Color-corrected optical systems

Claim 3

The method of claim 1 further comprising: a) determining absolute values of differences between a coefficient in said polynomial expression for said one optical material and corresponding coefficients in the polynomial expressions for those particular optical materials for which said corresponding ratios of coefficients are substantially equal to said ratio of coefficients for said one optical material; and b) selecting optical materials for designing said system from among those particular optical materials for which said corresponding ratios of coefficients are substantially equal, and for which the absolute values of differences between said corresponding coefficients are sufficiently large to permit construction of optical elements having dioptric powers of appropriate configuration for said system.

Claim 4

The method of claim 1 wherein the dispersive power of each optical material is represented by a polynomial expression of the form ##EQU79## where D(λ) is the dispersive power, λ is the wavelength, ω(λ) is said variable that is a function of wavelength; ω(λ) being defined by the expression ω(λ)=δλ/(1+αδλ), where δλ represents change in wavelength with respect to a base wavelength and α is a constant that is substantially independent of the dispersive power of the optical material; where η i are the coefficients in said polynomial expression; and where n is the degree of said polynomial.

Claim 5

The method of claim 3 wherein absolute values are determined for differences between a coefficient η i in the polynomial expression for said one optical material and corresponding coefficients η i in the polynomial expressions for the particular optical materials for which corresponding ratios (η i /η j ), where j≠i, are substantially equal to the ratio (η i /η j ) for said one optical material.

Claim 6

The method of claim 3 wherein said polynomial expression is of (n-1)th degree.

Claim 7

The method of claim 5 wherein, when said polynomial expression is quadratic, the ratio (η 1 /η 2 ) for said one optical material is compared with the corresponding ratios (η 1 /η 2 ) for the others of said optical materials.

Claim 8

The method of claim 6 wherein said optical materials for designing said system are selected from the group consisting of optical glasses listed in TABLE I, which is incorporated herein by reference, each optical glass listed in TABLE I being described in terms of refractive index at a base wavelength of 0.574 micrometer, and in terms of numerical values for said coefficients η i (i=1, 2) for a wavelength range extending from approximately 0.40 micrometer to approximately 0.70 micrometer.

Claim 9

The method of claim 5 wherein, when said polynomial expression is cubic, the ratios (η 1 /η 2 ), (η 2 /η 3 ) and (η 1 /η 3 ) for said one optical material are compared with the corresponding ratios (η 1 /η 3 ), (η 2 /η 3 ) and (η 1 /η 3 ) for the others of said optical materials.

Claim 10

The method of claim 8 wherein said optical materials for designing said system are selected from the group consisting of optical glasses listed in TABLE II, which is incorporated herein by reference, each optical glass listed in TABLE II being described in terms of refractive index at a base wavelength of 0.589 micrometer, and in terms of numerical values for said coefficients η i (i=1, 2, 3) for a wavelength range extending from approximately 0.36 micrometer to approximately 1.01 micrometers.

Claim 11

An optical system that is color-corrected at more than three wavelengths, said system comprising optical elements made of only two different optical materials, each of said optical materials having a characteristic dispersive power, said system being made by a process that includes selection of said optical materials, said optical materials being selected by: a) representing the dispersive power of each optical material by a polynomial expression in a variable that is a function of wavelength, the polynomial expression for each optical material being of a degree that is numerically one less than the number of wavelengths for which color correction is required; b) comparing a ratio of coefficients in the polynomial expression for one of said optical materials with corresponding ratios of coefficients in the polynomial expressions for others of said optical materials; c) identifying particular optical materials for which said corresponding ratios of coefficients in said polynomial expressions are substantially equal; and d) choosing optical materials for designing said system from among those particular optical materials for which said corresponding ratios of coefficients are substantially equal.

Claim 12

An optical system that is color-corrected at more than three wavelengths, said system comprising optical elements made of only two different optical materials, each of said optical materials having a characteristic dispersive power, said system being made by a process that includes selection of said optical materials, said optical materials being selected by: a) representing the dispersive power of each optical material by a polynomial expression in a variable that is a function of wavelength, the polynomial expression for each optical material being of a degree that is numerically one less than the number of wavelengths for which color correction is required; b) comparing a ratio of coefficients in the polynomial expression for one of said optical materials with corresponding ratios of coefficients in the polynomial expressions for others of said optical materials; c) identifying particular optical materials for which said corresponding ratios of coefficients in said polynomial expressions are substantially equal; and d) choosing optical materials for designing said system from among those particular optical materials for which said corresponding ratios of coefficients are substantially equal.

Claim 13

The optical system of claim 10 wherein said optical materials are further selected by: a) determining absolute values of differences between a coefficient in said polynomial expression for said one optical material and corresponding coefficients in the polynomial expressions for those particular optical materials for which said corresponding ratios of coefficients are substantially equal to said ratio of coefficients for said one optical material; and b) selecting optical materials for designing said system from among those particular optical materials for which said corresponding ratios of coefficients are substantially equal, and for which the absolute values of differences between said corresponding coefficients are sufficiently large to permit construction of optical elements having dioptric powers of appropriate configuration for said system.

Claim 14

The optical system of claim 10 wherein the dispersive power of each optical material is represented by a polynomial expression of the form ##EQU80## where D(λ) is the dispersive power, λ is the wavelength, ω(λ) is said variable that is a function of wavelength; ω(λ) being defined by the expression ω(λ)=δλ/(1+αδλ), where δλ represents change in wavelength with respect to a base wavelength and α is a constant that is substantially independent of the dispersive power of the optical material; where η i are the coefficients in said polynomial expression; and where n is the degree of said polynomial.

Claim 15

The optical system of claim 12 wherein absolute values are determined for differences between a coefficient η i in the polynomial expression for said one optical material and corresponding coefficients η i in the polynomial expressions for the particular optical materials for which corresponding ratios (η i /η j ), where j≠i, are substantially equal to the ratio (η i /η j ) for said one optical material.

Claim 16

The optical system of claim 12 wherein said polynomial expression is of (n-1)th degree.

Claim 17

The optical system of claim 14 wherein, when said polynomial expression is quadratic, the ratio (η 1 /η 2 ) for said one optical material is compared with the corresponding ratios (η 1 /η 2 ) for the others of said optical materials.

Claim 18

The optical system of claim 15 wherein said optical materials for designing said system are selected from the group consisting of optical glasses listed in TABLE I, which is incorporated herein by reference, each optical glass listed in TABLE I being described in terms of refractive index at a base wavelength of 0.574 micrometer and in terms of numerical values for said coefficients η i (i=1, 2) for a wavelength range extending from approximately 0.40 micrometer to approximately 0.70 micrometer.

Claim 19

The optical system of claim 14 wherein, when said polynomial expression is cubic, the ratios (η 1 /η 2 ), (η 2 /η 3 ) and (η 1 /η 3 ) for said one optical material are compared with the corresponding ratios (η 1 /η 2 ), (η 2 /η 3 ) and (η 1 /η 3 ) for the others of said optical materials.

Claim 20

The optical system of claim 17 wherein said optical materials for designing said system are selected from the group consisting of optical glasses listed in TABLE II, which is incorporated herein by reference, each optical glass listed in TABLE II being described in terms of refractive index at a base wavelength of 0.589 micrometers, and in terms of numerical values for said coefficients η i (i=1, 2, 3) for a wavelength range extending from approximately 0.36 micrometer to approximately 1.01 micrometer.

Claim 21

An optical system color-corrected at least at four wavelengths, said system comprising only two lens elements, each lens element being made of a different optical material, each optical material having a characteristic dispersive power, the dispersive power of each optical material being represented by a polynomial expression in a variable that is a function of wavelength, said polynomial expression being of the form D(λ)=η.sub.1 ω(λ)+η.sub.2 ω.sup. (80 ) where D(λ) is the dispersive power, λ is the wavelength, ω(λ) is the variable that is a function of wavelength, ω(λ) being defined by the expression ω(λ)=δλ/(1+αδλ), where δλ represents change in wavelength with respect to a base wavelength and α is effectively a constant that is substantially independent of the dispersive power of the optical material, and wherein η 1 and η 2 are coefficients in said polynomial expression, said optical system being made by a process that includes selection of said optical materials, said optical materials being selected by ascertaining that corresponding coefficients in the polynomial expressions for each of said optical materials have an absolute value difference that permits construction of optical elements having dioptric powers appropriate for said system.

Claim 22

An optical system color-corrected at least at four wavelengths, said system comprising only two lens elements, each lens element being made of a different optical material, each optical material having a characteristic dispersive power, the dispersive power of each optical material being represented by a polynomial expression in a variable that is a function of wavelength, said polynomial expression being of the form D(λ)=η.sub.1 ω(λ)+η.sub.2 ω.sup. (80 ) where D(λ) is the dispersive power, λ is the wavelength, ω(λ) is the variable that is a function of wavelength, ω(λ) being defined by the expression ω(λ)=δλ/(1+αδλ), where δλ represents change in wavelength with respect to a base wavelength and α is effectively a constant that is substantially independent of the dispersive power of the optical material, and wherein η 1 and η 2 are coefficients in said polynomial expression, said optical system being made by a process that includes selection of said optical materials, said optical materials being selected by ascertaining that corresponding coefficients in the polynomial expressions for each of said optical materials have an absolute value difference that permits construction of optical elements having dioptric powers appropriate for said system.

Claim 23

An optical system color-corrected at more than two wavelengths, said system comprising only two different optical materials.

Claim 24

An optical system color-corrected at more than two wavelengths, said system comprising only two different optical materials.

Claim 25

The optical system of claim 20 wherein said system is a lens system.

Claim 26

An optical system rotationally symmetric about an axis, said system comprising a lens doublet having a common focal length on said axis for three optical wavelengths, said lens doublet comprising a first lens element made of an optical material having refractive index of approximately 1.49 and an Abbe number of approximately 84.07 at a base wavelength of 0.546 micrometers, and a second lens element made of an optical material having a refractive index of approximately 1.50 and an Abbe number of approximately 59.34 at said base wavelength.

Claim 27

An optical system rotationally symmetric about an axis, said system comprising a lens doublet having a common focal length on said axis for three optical wavelengths, said lens doublet comprising a first lens element made of an optical material having refractive index of approximately 1.49 and an Abbe number of approximately 84.07 at a base wavelength of 0.546 micrometers, and a second lens element made of an optical material having a refractive index of approximately 1.50 and an Abbe number of approximately 59.34 at said base wavelength.

Claim 28

The optical system of claim 22 having a design form wherein said first and second lens elements are positioned in contact with each other to define first, second and third surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said second and third surfaces, said first surface having a positive radius of curvature of approximately 0.421 times the focal length of said doublet, said second surface having a negative radius of curvature of approximately 0.215 times said focal length, said third surface having a positive radius of curvature of approximately 7.034 times said focal length, said first lens element having a thickness along said axis of approximately 0.016 times said focal length, said second lens element having a thickness along said axis of approximately 0.009 times said focal length.

Claim 29

A lens doublet that is color-corrected at more than three wavelengths.

Claim 30

A lens doublet that is color-corrected at more than three wavelengths.

Claim 31

An optical system rotationally symmetric about an axis, said system comprising a lens doublet having a common focal length on said axis for four optical wavelengths, said lens doublet comprising a first lens element made of an optical material having a refractive index of approximately 1.49 and an Abbe number of approximately 81.40 at a base wavelength of 0.546 micrometers, and a second lens element made of an optical material having a refractive index of approximately 1.70 and an Abbe number of approximately 55.31 at said base wavelength.

Claim 32

An optical system rotationally symmetric about an axis, said system comprising a lens doublet having a common focal length on said axis for four optical wavelengths, said lens doublet comprising a first lens element made of an optical material having a refractive index of approximately 1.49 and an Abbe number of approximately 81.40 at a base wavelength of 0.546 micrometers, and a second lens element made of an optical material having a refractive index of approximately 1.70 and an Abbe number of approximately 55.31 at said base wavelength.

Claim 33

The optical system of claim 25 having a design form wherein said first and second lens elements are positioned in contact with each other to define first, second and third surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said second and third surfaces, said first surface having a positive radius of curvature of approximately 0.257 times the focal length of said doublet, said second surface having a negative radius of curvature of approximately 0.372 times said focal length, said third surface having a positive radius of curvature of approximately 2.022 times said focal length, said first lens element having a thickness along said axis of approximately 0.016 times said focal length, said second lens element having a thickness along said axis of approximately 0.009 times said focal length.

Claim 34

The optical system of claim 25 having a design form wherein said first and second lens elements are positioned with respect to each other to define first, second, third and fourth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said third and fourth surfaces, said first surface having a positive radius of curvature of approximately 0.598 times the focal length of said doublet, said second surface having a negative radius of curvature of approximately 0.207 times said focal length, said third surface having a negative radius of curvature of approximately 0.221 times said focal length, said fourth surface having a negative radius of curvature of approximately 0.699 times said focal length, said first lens element having a thickness along said axis of approximately 0.016 times said focal length, said second lens element being separated from said first lens element along said axis by approximately 0.0005 times said focal length, said second lens element having a thickness along said axis of approximately 0.009 times said focal length.

Claim 35

A lens doublet that is color-corrected at more than four optical wavelengths.

Claim 36

A lens doublet that is color-corrected at more than four optical wavelengths.

Claim 37

An optical system rotationally symmetric about an axis, said system comprising a lens doublet having a common focal length on said axis for five optical wavelengths, said lens doublet comprising a first lens element made of an optical material having a refractive index of approximately 1.53 and an Abbe number of approximately 76.57 at a base wavelength of 0.546 micrometers, and a second lens element made of an optical material having a refractive index of approximately 1.65 and an Abbe number of approximately 58.15 at said base wavelength.

Claim 38

An optical system rotationally symmetric about an axis, said system comprising a lens doublet having a common focal length on said axis for five optical wavelengths, said lens doublet comprising a first lens element made of an optical material having a refractive index of approximately 1.53 and an Abbe number of approximately 76.57 at a base wavelength of 0.546 micrometers, and a second lens element made of an optical material having a refractive index of approximately 1.65 and an Abbe number of approximately 58.15 at said base wavelength.

Claim 39

The optical system of claim 29 having a design form wherein said first and second lens elements are positioned with respect to each other to define first, second, third and fourth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said third and fourth surfaces, said first surface having a positive radius of curvature of approximately 0.753 times the focal length of said doublet, said second surface having a negative radius of curvature of approximately 0.151 times said focal length, said third surface having a negative radius of curvature of approximately 0.156 times said focal length, said fourth surface having a negative radius of curvature of approximately 0.680 times said focal length, said first lens element having a thickness along said axis of approximately 0.020 times said focal length, said second lens element being separated from said first lens element along said axis by approximately 0.0004 times said focal length, said second lens element having a thickness along said axis of approximately 0.010 times said focal length.

Claim 42

A dioptric optical system color-corrected at three wavelengths, said system comprising only two optical materials, namely, Schott FK51 glass and Schott K51 glass.

Claim 43

A dioptric optical system color-corrected at three wavelengths, said system comprising only two optical materials, namely, Schott FK51 glass and Schott K51 glass.

Claim 44

The optical system of claim 32, said system being a lens doublet.

Claim 45

A dioptric optical system color-corrected at four wavelengths, said system comprising only two optical materials, namely, Corning-France 486817 glass and Ohara LAK14 glass.

Claim 46

A dioptric optical system color-corrected at four wavelengths, said system comprising only two optical materials, namely, Corning-France 486817 glass and Ohara LAK14 glass.

Claim 47

The optical system of claim 34, said system being a lens doublet.

Claim 48

The optical system of claim 35, said lens doublet comprising two air-spaced lens elements.

Claim 49

A dioptric optical system precisely color-corrected at five wavelengths, said system comprising only two optical materials, namely, Schott PK5I glass and Hoya LAC7 glass.

Claim 50

A dioptric optical system precisely color-corrected at five wavelengths, said system comprising only two optical materials, namely, Schott PK5I glass and Hoya LAC7 glass.

Claim 51

The optical system of claim 37 said system being a lens doublet.

Claim 52

The optical system of claim 38, said lens doublet comprising two air-spaced lens elements.

Claim 55

The method of claim 40 wherein said coefficients η i are calculated using a least-squares technique.

Claim 56

The method of claim 40 wherein said polynomial is quadratic, the coefficients η 1 and η 2 being calculated for each optical material, and wherein said candidate optical materials for designing said system are identified from among those optical materials for which corresponding ratios η 1 /η 2 are substantially equal.

Claim 57

The method of claim 42 wherein optical materials for designing said system are selected by forming paired combinations of said candidate optical materials for which corresponding ratios η 1 /η 2 are substantially equal, subtracting corresponding values of η 1 for each paired combination of said candidate optical materials, and selecting optical materials for designing said system from among those paired combinations for which the absolute value of the difference between corresponding values of η 1 is greater than a specified value appropriate for said system.

Claim 58

The method of claim 40 wherein said polynomial is cubic, the coefficients nl, n2 and n3 being calculated for each optical material, and wherein said candidate optical materials for designing said system are identified from among those optical materials for which corresponding ratios (η 1 /η 2 ), (η 2 /η 3 ) and (η 1 /η 3 ) are substantially equal.

Claim 59

The method of claim 44, said method being used to select three different optical materials from among said candidate optical materials for designing said system, said method further comprising: a) locating each candidate optical material with respect to a three-dimensional coordinate system defined by axes corresponding to the coefficients η 1 , η 2 and η 3 ; b) designating a first one of said candidate optical materials as a reference optical material; c) defining a two-dimensional transformed coordinate system by axes μ 1 and μ 2 , with origin at the location of said reference optical material; d) locating the other candidate optical materials with respect to said transformed coordinate system; e) calculating the ratio μ 2 /μ 1 for each of said other candidate optical materials; and f) selecting a second one and a third one of said candidate optical materials from among those other candidate optical materials having substantially the same value as said reference optical material for the ratio μ 2 /μ 1 .

Claim 60

An optical system color-corrected at least at three wavelengths, said system comprising only two lens elements, each lens element being made of a different optical material exclusive of calcium fluoride, each optical material having a characteristic dispersive power, the dispersive power of each optical material being represented by a polynomial expression in a variable that is a function of wavelength, said polynomial expression being the form D(λ)=η.sub.1 ω(λ)+η.sub.2 ω.sup. (80 ) where D(λ) is the dispersive power, λ is the wavelength, ω(λ) is the variable that is a function of wavelength, ω(λ) being defined by the expression ω(λ)=δλ/(1+αδλ), where δλ represents change in wavelength with respect to a base wavelength and α is effectively a constant that is substantially independent of the dispersive power of the optical material, said optical system being made by a process that includes selection of said optic materials, said optical materials being selected by ascertaining that corresponding coefficients in the polynomial expressions for each of said optical materials have an absolute value difference that permits construction of optical elements having dioptric powers appropriate for said system.

Claim 61

An optical system color-corrected at least at three wavelengths, said system comprising only two lens elements, each lens element being made of a different optical material exclusive of calcium fluoride, each optical material having a characteristic dispersive power, the dispersive power of each optical material being represented by a polynomial expression in a variable that is a function of wavelength, said polynomial expression being the form D(λ)=η.sub.1 ω(λ)+η.sub.2 ω.sup. (80 ) where D(λ) is the dispersive power, λ is the wavelength, ω(λ) is the variable that is a function of wavelength, ω(λ) being defined by the expression ω(λ)=δλ/(1+αδλ), where δλ represents change in wavelength with respect to a base wavelength and α is effectively a constant that is substantially independent of the dispersive power of the optical material, said optical system being made by a process that includes selection of said optic materials, said optical materials being selected by ascertaining that corresponding coefficients in the polynomial expressions for each of said optical materials have an absolute value difference that permits construction of optical elements having dioptric powers appropriate for said system.