Abstract:
A light scanning system uses a tilting angle error correcting system, applying a conjugate relation from geometrical optics. A light beam from a light source is converged to a linear image near a deflecting surface of a deflector by a first converging optical system. The deflected light beam from the deflecting surface is converged to a light spot on a scanning plane by a second converging optical system. The first converging optical system provides the light converging effect only in a plane perpendicular to the direction of scan and also has an overcorrected spherical aberration, so that the spherical aberration of the entire system can be favorably corrected, thereby making it possible to obtain a high converging performance for realizing high resolution.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to a light scanning system for deflecting a light beam from a light source by means of a deflecting device, thereby scanning a scanning plane. 
     2. Description of the Prior Art 
     Conventionally, in a light scanning system using a deflecting device possessing a deflecting surface, such as rotating polygon mirror, various methods are known to prevent uneven pitches of scanning lines on the scanning plane even if the deflected and scanned light beam is changed within the plane perpendicular to the scanning plane due to tilting of the deflecting surface. For example, the light scanning systems disclosed in Japanese Laid-open Patent Application Nos. 56-36622, 57-144516, and U.S. Pat. Nos. 3,750,189, 4,123,135 are comprised of a light source for producing a light beam collimated to a proper beam diameter, a first converging optical system comprised of a single flat convex cylindrical lens for converging the light beam to a linear image, a deflecting device having a deflecting surface near the converging position of the linear image, and a second converging optical system comprised of a single spherical lens and a single toric lens for converging the deflected light beam to a spot image on the scanning plane. The deflecting surface and the scanning plane are in a conjugate relation from geometrical optics within a plane perpendicular to the direction of scan, and the tilt of the deflecting surface is optically corrected, whereby uneven pitches of the scanning lines are corrected. 
     However, in the conventional light scanning systems, the aperture ratio is small, being 1:60 in the plane parallel to the direction of scan and 1:100 in the plane perpendicular to the direction of scan, and the spot diameter on the scanning plane of the light beam is about 100 μm. Such corresponds to a resolution of only about 10 dots per 1 mm. To increase the aperture ratio while reducing the spot diameter, a sufficient aberration correction is needed. In the conventional light scanning system, the optical power in the plane perpendicular to the direction of scan of the second converging optical system must be strong in order to satisfy the conjugate relation from geometrical optics. Therefore, the spherical aberration in the plane perpendicular to the direction of scan is insufficiently corrected, and it is hard to increase the aperture ratio because the residual aberration is large, which is a great obstacle in enhancing the resolution. 
     SUMMARY OF THE INVENTION 
     It is hence a primary object of this invention to present a light scanning system exhibiting a high performance with respect to favorably correcting and reducing residual aberration, in particular, the spherical aberration in the plane perpendicular to the direction of scan. 
     In order to achieve this object, the light scanning system of this invention is arranged to converge a light beam from a light source to a linear image in the vicinity of a deflecting surface by means of a first converging optical system providing a light converging action only in the plane perpendicular to the direction of scan and being designed so as to generate an over-corrected spherical aberration. This over-corrected spherical aberration is canceled with an under-corrected spherical aberration in the plane perpendicular to the direction of scan of a second converging optical system. As a result, the residual aberration of the entire system is significantly decreased. It is hence possible to increase the aperture ratio, and to reduce the spot diameter on the scanning plane, so that a light scanning system suited to high printing quality can be realized. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a perspective view showing a first embodiment of a light scanning system of this invention; 
     FIGS. 2(a), (b) are schematic diagrams showing an optical element arrangement in the plane parallel to the direction of scan and in the plane perpendicular to the direction of scan, respectively, of the first embodiment; 
     FIGS. 3(a), (b) are schematic diagrams showing an optical element arrangement in the plane parallel to the direction of scan and in the plane perpendicular to the direction of scan, respectively, of a second embodiment; and 
     FIGS. 4 through 14 are graphs in which characteristic curves of first through eleventh examples of the present invention are plotted, in each of which (a) relates to the spherical aberration in the plane perpendicular to the direction of scan of the first converging optical system, (b) to the spherical aberration in the plane perpendicular to the direction of scan of the second converging optical system, (c) to the spherical aberration in the plane perpendicular to the direction of scan of the whole system, (d) to the astigmatism, and (e) to the linearity of scan. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1 is a perspective view showing a first embodiment of a light scanning system of this invention. A laser light source 17 is comprised of a laser oscillator 15 for generating a laser beam and a collimator lens 16 for forming a collimated light beam 1. This light beam 1 is linearly converted in the direction of scan in the vicinity of a deflecting surface 6, by means of a first converging optical system 5 comprised of, sequentially from the light source 17, a positive flat convex cylindrical lens 2, a negative flat concave cylindrical lens 3, and a positive flat convex cylindrical lens 4. 
     The deflecting surface 6 is one of the plural deflecting surfaces of a rotating polygon mirror 7. The mirror is rotated by a motor (not shown) to deflect the light beam. 
     The light beam deflected by this deflecting surface 6 forms a scanning spot on a scanning plane 12 defined on a rotating photosensitive drum 18, by means of a second converging optical system 11 comprised of two spherical lenses 8, 9 and a toric lens 10. It is preferable that these two spherical lenses 8, 9 and the toric lens 10 have external shapes large enough to accommodate the range of the light beam deflected by the rotating mirror 6 while allowing the size of the light scanning system to be reduced as shown in FIG. 1. 
     FIGS. 2(a), (b) show an arrangement of the optical elements in the plane parallel to the direction of scan and in the plane perpendicular to the direction of scan, respectively, of the first embodiment. As shown in FIG. 2(b), in the plane perpendicular to the direction of scan with respect to the second converging optical system 11, the deflecting surface 6 and the scanning surface 12 are in a conjugate relation from geometrical optics. Therefore, a correction in the tilt of the deflecting surface is facilitated. The second converging optical system facilitating such action has a greater optical power in the plane perpendicular to the direction of scan than in the deflecting direction, so that an under-corrected spherical aberration occurs in the plane perpendicular to the direction of scan. 
     In this embodiment, as mentioned above, the first converging optical system consisting of the cylindrical lens group generates an over-corrected spherical aberration in the plane perpendicular to the direction of scan, so as to cancel the under-corrected spherical aberration generated in the second converging optical system. As a result, the spherical aberration of the entire system is notably reduced, so that it is possible to increase the aperture ratio. 
     FIGS. 3(a), (b) show an arrangement of the optical elements in the plane parallel to the direction of scan and in the plane perpendicular to the direction of scan, respectively, of a light scanning system according to a second embodiment of this invention. A first converging optical system 5 is comprised of, sequentially from the light source 17, a negative meniscus lens 13 having a convex surface forming the light source, and a positive flat convex cylindrical lens 14. It is designed to converge the light beam in the vicinity of the deflecting surface 6 and, at the same time, generates an over-corrected spherical aberration. 
     A second converging optical system 11 is comprised of a meniscus spherical lens 8 having a concave surface facing the deflecting surface 6, a meniscus spherical lens 9 having a convex surface facing the deflecting surface, and one toric lens 10, and it focuses the light beam to a scanning spot on the scanning plane 12. This second converging optical system generates an under-corrected spherical aberration in the plane perpendicular to the direction of scan, which is canceled by the over-corrected spherical aberration of the first converging optical system 5. 
     Incidentally, in FIGS. 2(a), (b) and FIGS. 3(a), (b), the following symbols denote as the following parameters of the present invention: 
     r 1 , r 2 , . . . , r m  (m=11 or 13); radius of curvature of each surface with respect to refraction in the plane parallel to the direction of scan; 
     r&#39; 1 , r&#39; 2 , . . . , r&#39; m  (m=11 or 13): radius of curvature of each surface with respect to refraction in the plane perpendicular to the direction of scan; 
     d 1 , d 2 , . . . , d m-1  (m=11 or 13): distance between each adjacent two surfaces; and 
     n 1 , n 2 , . . . , n s  (s=5 or 6): refractive index of each lens taken with radiation having a wave length of 790 nm. 
     Furthermore, by satisfying the following conditions, the characteristics exhibited by the present invention can be further improved. 
     
         3.8&lt;f.sub.p /f.sub.v &lt;5.0                                  (1) 
    
     
         0.2&lt;L/f.sub.p &lt;0.4                                         (2) 
    
     
         0.45&lt;f.sub.p /r.sub.a &lt;0.1                                 (3) 
    
     where, 
     f p  : focal length with respect to refraction in the plane parallel to the direction of scan of the second converging optical system; 
     f v  : focal length with respect to refraction in the plane perpendicular to the direction of scan of the second convergiing optical system; 
     L: overall length of the lenses of the second converging optical system; and 
     r a  : radius of curvature, with respect to refraction in the plane parallel to the direction of scan of the deflecting surface of the third lens from the deflecting surface of the second converging optical system (r a  means r 12  of Example 2 and r 10  of Example 2 through 11 shown later) 
     Condition (1) defines the ratio of the focal length with respect to refraction in the plane parallel to the direction of scan to the focal length with respect to refraction in the plane perpendicular to the direction of scan of the second converging optical system. When exceeding the upper limit or lower limit, correction of astigmatism is difficult, which is an obstacle in the realization of high performance. 
     Condition (2) defines the overall length of the lenses of the second converging optical system. Parameter set below the lower limit are indicative of an advantageous compact design, but correction of astigmatism becomes difficult. When the parameters are set above the upper limit, the overall length of the second converging optical system increases, and, accordingly, the aperture of the lens having a toric plane increases, which may give rise to a significant cost increase. 
     Condition (3) is important for ensuring the linearity of scanning. The second converging optical system, with respect to refraction in the plane parallel to the direction of scan, generates a negative distortion characteristic on the deflecting surface end plane of the third lens from the deflecting surface, and produces a favorable linearity in the whole system. If the radius of curvature r a  of this plane exceeds the upper limit or lower limit, it is hard to maintain an excellent degree of linearity. 
     Hereinafter, examples of practical designs are shown. Example 1 corresponds to the first embodiment shown in FIGS. 2(a), (b), and Examples 2 to 11 correspond to the second embodiment shown in FIGS. 3(a), (b). 
     EXAMPLE 1 
     aperture ratio in the plane parallel to the direction of scan=1:49 
     aperture ratio in the plane perpendicular to the direction of scan=1:49 
     half deflecting angle=±33° 
     
         __________________________________________________________________________f.sub.p = 284.78 f.sub.p /f.sub.v = 4.15L/f.sub.p = 0.31 f.sub.p /r.sub.a ( = f.sub.p /r.sub.12)__________________________________________________________________________= 0          r.sub.1 = ∞&#39;                  r.sub.1 &#39; = 46.587                          d.sub.1 = 2.40                                n.sub.1 = 1.765299          r.sub.2 = ∞                  r.sub.2 &#39; = ∞                          d.sub.2 = 14.28          r.sub.3 = ∞                  r.sub.3 &#39; = -29.870                          d.sub.3 = 2.20                                n.sub.2 = 1.510516first converging means          r.sub.4 = ∞                  r.sub.4 &#39; = ∞                          d.sub.4 = 33.89          r.sub.5 = ∞                  r.sub.5 &#39; = 60.000                          d.sub.5 = 3.00                                n.sub.3 = 1.765299          r.sub.6 = ∞                  r.sub.6 &#39; = ∞                          d.sub.6 = 51.35deflecting surface          r.sub.7 = ∞                  r.sub.7 &#39; = ∞                          d.sub.7 = 20.48          r.sub.8 = -70.606                  r.sub.8 &#39; = -70.606                          d.sub.8 = 17.28                                n.sub.4 = 1.765299          r.sub.9 = -77.654                  r.sub.9 &#39; = -77.654                          d.sub.9 = 0.66          r.sub.10 = 354.042                  r.sub.10 &#39; = 354.042                          d.sub.10 = 14.21                                n.sub.5 = 1.532883second converging means          r.sub.11 = 431.786                  r.sub.11 &#39; = 431.786                          d.sub.11 = 39.29          r.sub.12 = ∞                  r.sub.12 &#39; = -83.615                          d.sub.12 = 18.19                                n.sub.6 = 1.674497          r.sub.13 = -230.766                  r.sub.13 &#39; = -34.394__________________________________________________________________________ 
    
     EXAMPLE 2 
     aperture ratio in the plane parallel to the direction of scan=1:49 
     aperture ratio in the plane perpendicular to the direction of scan=1:49 
     half deflecting angle=±33° 
     
         __________________________________________________________________________f.sub.p = 284.78 f.sub.p /f.sub.v = 4.15L/f.sub.p = 0.31 f.sub.p /r.sub.a ( = f.sub.p /r.sub.10)__________________________________________________________________________= 0          r.sub.1 = ∞                  r.sub.1 &#39; = 21.000                          d.sub.1 = 4.00                                n.sub.1 = 1.765299          r.sub.2 = ∞                  r.sub.2 &#39; = 17.545                          d.sub.2 = 5.00first converging means          r.sub.3 = ∞                  r.sub.3 &#39; = 47.389                          d.sub.3 = 3.72                                n.sub.2 = 1.765299          r.sub.4 = ∞                  r.sub.4 &#39; = ∞                          d.sub.4 = 79.01deflecting means          r.sub.5 = ∞                  r.sub.5 &#39; = ∞                          d.sub.5 = 20.48          r.sub.6 = -70.606                  r.sub.6 &#39; = -70.606                          d.sub.6 = 17.28                                n.sub. 3 = 1.765299          r.sub.7 = -77.654                  r.sub.7 &#39; = -77.654                          d.sub.7 = 0.66          r.sub.8 = 354.042                  r.sub.8 &#39; = 354.042                          d.sub.8 = 14.21                                n.sub.4 = 1.532883second converging means          r.sub.9 = 431.786                  r.sub.9 &#39; = 431.786                          d.sub.9 = 39.29          r.sub.10 = ∞                  r.sub.10 &#39; = -83.615                          d.sub.10 = 18.19                                n.sub.5 = 1.674497          r.sub.11 = -230.766                  r.sub.11 &#39; = -34.394__________________________________________________________________________ 
    
     EXAMPLE 3 
     aperture ratio in the plane parallel to the direction of scan=1:50 
     aperture ratio in the plane perpendicular to the direction of scan=1:50 
     half deflecting angle=±30° 
     
         ______________________________________f.sub.p = 287.66 f/f = 4.20L/f.sub.p = 0.30 f.sub.p /r.sub.a ( = f.sub.p /r.sub.10)______________________________________= -0.15            r.sub.1 = ∞                          r.sub.1 &#39; = 15.044            d.sub.1 = 4.00                          n.sub.1 &#39; = 1.76530            r.sub.2 = ∞                          r.sub.2 &#39; = 12.773first converging d.sub.2 = 5.00means            r.sub.3 = ∞                          r.sub.3 &#39; = 48.842 -  d.sub.3                          = 3.72 n.sub.2 = 1.76530            r.sub.4 = ∞                          r.sub.4 &#39; = ∞            d.sub.4  = 73.19deflecting surface            r.sub.5 = ∞                          r.sub.5 &#39; = ∞            d.sub.5 = 20.00            r.sub.6 = -70.189                          r.sub.6 &#39; = -70.189            d.sub. 6 = 18.85                          n.sub.3 = 1.76530            r.sub.7 = -77.471                          r.sub.7 &#39; = -77.471            d.sub.7 = 10.00            r.sub.8 = 369.975                          r.sub.8 &#39; = 369.975second converging            d.sub.8 = 6.15                          n.sub.4 = 1.53288means            r.sub.9 = 554.244                          r.sub.9 &#39; = 554.244            d.sub.9 = 39.51            r.sub.10 = -1859.183                          r.sub.10 &#39; = -78.953            d.sub.10 = 12.34                          n.sub.5 = 1.67450            r.sub.11 = -227.419                          r.sub.11 &#39; = -33.306______________________________________ 
    
     EXAMPLE 4 
     aperture ratio in the plane parallel to the direction of scan=1:50 
     aperture ratio in the plane perpendicular to the direction of scan=1:50 
     half deflecting angle=±30° 
     
         ______________________________________f.sub.p = 287.66 f.sub.p /f.sub.v = 4.13L/f.sub.p = 0.32 f.sub.p /r.sub.a ( = f.sub.p /r.sub.10)______________________________________= 0            r.sub.1 = ∞                          r.sub.1 &#39; = 38.410            d.sub.1 = 4.00                          n.sub.1 = 1.76530            r.sub.2 = ∞                          r.sub.2 &#39; = 26.065first converging d.sub.2 = 5.00means            r.sub.3 = ∞                          r.sub.3 &#39; = 39.264            d.sub.3 = 3.72                          n.sub.2 = 1.765299            r.sub.4 = ∞                          r.sub.4 &#39; = ∞            d.sub.4 = 86.06deflecting surface            r.sub.5 = ∞                          r.sub.5 &#39; = ∞            d.sub.5 = 20.00            r.sub.6 = -83.583                          r.sub.6 &#39; = -83.583            d.sub.6 = 25.24                          n.sub.3 = 1.73759            r.sub.7 = -87.678                          r.sub.7 &#39; = -87.678            d.sub.7 = 10.00            r.sub.8 = 336.361                          r.sub.8 &#39; = 336.361second converging            d.sub.8 = 6.00                          n.sub.4 = 1.76167means            r.sub.9 = 432.403                          r.sub.9 &#39; = 432.403            d.sub.9 = 39.58            r.sub.10 = ∞                          r.sub.10 &#39; = -65.724            d.sub.10 = 12.00                          n.sub.5 = 1.60659            r.sub.11 = -286.512                          r.sub.11 &#39; = -29.803______________________________________ 
    
     EXAMPLE 5 
     aperture ratio in the plane parallel to the direction of scan=1:50 
     aperture ratio in the plane perpendicular to the direction of scan=1:50 
     half deflecting angle=±30° 
     
         ______________________________________f.sub.p = 287.87 f.sub.p /f.sub.v = 3.97L/f.sub.p = 0.30 f.sub.p /r.sub.a ( = f.sub.p /r.sub.10)______________________________________= 0            r.sub.1 = ∞                          r.sub.1 &#39; = 23.564            d.sub.1 = 4.05                          n.sub.1 = 1.765299            r.sub.2 = ∞                          r.sub.2 &#39; = 20.286first converging d.sub.2 = 5.06means            r.sub.3 = ∞                          r.sub.3 &#39; = 54.574            d.sub.3 = 3.77                          n.sub.2 = 1.765299            r.sub.4 = ∞                          r.sub.4 &#39; = ∞            d.sub.4 = 85.42deflecting surface            r.sub.5 = ∞                          r.sub.5 &#39; = ∞            d.sub.5 = 25.00            r.sub.6 = -72.763                          r.sub.6 &#39; = -72.763            d.sub.6 = 19.00                          n.sub.3 = 1.76167            r.sub.7 = -77.288                          r.sub.7 &#39; = =77.288            d.sub.7 = 10.00            r.sub.8 = 643.375                          r.sub.8 &#39; = 643.375second converging            d.sub.8 = 11.15                          n.sub.4 = 1.5119means            r.sub.9 = 2849.379                          r.sub.9 &#39; = 2849.379            d.sub.9 = 45.00            r.sub.10 = ∞                          r.sub.10 &#39; = -82.637            d.sub.10 = 6.00                          n.sub.5 = 1.67450            r.sub.11 = -306.407                          r.sub.11 &#39; = -34.194______________________________________ 
    
     EXAMPLE 6 
     aperture ratio in the plane parallel to the direction of scan=1:50 
     aperture ratio in the plane perpendicular to the direction of scan=1:50 
     half deflecting angle=±30° 
     
         ______________________________________f.sub.p = 295.12 f.sub.p /f.sub.v = 4.38L/f.sub.p = 0.27 f.sub.p /r.sub.a ( = f.sub.p /r.sub.10)______________________________________= -0.055            r.sub.1 = ∞                          r.sub.1 &#39; = 23.636            d.sub.1 = 4.55                          n.sub.1 = 1.76530            r.sub.2 = ∞                          r.sub.2 &#39; = 20.007first converging d.sub.2 = 5.68means            r.sub.3 = ∞                          r.sub.3 &#39; = 46.669            d.sub.3 = 3.72                          n.sub.2 = 1.76530            r.sub.4 = ∞                          r.sub.4 = ∞            d.sub.4 = 71.86deflecting surface            r.sub.5 = ∞                          r.sub.5 &#39; = ∞            d.sub.5 = 20.00            r.sub.6 = -65.003                          r.sub.6 &#39; = -65.003            d.sub.6 = 8.01                          n.sub.3 = 1.78506            r.sub.7 = -73.811                          r.sub.7 &#39; = -73.811            d.sub.7 = 0.23            r.sub.8 = 607.287                          r.sub.8 &#39; = 607.287second converging            d.sub.8 = 12.92                          n.sub.4 = 1.510516means            r.sub.9 = 407.327                          r.sub.9 &#39; = 407.327            d.sub.9 = 39.47            r.sub.10 = -5379.689                          r.sub.10 &#39; = -117.403            d.sub.10 = 19.93                          n.sub.5 = 1.72367            r.sub.11 = -167.907                          r.sub.11 &#39; = -37.807______________________________________ 
    
     EXAMPLE 7 
     aperture ratio in the plane parallel to the direction of scan=1:50 
     aperture ratio in the plane perpendicular to the direction of scan=1:50 
     half deflecting angle=±30° 
     
         ______________________________________f.sub.p = 288.01 f.sub.p /f.sub.v = 3.98L/f.sub.p = 0.34 f.sub.p /r.sub.a ( = f.sub.p /r.sub.10)______________________________________= 0.014            r.sub.1 = ∞                          r.sub.1 &#39; = 25.637            d.sub.1 = 4.83                          n.sub.1 = 1.76530            r.sub.2 = ∞                          r.sub.2 &#39; = 21.020first converging d.sub.2 = 6.40means            r.sub.3 = ∞                          r.sub.3 &#39; = 48.017            d.sub.3 = 4.50                          n.sub.2 = 1.76530            r.sub.4 = ∞                          r.sub.4 &#39; = ∞            d.sub.4 = 79.87deflecting surface            r.sub.5 = ∞                          r.sub.5 &#39; = ∞            d.sub.5 = 20.00            r.sub.6 = -68.359                          r.sub.6 &#39; = -68.359            d.sub.6 = 12.20                          n.sub.3 = 1.67450            r.sub.7 = -78.902                          r.sub.7 &#39; = -78.902            d.sub.7 = 1.74            r.sub.8 = 740.172                          r.sub.8 &#39; = 740.172second converging            d.sub.8 = 23.55                          n.sub.4 = 1.65903means            r.sub.9 = 574.503                          r.sub.9 &#39; = 574.503            d.sub.9 = 38.89            r.sub.10 = 20901.200                          r.sub.10 &#39; = -149.805            d.sub.10 = 20.94                          n.sub.5 = 1.63512            r.sub.11 = -161.094                          r.sub.11 &#39; = -38.452______________________________________ 
    
     EXAMPLE 8 
     aperture ratio in the plane parallel to the direction of scan=1:50 
     aperture ratio in the plane perpendicular to the direction of scan=1:50 
     half deflecting angle=±30° 
     
         ______________________________________f.sub.p = 291.69 f.sub.p /f.sub.v = 4.12L/f.sub.p = 0.32 f.sub.p /r.sub.a (= f.sub.p /r.sub.10)______________________________________= 0;            r.sub.1 = ∞                          r.sub.1 &#39; = 25.357            d.sub.1 = 4.83                          n.sub.1 = 1.76530            r.sub.2 = ∞                          r.sub.2 &#39; = 21.316first converging d.sub.2 = 6.40means            r.sub.3 = ∞                          r.sub.3 &#39; = 49.817            d.sub.3 = 4.50                          n.sub.2 = 1.76530            r.sub.4 = ∞                          r.sub.4 &#39; = ∞            d.sub.4 = 77.99deflecting surface            r.sub.5 = ∞                          r.sub.5 &#39; = ∞            d.sub.5 = 20.00            r.sub.6 = -67.946                          r.sub.6 &#39; = -67.946            d.sub.6 = 11.05                          n.sub.3 = 1.76167            r.sub.7 = -78.402                          r.sub.7 &#39; = -78.402            d.sub.7 = 2.66            r.sub.8 = 743.300                          r.sub.8 &#39; = 743.300second converging            d.sub.8 = 22.88                          n.sub.4 = 1.65903means            r.sub.9 = 542.759                          r.sub.9 &#39; = 542.759            d.sub.9 = 37.26            r.sub.10 = ∞                          r.sub.10 &#39; = -146.768            d.sub.10 = 19.73                          n.sub.5 = 1.67150            r.sub.11 = -165.713                          r.sub.11 &#39;= -39.239______________________________________ 
    
     EXAMPLE 9 
     aperture ratio in the plane parallel to the direction of scan=1:50 
     aperture ratio in the plane perpendicular to the direction of scan=1:50 
     half deflecting angle=±30° 
     
         ______________________________________f.sub.p = 287.89 f.sub.p /f.sub.v = 4.24L/f.sub.p = 0.30 f.sub.p /r.sub.a (= f.sub.p /r.sub.10)______________________________________            r.sub.1 = ∞                          r.sub.1 &#39; = 20.956            d.sub.1 = 4.00                          n.sub.1 = 1.76530            r.sub.2 = ∞                          r.sub.2 &#39; = 17.812first converging d.sub.2 = 5.00means            r.sub.3 = ∞                          r.sub.3 &#39; = 46.210            d.sub.3 = 3.72                          n.sub.2 = 1.76530            r.sub.4 = ∞                          r.sub.4 &#39; = ∞            d.sub.4 = 72.19deflecting surface            r.sub.5 = ∞                          r.sub.5 &#39; = ∞            d.sub.5 = 20.48            r.sub.6 = -68.143                          r.sub.6 &#39; = -68.143            d.sub. 6 = 20.64                          n.sub.3 = 1.78506            r.sub.7 = -80.684                          r.sub.7 &#34; = -80.684            d.sub.7 = 6.77            r.sub.8 = 918.262                          r.sub.8 &#39; = 918.262second converging            d.sub.8 = 7.38                          n.sub.4 = 1.53288means            r.sub.9 = -4001.818                          r.sub.9 &#39; = -4001.818            d.sub.9 = 37.59            r.sub.10 = -1047.105                          r.sub.10 &#39; = -85.234            d.sub.10 = 14.29                          n.sub.5 = 1.67450            r.sub.11 = -195.914                          r.sub.11 &#39; = -34.629______________________________________ 
    
     EXAMPLE 10 
     aperture ratio in the plane parallel to the direction of scan=1:50 
     aperture ratio in the plane perpendicular to the direction of scan=1:50 
     half deflecting angle=±30° 
     
         ______________________________________f.sub.p = 287.69 f.sub.p /f.sub.v = 4.49L/f.sub.p = 0.28 f.sub.p /r.sub.a (= f.sub.p /r.sub.10)______________________________________            r.sub.1 = ∞                          r.sub.1 &#39; = 21.193            d.sub.1 = 4.00                          n.sub.1 = 1.76530            r.sub.2 = ∞                          r.sub.2 &#39; = 17.851first converging d.sub.2 = 5.00means            r.sub.3 = ∞                          r.sub.3 &#39; = 41.662            d.sub.3 = 3.72                          n.sub.2 = 1.76530            r.sub.4 = ∞                          r.sub.4 &#39; = ∞            d.sub.4 = 65.06deflecting surface            r.sub.5 = ∞                          r.sub.5 &#39; = ∞            d.sub.5 = 20.48            r.sub.6 = -65.855                          r.sub.6 &#39; = -65.855            d.sub. 6 = 22.11                          n.sub.3 = 1.78506            r.sub.7 = -82.458                          r.sub.7 &#39; = -82.458            d.sub.7 = 0.00            r.sub.8 = 11290.889                          r.sub.8 &#39; = 11290.889second converging            d.sub.8 = 9.89                          r.sub.4 = 1.78506means            r.sub.9 = -1046.936                          r.sub.9 &#39; = -1046.936            d.sub.9 = 34.50            r.sub.10 = -746.887                          r.sub.10 &#39;= -78.255            d.sub.10 = 15.00                          n.sub.5 = 1.78506            r.sub.11 = -192.977                          r.sub.11 &#39; =-36.101______________________________________ 
    
     EXAMPLE 11 
     aperture ratio in the plane parallel to the direction of scan=1:50 
     aperture ratio in the plane perpendicular to the direction of scan=1:50 
     half deflecting angle=±30° 
     
         ______________________________________f.sub.p = 287.66 f.sub.p /f.sub.v = 4.35L/f.sub.p = 0.30 f.sub.p /r.sub.a (= f.sub.p /r.sub.10)______________________________________= 0            r.sub.1 = ∞                          r.sub.1 &#39; = 21.004            d.sub.1 = 4.00                          n.sub.1 = 1.76530            r.sub.2 = ∞                          r.sub.2 &#39; = 17.845first converging d.sub.2 = 5.00means            r.sub.3 = ∞                          r.sub.3 &#39; = 45.422            d.sub.3 = 3.72                          n.sub.2 = 1.76530            r.sub.4 = ∞                          r.sub.4 &#39; = ∞            d.sub.4 = 70.73            r.sub.5 = ∞                          r.sub.5 &#39; = ∞deflecting surface            d.sub.5 = 20.48            r.sub.6 = -68.363                          r.sub.6 &#39; = -68.363            d.sub. 6 = 16.61                          n.sub.3 = 1.78506            r.sub.7 =  -77.695                          r.sub.7 &#39; = -77.695            d.sub.7 = 0.00            r.sub.8 = 11425.394                          r.sub.8 &#39; = 11425.394second converging            d.sub.8 = 17.01                          n.sub.4 = 1.78506means            r.sub.9 = -8531.994                          r.sub.9 &#39; = -8531.994            d.sub.9 = 35.96            r.sub.10 = ∞                          r.sub.10 &#39; = -89.050            d.sub.10 = 16.53                          n.sub.5 = 1.67450            r.sub.11 = -208.951                          r.sub.11 &#39; = -34.131______________________________________ 
    
     FIGS. 4 through 14 show characteristic curves of the above Examples 1 through 11, in each of which (a) relates to the spherical aberration in the plane perpendicular to the direction of scan of the first converging optical system, (b) to the spherical aberration in the plane perpendicular to the direction of scan of the second converging optical system, (c) to the spherical aberration in the plane perpendicular to the direction of scan of the whole system, (d) to the astigmatism, and (e) to the characteristics of linearity of scan. Furthermore, F denotes F number, ω denotes half deflecting angle, S denotes sagittal aberration, and M denotes meridional aberration. 
     As apparent from FIGS. 4 through 14, the residual aberration of the whole system is remarkably corrected, the aperture ratio is large, and the deflecting angle is large. As the result of this, the light scanning system of the invention can exhibit a highly accurate converging performance facilitated by a simple structure.