JPS63157122A - Scanning optical system - Google Patents

Abstract

PURPOSE:To obtain an optical system in which a view angle is >=30 deg. in one side and an aberration scarcely occurs, by a lens constituted of one piece, by providing a necessary f.theta lens between an optical deflector and an image surface. CONSTITUTION:A laser beam 13 which is deflected at an equal angular velocity by a rotary polygon mirror 10 passes through an f.theta lens 12 provided between the polygon mirror 10 and an image surface 11 and forms an image on the surface 11. This lens 12 is formed by one piece of aspherical lens and goes to a meniscus lens of a convex part to the image surface side, and approximate curvatures r1, r2 of first and second faces are selected so as to satisfy a condition of the expression I. In such a way, the astigmatism and the image surface curvature aberration are corrected, and even when a light source is in an infinity, a scanning optical system in which a view angle is >=30 deg. in one side and the aberration scarcely occurs is obtained by a lens constituted of one piece.

Description

[Detailed Description of the Invention] [General Work] By using an f/θ lens consisting of a single aspherical lens with a convex surface on the image plane side as a scanning optical system, the number of parts is small and the number of parts is sufficient. It makes it possible to obtain imaging performance.

[Industrial application field]

The present invention relates to a device that records characters or images by scanning light such as a laser beam, or a device that reads characters or images, and more specifically relates to a scanning lens that focuses light into a small spot and scans it. It is.

Optical systems in which a laser beam is scanned by an optical deflector and then imaged by a lens system to scan the image point are used in a wide variety of fields, including printers, displays, pattern generators, and image reading devices. For example, as shown in FIG. 2, a laser printer that modulates laser light according to the dot pattern of characters to form and record latent images of characters on a photosensitive drum is equipped with a rotating polygon mirror 1, a scanning lens 2, The image point 4 of the incident laser 3 by the scanning lens can be repeatedly scanned linearly from one end of the drum 5 to the other end.

Now, if the focal length of the scanning lens is f, and the angle between the beam incident on the lens and the optical axis is θ, then the ideal image height of a general lens is defined as f-tan θ, while the ideal image height is A lens in which is defined by f·θ is called an f·θ lens. The present invention relates to this f/θ lens. r
- If a θ lens is used, the velocity V of the beam on the image plane is expressed as. If the optical deflector is a rotating polygon mirror that rotates at a constant angular speed, the image point is scanned at a constant speed. In this way, the .theta lens has the characteristic of maintaining a linear relationship between the scanning angle and the scanning position.

[Prior art and problems to be solved by the invention] Conventional scanning lenses use two or three lenses (JP-A-53-137631, JP-A-51-9463, JP-A-Sho 54- 41149, JP-A No. 54-109457, and JP-A No. 54-150144), but all of these had the disadvantage of having a large number of parts.

Further, as a scanning lens using a single lens, there are Japanese Patent Application Laid-Open No. 55-7727 and ■ Japanese Patent Application Laid-open No. 54-87540.

(2) is a spherical lens, which can correct distortion to a small extent, but as the angle of view increases, the curvature of the field increases and plane imaging performance deteriorates, so there is a limit to the angle of view that can be used. (2) selects the conjugate image position of the light emitting point of the beam incident on the optical deflector at a finite distance, and is not intended to cover the use of multiple mirrors (rotating polygon mirrors) in the optical deflector.

The performances required of f/theta lenses can be roughly classified as follows.

■Good imaging performance (small spherical aberration, comatic aberration) ■Good planar imaging performance (small astigmatism, small curvature of field) ■Good f/θ characteristics (small distortion) - For FIH ,
For an f/θ lens, the focal length f and the ratio of the incident beam diameter f
/D, that is, the F number is thick (when it's dark, you don't need to pay much attention to ■).

■ is important.

Here, in aberration theory, the third-order aberration coefficients related to ■ are astigmatism: ■, field curvature: ■, and Petzval sum: P
and has the following relationship.

rv=m+p (1) JP-A-54-87540 has the following description. "
When the light source position is at an infinite distance from the deflector, ■=0 and IV=0 must be satisfied in order to scan the scanned plane, which is the imaging surface of the scanning lens, without field curvature. However, when the scanning lens is a single lens made of a glass material with a refractive index of N,
Assuming that the focal length of the lens is f=1, P = 1/N...
・(2) (N: refractive index of the lens), so m =
It is impossible to satisfy both o and IV=O. In other words, in the case of a single lens, the Petzval sum remains, so
Only either astigmatism ■ or curvature of the field field ■ can be corrected. ...(omitted)... On the other hand, if the light source position is placed at a finite distance, both astigmatism and spherical field curvature can be corrected even if the Petzval sum remains, and the imaging position can be fixed on the scanned plane. Is possible. '', which states that when the light source is at infinity, it is not possible to correct both astigmatism and spherical aberration at the same time with a single lens.

The present invention was created in view of these points, and is an optical system in which the conjugate image position of the light emitting point incident on the optical deflector is located at an almost infinite distance, and an optical system that uses a rotating polygon mirror as the optical deflector. The object of the present invention is to provide a single-lens lens having an angle of view of 30° or more on one side and having few aberrations.

[Means for solving problems]

Therefore, in the present invention, as illustrated in FIG. 1, an optical deflector 1o that deflects light at a constant angular velocity,
In a scanning optical system that includes an f/θ lens 12 between 0 and an image plane 11 and scans a parallel beam, the f/θ lens 1
2 is composed of one aspherical lens, and the f/θ lens 12 is characterized in that it is a meniscus lens with a convex surface on the image plane side.

[For production]

The curvature of the first surface of the f/θ lens 12 near the optical axis is rl
, when the curvature near the optical axis of the second surface is r2, inequality 1
When ≦□<1.5 is satisfied, both g astigmatism and field curvature can be corrected.

〔Example〕

The present invention deals with cases where the light source position is at an infinite distance from the deflector, but contrary to the description in the above-mentioned Japanese Patent Application Laid-Open No. 54-87540, we designed a single aspherical lens that could be put into practical use for the following reasons. There is a possibility that it can be done.

i) There is a tolerance range in the actual planar imaging performance ■=0, I
There is also a certain tolerance range for V=0.

ii) Equation (2) P=1/N applies when considering a thin wall system, but when considering a thick wall system, the following equation is obtained.

If we set p=o in equation (3), rl = r.

That is, when the radii of curvature of the first surface and the second surface are the same, P=0. But r,! Since rt is a major restriction during design, P can be brought close to O to some extent by actually setting rl and r2 to relatively close values. Therefore, it is considered that r and r2 have the same sign, that is, a meniscus lens is easier to correct astigmatism and field curvature at the same time.

In addition, for high-order aberration correction when the angle of view is large, an aspheric surface is used to increase the degree of freedom in design.

Conventionally, in lens design, a computer is used to calculate the merit function value, which is the sum of each lens aberration multiplied by weight. The method used is to recalculate and repeat this operation many times until the merit function value satisfies the target value. However, in the case of an aspheric lens, there are many optical parameters for designing a lens, such as refractive index, thickness, radius of curvature, aspheric coefficient entrance pupil position, etc. The optimal design of a lens is an optimization problem of a multivariable function. Become.

Generally, the merit function, which is the sum of various aberrations, has many extreme values, so no matter how much optimization is performed using a computer, if the initial values are wrong, a good lens cannot be obtained. Therefore, it is a well-known method to set the initial value using aberration theory as a guideline or using past data. In the present invention as well, we were able to obtain a good lens by performing optimal design through trial and error using a computer using such a procedure.

Figure 1 shows a model of a single aspherical f/θ lens. In this figure, a parallel incident beam 13 is reflected by an optical deflector 10 using a rotating polygon mirror, passes through the optical axis of an f/θ lens, and reaches an image plane. The constituent parameters of the lens are: refractive index 2N, center thickness: d1, radius of curvature of the n-th surface and aspheric coefficient: rn
, Bn, Cn +Dn, En, Fn, Gn
It is. However, the shape of the n-plane is +'CnSn'+DnSn''+'CnSn'+DnSn''+'CnSn'+DnSn''+'CnSn'+DnSn' +EnSnI0+
It has a rotationally symmetrical shape with the optical axis formed by FnSnI2+GnSn'4 as the central axis. Other parameters related to the entrance pupil position and its changes include the distance d0 between the rotating polygon mirror and the first surface of the lens, the angle ψ between the incident beam and the optical axis, the diameter of the inscribed circle (size of the rotating mirror): RO1 rotating mirror center position Distance related to: ΔX. In the case of a rotating polygon mirror, the position of the reflection point changes depending on the scanning angle θ (the angle between the optical axis and the angle of incidence on the lens) based on the difference between the inscribed circle and the circumscribed circle. That is, the entrance pupil position changes depending on the scanning angle θ. The f/theta lens needs to have characteristics such that its performance does not deteriorate even if the entrance pupil position changes in this way.

The important performances required of the f/theta lens are as follows.

■Small astigmatism and curvature of field.

■Distortion aberration is small (f/θ characteristics are good) ■■Characteristics are good even when the entrance pupil position changes due to changes in the scanning angle.

Taking the above into account, we performed an optimal design using a computer through repeated trial and error. As a result, as expected from the theory of aberrations mentioned above, it was found that aberrations cannot be corrected at the same time unless a meniscus lens (convex in the image plane direction) has relatively close values of rl and r2. r, and r
As a result of repeated optimal design, it was found that the following inequality must be satisfied:

1≦(−)<1.5 z Outside this range, it is difficult to correct each aberration at the same time.

Examples will be described below.

We selected several elements that greatly influence the optimal design of a single aspherical lens, and performed the optimal design by varying each of them.

The selected elements are:

0 angle of view (θmax) ■Refractive index (N) ■Lens thickness (dl) ■ is the maximum angle θm between the optical axis and the beam incident on the lens
ax (θmax>O), and −θmax ~θm
The incident beam between ax is valid.

θmax is 33°, 44°, 52°, respectively 8
Compatible with rotating polygon mirrors such as a hexahedron, a hexahedron, and a pentahedron. Table 1 shows values such as focal length corresponding to the angle of view.

Regarding the refractive index N in Table 1, the optical materials currently used for lenses are about 1.4 to 1.9. In the present invention, the optimal design was carried out using approximately 1.5 as a representative of a low refractive index and approximately 1.8 as a representative of a high refractive index. As a result of repeatedly performing optimal design, it was found that a larger N is advantageous in correcting each aberration. This is clearly seen in the embodiments described below.

In addition, as a result of repeatedly performing optimal design, we found that the thickness dl of the lens has a large effect on aberration correction, and that if d is too small, it will not be possible to correct each aberration at the same time, so a certain amount of thickness is necessary. Understood.

Examples are shown below. Table 2 shows the relationship between the example number and 0 angle of view, ■ refractive index, ■ lens thickness, Table 3 shows the specifications of each example, and Figs. It showed aberrations. From the figure, it can be seen that the present embodiments satisfying 1≦□<1.5 have small aberrations and are suitable for practical use. Although not shown in the drawings, "those outside the above conditions have large aberrations and are not suitable for practical use.

Table 2 with blank space below: [Example 1] f = 220.0000 d
O=r1=-45,3668d1ar2
= −41,0367d 2 ; B 1 = −2,5
64104Xl0-'C1miE1=5.
990942XlO−” F1=82=−1
,200928Xl0-6G2・E2=-9,
098427xlO-IbF 2 =l −-1,ioez The aberration diagram is shown in FIG.

However, the distortion aberration is the value of the following equation when focal length f, step angle θ, and y.

fθ Table 1 (1) ・ 11.0000 ・ 40.0000 N=
1.48600・283.4399・1.724664xlO-' D1=-1
,734847xlo-'・0.0
G1= 0.0・-2゜225062X
10-” D2=8.369305X10-
”・0.0 G2=
0.0 image height [Example 2] f = 220.0000 d
Or 1 = -50,9850d 1 r 2 = 45.5954 d
2B 1 = -1,742203Xl0-5
CIE1=3.712757XIO-”
FIB2=-5,244683Xl0-'
C2E 2 =-2,030129xlO-”
F 2−− =1.118 I The aberration diagram is shown in FIG.

[Example 3] f = 220.0000 dO
r 1 = -57,0081d 1 r 2 = -49,9818d 2 B 1 = -1,264485Xl0-'
CIEl=1.540421XIO-”F
IB 2--2.392693 Xl0-'
C2E2 = -6,018082xlO-I7F
2--1.141 The aberration diagram is shown in Figure 5 Table 3 (2) = 11.0000 = 50.0000 N=
1.48600=290.5615=1.015482X10-' DI=-
1,057879X10-'=0.0
G1= 0.0=-1,056290
xlO-10D2= 1.565872xlO-14
= 0.0 G2= 0
．． 0= 12.0000 = 60.0000 N=
1.48600=295.7277=5.503187X10-' D1=-
5,097621X10-16-0.0
G1= 0.0=-6,329331X
10-” D2= 3.516849X10-
”-0,0G2 reed 0.0.

[Example 4] f = 220.0000 dO
r 1 = -66,5182d 1 r 2 = -57,5658d 2 B 1 = -5,240528Xl0-"
CIE1=2.222347X10-”F
IB 2 = -1,068260Xl0-'
C2E 2 = -2,052871Xl0-'6
F2-=1.156z The aberration diagram is shown in FIG.

[Example 5] r = 220.0000 d
Or 1 = -69,1807d 1 r 2 = -61,9764d 2 B l = -5,668784Xl0-'
CIE 1 = 8.531304 Xl0-”
F t82 =-6,606470Xl0-'
C2E 2 = −4,906209Xl0−”
FZr! -=1.116 The aberration diagram is shown in Figure 7 (Table 3 (3) = 26.0000" 30.0000 N
= 1.78571=263.6571 = 9.635758X10-” D1=-6
,297802X10'2=0.0
G1= 0.0=-3,0O0
820X10-”D2=5.95708
4X10-14=0.0
G2= 0.0= 17.0000 = 40.0000 N=
1.78571=275.9692=1.603355xlO-' DI
=-6,24265xlo-”=0.0
G1= 0.0= 1.1
48118X10-” D2=-1,6634
01X10 3= 0.0
G2=0.0 is shown.

[Example 6] f = 220.0000 dr 1
= -74,7753d r 2 = -67,5528d B 1--3.178875 xlO-' C
E 1 = 4.805572 xlO-14FB
2--2.869785 Xl0-' CB
2--4.013730 XIO””Fr.

--=1.10? The aberration diagram is shown in FIG.

[Example 7] f -220,0000d I r 1--77.4896 dr 2
= −71,7326d'.

B 1--1.904874 XIO″h c
El Den 4.334901 Xl0-1SF lB2-
-1.327272X10-' C:B2--
4.460741X10-” FS-t, oso
The aberration diagram is shown in Figure 9. Table 3 (4) 0 = 17.2386 1 = 50.0000 N
1.785712-284.7271 1= 6.646437xlO-' DI heat-3,236906x 10- "1- 0.0
Gl-0,02=2.5388
32X10-” D2=-4,399395X1
0-”2- 0.0 G2=
0.01 = 23.2564 1 bottle 60.0000 N = 1.
78571! =294.9517 4 6.175538xlO-” DI--5,
110941xlO-”-0,0G1=0.0!--2,351038X10-”D2--3
．． 112747X1 (1”: Electric 0.OG2=0.
0.

[Example 8] r = 165.5000 dr 1
= -'48.7381 dr
2 = -38,4946d B 1 = -3,482473xlO-' C
E1= 8.707567X10-” FB
2 = -8,861466Xl0-'C
E2=-1,754637xlo-1F:r.

--1,266 The aberration diagram is shown in Figure 1O.

[Example 9] f -165,5000d 1 r 1 = -53,2086d r 2 = -41,8659d : B1--2.256799xlO-' C:E 1
= 2.413553xlO-”F)B
2 = -2,057704x 10-' C:
E2=-5,260583xlo-”F:
- = 1.271 The aberration diagram is shown in Figure 11.
．． 9229 [= 5.072485xlO-' DI-
-9,376305xlO-'1=-4.439226
XIO-13G1= 1.002868X10-”≧
= -2,101010xlO-” 02-7
．． 557104x10-th! -1,815009X10
-” G2=-8,403720X10-”1=
7.2970 = 50.0000 N=
1.48600: =216.3631
D I = −3,630719X10−”=
2.223478X10-' Gl=6
．． 743042X10-" and -7,046832X10
−”D2=3.239996X10−”!
=-1.196650X10-” G2--1
．． 344378X10-”1 = 4.028875
X 10-'”: Show.

[Example 10] f = 165.5000 r L = -56,8958 r 2 = -44,8169 B 1 = 1.909148 xlO-'
IE 1 = 1.520780 xlO-”
IB 2 = 6.279218 xlo-9+
E2=-1,641882X10-” 1-=
1.270 The aberration diagram is shown in FIG.

[Example 11] f = 165.5000 r 1 = -65,1473 r 2 = -52, 1968 B1 = -8, 134037Xl0-h (E1 = 2.
870138X10-”IB2=-1,
217566Xl0-h (E2 = -1,6014
73Xl0-1S1I = 1.248 The aberration diagram is shown in Table 13 and Table 3 (6) 10 = 7.6444 11 = 60.0000
N= 1.4860012 =222.5803 11:1= 1.660395xlO-'
DI=-2,524011xlO-'r l=-3
,846042X10-th G1= 2.4474
31X10-”1=-5,871182xlO-”
D2= 1.355357xlO-+21=
9.679337X10-I9G2=-2,40814
5X10-”! 0 = 15.3378 11 = 30.0000 N
= 1.78571L 2 =199.0332 1=9.487563xlO-' DI=-6
,791407xlO−”' 1 = −8,3
75036xlO-lb G 1 =
8.824204xlO-”2 2=-4,780
826xlO-10D2= 4.438801xl
O-13"2= 1.529839xlO-"
G2=-7,533866xlO-" is shown in FIG.

3rd degree [Example 12] f = 165.5000
d O−IEr 1 = −65,9158d l
= 4Cr 2 = -55,4219d 2 =
20981 = -4,816877xlL'
CI = 5E 1 = 9.075982
xlO−” F 1 = −282=
-4,602700Xl0-' C2= -
2E 2 = -5,968362xlO-I'F 2
= 3=1.189 The aberration diagram is shown in FIG.

z [Example 13] f = 165.5000 d O
= 18r 1 = -70,2339d l = 5
Cr2=-59,8876d2=217B
l=-3,601022Xl0-hC1=EE1
= 1.690907X10-” F1=-3
82=-2,166960Xl0-'C2
= −IE 2 = −2,803466Xl0−”
F 2 = 1I −=1.172 The aberration diagram is shown in FIG. 15.

Zetsu (7), 2892. 0000 N= 1.78
571.6895. 191031X10-9DI=-3,250581X
lO-”, 345027X10-1” G1=
2.339426X10-”, 942563X10-
IoD2 = 3.714396xlO-”, 6951
59
22.4312. 0000 N= 1.78
571.3409. 311956 X 10-” DI=-
5,513907X 10th, 032890X10-
”G1=2.137596X10-19.
547980 x 10' D2 = 2.3
90081xlO-Iff, 340327X10-”
G 2 = -2,833385X10-” [Example 14] f = 165.5000
dr 1 = -73,9872d r 2 = -63,9824d B 1 = -3,514309xlO-h
cE 1 = 2.387407 xlO-”
FB2 = -1,244709xlo
−' CE 2 = −1,473841
Xl0-16 F: -=1.156 The aberration diagram is shown in Figure 16 B [Example 15] f = 140.0000 d +
r1=-58,1510d r2=-41,9345'djB1=
-2,491429X10-' CE1=-3
, 330604X10-"F'B2=4.
179378XIO-” (,:E2=-2,
573251X10-I6F:- = 1.387 The aberration diagram is number 17.

Table 3 (8) ) = 19.4385 1 = 60.0000 N
= 1.78571≧=224.5533 1 = 1.451175xlO” DI
--8,487944X10-th L=-3,5983
32X10-IhG1= 2.145000X10-
"≧=-8.226158X10-" D2=
1.587217X10-”!= 5.5895
77X10-”°G2=-8,7654
93X 1O-24=shown.

) = 7.2443', = 60.000ON = 1.48600!
= 187.2432, = 1.805369X10-' D1=-
1,499721X10-'= 4.299494X
10-1' G1=-1,486034X10-I
h! =-1,590367xlO-”D2=
3.338246xlO-13:= 1.21573
9X10-''' G 2 = -2,221703X
10d3: Show.

[Example 16] (= 140.0000
dOr! = -63,4297d 1r 2
= -48,6415d 2 B1=-1,258949X10-' C
IEl Tomi 1.817489 Xl0-”
F IB 2 = −1,363431Xl0−”
C2E2=-6,254525X10-
"F2- = 1.304 The aberration diagram is the first
In Figure 8 [Example 17] r = 140.0000 d O
r 1 = −66,0795d i r 2 = −52,3199d 2 B 1 = −5,609556Xl0−”
CIE l = 8.466122 Xl0-th
FIB2 = -3,993857Xl0-'
C2E 2 = -1,338344XIO'
F2r.

-=1.263 r.

The aberration diagram is shown in FIG. 19.

Table 3 (9) = 11.4681 = 30.0000 N-1
,78705=169.1624=6.839530X10-” D1=-
4,664560X10-'.

4.353678xlO-” Gl=4
．． 439959xlO-”=-6,882926X10
-”D2=2.626494X10-12
= 5.687494x10-18G2=-2,34
3089xlO-”.

Mi12.8452 = 40.0000 N= 1.7
8705=177.3239=1.544548×1O-1lDI=-6,15
0223
100006X 10th edition' D2 Tomi 9.8076
53 x 10-” = 8.273120x10-
19G2=-2,424213xlO-” 3rd [Example 18] f = 140.0000 d O
r 1--64.4613 d 1r
2 = -54,5623d 2 B 1--4.312118 Xl0-"C
IE1= 1.784064X10-” FI
B2=-1,124136X10-' C2E
2--7.416259X10-''F2I-=1.181 The aberration diagram is shown in FIG.

Table (10) = 12.1043 = 50.0000 N-
1,78705=187.8261=1.922232X10-” DI=-
8,932850X10-”=-3,262454X1
0-” G1= 3.517197X10-
”=-4,290317X10-” D2=
7.609930X10-'Koni 3.503699
X10-” G2=-7,348855X10-
[Effect of the Invention] As described above, according to the present invention, by using 18 aspherical lenses, the number of parts can be reduced by 4, and in addition, it is possible to provide 9 scanning light systems with sufficient imaging performance. , which is extremely useful in practice.

[Brief explanation of the drawing]

Fig. 1 is a diagram showing a model of the aspherical f/θ lens of the present invention, Fig. 2 is a C diagram for explaining the principle of the f/θ lens, and Figs. It is a figure which shows the aberration of 18th Example. In FIG. 1, 10 is a light deflector (rotating polygon mirror), 11 is an image plane, 12 is an f/θ lens, and 13 is a parallel beam. Figure 1o shows a model of the aspherical f/θ lens of the present invention.
Optical deflector (rotating polygon mirror) 11, image plane 12, f/θ lens 13 Parallel beam salvage aberration (mm) Aberration diagram of Example 7 Spherical aberration (mm) Aberration diagram of Example 14 Fig. 16

Claims (1)

[Claims] 1. An optical deflector (10) that deflects light at a constant angular velocity, and an f/θ lens (12) between the optical deflector (10) and an image plane (11). , in a scanning optical system that optically scans a parallel beam, the f/θ lens (12) is composed of a single aspherical lens, and the f/θ lens (12) is a meniscus lens having a convex surface on the image plane side. A scanning optical system characterized by: 2. When the curvature of the first surface of the f/θ lens (12) near the optical axis is r_1, and the curvature of the second surface near the optical axis is r_2, inequality 1≦r_1/r_2<1.5 is satisfied. A scanning optical system according to claim 1, characterized in that: