BACKGROUND OF THE INVENTION 0001 1. Field of the Invention 0002 This invention relates to a light scanning system, and more particularly to a light scanning system in which a deflected light bundle is imaged as a light spot on a surface to be scanned (will be referred to as a scan surface, hereinbelow) by a catoptric system and the light spot is caused to scan the scan surface. 0003 2. Description of the Related Art 0004 There has been known a light scanning system in which a light bundle is once imaged as a line image on a deflecting surface of a deflecting means (e.g., a rotational polygonal mirror) and the line image of the light bundle is further focused on a scan surface as a light spot and the light spot is caused to scan the scan surface at a constant speed. The performance of an imaging optical system of such a light scanning system is generally evaluated mainly on the f characteristic, bow of the scanning line, field curvature and/or the like, and various imaging optical systems have been designed for this purpose. For example, there has been disclosed, in Japanese Unexamined Patent Publication No. 11(2099)-153764, an optical system in which the line image on the deflecting surface is focused on the scan surface by a free curve mirror, and there has been disclosed, in Japanese Unexamined Patent Publication No. 8(1996)-220440, an optical system in which the line image is focused on the scan surface as a light spot by once reflecting the line image by a positive mirror and then reflecting the same by a negative mirror. Further, there has been disclosed, in Japanese Unexamined Patent Publication No. 8(1996)-211315, an optical system in which the line image is focused on the scan surface as a light spot by reflecting the line image by a pair of positive mirrors. 0005 In a light scanning system for use in medical diagnosis, e.g., a laser printer for showing an image for medical diagnosis, there has been a demand that the light spot should scan the scan surface at a constant speed or that an error in f characteristic (will be referred to as an f error, hereinbelow) should be as small as possible, in order to suppress distortion of the reproduced image. However, in accordance with the catoptric system designing method based on the conventional (positive and negative) power distribution, it is difficult to design a scanning optical system which is sufficiently small in the f error and can cause the light spot to scan the scan surface at a satisfactory constant speed.

SUMMARY OF THE INVENTION 0006 In view of the foregoing observations and description, the primary object of the present invention is to provide a light scanning system which is sufficiently small in f error. 0007 In accordance with the present invention, there is provided a light scanning system for causing a light spot to scan a scan surface at a constant speed comprising a light source, a deflecting means which deflects a light bundle radiated from the light source, a line image imaging optical system which is disposed between the light source and the deflecting means and images a light bundle radiated from the light source on a deflecting surface of the deflecting means as a line image extending in a direction in which the light bundle is deflected, and a scanning/imaging optical system which is disposed between the deflecting means and the scan surface and images the light bundle deflected by the deflecting means on the scan surface as a light spot, wherein the improvement comprises that 0008 the scanning/imaging optical system comprises a first aspheric mirror which is symmetric with respect to an axis of rotation and is disposed on the light inlet side of the scanning/imaging optical system and a second aspheric mirror which is anamorphic and is disposed on the light outlet side of the scanning/imaging optical system, the first aspheric mirror having a negative power in the direction in which a light bundle impinging upon the first aspheric mirror is deflected and the second aspheric mirror having a positive power in the direction in which a light bundle impinging upon the second aspheric mirror is deflected. 0009 The line image imaging optical system may have a positive power in the direction in which the line image of the light bundle extends. 0010 It is preferred that the scanning/imaging optical system satisfies the following formulae (1) and (2),

(m1efym1m2efym2)/efy<35(1)

d0/efx>0.4(2)

0011 wherein m1 represents the inclination to Z-direction of the optical axis of the first aspheric mirror in YZ plane, efym1 represents the focal length of the first aspheric mirror, m2 represents the inclination to the Z-direction of the optical axis of the second aspheric mirror in Y-Z plane, efym2 represents the focal length of the second aspheric mirror on a cross-section along the Y-Z plane, efy represents the focal length of the scanning/imaging optical system on a cross-section along the Y-Z plane, efx represents the focal length of the scanning/imaging optical system on a plane normal to the Y-Z plane, and d0 represents the distance between the deflecting surface of the deflecting means on which the line image is imaged and the front principal point of the scanning/imaging optical system on a plane normal to the Y-Z plane, assuming that a direction in which the light spot is caused to scan the scan surface is the X-direction, a direction which is normal to the X-direction on the scan surface is Y-direction and a direction normal to both the X-direction and the Y-direction (i.e., a direction normal to the scan surface) is the Z-direction. 0012 In the light scanning system of the present invention, since the scanning/imaging optical system comprises a first aspheric mirror which is symmetric with respect to an axis of rotation and is disposed on the light inlet side of the scanning/imaging optical system and a second aspheric mirror which is anamorphic and is disposed on the light outlet side of the scanning/imaging optical system, and the first aspheric mirror has a negative power in the direction in which a light bundle impinging upon the first aspheric mirror is deflected with the second aspheric mirror having a positive power in the direction in which a light bundle impinging upon the second aspheric mirror is deflected, that is, since the catoptric system is designed on the basis of a (positive and negative) power distribution different from that in the conventional catoptric system, a negative distortion is generated. As a result, the f error can be smaller as compared with the conventional light scanning system. When the aforesaid formula (2) is satisfied, the f error can be further smaller. 0013 When the line image imaging optical system has a positive power in the direction in which the line image of the light bundle extends on the deflecting surface, the field curvature can be smaller. 0014 Further, when the scanning/imaging optical system satisfies the aforesaid formula (1), bow of the scanning line can be suppressed.

BRIEF DESCRIPTION OF THE DRAWINGS 0015 FIG. 1 is a perspective view showing a light scanning system in accordance with an embodiment of the present invention, 0016 FIG. 2 is a graph showing f errors in various examples of designing of the light scanning system shown in FIG. 1, 0017 FIG. 3 is a graph showing bows of the scanning line in various examples of designing of the light scanning system shown in FIG. 1, 0018 FIG. 4 is a side view briefly showing a first example of designing (example G) of the light scanning system shown in FIG. 1, 0019 FIG. 5 is a plan view briefly showing the first example of designing of the light scanning system shown in FIG. 1, 0020 FIG. 6 is a graph showing the width of f error in the first example of designing, 0021 FIG. 7 is a graph showing the bow of the light spot in the Y-direction in the first example of designing, 0022 FIG. 8 is a graph showing the field curvature in the first example of designing, 0023 FIG. 9 is a side view briefly showing a second example of designing (example H) of the light scanning system shown in FIG. 1, 0024 FIG. 10 is a plan view briefly showing the second example of designing of the light scanning system shown in FIG. 1, 0025 FIG. 11 is a graph showing the width of f error in the second example of designing, 0026 FIG. 12 is a graph showing the bow of the light spot in the Y-direction in the second example of designing, 0027 FIG. 13 is a graph showing the field curvature in the second example of designing, 0028 FIG. 14 is a side view briefly showing a third example of designing (example A) of the light scanning system shown in FIG. 1, 0029 FIG. 15 is a plan view briefly showing the third example of designing of the light scanning system shown in FIG. 1, 0030 FIG. 16 is a graph showing the width of f error in the third example of designing, 0031 FIG. 17 is a graph showing the bow of the light spot in the Y-direction in the third example of designing, and 0032 FIG. 18 is a graph showing the field curvature in the third example of designing.

DESCRIPTION OF THE PREFERRED EMBODIMENT 0033 In FIG. 1, a light scanning system in accordance with an embodiment of the present invention comprises a light source 10, a rotary polygonal mirror 11 which is rotated by a drive means such as an electric motor (not shown) to deflect a light bundle radiated from the light source 10, a line image imaging optical system 20 which is disposed between the light source 10 and the rotary polygonal mirror 11 which images a light bundle radiated from the light source 10 on a deflecting surface S of the mirror 11 as a line image L extending in a direction in which the light bundle is deflected, and a scanning/imaging optical system 30 which is disposed between the polygonal mirror 11 and a scan surface 12 and images on the scan surface 12 as a light spot P the light bundle deflected by the rotary polygonal mirror 11, and causes the light spot P to scan the scan surface 12 at a constant speed in a direction of arrow X in FIG. 1. 0034 As shown in FIG. 1, the direction normal to the X-direction in which the light spot P is moved on the scan surface 12 is taken as a Y-direction and the direction normal to both the X-direction and the Y-direction (normal to the scan surface 12) is taken as Z-direction. 0035 The light source 10 comprises a semiconductor laser 9 which emits a laser beam and a collimator lens 8 which converts the laser beam emitted from the laser 9 into a parallel beam and a parallel laser beam is radiated from the light source 10. 0036 The line image imaging optical system 20 has a positive power in the Y-direction and images the parallel laser beam radiated from the light source 10 on the deflecting surface S as a line image L. The line image imaging optical system 20 has a positive power also in the direction in which the line image L extends weaker than that in the Y-direction. 0037 The scanning/imaging optical system 30 comprises a first aspheric mirror 31 which is symmetric with respect to an axis of rotation and is disposed on the light inlet side of the scanning/imaging optical system 30 and a second aspheric mirror 32 which is anamorphic and is disposed on the light outlet side of the scanning/imaging optical system 30. The first aspheric mirror 31 has a negative power in the direction in which a light bundle impinging thereupon is deflected and the second aspheric mirror 32 has a positive power in the direction in which a light bundle impinging thereupon is deflected. 0038 The first aspheric mirror 31 reflects a light bundle which is deflected by the rotary polygonal mirror 11 to impinge upon the first aspheric mirror 31 as a light bundle deflected at a larger angle. The second aspheric mirror 32 reflects the light bundle which is reflected by the first aspheric mirror 31 to impinge upon the second aspheric mirror 32 as a light bundle deflected at a smaller angle. 0039 Operation of the light scanning system of this embodiment will be described, hereinbelow. 0040 A parallel light bundle radiated from the light source 10 is imaged on a light deflecting surface S of the rotary polygonal mirror 11 as a line image L by the line image imaging optical system 20 and is further focused on the scan surface 12 as a light spot P by the scanning/imaging optical system 30 comprising the first and second aspheric mirrors 31 and 32. When the parallel light bundle is imaged on the light deflecting surface S as a line image L, the light bundle is slightly converged in the direction in which the line image L extends. 0041 The parallel light bundle is imaged on the scan surface 12 as a light spot P and at the same time, is deflected by the light deflecting surface S of the rotary polygonal mirror 11 to cause the light spot P to repeatedly scan the scan surface 12 in the X-direction through the scanning/imaging optical system 30 comprising the first and second aspheric mirrors 31 and 32 as the rotary polygonal mirror 11 is rotated about an axis of rotation O. 0042 The f error of the light scanning system of this embodiment will be discussed, hereinbelow. 0043 FIG. 2 is a graph showing f errors in fifteen examples of designing (examples of designing A to O) of the light scanning system shown in FIG. 1. In FIG. 2, the left ordinate represents the fluctuation in f errors ft, the right ordinate represents the value of Q(d0/efx in the aforesaid formula (2)), and the abscissa represents the examples of designing. The examples of designing A to O are arranged along the abscissa in the order of decreasing fluctuation in f errors ft. 0044 The f characteristic is a value represented by the following formula.

f characteristic(a distance between a reference scanning position X0 in which the scanning angle is 0 and an actual scanning positiona distance between the reference scanning position X0 and an ideal scanning position)/(a distance between the reference scanning position X0 and the actual scanning position100(%)

0045 The fluctuation in f errors ft represents a p-p (peak-to-peak) value of values representing f characteristics at various evaluation angles, and the scanning length means a length by which the light spot is caused to scan the scan surface. 0046 In the following table 1, the examples of designing A to O are arranged in the order of decreasing fluctuation in f errors ft. 1TABLE 1example of designingft (%)QA0.0000.495B0.0000.445C0.0000.428D0.0000.446E0.0000.460F0.0000.462G0.0010.461H0.0010.473I0.0010.459J0.0030.461K0.0140.302L0.2130.524N0.2250.432N1.0130.508O8.0830.178

0047 As can be seen from FIG. 2 and table 1, the fluctuation in f errors ft are substantially not larger than 1% in the examples of designing A to O except the example of designing O and smaller than 0.3% in the examples of designing A to O except the examples of designing N and O. Especially, in the examples of designing A to J, the fluctuation in f errors ft are as small as not larger than 0.003%. 0048 The aforesaid formulae (1) and (2) (equal to the following formulae (1) and (2)) will be discussed, hereinbelow.

P(am1efym1m2efym2)/efy<35(1)

Qd0/efx>0.4(2)

0049 wherein m1 represents the inclination to Z-direction of the optical axis of the first aspheric mirror in YZ plane, efym1 represents the focal length of the first aspheric mirror, m2 represents the inclination to the Z-direction of the optical axis of the second aspheric mirror in Y-Z plane, efym2 represents the focal length of the second aspheric mirror on a cross-section along the Y-Z plane, efy represents the focal length of the scanning/imaging optical system on a cross-section along the Y-Z plane, efx represents the focal length of the scanning/imaging optical system on a plane normal to the Y-Z plane, and d0 represents the distance between the deflecting surface of the deflecting means on which the line image is imaged and the front principal point of the scanning/imaging optical system on a plane normal to the Y-Z plane. 0050 FIG. 3 is a graph showing the fluctuation in bows of scanning lines in fifteen examples of designing (examples of designing A to O) of the light scanning system shown in FIG. 1. In FIG. 3, the left ordinate represents the fluctuation in bows of the scanning line ypos (a p-p (peak-to-peak) value of the variation of the position of the light spot on the scan surface in the Y-direction) in mm, the right ordinate represents the value of P in the formula (1), and the abscissa represents the examples of designing. The examples of designing A to O are arranged along the abscissa in the order of decreasing fluctuation in bows of the scanning line ypos. 0051 In the following table 2, the examples of designing A to O are arranged in the order of decreasing fluctuation in bows of the scanning line ypos. 2TABLE 2example of designingypos (mm)PD0.00417.45151A0.00812.41585C0.00818.71052I0.00812.94674G0.00911.66628F0.00911.17610B0.01017.89876E0.01016.04585H0.01214.70069J0.01716.37963L0.0448.72916N0.08312.12624M0.10218.13760K0.15576.32608O0.408113.64389

0052 As can be seen from FIGS. 2 and 3 and tables 1 and 2, the examples of designing which satisfy both the conditions P<35 and Q>0.4 (the examples of designing but K and O) are all very small in bow of scanning line in the Y-direction (ypos is substantially smaller than 0.1 mm). Especially, in eight examples of designing (D, A, C, I, G, F, B and E), the value of ypos is as small as not larger than 0.01, that is, bow of the scanning line in the Y-direction is very small. 0053 The example of designing G (first example of designing), the example of designing H (second example of designing) and the example of designing A (third example of designing) will be described in more detail, hereinbelow. 0054 The aspheric surfaces of the first and second aspheric mirrors are represents as follows. 0055 first aspheric mirror

zch2/1SQR1(1K)c2h2Ah4Bh6Ch8Dh10

0056 wherein c represents the curvature (c1/rdy), h represents the height from the optical axis (hSQR(x2y2)), K represents the conic constant, and A,B, C and D respectively represent 4th, 6th, 8th and 10th order aspheric coefficients, SQR being a sign representing {square root}{square root over ( )}. 0057 second aspheric mirror

z(CUXx2CUYy2)/1SQR1(1KX)CUX2x2(1KY)CUY2y2AR(1AP)x2(1AP)y22BR(1BP)x2(1BP)y23CR(1CP)x2(1CP)y24DR(1DP)x2(1DP)y25

0058 wherein CUX represents the curvature in the X-Z section (CUX1/rdx), CUY represents the curvature in the Y-Z section (CUY1/rdy), KX represents the conic constant in the X-Z section, KY represents the conic constant in the Y-Z section, AR,BR, CR and DR respectively represent the symmetry components of rotation of 4th, 6th, 8th and 10th order deformation coefficients for the respective cones, and AP, BP, CP and DP respectively represent the symmetry components of rotation of 4th, 6th, 8th and 10th order deformation coefficients for the respective cones. It should be noted that a common aspheric surface is obtained when CUXCUY, KXKY, APBPCPDP0. 0059 <First Example of Designing (Example of Designing G)>0060 FIG. 4 is a side view of the example of designing G and FIG. 5 is a plan view of the same. The optical axis of the line image imaging optical system 20G is moved to the Y-Z plane so that the optical path length from the line image imaging optical system 20G to the rotary polygonal mirror 11G does not change. 0061 The specification of the respective optical elements ((1) to (5)), design performance (6) and calculation of the values of P and Q (7) in the example of designing G will be described, hereinbelow. 0062 F characteristics of the light spots imaged on the scan surface at a plurality of rotating angles of the rotary polygonal mirror (i.e., 0, 21, 29.4 and 42), the positions yp of the light spots in the Y-direction at the respective rotating angles of the rotary polygonal mirror, fluctuation in bows of the scanning line ypos, the amount of field curvature xfo in converging the light bundle in the X-direction at the respective rotating angles of the rotary polygonal mirror, fluctuation in amounts of field curvature xfo in converging the light bundle in the X-direction (peak-to-peak value of the amounts of field curvature xfo), the amount of field curvature yfo in converging the light bundle in the Y-direction at the respective rotating angles of the rotary polygonal mirror, fluctuation in amounts of field curvature yfo in converging the light bundle in the Y-direction (peak-to-peak value of the amounts of field curvature yfo) are shown in the following table 3. 3TABLE 3light spotanglepositionfypxfoyfo4217602.1270.2850.22329.4123.202.1340.1290.035218802.1260.1790.40002.1290.10.1218802.1260.1790.02529.4123.202.1340.130.0254217602.1270.2850.223p-pft 0ypos 0.009Max:0.465Max:0.623

0063 FIGS. 6, 7 and 8 respectively show f characteristics of the light spots imaged on the scan surface at the aforesaid rotating angles of the rotary polygonal mirror, the positions yp of the light spots in the Y-direction at the aforesaid rotating angles of the rotary polygonal mirror, and the amount of field curvature xfo in converging the light bundle in the X-direction and the amount of field curvature yfo in converging the light bundle in the Y-direction at the respective rotating angles of the rotary polygonal mirror. 0064 (1) The Specification of the Line Image Imaging Optical System 20G 0065 lens system: single lens 0066 thickness: 8.625837 mm 0067 glass: BSC7 HOYA 0068 radius of curvature of the first face in the Y-Z section, rdy1: 88.73457 mm 0069 radius of curvature of the first face in a cross-section which includes the optical axis and is normal to the Y-Z section, rdx1: 310.2599 mm 0070 radius of curvature of the second face in the Y-Z section, rdy2radius of curvature of the second face in a cross-section which includes the optical axis and is normal to the Y-Z section, rdx2 (plane) 0071 (2) The Specification of the First Aspheric Mirror 31G 0072 focal length in the Y-Z section, efym1focal length in a cross-section which includes the optical axis and is normal to the Y-Z section, efxm1272.354 mm 0073 rdy554.70842 mm 0074 aspheric coefficients 0075 K51.928874 0076 A0.7630001E-7 0077 B0.197933E-10 0078 C0.145888E-13 0079 D0.725540E-17 0080 inclination to the Z-direction of the aspheric axis in the YZ section, m1: 3.4370081 (3) The Specification of the Second Aspheric Mirror 32G 0082 focal length in the Y-Z section, efym266.187 mm 0083 focal length in a cross-section which includes the optical axis and is normal to the Y-Z section, efxm2185.074 mm 0084 rdy132.37387 mm 0085 rdx370.14752 mm 0086 aspheric parameters 0087 KY2.005179 0088 KX1.494253 0089 AR0.550051E-08 0090 BR0.728624E-12 0091 CR0.279367E-14 0092 DR0.56269E-18 0093 AP0.411218E-01 0094 BP0.330127E00 0095 CP0.858727E00 0096 DP0.898273E00 0097 inclination to the Z-direction of the aspheric axis in the YZ section, m2: 2.4550098 (4) The Specification of the Scanning/imaging Optical System 30G (The Combined Specification of the First and Second Aspheric Mirrors 31G and 32G) 0099 focal length in the Y-Z section, efy66.305 mm 0100 focal length in a cross-section which includes the optical axis and is normal to the Y-Z section, efx329.484 mm 0101 distance between the reflecting surface in a plane which includes the optical axis and is normal to the Y-Z section and the front principal point of the scanning/imaging optical system, H: 116.971 mm 0102 (5) Other Data 0103 the distance from the rear end of the line image imaging optical system 20G to the deflecting face of the rotary polygonal mirror 11G: 166.555 mm 0104 distance from the deflecting face of the rotary polygonal mirror 11G to the first aspheric mirror 31G, dpmm1: 35.000 mm 0105 distance from the first aspheric mirror 31G to the second aspheric mirror 32G, dm1m2: 65.704 mm 0106 distance from the second aspheric mirror 32G to the scan surface 12G: 237.899 mm 0107 inclination to the Y-direction of the axis of rotation of the rotary polygonal mirror 11G in the YZ section: 5.00108 length of the first aspheric mirror 31G in the X-direction (corresponding to the whole scanning angle): 70 mm 0109 length of the second aspheric mirror 32G in the X-direction (corresponding to the whole scanning angle): 200 mm 0110 (6) Design Performance 0111 fluctuation in bows of scanning lines (p-p): 0.009 mm 0112 fluctuation in f errors (%): 0.000(%) 0113 fluctuation in amounts of field curvature in converging the light bundle in the Y-direction (p-p): 0.465 mm 0114 fluctuation in amounts of field curvature in converging the light bundle in the X-direction (p-p): 0.623 mm 0115 (7) Calculation of the Values of P and Q 1

\begin{matrix} P = (m1 e f y m1 - m2 efym2) / efy \\ = (3.437 (- 272.354) - (- 2.455) 66.187) / 66.305 \\ = 11.667 < 35 \end{matrix}

\begin{matrix} Q = d0 / efx \\ = (d_{pmm1} + H) / efx \\ = (35.000 + 116.971) / 329.484 \\ = 0.461 > 0.4 \end{matrix}

0116 <Second Example of Designing (Example of Designing H)>0117 FIG. 9 is a side view of the example of designing G and FIG. 10 is a plan view of the same. The optical axis of the line image imaging optical system 20H is moved to the Y-Z plane so that the optical path length from the line image imaging optical system 20H to the rotary polygonal mirror 11H does not change. 0118 The specification of the respective optical elements ((1) to (5)), design performance (6) and calculation of the values of P and Q (7) in the example of designing H will be described, hereinbelow. 0119 F characteristics of the light spots imaged on the scan surface at a plurality of rotating angles of the rotary polygonal mirror (i.e., 0, 21, 29.4 and 42), the positions yp of the light spots in the Y-direction at the respective rotating angles of the rotary polygonal mirror, fluctuation in bows of the scanning line ypos, the amount of field curvature xfo in converging the light bundle in the X-direction at the respective rotating angles of the rotary polygonal mirror, fluctuation in amounts of field curvature xfo in converging the light bundle in the X-direction (peak-to-peak value of the amounts of field curvature xfo), the amount of field curvature yfo in converging the light bundle in the Y-direction at the respective rotating angles of the rotary polygonal mirror, fluctuation in amounts of field curvature yfo in converging the light bundle in the Y-direction (peak-to-peak value of the amounts of field curvature yfo) are shown in the following table 4. 4TABLE 4light spotanglepositionfypxfoyfo4217601.3680.0320.48129.4123.201.3730.2850.148218801.3610.2950.2470001.3680.0710.099218801.3610.2950.24729.4123.201.3730.2860.1484217601.3680.0320.481p-pft 0ypos 0.012Max:0.581Max:0.729

0120 FIGS. 11, 12 and 13 respectively show f characteristics of the light spots imaged on the scan surface at the aforesaid rotating angles of the rotary polygonal mirror, the positions yp of the light spots in the Y-direction at the aforesaid rotating angles of the rotary polygonal mirror, and the amount of field curvature xfo in converging the light bundle in the X-direction and the amount of field curvature yfo in converging the light bundle in the Y-direction at the respective rotating angles of the rotary polygonal mirror. 0121 (1) The Specification of the Line Image Imaging Optical System 20H 0122 lens system: single lens 0123 thickness: 8.625837 mm 0124 glass: BSC7 HOYA 0125 radius of curvature of the first face in the Y-Z section, rdy1: 88.73457 mm 0126 radius of curvature of the first face in a cross-section which includes the optical axis and is normal to the Y-Z section, rdx1: 388.42515 mm 0127 radius of curvature of the second face in the Y-Z section, rdy2radius of curvature of the second face in a cross-section which includes the optical axis and is normal to the Y-Z section, rdx2 (plane) 0128 (2) The Specification of the First Aspheric Mirror 31H 0129 focal length in the Y-Z section, efym1focal length in a cross-section which includes the optical axis and is normal to the Y-Z section, efxm1376.227 mm 0130 rdy752.45455 mm 0131 aspheric coefficients 0132 K100.775715 0133 A0.578683E-7 0134 B0.616175E-11 0135 C0.255522E-15 0136 D0.197146E-20 0137 inclination to the Z-direction of the aspheric axis in the YZ section, m1: 3.20700138 (3) The Specification of the Second Aspheric Mirror 32H 0139 focal length in the Y-Z section, efym269.235 mm 0140 focal length in a cross-section which includes the optical axis and is normal to the Y-Z section, efxm2185.028 mm 0141 rdy138.47086 mm 0142 rdx370.05529 mm 0143 aspheric parameters 0144 KY2.182209 0145 KX0.851945 0146 AR0.727070E-08 0147 BR0.417889E-12 0148 CR0.494209E-14 0149 DR0.120920E-17 0150 AP0.967812E-01 0151 BP0.170026E00 0152 CP0.912777E00 0153 DP0.943001E00 0154 inclination to the Z-direction of the aspheric axis in the YZ section, m2: 1.6580155 (4) The Specification of the Scanning/imaging Optical System 30H (The Combined Specification of the First and Second Aspheric Mirrors 31H and 32H) 0156 focal length in the Y-Z section, efy74.261 mm 0157 focal length in a cross-section which includes the optical axis and is normal to the Y-Z section, efx296.257 mm 0158 distance between the reflecting surface in a plane which includes the optical axis and is normal to the Y-Z section and the front principal point of the scanning/imaging optical system, H: 70.090 mm 0159 (5) Other Data 0160 the distance from the rear end of the line image imaging optical system 20H to the deflecting face of the rotary polygonal mirror 11H: 166.555 mm 0161 distance from the deflecting face of the rotary polygonal mirror 11H to the first aspheric mirror 31H, dpmm1: 70.000 mm 0162 distance from the first aspheric mirror 31H to the second aspheric mirror 32H, dm1m2: 43.775 mm 0163 distance from the second aspheric mirror 32H to the scan surface 12H: 219.011 mm 0164 inclination to the Y-direction of the axis of rotation of the rotary polygonal mirror 11H in the YZ section: 5.00165 length of the first aspheric mirror 31H in the X-direction (corresponding to the whole scanning angle): 140 mm 0166 length of the second aspheric mirror 32H in the X-direction (corresponding to the whole scanning angle): 220 mm 0167 (6) Design Performance 0168 fluctuation in bows of scanning lines (p-p): 0.012 mm 0169 fluctuation in f errors (%): 0.000(%) 0170 fluctuation in amounts of field curvature in converging the light bundle in the Y-direction (p-p): 0.581 mm 0171 fluctuation in amounts of field curvature in converging the light bundle in the X-direction (p-p): 0.729 mm 0172 (7) Calculation of the Values of P and Q 2

\begin{matrix} P = (m1 e f y m1 - m2 efym2) / efy \\ = (3.207 (- 376.277) - (- 1.685) 69.235) / 74.261 \\ = 14.702 < 35 \end{matrix}

\begin{matrix} Q = d0 / efx \\ = (d_{pmm1} + H) / efx \\ = (70.000 + 70.090) / 296.257 \\ = 0.473 > 0.4 \end{matrix}

0173 <Third Example of Designing (Example of Designing A)>0174 FIG. 14 is a side view of the example of designing A and FIG. 15 is a plan view of the same. The optical axis of the line image imaging optical system 20A is moved to the Y-Z plane so that the optical path length from the line image imaging optical system 20A to the rotary polygonal mirror 11A does not change. 0175 The specification of the respective optical elements ((1) to (5)), design performance (6) and calculation of the values of P and Q (7) in the example of designing A will be described, hereinbelow. 0176 F characteristics of the light spots imaged on the scan surface at a plurality of rotating angles of the rotary polygonal mirror (i.e., 0, 21, 29.4 and 42), the positions yp of the light spots in the Y-direction at the respective rotating angles of the rotary polygonal mirror, fluctuation in bows of the scanning line ypos, the amount of field curvature xfo in converging the light bundle in the X-direction at the respective rotating angles of the rotary polygonal mirror, fluctuation in amounts of field curvature xfo in converging the light bundle in the X-direction (peak-to-peak value of the amounts of field curvature xfo), the amount of field curvature yfo in converging the light bundle in the Y-direction at the respective rotating angles of the rotary polygonal mirror, fluctuation in amounts of field curvature yfo in converging the light bundle in the Y-direction (peak-to-peak value of the amounts of field curvature yfo) are shown in the following table 5. 5TABLE 5light spotanglepositionfypxfoyfo4217603.5180.0920.36629.4123.203.5210.3510.214218803.5140.420.1560003.5180.10.1218803.5140.420.15629.4123.203.5210.3520.2144217603.5180.0920.366p-pft 0ypos 0.008Max:0.772Max:0.522

0177 FIGS. 16, 17 and 18 respectively show f characteristics of the light spots imaged on the scan surface at the aforesaid rotating angles of the rotary polygonal mirror, the positions yp of the light spots in the Y-direction at the aforesaid rotating angles of the rotary polygonal mirror, and the amount of field curvature xfo in converging the light bundle in the X-direction and the amount of field curvature yfo in converging the light bundle in the Y-direction at the respective rotating angles of the rotary polygonal mirror. 0178 (1) The Specification of the Line Image Imaging Optical System 20A 0179 lens system: single lens 0180 thickness: 8.625837 mm 0181 glass: BSC7 HOYA 0182 radius of curvature of the first face in the Y-Z section, rdy1: 88.73457 mm 0183 radius of curvature of the first face in a cross-section which includes the optical axis and is normal to the Y-Z section, rdx1: 333.66044 mm 0184 radius of curvature of the second face in the Y-Z section, rdy2radius of curvature of the second face in a cross-section which includes the optical axis and is normal to the Y-Z section, rdx2 (plane) 0185 (2) The Specification of the First Aspheric Mirror 31A 0186 focal length in the Y-Z section, efym1focal length in a cross-section which includes the optical axis and is normal to the Y-Z section, efxm1396.485 mm 0187 rdy792.96954 mm 0188 aspheric coefficients 0189 K132.894650 0190 A0.530960E-07 0191 B0.53854E-11 0192 C0.327988E-15 0193 D0.934694E-20 0194 inclination to the Z-direction of the aspheric axis in the YZ section, m1: 2.8050195 (3) The Specification of the Second Aspheric Mirror 32A 0196 focal length in the Y-Z section, efym270.291 mm 0197 focal length in a cross-section which includes the optical axis and is normal to the Y-Z section, efxm2194.928 mm 0198 rdy140.58269 mm 0199 rdx389.85648 mm 0200 aspheric parameters 0201 KY2.366281 0202 KX0.066032 0203 AR0.746007E-08 0204 BR0.194695E-12 0205 CR0.315989E-14 0206 DR0.66931E-18 0207 AP0.162771E-00 0208 BP0.925186E01 0209 CP0.915259E00 0210 DP0.945526E00 0211 inclination to the Z-direction of the aspheric axis in the YZ section, m2: 2.6110212 (4) The Specification of the Scanning/imaging Optical System 30A (The Combined Specification of the First and Second Aspheric Mirrors 31A and 32A) 0213 focal length in the Y-Z section, efy74.781 mm 0214 focal length in a cross-section which includes the optical axis and is normal to the Y-Z section, efx311.578 mm 0215 distance between the reflecting surface in a plane which includes the optical axis and is normal to the Y-Z section and the front principal point of the scanning/imaging optical system, H: 74.311 mm 0216 (5) Other Data 0217 the distance from the rear end of the line image imaging optical system 20A to the deflecting face of the rotary polygonal mirror 11A: 166.555 mm 0218 distance from the deflecting face of the rotary polygonal mirror 11A to the first aspheric mirror 31A, dpmm1: 80.000 mm 0219 distance from the first aspheric mirror 31A to the second aspheric mirror 32A, dm1m2: 46.490 mm 0220 distance from the second aspheric mirror 32A to the scan surface 12A: 200.235 mm 0221 inclination to the Y-direction of the axis of rotation of the rotary polygonal mirror 11A in the YZ section: 5.00222 length of the first aspheric mirror 31A in the X-direction (corresponding to the whole scanning angle): 160 mm 0223 length of the second aspheric mirror 32A in the X-direction (corresponding to the whole scanning angle): 250 mm 0224 (6) Design Performance 0225 fluctuation in bows of scanning lines (p-p): 0.008 mm 0226 fluctuation in f errors (%): 0.000(%) 0227 fluctuation in amounts of field curvature in converging the light bundle in the Y-direction (p-p): 0.772 mm 0228 fluctuation in amounts of field curvature in converging the light bundle in the X-direction (p-p): 0.522 mm 0229 (7) Calculation of the Values of P and Q 3

\begin{matrix} P = (m1 e f y m1 - m2 efym2) / efy \\ = (2.805 (- 396.485) - (- 2.611) 70.291) / 74.781 \\ = 12.418 < 35 \end{matrix}

\begin{matrix} Q = d0 / efx \\ = (d_{pmm1} + H) / efx \\ = (80.000 + 74.311) / 311.578 \\ = 0.495 > 0.4 \end{matrix}

0230 Though, in the embodiment described above, the line image imaging optical system has a positive power in the direction in which the line image L extends, the f error can be suppressed even if the line image imaging optical system has no power or a negative power in the direction in which the line image L extends.