Optical system

An optical system comprising

• N lenses sequentially disposed along an optical axis from an object-side toward a sensor-side,
• wherein a first axis perpendicular to the optical axis is defined and a second axis perpendicular to the optical axis and the first axis is defined in an nth lens which is any one of the N lenses,
• a first surface of the nth lens has a first sag value S1 at coordinates spaced apart from the optical axis by a first distance d1 in the first axis direction and a second sag value S2 at coordinates spaced apart from the optical axis by the first distance d1 in the second axis direction,
• a second surface of the nth lens has a third sag value S3 at coordinates spaced apart from the optical axis by the first distance in the first axis direction and a fourth sag value S4 at coordinates spaced from the optical axis by the first distance in the second axis direction, and
• the nth lens satisfies Equations 8 and 9 below:
• d
• ⁢
• 1
• >
• 0
• ⁢
• S
• ⁢
• 2
• -
• S
• ⁢
• 1
• ≠
• 0
• ⁢
• S
• ⁢
• 4
• -
• S
• ⁢
• 3
• ≠
• 0
• [
• Equation
• ⁢
• 8
• ]
• ❘
• "\[LeftBracketingBar]"
• S
• ⁢
• 2
• -
• S
• ⁢
• 1
• ❘
• "\[RightBracketingBar]"
• <
• ❘
• "\[LeftBracketingBar]"
• S
• ⁢
• 4
• -
• S
• ⁢
• 3
• ❘
• "\[RightBracketingBar]"
• .
• [
• Equation
• ⁢
• 9
• ]

An optical system comprising:

• N lenses sequentially disposed along an optical axis from an object-side toward a sensor-side,
• wherein a first axis perpendicular to the optical axis in a major axis direction of a sensor;
• a second axis perpendicular to the optical axis and the first axis in a minor axis direction of the sensor;
• and a third axis perpendicular to the optical axis in a diagonal direction of the sensor;
• and a fourth axis perpendicular to the optical axis is defined in an nth lens which is any one of the N lenses,
• a shape of a first surface of the nth lens is symmetrical in the first axis direction and the second axis direction,
• wherein a sag value of a first surface of the nth lens is set by Equation 2 below,
• Z
• =
• cr
• 2
• 1
• +
• (
• 1
• +
• k
• )
• ⁢
• c
• 2
• ⁢
• r
• 2
• +
• ∑
• i
• =
• 1
• n
• C
• j
• ⁢
• Z
• j
• [
• Equation
• ⁢
• 2
• ]
• (In Equation 2, Z is a sag value of an nth lens, c is a curvature value of an nth lens, r is an effective diameter value of an nth lens, k is a conic constant, and Cj is a Zernike coefficient at the j order, and Zj is a Zernike basis at the j order);
• wherein a plurality of first coordinates (±v1,0) set by Equation 13-1 and Equation 13-2 below are set on the first axis of the first surface of the nth lens,
• v
• 1
• ′
• =
• V
• -
• t
• 1
• *
• tan
• ⁡
• (
• θ
• v
• -
• α
• )
• [
• Equation
• ⁢
• 13
• -
• 1
• ]
• 0.7
• *
• v
• 1
• ′
• <
• v
• 1
• <
• 1.3
• *
• v
• 1
• ′
• [
• Equation
• ⁢
• 13
• -
• 2
• ]
• (In Equation 13-1, v1′ is a distance spaced apart from the optical axis in the negative or positive direction of the first axis, V is a half of the major axis of the image sensor unit, t1 is a distance from the eleventh surface S11 to the image sensor unit, θv is the chief ray angle in the 0.8 field of the image sensor unit, and α is sin−1(1/(2*F number)));
• wherein a plurality of second coordinates (0,±h1) set by Equation 14-1 and Equation 14-2 below are set on the second axis of the first surface of the nth lens,
• h
• 1
• ′
• :
• H
• -
• t
• 1
• *
• tan
• ⁡
• (
• θ
• h
• -
• α
• )
• ⁢
• h
• 1
• ′
• <
• v
• 1
• ′
• [
• Equation
• ⁢
• 14
• -
• 1
• ]
• 0.7
• *
• h
• 1
• ′
• <
• h
• 1
• <
• 1.3
• *
• h
• 1
• ′
• ⁢
• h
• 1
• <
• v
• 1
• [
• Equation
• ⁢
• 14
• -
• 2
• ]
• (In Equation 14-1, h1′ is a distance spaced apart from the optical axis in the negative or positive direction of the first axis, H is a half of the minor axis length of the image sensor unit, t1 is a distance from the eleventh surface S11 to the image sensor unit, θh is the chief ray angle in the 0.6 field of the image sensor unit, and α is sin−1(1/(2*F number)));
• wherein a plurality of third coordinates (x1,y1/−x1,−y1) and the fourth coordinates (−x1,y1/x1,−y1) set respectively by Equation 15-1 and Equation 15-2 below are set on the third axis and the fourth axis of the first surface of the nth lens,
• d
• 1
• ′
• :
• D
• -
• t
• 1
• *
• tan
• ⁡
• (
• θ
• d
• -
• α
• )
• ⁢
• h
• 1
• ′
• <
• v
• 1
• ′
• <
• d
• 1
• ′
• ⁢
• ❘
• "\[LeftBracketingBar]"
• d
• 1
• ′
• ❘
• "\[RightBracketingBar]"
• 2
• =
• ❘
• "\[LeftBracketingBar]"
• x
• 1
• ′
• ❘
• "\[RightBracketingBar]"
• 2
• +
• ❘
• "\[LeftBracketingBar]"
• y
• 1
• ′
• ❘
• "\[RightBracketingBar]"
• 2
• [
• Equation
• ⁢
• 15
• -
• 1
• ]
• 0.7
• *
• d
• 1
• ′
• <
• d
• 1
• <
• 1.3
• *
• d
• 1
• ′
• ⁢
• h
• 1
• <
• v
• 1
• <
• d
• 1
• ⁢
• ❘
• "\[LeftBracketingBar]"
• d
• 1
• ❘
• "\[RightBracketingBar]"
• 2
• =
• ❘
• "\[LeftBracketingBar]"
• x
• 1
• ❘
• "\[RightBracketingBar]"
• 2
• +
• ❘
• "\[LeftBracketingBar]"
• y
• 1
• ❘
• "\[RightBracketingBar]"
• 2
• [
• Equation
• ⁢
• 15
• -
• 2
• ]
• (In Equation 15-1, d1′ is a diagonal distance extending from the optical axis in third and fourth axis directions, D is a half of a diagonal length of the image sensor unit, t1 is a distance from the eleventh surface S11 to the image sensor unit, θd is the chief ray angle in the 1.0 field of the image sensor unit, and α is sin−1(1/(2*F number)));
• wherein the first surface of the nth lens includes a first effective surface formed by connecting the first coordinate, the second coordinate, the third coordinate, and the fourth coordinate,
• wherein |second sag value-first sag value| is the difference between the second sag value at the second coordinate of the second axis equidistant from the optical axis and the first sag value at the first coordinate of the first axis, and
• wherein an average deviation between |second sag value-first sag value| inside the first effective surface is smaller than an average deviation between |second sag value−first sag value| outside the first effective surface.