GB2104240A

GB2104240A - Mono aspherical lens

Info

Publication number: GB2104240A
Application number: GB08219174A
Authority: GB
Inventors: Jan Haisma; Josephus Johannes Maria Braat; Gijsbert Prast
Original assignee: Philips Gloeilampenfabrieken NV
Current assignee: Koninklijke Philips NV
Priority date: 1982-07-02
Filing date: 1982-07-02
Publication date: 1983-03-02
Also published as: GB2104240B

Abstract

Mono aspherical lenses comprising a single refracting element are attractive for use in, for example, optical disc players, where light of a single wavelength is focussed by the lens to a diffraction limited read spot. It has now been found possible to achieve both a large numerical aperture needed to obtain a small read spot and a wide enough field of view within which the tracking purposes, with a lens 10 having only one aspheric surface 12, provided that the following conditions are met:- <IMAGE> where c1 is the curvature of the aspherical surface 12 at the intersection with the optical axis, c2 the curvature of the spherical surface 13, d the thickness of the lens, n the refractive index in the range 1.5</=n</=2.0, for the focal length, and NA the numerical aperture in the range 0.3</=NA</=0.5, the magnification V lying in the range V</=0.1. <IMAGE>

Description

SPECIFICATION Mono-aspherical lens The invention relates to a single lens having one spherical and one aspherical refractive surface. Such a lens, briefly referred to as a mon-aspherical lens, is known, for example, from British Patent Specification 1,499,861. The known mono-aspherical lens has a small numerical aperture and a small diffraction-limited field.

A conventional lens having two spherical surfaces produces an image of an axial point, which image is not diffraction-limited, especially at larger numerical apertures. If one surface of the lens is made aspherical a perfect (abberation free) image of the axial point can be obtained. Making only one surface aspherical does not guarantee a high image quality for non-axial object points.

In order to satisfy the Abbe sine condition strictly it is known, for example, from British Patent Specification 1,512,652, to make both refractive surfaces of the lens aspherical.

Surprisingly, it has been found possible to meet the Abbe sine condition substantially for mono-aspherical lenses having a large numerical aperture by making a selection from the multitude of possible mono-aspherics. To achieve a maximum diffraction-limited field coma must be minimised. By means of third-order aberration theory it is possible to calculate the lens shape for which third-order coma disappears in the case of a mono-aspherical lens whose focal length, refractive index, thickness and object and image conjugates are given.

It is found that for large numerical apertures (NA > 0.25) the third-order aberration theory is inadequate.

Then, in order to obtain mon-aspherical lenses with a large diffraction-limited field, a specific amount of third-order coma has to be accepted, which might seem to be a conflicting requirement.

The invention is based on the recognition that for a large diffraction-limited field and a large numerical aperture third-order coma can be compensated for by higher-order coma.

The lens shapes having this compensating effect are selected from a number of mono-aspherical lenses by determining when the diffraction-limited field is as large as possible by means of exact ray calculation.

The lens shape having the property that the third-order coma is zero may serve as a basis for the calculation. The result of the calculation is a lens which substantially complies with the Abbe sine condition and which consequently has a large diffraction-limited field.

The invention provides a mon-aspherical lens having one spherical and one aspherical refractive surface, wherein the parameters of the spherical refractive surface and of the aspherical refractive surface are related by the equation:

in which: 1.00 I)f 1.35, a = 4.85 (NA) - 0.32 n - 2.39, and b = -4.10 (NA) + 1.20 n + 0.46, where c1 is the curvature of the aspherical surface at the intersection with the optical axis, c2 the curvature of the spherical surface, d the thickness of the lens, n the refractive index in the range 1.5 S n S 2.0, f the focal length, and NA the numerical aperture in the range 0.3 S NA S 0.5, the magnification V lying the range V60.1.

The calculation for an arbitrary mono-aspherical lens are effected in accordance with the criterion that the lens should be free from spherical aberration. In that case the optical path-lengths of all rays from the axial object point to the associated axial image point are equal.

In general it is not possible to find analytical expressions for the co-ordinates of the desired aspherical surface. However, by means of modern computing devices it is no problem to make the path-lengths iteratively equal to each other for a number of rays, or, which is the same thing, to have all rays from a point object pass through one image point.

In order to minimize the computing time it is alternatively possible to work out the problem analytically as far as this is possible and to effect only the last step numerically, namely solving one transcendental equation, compare E. Wolf, Proc. Phys. Soc., 61494(1948).

Both methods ultimately lead to a set of discrete points on the desired aspherical surface. At option, an approximate curve may be constructed through this set of points, which is represented by a series expansion. The coefficients of this expansion then uniquely define the aspherical surface.

Two embodiments of the invention will be described in more detail, by way of example, with reference to the accompanying drawing, which represents a lens in accordance with the invention showing the path of rays from an object at infinity through the lens to the image plane.

In the Figure a mono-aspherical lens in accordance with the invention is designated 10. Starting from an object disposed at infinity (s = - cm) two pairs of marginal rays are shown, one pair parallel to the optical axis 00', the other pair at an angle ss to the optical axis. "Marginal rays" are to be understood to mean those rays at the edge of the pupil 11. The marginal rays refracted by the aspherical surface 12 pass through the lens 10 of a thickness d and after being refracted by the spherical surface 13 of the lens 10 they converge in the image plane 14. The convergence point of the marginal rays which are parallel to the optical axis 00' is disposed on said axis and the convergence point of the marginal rays which are incident at an angle ss to the optical axis 00' is at a distance r from the axis.The diameter of the pupil 11 and thus the effective diameter of the lens loins designated 2may, the diffraction-limited image area in the image plane having a diameter 2r.

The distance between the spherical surface 13 and the image plane 4 is s'. The angle a is the angle between the optical axis 00' and the marginal rays which have been refracted by the surface 13 and which are incident on the surface 12 parallel to the optical axis. The numeral aperture NA is given by the relationship NA = sin a.

In the following examples a specific refractive index n, a specific thickness d and a specific focus length f of the lens were selected as a basis for the calculations.

The paraxial curvatures c1 and c2 of the lens surfaces were varied using those curvature values for which the third-order coma is zero as starting point. Subsequently, the lens shape was determined by means of exact ray calculations (by varying c1 and c2) for which, at a large numerical aperture, the off-axis image quality of the lens was optimum.

In a first embodiment the lens 10 had a refractive index n = 2.0, a thickness d = 9.0 mm, a focal length f = 8 mm, and a numerical aperture NA = 0.4. The distance between the object and the lens 10 was s = -160 mm and the distance between the lens 10 and the image plane was s' = 3.94 mm.

At the intersection 15 with the optical axis 00' the aspherical surface 12 had a curvature c1 = 0.1245 mm-1, whilst the spherical surface 13 had a curvature c2 = -0.00125 mm-'.

The effective diameter of the lens 2ymax = 6.50 mm. The pupil 11 was disposed at the location of the surface 12. The diffraction-limited image area in the image plane 14 had a radius r = 1001lem.

The curve which approximates the aspherical surface 12 is represented by a series expansion with terms in which even Tschebycheff polynomials occur:

Here z is the abscissa of the point on the aspherical surface with the ordinate y, the abscissa being reckoned from the intersection 15. The coefficients of the terms are: g, = 0.413384 g, = 0.415212 g2 = 0.001803 g3 = -0.000027 g4 = -0.000001 whilst k = 0.276274 In a second embodiment the lens 10 had a refractive index n = 1.51, a thickness d = 5.0 mm, a focal length f = 8 mm, and a numerical aperture NA = 0.5. The distance between the object and the lens 10 was s = - 1 60mm and the distance between the lens and the image plane 14 was s' = 5.685 mm.

At the point of intersection 15 with the optical axis 00' the aspherical surface 12 has a curvature c, = 0.205 mm-', whilst the spherical surface 13 had a curvature c2 = -0.06835 mm-' The effective diameter of the lens was 2ymax = 8.624 mm. The pupil 11 was disposed at the location of the surface 12. The diffraction-limited image area in the image plane 14 had a radius r = 50 fly The curve which approximates the aspherical surface 12 is represented by a series expansion with terms in which even Tschebycheff polynomials occur:

The coefficients of the terms are: g0 = 0.956078 g1 = 0.953333 g2 = -0.005314 g3 = -0.002753 g4 = 0.000175 95 = 0.000012 g6 = 0.000003 whilst k = 0.23193.

Claims

1. A mon-aspherical lens having one spherical and one aspherical refractive surface, wherein the parameters of the spherical refractive surface and of the aspherical refractive surface are related by the equation:

in which: d 1.00 S ( 1) f < 1.35,(n-1)f # 1.35 a = 4.85 (NA) - 0.32 n - 2.39, and b = -4.10 (NA) + 1.20 n + 0.46, where c1 is the curvature of the aspherical surface at the intersection with the optical axis, c2 the curvature of the spherical surface, d the thickness of the lens, n the refractive index in the range 1.5 S n S 2.0, f the focal length, and NA the numerical aperture in the range 0.3 # NA # 0.5, the magnification V lying in the range V # 0.1.

2. A mono-spherical lens as claimed in Claim 1, wherein the aspheric surface is represented by a series expansion with terms in which Tschebyscheff polynomials T occur, given by:

where z is the abscissa of a point, of ordinate y, on the aspherical surface measured from the pole of the surface, gn are the coefficients of the terms and k is a constant.

3. A mono-aspherical lens substantially as described as the first embodiment and with reference to the accompanying Figure.

4. A mon-aspherical lens substantially as described as the second embodiment and with reference to the accompanying Figure.