# US 4,400,063 A · F(.theta.) Lens system of four-group construction

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- Number: US 4,400,063 A
- Document ID: US4400063A
- Status: Granted
- Kind: A
- Application number: 06/271,284
- Filed: 1981-06-08
- Granted: 1983-08-23
- Earliest claimed: 1980-06-20
- Assignees: Nippon Kogaku K.K.
- Inventors: Bun Hayashida
- Web page: https://patentgrep.com/patent/US4400063A

## CPC

- G02B 9/34: having four components only
- G02B 13/00: Optical objectives specially designed for the purposes specified below (with variable magnification {in general} G02B15/00)
- G02B 13/0005: {having F-Theta characteristic (scanning systems employing movable or deformable optical elements G02B26/10)}
- G02B 26/125: {Details of the optical system between the polygonal mirror and the image plane (G02B26/123, G02B26/127 take precedence; F-Theta lenses G02B13/0005)}
- G02B 27/0025: {for optical correction, e.g. distorsion, aberration}
- G02B: OPTICAL ELEMENTS, SYSTEMS OR APPARATUS

## Abstract

This specification discloses an f.theta. lens system having an entrance pupil at a remote position on the incident light side of the lens system and having such a negative distortion that the image height H of a parallel light beam incident at an angle .theta. with respect to the optical axis with the entrance pupil as the center is H=f.theta., where f is the focal length of the entire system. The lens system includes, in succession from the entrance pupil side, a first group having at least one negative lens and having a composite negative refractive power, a second and a third group each having a meniscus lens component having its concave surface facing the entrance pupil side, and a fourth group having at least one positive lens and having a composite positive refractive power.

## Claims

### Claim 1

An f.theta. lens system having an entrance pupil at a remote position on the incident light side of the lens system and having negative distortion such that the image height H of a parallel light beam incident at an angle .theta. with respect to the optical axis with said entrance pupil as the center is H=f.theta., where f is the focal length of the entire system, said lens system including, in succession from the entrance pupil side:
a first group having at least one negative lens and having a composite negative refractive power;
a second and a third group each having a meniscus lens component having its concave surface facing said entrance pupil side; and
a fourth group having at least one positive lens and having a composite positive refractive power;
and wherein the lens system satisfies the following conditions:
0.08f<R.sub.III <0.35f
.vertline.R.sub.III .vertline.<.vertline.R.sub.II .vertline.
f<f.sub.II
f<f.sub.III
0.8<R.sub.4 /R.sub.3 <1.2
0.7<R.sub.6 /R.sub.5 <1.5
where R.sub.3 and R.sub.4 represent the radii of curvature of the opposite lens surfaces of said second group from said entrance pupil side, R.sub.5 and R.sub.6 represent the radii of curvature of the opposite lens surfaces of said third group from said entrance pupil side, R.sub.II =(R.sub.3+ R.sub.4)/2, R.sub.III =(R.sub.5+ R.sub.6)/2, and f.sub.II and f.sub.III represent the focal lengths of said second group and said third group, respectively.

### Claim 2 (depends on 1)

An f.theta. lens system according to claim 1, wherein the radii of curvature of the opposite lens surfaces of each meniscus lens of said second and third groups are substantially equal.

### Claim 3 (depends on 1)

An f.theta. lens system according to claim 1, wherein said first group has, in succession from said entrance pupil side, a positive lens and a negative lens, and said fourth group has a single positive lens.

### Claim 4 (depends on 3)

An f.theta. lens system according to claim 3, wherein numerical data are as follows:
f=100 mm, 2.omega.=45.degree.
The entrance pupil lies 7.095 mm ahead of the first lens surface .gamma..sub.1 ;
______________________________________ .gamma..sub.1 = -152.993 d.sub.1 = 1.5 n.sub.1 = 1.51508 .gamma..sub.2 = -13.156 d.sub.2 = 0.4 G.sub.1 .gamma..sub.3 = -12.495 d.sub.3 = 2.4 n.sub.2 = 1.51508 .gamma..sub.4 = 120.668 d.sub.4 = 2.4 .gamma..sub.5 = -33.261 d.sub.5 = 1.8 n.sub.3 = 1.51508 G.sub.2 .gamma..sub.6 = -33.113 d.sub.6 = 2.4 .gamma..sub.7 = -15.508 d.sub.7 = 5.5 n.sub.4 = 1.51508 G.sub.3 .gamma..sub.8 = -18.472 d.sub.8 = 2.0 .gamma..sub.9 = 238.413 d.sub.9 = 4.5 n.sub.5 = 1.51508 G.sub. 4 .gamma..sub.10 = -37.308 f.sub.I = -109.8 f.sub.II = 2814 f.sub.III = -508.0 f.sub.IV = 64.0 ______________________________________
where .gamma..sub.1, .gamma..sub.2, . . . , .gamma..sub.10 represent the radii of curvature of the successive lens surfaces from said entrance pupil side, d.sub.1, d.sub.2, . . . , d.sub.9 represent the center thicknesses and air spaces of the successive lenses, n.sub.1, n.sub.2, . . . , n.sub.5 represent the refractive indices of the successive lenses for light of wavelength 6328 A, and f.sub.I, . . . , f.sub.IV represent the focal lengths of said groups.