Lens system for optical beam scanner

Abstract: The present invention relates to a lens system for an optical beam scanner which scans a plurality of optical beams. The lens system comprises: a first lens group (F L ) having an entrance pupil and including first and third lenses (L₁, L₃) each in the form of meniscus having a positive power, a fourth lens (L₄) having a positive power, and a second lens (L₂) having a negative power; and a second lens group (R L ) including a fifth lens (L₅) having a positive power. The first to fifth lenses are successively disposed in that order from the entrance pupil side. The resulting lens system has a telecentric and an f-sinϑ characteristic.

Description: The present invention relates to a telecentric f-sin ϑ lens system, and more particularly to a lens system which is applied to an optical beam scanner, such as a laser printer, which scans a plurality of optical beams on a recording surface. Japanese Patent Laying-Open Gazettes Nos. 195211/1984 and 267910/1988 disclose lens systems which can be applied to an optical beam scanner such as a laser printer, respectively. Fig. 1 illustrates the structure of a conventional telecentric f-ϑ lens system, which is disclosed in the former gazette (Japanese Patent Laying-Open Gazette No. 195211/1984). Another telecentric f-ϑ lens system is disclosed in the European Patent Application EP-A-0 360 233, of which the date of filing is prior to the date of this application, but which was published under Article 93 EPC after that date (Art. 54 (3) EPC). As shown in Fig. 1, the conventional telecentric f-ϑ lens system is formed with a negative meniscus lens L₁₂ whose concave surface S₁₂ is directed toward an entrance pupil EP, positive meniscus lenses L₁₃ and L₁₄ and a positive plano-convex lens L₁₅, and these lenses L₁₂ to L₁₅ are arranged in order from the entrance pupil EP side toward a recording surface RS side. The aforementioned lens system satisfies: h = f·ϑ assuming that h represents a distance from an optioal axis Z of the lens system to a beam spot on the recording surface RS, f represents the focal length of the lens system and ϑ represents an incident angle of the beam upon the lens system. A laser beam is generally deflected by a polygon mirror, so that the laser beam is impinged on the recording surface RS through the lens syetem. Since the polygon mirror is rotated at a constant angular velocity, the beam spot moves on the recording surface RS at a constant speed. Further, the lens system has a telecentric characteristic that all principal rays substantially vertically enter the recording surface RS, so that an image size in a main scanning direction does not vary even if the recording surface RS is displaced in the direction of the optical axis Z, for example as is well known in the art. Therefore, a telecentric f-ϑ lens system is employed in a laser printer etc. particularly requiring that a laser beam is projected onto the recording surface in high accuracy. Fig. 2 shows a schematic illustration of the optical path deflected by a deflector 1. A plurality of laser beams B₀ to B n are projected onto a point O of the deflector 1 which rotates in the forward and reverse directions around a Y-axis, while laser beams b₀ to b n deflected by the deflector 1 are directed toward a recording surface RS (X-Y plane) through a lens system 2a. In the figure, symbols i₀ to i n represent beam spots of the laser beams b₀ to b n on the recording surface RS, respectively. In the case that an f-ϑ lens system shown in Fig. 1 is employed as the lens system 2a, the following equation is obtained: Where y is a distance between the beam spots i₀ and i n , f is a focal length of the f-ϑ lens system 2a, α is an angle between the laser beam B n and an optical axis X, and β is an angle between the laser beam b₀ and an optical axis Z of the f-ϑ lens system 2a. When the deflector 1 rotates around the Y-axis, the angle β varies corresponding to the rotation of the deflector 1, whereby the distance y varies with the angle β. Therefore, the locus of the laser beams focusing on the recording surface RS by the f-ϑ lens system 2a will not straight as shown in Fig. 3, so that the quality of an image recording on the recording surface RS is lowered. Fig. 4 illustrates the structure of an f-sinϑ lens system, which is disclosed in latter gazette (Japanese Patent Laying-Open Gazette No. 267910/1988). As shown in Fig. 4, the f-sinϑ lens system is formed with a first lens group G₁ having a negative focal length and a second lens group G₂ having a positive focal length, to satisfy: h = f · sinϑ where h is a distance between an optical axis Z of the f-sinϑ lens system and a beam spot b on a recording surface RS, f is a focal length of the f-sinϑ lens system and ϑ is an incident angle that the optical beam entering the lens system forms with respect to the optical axis Z thereof. In the case that the f-sinϑ lens system 2 is used instead of the lens system 2a as shown in Fig. 2, the following equation is obtained: Y = f·sinα As understood the above equation, the distance y is a constant even if the deflector 1 rotates in the forward and reverse direction around the Y-axis. Therefore, the loci of the plural laser beams will be straight as shown in Fig. 5, when the laser beams are directed to the recording surface RS through the f-sinϑ lens system. However, the f-sinϑ lens system shown in Fig. 5 has no telecentric characteristic, so that an image size in a main scanning direction varies with the displacement of the recording surface RS in the direction of the optical axis Z of the f-sinϑ lens system. Therefore, the lens system can't be employed in the optical beam scanner such as a laser printer requiring that the image can be recorded on the recording surface RS in high accuracy. SUMMARY OF THE INVENTION The present invention is directed to a lens system for an optical beam scanner which scans a plurality of optical beams on a recording surface. The lens system comprises: (a) a first lens group having an entrance pupil, which includes (a-1) a first lens in the form of meniscus having a positive power and having a concave surface which is directed to the entrance pupil, (a-2) a second lens having a negative power, (a-3) a third lens in the form of meniscus having a positive power, and a fourth lens having positive power; and (b) a second lens group including a fifth lens having a positive power. Further, the first through fifth lenses are successively disposed in order from the entrance pupil side. In an aspect of the present invention, the above lens system satisfies following: 0.6 < (r₂/r₃) ≦ 2.1 -0.43 < (f₂/f) < -0.21 1.3 < (f₅/f) ≦ 2.6 where r₂ is a radius of curvature of a surface of the first lens, which is directed to the recording surface; r₃ is a radius of curvature of a surface of the second lens, which is directed to the entrance pupil; f₂ is a focal length of the second lens; f₅ is a focal length of the fifth lens.. and f is a focal length of the lens system. Further, the present invention is directed to an optical beam scanner for scanning a plurality of optical beams on a recording surface. The optical beam scanner comprises: a light source for generating the plurality of optical beams; a deflector for deflecting the optical beams outgoing from the light source; and a lens system for imaging the optical beams deflected by the deflector on the recording surface. The lens system comprises: (a) a first lens group having an entrance pupil, which includes (a-1) a first lens in the form of meniscus having a positive power and having a concave surface which is directed to the entrance pupil, (a-2) a second lens having a negative power, (a-3) a third lens in the form of meniscus having a positive power, and a fourth lens having positive power; and (b) a second lens group including a fifth lens having a positive power. Further, the first through fifth lenses are successively disposed in order from the entrance pupil side. A principal object of the present invention is to provide a lens system which has a telecentric property and an excellent f-sinϑ characteristic. Another object of the present invention is to provide an optical beam scanner which can scan the plurality of optical beams on the recording surface in high accuracy while improving a quality of an image formed on the recording surface. These and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 illustrates the structure of a conventional telecentric f-ϑ lens system: Fig. 2 is a schematic illustration of optical paths deflected by a deflector; Fig. 3 is a diagram showing a scanning locus made by the telecentric f-ϑ lens system where a plurality of optical beams are applied; Fig. 4 illustrates the structure of a conventional f-sinϑ lens system; Fig. 5 is a diagram showing a scanning locus made by the f-sinϑ lens system where a plurality of optical beams are applied; Fig. 6 illustrates a preferred embodiment of a lens system according to the present invention; Figs. 7A, 7B and 7C illustrate spherical aberration, astigmatism and f-sinϑ characteristic of a first example, respectively; Figs. 8A, 8B and 8C illustrate spherical aberration, astigmatism and f-sinϑ characteristic of a second example, respectively; Figs. 9A, 9B and 9C illustrate spherical aberration, astigmatism and f-sinϑ characteristic of a third example, respectively; Figs. 10A, 10B and 10C illustrate spherical aberration, astigmatism and f-sinϑ characteristic of a fourth example, respectively; Figs. 11A, 11B and 11C illustrate spherical aberration, astigmatism and f-sinϑ characteristic of a fifth example, respectively: Figs. 12A, 12B and 12c illustrate spherical aberration, astigmatism and f-sinϑ characteristic of a sixth example, respectively; Figs. 13A, 13B and 13C illustrate spherical aberration, astigmatism and f-sinϑ characteristic of a seventh example, respectively; and Figs 14 is a perspective view showing an optical system of an optical beam scanner to which the lens system structured along Fig. 6 is applied. DESCRIPTION OF THE PREFERRED EMBODIMENTS Fig. 6 illustrates a preferred embodiment of a lens system according to the present invention. The lens system is formed with a rear lens group R L and a front lens group F L , which are arranged in order from a recording surface RS side at a prescribed interval. The front lens group F L is formed with first, third and fourth meniscus lenses L₁, L₃ and L₄ having positive power and a second lens L₂ having negative power, as shown in Fig. 6. The first to fourth lenses L₁ to L₄ are arranged in order from an entrance pupil EP side at prescribed intervals, while all of concave surfaces S₁, S₃ S₅ and S₇ of the first to fourth lenses L₁ to L₄ are directed toward the entrance pupil EP. On the other hand, the rear lens group R L is formed with a fifth lens L₅ having positive power, and a convex surface S₁₀ of the fifth lens L₅ is directed toward the recording surface RS. The lens system having the aforementioned structure satisfies: 0.6 < (r₂/r₃) ≦ 2.1 (1) -0.43 < (f₂/f) < -0.21 (2) 1.3 < (f₅/f) ≦ 2.6 (3) where r₂ is a radius of curvature of a surface S₂ of the first lens L₁, which is directed toward the recording surface RS; r₃ is a radius of curvature of the surface S₃ of the second lens L₂; f₂ is a focal length of the second lens L₂; f₅ is a focal length of the fifth lens L₅; and f is a focal length of the lens system. The inequality (1) shows the condition for correcting the spherical aberration, astigmatism and curvature of image surface. That is, when the value (r₂/r₃) is not more that 0.6, both of the meridional and sagittal image surfaces are inclined toward the negative (-) side while correction of the spherical aberration is insufficient. When value (r₂/r₃) is more than 2.1, the spherical aberration is excessively corrected while the meridional image surface is inclined toward the positive (+) side, whereby astigmatism at an end of a field angle is increased. Further, the f-sinϑ characteristic is degraded also. The inequality (2) shows the condition for the curvature of image surface. That is, when the value (f₂/f) is not more than -0.43 the curvature of the sagittal image surface is increased. When the value (f₂/f) is not less than -0.21, both of the meridional and sagittal image surfaces are inclined toward the negative (-) side. The inequality (3) shows the condition for the curvature of image surface and the condition that the lens system has a telecentric property. That is, when the value (f₅/f) is not more that 1.3, the meridional image surface is inclined toward the negative (-) side while the telecentric characteristic is degraded. On the other hand, when the value (f₅/f) is more than 2.6, the sagittal image surface is inclined in spite of improving the telecentric characteristic of the lens system. When, to the contrary, a lens system is formed with the first to fifth lenses L₁ to L₅ and the lens system satisfies the inequality (1) to (3) (Examples 1 to 8 described below), the lens system which has both of telecentric and f-sinϑ characteristics can be obtained, which further has the following characteristics; (1) F-number is not more than 20; (2) spherical aberration, astigmatism etc. are small; and (3) image surface is flat. Example 1 Table 1 shows lens data of a first example according to a lens system structured along Fig. 6. Referring to Table 1, symbol r i (i = 1, 2, ..., 10) represents radius of curvature of lens surfaces S i , such that r₁ represents the radius of curvature of tbe concave surface S₁ of the first lens L₁ and r₂ represents the radius of curvature of the convex surface S₂ thereof directed toward the recording surface, for example. Symbol d i (i = 1, 3, 5, 7, 9) represents thickness values of the first to fifth lenses L₁ to L₅, respectively. On the other hand, d i (i = 2, 4, 6, 8) represents spaces between pairs of the first to fifth lenses L₁ to L₅, respectively, such that d₂ represents the space between the first and second lenses L₁ and L₂, for example. Symbol n i (i = 1, 3, 5, 7, 9) represents indexes of refraction of the first to fifth lenses L₁ to L₅ with respect to a line d (587.6 nm). The focal length f , the F-number F NO etc. of the lens system having the aforementioned lens data are set as shown in Table 2. f F NO λ d₀ 100.00 20.00 632.8 nm 10.00 Referring to Table 2, λ represents a wavelength of a laser beam, and d₀ represents a space between the entrance pupil EP and the concave surface S₁ of the first lens L₁. The focal length f₂, f₅ of the second and fifth lens L₂, L₅ is -30.9, 190.8, respectively, although this is not shown in Tables 1 and 2. Thus, r₂ / r₃ = 1.202 f₂ / f = -0.309 f₅ / f = 1.908 and it is apparent that the lens system satisfies the inequalities (1) to (3). Figs. 7A, 7B and 7C illustrate spherical aberration, astigmatism and f-sinϑ characteristic of the lens system having the aforementioned structure, respectively. The results shown in these figures and Figs. 8A-13A, 8B-13B and 8C-13C, which are hereinafter described in detail, have been obtained with respect to light of 632.8 nm in wavelength. In each of Fig. 7B and Figs. 8B, 9B, 10B, 11B, 12B and 13B, symbol S denotes a sagittal image surface and symbol M denotes a meridional image surface, respectively. The f-sinϑ characteristic shown in each of Figs. 7C, 8C, 9C, 10C, 11C, 12C and 13C is obtained by the following equation in which ϑ represents an angle of incidence of the optical beam upon the lens system and h represents a distance between a beam spot on a recording surface and an optical axis of the lens system: Example 2 Table 3 shows lens data of a second example according to the lens system. The focal length f , the F-number F NO etc. of the lens system having the aforementioned lens data are set as shown in Table 4. f F NO λ d₀ 100.00 20.00 632.8 nm 11.00 The focal length f₂, f₅ of the second and fifth lens L₂, L₅ is -31.9, 203.4, respectively, although this is now shown in Tables 3 and 4. Thus, r₂ / r₃ = 0.606 f₂ / f = -0.319 f₅ / f = 2.034 and it is apparent that the lens system satisfies the inequalities (1) to (3). Figs 8A, 8B and 8C illustrate spherical aberration, astigmatism and f-sinϑ characterisric of the lens system having the aforementioned structure, respectively. Example 3 Table 5 shows lens data of a third example according to the lens system. The focal length f , the F-number F NO etc. of the lens system having the aforementioned lens data are set as shown in Table 6. f F NO λ d₀ 100.00 20.00 632.8 nm 10.10 The focal length f₂, f₅ of the second and fifth lens L₂, L₅ is -32.8, 183.8, respectively, although this is not shown in Tables 5 and 6. Thus, r₂ / r₃ = 2.100 f₂ / f = -0.328 f₅ / f = 1.838 and it is apparent that the lens system satisfies the inequalities (1) to (3). Figs 9A, 9B and 9C illustrate spherical aberration, astigmatism and f-sinϑ characteristic of the lens system having the aforementioned structure, respectively. Example 4 Table 7 shows lens data of a fourth example according to the lens systems The focal length f , the F-number F NO etc. of the lens system having the aforementioned lens data are set as shown in Table 8. f F NO λ d₀ 100.00 20.00 632.8 nm 10.00 The focal length f₂, f₅ of the second and fifth lens L₂, L₅ is -21.1, 192.3, respectively, although this is not shown in Tables 7 and 8. Thus, r₂ / r₃ = 1.240 f₂ / f = -0.211 f₅ / f = 1.923 and it is apparent that the lens system satisfies the inequalities (1) to (3). Figs 10A, 10B and 10C illustrate spherical aberration, astigmatism and f-sinϑ characteristic of the lens system having the aforementioned structure, respectively. Example 5 Table 9 shows lens data of a fifth example according to the lens system. The focal length f , the F-number F NO etc. of the lens system having the aforementioned lens data are set as shown in Table 10. f F NO λ d₀ 100.00 20.00 632.8 nm 10.00 The focal length f₂, f₅ of the second and fifth lens L₂, L₅ is -42.6, 170.6, respectively, although this is not shown in Tables 9 and 10. Thus, r₂ / r₃ = 0.791 f₂ / f = -0.426 f₅ / f = 1.706 and it is apparent that the lens system satisfies the inequalities (1) to (3). Figs 11A, 11b and 11C illustrate spherical aberration, astigmatism and f-sinϑ characteristic of the lens system having the aforementioned structure, respectively. Example 6 Table 11 shows lens data of a sixth example according to the lens system. The focal length f , the F-number F NO etc. of the lens system having the aforementioned lens data are set as shown in Table 12. f F NO λ d₀ 100.00 20.00 632.8 nm 10.00 The focal length f₂, f₅ of the second and fifth lens L₂, L₅ is -39.9, 133.0, respectively, although this is not shown in Tables 11 and 12. Thus, r₂ / r₃ = 0.779 f₂ / f = -0.399 f₅ / f = 1.330 and it is apparent that the lens system satisfies the inequalities (1) to (3). Figs 12A, 12B and 12C illustrate spherical aberration, astigmatism and f-sinϑ characteristic of the lens system having the aforementioned structure, respectively. Example 7 Table 13 shows lens data of a seventh example according to the lens system. The focal length f , the F-number F NO etc. of the lens system having the aforementioned lens data are set as shown in Table 14. f F NO λ d₀ 100.01 20.00 632.8 nm 10.00 The focal length f₂, f₅ of the second and fifth lens L₂, L₅ is -26.7, 260.0, respectively, although this is not shown in Tables 13 and 14. Thus, r₂ / r₃ = 1.108 f₂ / f = -0.267 f₅ / f = 2.600 and it is apparent that the lens system satisfies the inequalities (1) to (3). Figs 13A, 13B and 13C illustrate spherical aberration, astigmatism and f-sinϑ characteristic of the lens system having the aforementioned structure, respectively. The spherical aberration of the lens system is extremely small as understood from the spherical aberration diagrams (Figs. 7A, 8A, 9A, 10A, 11A, 12A, and 13A), and the astigmatism thereof is also extremely small as understood from the astigmatism diagrams (Figs. 7B, 8B, 9B, 10B, 11B, 12B, and 13B). Further, the lens system structured as above has an excellent f-sinϑ characteristic, as understood from the f-sinϑ characteristic diagrams (Figs. 7C, 8C, 9C, 10C, 11C, 12C and 13C). Further, all the F-numbers F NO of the lens systems are not more than 20 in Examples 1 to 7, as hereinabove described. Fig. 14 is a perspective view showing an optical system of an optical beam scanner, which scans a plurality of laser beams on a recording surface, to which the aforementioned lens system can be applied. Referring to Fig. 14, a laser beam B₁ outgoing from a laser tube 11 is projected onto a non-polarizing beam splitter 12, to be divided into a scanning beam B₂ and a reference beam B₃. The scanning beam B₂ reflected by the beam splitter 12 enters an optical modulator system 13 for dividing the scanning beam B₂ into a plurality of laser beams and individually modulating the plurality of laser beams in response to image signals being inputted into the optical modulator system 13. The optical modulator system 13 includes a non-polarizing beam splitter 14 and two polarizing beam splitters 15, 16 so as to divide the scanning beam B₂ into four laser beams B₂₁, B₂₂, B₂₃, B₂₄. The scanning beam B₂ is divided into two laser beams by the beam splitter 14, and then the two laser beams are directed to the beam splitter 15, 16, respectively. The laser beam entering the beam splitter 15 is dividied into two laser beams B₂₁, B₂₂ while the laser beam entering the beam splitter 16 is dividied into two laser beam B₂₃, B₂₄, so that the four laser beams B₂₁, B₂₂, B₂₃, B₂₄ then enter optical modulation elements (e.g. acoustic optical modulators) 17 to 20 disposed on optical axes of the laser beams B₂₁, B₂₂, B₂₃, B₂₄, respectively. Thus, the respective laser beams B₂₁, B₂₂, B₂₃, B₂₄ are modulated in response to the image signals from a control unit (not shown) for controlling the optical beam scanner. The structure and, operation of the optical modulation elements 17 to 20 are well known to these skilled in the art, and hence redundant description is omitted. Further, two polarizing beam splitter 21, 22 and a non-polarizing beam splitter 23 are provided in the optical modulator svstem 13, so that modulated laser beams B₂₁′, B₂₂′, B₂₃′, B₂₄′ are bundled, to generate a multibeam B₄ consisting of them which are not parallel each other. The multibeam B₄ outgoing from the opitcal modulator system 13 are reflected by reflecting mirrors 24, 25, and then projected onto a polygon mirror 28, which is rotated at a constant angular velocity, through a beam expander 26 and a cylindrical lens 27. A multibeam B₅ deflected by the polygon mirror 28 is focused on a photosensitive material (not shown), which is wound on a rotating cylinder 31, by the lens system 29 as shown in Fig. 6 and a cylindrical lens 30, thereby to record a desired image on the photosensitive material. On the other hand, the reference beam B₃ is projected onto a reflecting mirror 33 disposed in the vicinity of the cylindrical lens 27 through a beam expander 32. A reference beam B₃′ reflected by the reflecting mirror 33 enters the polygon mirror 28 through the cylindrical lens 27, and is then directed by the lens system 29 and the cylindrical lens 30 toward a reflecting mirror 34. Thus, the multibeam B₅ impinges on the photosensitive material provided on the rotating cylinder 31, while only the corresponding reference beam B₃′ is reflected by the reflecting mirror 34 onto a linear encorder 35 which is disposed substantially parallel to the scanning line on the photosensitive material. The lens system 29 is structured as shown in Fig. 6 and satisfies the above inequation (1) to (3), so as to have a telecentric characteristic. Therefore, the image is recorded on the photosensitive material in high accuracy. Further, the lens system has also an excellent f-sinϑ characteristic. Thus, each of scanning locus of the respective laser beams forming the multibeam B₅ is made straight. Consequently, the image can be recorded on the photosensitive material not only in high accuracy but also in high quality. Although the present invention has been described and illustrated in detail, it is clearly understood that the same is by way of illustration and example only and is not to be taken by way of limitation. The scope of the present invention should be limited only by the terms of the appended claims.

Claims: A telecentric f-sin ϑ lens system for an optical beam scanner which scans a plurality of optical beams over a recording surface (RS), said lens system comprising a first lens group and a second lens group, the first lens group having an entrance pupil (EP), which lens system is characterized in that said first lens group (F L ) includes a first lens (L₁) in the form of meniscus having a positive power and a concave surface (S₁) directed towards said entrance pupil (EP), a second lens (L₂) having negative power, a third lens (L₃) in the form of meniscus having a positive power, and a fourth lens (L₄) having a positive power, and said second lens group (F R ) includes a fifth lens (L₅) having a positive power, said first to fifth lenses (L₁ to L₅) being successively disposed in that order from said entrance pupil (EP). A telecentric f-sin ϑ lens system according to claim 1, wherein said lens system satisfies the following inequalities: 0.6 < (r₂/r₃) ≦ 2.1 - 0.43 < (f₂/f) < - 0.21 1.3 < (f₅/f) ≦ 2.6 where r₂ is the radius of curvature of the surface (S₂) of said first lens (L₁) which is directed towards said recording surface (RS), r₃ is the radius of curvature of the surface (S₃) of said second lens (L₂) which is directed towards said entrance pupil (EP), f₂ is the focal length of said second lens (L₂), f₅ is the focal length of said fifth lens (L₅) and f is the focal length of the lens system. A telecentric f-sin ϑ lens system according to claim 1 or 2, wherein said fifth lens (L₅) is a planoconvex lens having a flat surface which is directed towards said entrance pupil (EP). An optical beam scanner for scanning a plurality of optical beams over a recording surface (RS), said optical beam scanner comprising a light source (11, 13) for generating a plurality of optical beams, a deflector (28) for deflecting the optical beams from said light source, and a telecentric f-sin ϑ lens system as defined in one of the preceding claims.

Inventors: SHIROTA HIROYUKI DAINIPPON SCR, SHIROTA, HIROYUKI DAINIPPON SCREEN MFG. CO., LTD.
Applicants: DAINIPPON SCREEN MFG, DAINIPPON SCREEN MFG. CO., LTD.
Application year: 1989
Main classification: G02B13
IPC codes: G02B26, G02B13