a nonzero term of at least 4th order, said surfaces of said elements being structured so that said elements can be displaced generally laterally relative to one another by rotation of one or more of said elements about one or more axes of revolution, other than said optical axis, such that said nonrotationally symmetric aspheric surfaces of said elements operate to continuously change certain optical properties of said optical system as said elements move relative to one another while said outer surfaces of said outer elements remain optically invariant, not effecting any changes in any optical properties of said optical system as said elements move relative to one another.

Claim 37

The component of claim 30 wherein said first surface is planar.

Claim 38

The component of claim 30 wherein said axis or axes of revolution is offset and parallel with respect to said optical axis.

Claim 39

The component of claim 30 wherein said polynomial equation describing said second surface is in Cartesian coordinates of the form: z=K.sub.1 (xy.sup.2 +1/3x.sup.3)-K.sub.2 x.sup.3 y+K.sub.3 xy.sup.3 where K 1 is assignable constants and ##EQU15##

Claim 40

The component of claim 30 wherein said polynomial equation describing said second surface is in Cartesian coordinates of the form: z=K.sub.1 (xy.sup.2 +1/3x.sup.3)-K.sub.2 x.sup.3 y+K.sub.3 xy.sup.3 +K.sub.4 x.sup.4 +K.sub.5 x.sup.2 y.sup.2 where K 1 -K 4 are assignable constants and K 5 =2K 4 plus residue conveniently set to zero.

Claim 41

An analytic function optical component comprising a plurality of transparent elements that are disposed in tandem along an optical axis, the outwardly facing side of one of the outer ones of said elements having a surface that has a predetermined shape which is at least a part of a surface of revolution while the outwardly facing side of the remaining outer element and the inwardly facing sides of said outer elements and each of the oppositely facing sides of the remaining ones of said elements have an aspheric surface that is nonrotationally symmetric and mathematically described by a preselected polynomial equation having a nonzero term of at least 4th order, said surfaces of said elements being structured so that said elements can be displaced generally laterally relative to one another by rotation of one or more of said elements about one or more axes of revolution, other than said optical axis, such that said nonrotationally symmetric aspheric surfaces of said elements operate to continuously change certain optical properties of said component as said elements move relative to one another while said outer surface of said one outer element remains optically invariant, not effecting any changes in any optical properties of said component, as said elements move relative to one another.

Claim 42

An analytic function optical component comprising a plurality of transparent elements that are disposed in tandem along an optical axis, the outwardly facing side of one of the outer ones of said elements having a surface that has a predetermined shape which is at least a part of a surface of revolution while the outwardly facing side of the remaining outer element and the inwardly facing sides of said outer elements and each of the oppositely facing sides of the remaining ones of said elements have an aspheric surface that is nonrotationally symmetric and mathematically described by a preselected polynomial equation having a nonzero term of at least 4th order, said surfaces of said elements being structured so that said elements can be displaced generally laterally relative to one another by rotation of one or more of said elements about one or more axes of revolution, other than said optical axis, such that said nonrotationally symmetric aspheric surfaces of said elements operate to continuously change certain optical properties of said component as said elements move relative to one another while said outer surface of said one outer element remains optically invariant, not effecting any changes in any optical properties of said component, as said elements move relative to one another.

Claim 43

The component of claim 35 wherein said first surface is planar.

Claim 44

The component of claim 35 wherein said polynomial equation describing said second surface is in Cartesian coordinates of the form: z=K.sub.1 (xy.sup.2 +1/3x.sup.3)-K.sub.2 x.sup.3 y+K.sub.3 xy.sup.3 where K 1 is assignable constants and ##EQU16##

Claim 45

The component of claim 35 wherein said polynomial equation describing said second surface is in Cartesian coordinates of the form: z=K.sub.1 (xy.sup.2 +1/3x.sup.3)-K.sub.2 x.sup.3 y+K.sub.3 xy.sup.3 +K.sub.4 x.sup.4 +K.sub.5 x.sup.2 y.sup.2 where K 1 -K 4 are assignable constants and K 5 =2K 4 plus residue conveniently set to zero.