Patent ID: 8422141

Claim:
A radial gradient-index optical element having a refractive index that varies in a direction perpendicular to an optical axis, wherein the following conditional expressions are satisfied: |θ dCgi ( re )−(−0.1968θ gdgi ( re )+0.5480)|<0.02; |Δθ gdgi ( r )|>0.025; |Δθ gd ( re )−Δθ gd (0)|>0.025; |θ gdgi ( re )−θ gdgi (0.1 re )|<0.1; δ n λ( r )= n λ( r )− n λ(0); ν dgi ( r )=δ nd ( r )/{δ nF ( r )−δ nC ( r )}; θ gdgi ( r )={δ ng ( r )−δ nd ( r )}/{δ nF ( r )−δ nC ( r )}; θ dCgi ( r )={δ nd ( r )−δ nC ( r )}/{δ nF ( r )−δ nC ( r )}; Δθ gdgi ( r )=θ gdgi ( r )−{−1.687×10 −7 νdgi ( r ) 3 +5.702×10 −5 νdgi ( r ) 2 −6.603×10 −3 νdgi ( r )+1.462}; and Δθ gd ( r )=θ gd ( r )−{−1.687×10 −7 νd ( r ) 3 +5.702×10 −5 νd ( r ) 2 −6.603×10 −3 νd ( r )+1.462}, where r is a distance from the optical axis in the direction perpendicular to the optical axis, re is a maximum value of an effective beam diameter of a beam that transmits through the radial gradient-index optical element, nλ(r) is a refractive index of a medium of the radial gradient-index optical element at the distance r from the optical axis for one of g-line, F-line, d-line, and C-line, δnλ(r) is a refractive index difference of a medium between the optical axis and the distance r, νd(r) is an Abbe number of the medium at the distance r from the optical axis, θgd(r) is a partial dispersion ratio for the g-line and the d-line of the medium at the distance r, Δθgd(r) is a deviation of θgd(r) from a normal curve which is made by approximating a relationship between the Abbe number of a general glass and the partial dispersion ratio for the g-line and the d-line of the general glass, θgdgi(r) is an equivalent partial dispersion ratio for the g-line and the d-line of the radial gradient-index optical element at the distance r f, θdCgi(r) is an equivalent partial dispersion ratio for the d-line and the C-line of the radial gradient-index optical element at the distance r, Δθgdgi(r) is a deviation of θgdgi(r) from the normal curve which is made by approximating a relationship between the Abbe number of a general glass and the partial dispersion ratio for the g-line and the d-line of the general glass, νdgi(r) is an equivalent Abbe number of the radial gradient-index optical element at the distance r, the equivalent partial dispersion ratio is a partial dispersion ratio of virtual glass having a chromatic aberration equal to that of the radial gradient-index optical element, and the equivalent Abbe number is an Abbe number of the virtual glass.