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SCANNING OPTICAL APPARATUS AND IMAGE FORMING APPARATUS

20180157190 ยท 2018-06-07

    Inventors

    Cpc classification

    International classification

    Abstract

    A scanning optical apparatus includes a light source, a deflector and an imaging optical system. The deflector deflects a beam emitted from the light source to scan a scanning surface with the beam in a main scanning direction. The imaging optical system focuses the beam on the scanning surface. The imaging optical system includes a first lens having negative power in a sub scanning direction and a second lens having positive power in the sub scanning direction, in which the sub scanning direction is parallel to the scanning surface and perpendicular to the main scanning direction. The power 1 of the first lens, the power 2 of the second lens and a magnification in the sub scanning direction of the imaging optical system satisfy the conditions 1.21/20.9 and 1.30.8.

    Claims

    1. A scanning optical apparatus, comprising: a light source; a deflector which deflects a beam emitted from the light source to scan a scanning surface with the beam in a main scanning direction; and an imaging optical system which focuses the beam deflected by the deflector on the scanning surface, wherein the imaging optical system comprises a first lens having negative power in a sub scanning direction and a second lens having positive power in the sub scanning direction, in which the sub scanning direction is parallel to the scanning surface and perpendicular to the main scanning direction, and wherein the power 1 in the sub scanning direction of the first lens, the power 2 in the sub scanning direction of the second lens and a magnification in the sub scanning direction of the imaging optical system satisfy the following conditions.
    1.21/20.9
    1.30.8

    2. The scanning optical apparatus according to claim 1, wherein the distance L from a point where the deflector reflects the beam to the scanning surface is 350 mmL405 mm.

    3. The scanning optical apparatus according to claim 1, wherein the light source comprises two or more light sources, and beams emitted from the respective light sources are reflected on different faces of the same deflector and then focused on different scanning surfaces.

    4. The scanning optical apparatus according to claim 1, wherein the beam deflected by the deflector is reflected on one or more turn-back mirrors and then focused on the scanning surface.

    5. An image forming apparatus, comprising: a scanning optical apparatus which forms an electrostatic latent image on an image carrier; and a developer which develops the electrostatic latent image, in which the image forming apparatus forms an image on a recording medium by transferring the image developed by the developer to the recording medium, wherein the scanning optical apparatus comprises: a light source; a deflector which deflects a beam emitted from the light source to scan a scanning surface with the beam in a main scanning direction; and an imaging optical system which focuses the beam deflected by the deflector on the scanning surface, wherein the imaging optical system comprises a first lens having negative power in a sub scanning direction and a second lens having positive power in the sub scanning direction, in which the sub scanning direction is parallel to the scanning surface and perpendicular to the main scanning direction, and wherein the power 1 in the sub scanning direction of the first lens, the power 2 in the sub scanning direction of the second lens and a magnification in the sub scanning direction of the imaging optical system satisfy the following conditions.
    1.21/20.9
    1.30.8

    6. The image forming apparatus according to claim 5, wherein the distance L from a point where the deflector reflects the beam to the scanning surface is 350 mmL405 mm.

    7. The image forming apparatus according to claim 5, wherein the light source comprises two or more light sources, and beams emitted from the respective light sources are reflected on different faces of the same deflector and then focused on different scanning surfaces.

    8. The image forming apparatus according to claim 5, wherein the beam deflected by the deflector is reflected on one or more turn-back mirrors and then focused on the scanning surface.

    Description

    BRIEF DESCRIPTION OF THE DRAWINGS

    [0017] The advantages and features provided by one or more embodiments of the invention will become more fully understood from the detailed description given hereinbelow and the appended drawings which are given by way of illustration only, and thus are not intended as a definition of the limits of the present invention, and wherein:

    [0018] FIG. 1 illustrates the configuration of a scanning optical system according to an embodiment of the present invention;

    [0019] FIG. 2 is a graph of sub image plane shift in Example 1 when a scanning optical apparatus experiences a temperature change of 15 C.;

    [0020] FIG. 3 is a graph of sub image plane shift in Comparison 1 and Comparison 2 when a scanning optical apparatus experiences a temperature change of 15 C.;

    [0021] FIG. 4 is a graph of sub image plane shift in Example 2, Example 3, Example 4 and Example 5 when a scanning optical apparatus experience a temperature change of 15 C.;

    [0022] FIG. 5 is a graph of sub image plane shift in Example 6, Example 7, Comparison 3 and Comparison 4 when a scanning optical apparatus experiences a temperature change of 15 C.;

    [0023] FIG. 6 is a graph of sub image plane shift in Example 1a when a scanning optical apparatus experiences a temperature change of 15 C.;

    [0024] FIG. 7 is a graph of sub image plane shift in Comparison 1a, Comparison 2a and Comparison 3a when a scanning optical apparatus experiences a temperature change of 15 C.;

    [0025] FIG. 8 is a graph of sub image plane shift in Example 2a, Example 3a and Example 4a when a scanning optical apparatus experiences a temperature change of 15 C.;

    [0026] FIG. 9 is a graph of sub image plane shift in Example 5a, Example 6a, Comparison 4a and Comparison 5a when a scanning optical apparatus experiences a temperature change of 15 C.;

    [0027] FIG. 10 is a graph of sub image plane shift in Example 1b, Example 2b, Example 3b, Example 4b and Example 5b when a scanning optical apparatus experiences a temperature change of 15 C.;

    [0028] FIG. 11 illustrates the configuration of a scanning optical system according to another embodiment of the present invention; and

    [0029] FIG. 12 illustrates the configuration of a scanning optical system according to still another embodiment of the present invention.

    DETAILED DESCRIPTION OF EMBODIMENTS

    [0030] Hereinafter, one or more embodiments of the present invention will be described with reference to the drawings. However, the scope of the invention is not limited to the disclosed embodiments.

    [0031] FIG. 1 illustrates the scanning optical system of a scanning optical apparatus according to an embodiment of the present invention. The triaxial coordinate XYZ is shown in FIG. 1. A laser light 10 is emitted from a light source and collimated. The laser light 10 condensed in a sub scanning z direction (i.e. the direction normal to the sheet) enters a deflector 1, is deflected by the deflector 1, passes through a first lens 2 and a second lens 3, and is then incident on a scanning surface 4.

    [0032] The scanning optical apparatus is applied to an image forming apparatus such as a printer or a copier that forms an image on a recording medium. The image forming apparatus includes an image carrier, a charger, the scanning optical apparatus, a developer, a transfer section and a fixation section.

    [0033] The charger charges the image carrier, and the scanning optical apparatus emits a beam to the image carrier charged by the charger based on image data, so that an electrostatic latent image is formed on the image carrier. The image data may be based on external input data or data read by an original reader.

    [0034] The developer applies a developing agent to the image carrier on which the electrostatic latent image is formed, so as to develop an image with the developing agent from the electrostatic latent image.

    [0035] The transfer section transfers the developed image to a recording medium, and the fixation section heats and presses the transferred image to fix it on the recording medium.

    [0036] In this way, the image forming apparatus forms an image on a recording medium.

    [0037] Example 1 to Example 7, Example 1a to Example 6a and Example 1b to 5b of the present invention and Comparison 1 to Comparison 4 and Comparison 1a to Comparison 5a for comparison are all based on the scanning optical system as illustrated in FIG. 1 but have different configurations as listed in Table 4 to Table 9. The power ratio 1/2, the magnification in the sub scanning direction and the conjugation length L of these samples were calculated. The results are shown in Table 1 to 3. The conjugation length L is 373.2 mm in Example 1 to Example 7 and Comparison 1 to Comparison 4 as illustrated in Table 1, 405 mm in Example 1a to Example 6a, Comparison 1a, Comparison 2a, Comparison 4a and Comparison 5a, 410 nm in Comparison 3a, and 350 mm in Example 1b to Example 5b as illustrated in Table 2.

    [0038] In all examples and comparisons, the maximum image height in the main scanning direction is 164.5 mm, the deflector 1 has a regular heptagonal shape with an inscribed circle diameter of 48 mm, the incident angle to the deflector 1 is 60 with respect to the optical axis, the wavelength of the scanning beam is 780 nm, the ambient temperature is 25, and the lens material of the first lens 2 and the second lens 3 is respectively ZEONEX 330R and ZEONEX E48R, the F number of the image plane is 47.6 in the main scanning y direction and 53.3 in the sub scanning z direction.

    [0039] The planar aspect is determined by the following Expression 1.

    [00001] x = .Math. i .Math. .Math. A i .Math. y i + z 2 .Math. .Math. i .Math. .Math. B i .Math. y i

    [0040] In the expression, x is the direction of the optical axis, y is the main scanning direction perpendicular to the x direction, z is the sub scanning direction perpendicular to the x and y directions (corresponding to the triaxial coordinate in FIG. 1).

    TABLE-US-00001 TABLE 1 POWER RATIO MAGNIFI- CONJUGATION 1/2 CATION LENGTH L COMPARISON 1 1.2 1.4 373.2 COMPARISON 2 1.4 1.3 373.2 EXAMPLE 1 1.2 1.3 373.2 EXAMPLE 2 1.2 1.15 373.2 EXAMPLE 3 1.2 0.8 373.2 EXAMPLE 4 1 1.3 373.2 EXAMPLE 5 0.9 1.3 373.2 EXAMPLE 6 1.05 1.15 373.2 EXAMPLE 7 0.9 0.8 373.2 COMPARISON 3 0.9 0.7 373.2 COMPARISON 4 0.8 0.8 373.2

    TABLE-US-00002 TABLE 2 POWER RATIO MAGNIFI- CONJUGATION 1/2 CATION LENGTH L COMPARISON 1a 1.2 1.4 405 COMPARISON 2a 1.4 1.3 405 COMPARISON 3a 1.2 1.3 410 EXAMPLE 1a 1.2 1.3 405 EXAMPLE 2a 1.2 1.15 405 EXAMPLE 3a 1.2 0.8 405 EXAMPLE 4a 1 1.3 405 EXAMPLE 5a 0.9 1.3 405 EXAMPLE 6a 0.9 0.8 405 COMPARISON 4a 0.9 0.7 405 COMPARISON 5a 0.8 0.8 405

    TABLE-US-00003 TABLE 3 POWER RATIO MAGNIFI- CONJUGATION 1/2 CATION LENGTH L EXAMPLE 1b 1.2 1.3 350 EXAMPLE 2b 1.2 0.8 350 EXAMPLE 3b 0.9 1.3 350 EXAMPLE 4b 1.05 1.15 350 EXAMPLE 5b 0.9 0.8 350

    TABLE-US-00004 TABLE 4 DEGREE EXAMPLE 1 EXAMPLE 2 EXAMPLE 3 EXAMPLE 4 EXAMPLE 5 EXAMPLE 6 EXAMPLE 7 COMPARISON 1 COMPARISON 2 COMPARISON 3 COMPARISON 4 FIRST LENS, FIRST SURFACE, COEFFICIENT A 2 6.4688E03 6.6166E03 5.8000E03 6.5713E03 5.7971E03 6.4688E03 5.5992E03 6.7629E03 7.6277E03 3.9199E03 5.2368E03 4 1.8055E08 8.0709E08 8.2706E07 7.2757E07 2.2413E07 1.8055E08 4.0891E07 7.7733E07 1.2795E06 4.0098E07 3.1847E07 6 2.5336E10 4.1320E10 1.0333E09 2.1138E10 2.1565E10 2.5336E10 5.3926E10 4.1102E11 6.1560E10 4.0864E10 4.1360E10 8 1.8679E13 6.5924E14 1.0239E13 3.9348E14 1.2142E13 1.8679E13 1.9384E13 6.4676E14 7.9534E14 1.1108E13 2.4910E13 10 4.5605E17 3.4677E17 2.4193E17 1.3958E17 4.1763E17 4.5605E17 7.3536E17 1.8291E18 1.1139E18 3.7785E17 7.1313E17 FIRST LENS, FIRST SURFACE, COEFFICIENT B 0 2.7000E02 2.7000E02 2.7000E02 2.7000E02 2.7000E02 2.7000E02 2.7000E02 2.7000E02 2.7000E02 2.7000E02 2.7000E02 1 1.7037E04 4.0583E04 3.6518E03 5.0494E04 2.7196E04 1.7037E04 8.2013E04 2.3012E04 1.9552E04 3.6949E03 6.3578E04 2 1.6292E05 1.8572E05 3.3622E06 9.2855E06 3.4533E06 1.6292E05 2.4216E06 1.2958E05 1.2770E05 4.4668E05 1.3501E05 3 1.5139E07 6.8626E08 3.0850E07 1.8187E07 3.8440E08 1.5139E07 1.9848E07 3.1023E08 4.6186E08 4.6988E07 3.2299E08 4 1.5946E08 9.0813E09 2.4484E08 1.8351E08 1.8781E08 1.5946E08 8.5913E09 2.3549E08 1.8548E08 2.6043E08 7.6378E09 5 1.5823E11 2.2901E11 1.0243E09 1.7012E10 2.7695E11 1.5823E11 3.9263E11 9.1149E11 1.8214E11 5.7428E10 1.7134E11 6 9.7612E12 1.0612E11 5.5574E12 1.1585E12 2.4175E12 9.7612E12 1.4156E12 5.6079E12 1.4631E11 6.6530E13 3.5987E12 7 2.1339E14 3.7638E14 3.4574E13 1.7888E14 1.1310E14 2.1339E14 1.2935E13 1.6979E14 1.0800E14 3.7454E13 1.9100E13 8 5.3069E15 2.5153E15 4.0831E15 1.1059E15 3.2547E15 5.3069E15 8.2138E15 2.6776E15 4.4513E15 6.4644E15 1.4985E14 FIRST LENS, SECOND SURFACE, COEFFICIENT A 1 1.0270E04 3.7149E06 2.1495E04 6.2392E04 3.2586E05 1.0270E04 2.3620E04 1.9213E04 1.6091E04 6.4434E05 1.7265E04 2 1.0090E02 1.0294E02 9.1960E03 1.0328E02 9.5084E03 1.0090E02 8.9500E03 1.0780E02 1.1636E02 7.2911E03 8.5881E03 3 1.3791E07 9.0041E08 4.5044E07 1.2438E08 7.7583E08 1.3791E07 3.1346E07 2.5240E07 2.1499E07 7.6177E08 2.5968E07 4 2.4290E07 2.6768E07 2.3464E07 6.4196E07 2.8997E07 2.4290E07 3.3121E08 5.6945E07 8.4699E07 9.1664E08 6.9730E08 5 1.3903E10 1.5218E10 4.9865E10 1.2395E10 2.7673E11 1.3903E10 2.4997E10 6.1631E12 6.7737E11 1.7781E10 2.3964E10 6 1.1870E10 1.8417E10 3.2065E10 2.0347E10 1.2701E10 1.1870E10 1.8860E10 1.3566E10 4.3721E10 1.3960E10 1.4750E10 7 4.4228E14 9.9147E14 2.2886E13 1.2942E13 5.1983E14 4.4228E14 6.6780E14 5.2075E14 1.8914E13 8.1642E14 7.3920E14 8 1.0020E13 1.0931E13 1.5338E13 5.8122E14 8.4511E14 1.0020E13 1.5219E13 1.9866E14 9.1310E14 1.0869E13 1.4186E13 9 1.5630E18 2.2472E17 3.2875E17 5.8534E17 7.6411E18 1.5630E18 4.2787E18 5.2431E18 6.0560E17 9.9610E18 9.3087E19 10 2.6421E17 5.5359E18 1.6016E17 1.4550E17 8.8329E18 2.6421E17 9.9882E18 2.9011E17 2.9906E17 1.9785E18 2.1704E17 FIRST LENS, SECOND SURFACE, COEFFICIENT B 0 1.0980E02 8.9515E03 1.0327E02 1.1091E02 1.2434E02 1.0980E02 1.3437E02 7.4169E03 4.5576E03 1.3491E02 1.4409E02 1 1.0534E04 2.3524E04 2.0774E03 2.9767E04 1.5540E04 1.0534E04 4.5137E04 1.3715E04 1.1611E04 2.0315E03 3.4818E04 2 8.1503E06 8.9676E06 2.6115E05 4.5409E06 2.8662E06 8.1503E06 2.2925E07 6.3842E06 5.6176E06 2.1125E05 6.2962E06 3 6.5383E08 5.9152E08 6.6835E07 1.3314E07 5.6243E08 6.5383E08 1.6834E07 4.2687E08 7.7719E09 7.0468E07 6.1551E08 4 1.1430E09 4.1741E10 1.1988E09 4.0320E09 4.7169E09 1.1430E09 1.2696E09 4.6892E09 4.0416E09 7.0188E09 5.1275E09 5 3.2689E11 2.5194E11 2.7756E10 1.0541E10 3.0977E11 3.2689E11 7.3034E11 4.4219E11 1.5454E11 1.3870E10 1.1087E11 6 6.9023E16 1.7765E12 8.7724E12 2.1895E12 2.1191E12 6.9023E16 1.9237E12 3.5858E12 4.4248E12 5.6301E12 7.3231E13 7 6.2056E16 6.3155E15 1.8486E13 3.0156E14 1.1617E14 6.2056E16 5.4986E14 1.5881E14 5.6407E15 1.9287E13 3.5929E14 8 5.8496E16 6.3504E16 8.5992E16 6.3691E16 1.2309E15 5.8496E16 6.8789E16 1.1599E15 1.4875E15 8.4471E18 3.2096E16 9 4.8346E18 1.5419E18 8.8083E17 2.4443E17 6.7510E18 4.8346E18 8.7050E18 7.8755E18 4.0015E18 7.3957E17 6.6331E18 10 6.2573E19 2.1238E19 1.5835E18 2.4573E19 4.3557E18 6.2573E19 1.9270E18 2.6104E19 1.0402E18 2.1152E18 2.3165E18 SECOND LENS, FIRST SURFACE, COEFFICIENT A 1 1.2252E04 5.0720E05 2.3272E04 5.0852E03 1.1104E03 1.2252E04 4.5541E04 2.0880E04 1.7429E04 5.5076E05 4.1735E04 2 1.2568E03 1.3388E03 9.3709E04 1.4050E03 1.2138E03 1.2568E03 8.7096E04 1.6969E03 1.8706E03 6.2086E04 8.0895E04 3 6.4626E08 2.2051E08 1.6329E07 1.2346E07 2.7246E08 6.4626E08 1.2070E07 1.7312E07 1.6721E07 6.2504E09 9.0443E08 4 2.6933E07 3.0441E07 1.5751E07 3.1412E07 2.7135E07 2.6933E07 1.2603E07 4.6136E07 4.8925E07 8.2835E08 1.0813E07 5 2.0263E11 1.0208E11 4.0853E11 5.7486E11 1.5544E11 2.0263E11 2.2165E11 3.9600E11 4.9154E11 3.6510E12 1.5832E11 6 2.6847E11 3.3689E11 1.3968E11 3.1231E11 2.6914E11 2.6847E11 9.3610E12 5.2034E11 5.8355E11 4.7927E12 6.3410E12 7 2.7894E15 1.7367E15 4.3723E15 1.1257E14 1.9393E15 2.7894E15 1.8133E15 3.9658E15 5.8177E15 1.9041E16 1.1146E15 8 1.8983E15 2.7992E15 9.0368E16 2.3644E15 1.9967E15 1.8983E15 5.1644E16 3.6633E15 5.1789E15 1.8264E16 2.2141E16 9 1.2954E19 1.0222E19 1.6363E19 6.3539E19 1.0585E19 1.2954E19 4.7675E20 1.7270E19 2.4320E19 1.9745E21 1.9218E20 10 6.1478E20 1.1160E18 2.4479E20 9.0095E20 7.4730E20 6.1478E20 1.1544E20 1.1073E19 2.3600E19 1.9234E21 7.9017E22 SECOND LENS, FIRST SURFACE, COEFFICIENT B 0 1.2005E02 1.2551E02 1.1163E02 1.2471E02 1.2050E02 1.2005E02 1.0700E02 1.4099E02 1.4558E02 1.0627E02 1.0567E02 1 3.4330E06 7.1749E06 3.1962E05 1.2464E05 5.9436E06 3.4330E06 6.3587E06 6.3794E06 4.6711E06 2.3121E05 4.8429E06 2 2.7826E07 3.7064E07 2.5684E07 2.5940E07 2.0389E07 2.7826E07 1.2996E07 4.4238E07 4.8085E07 2.2678E07 1.6381E07 3 2.2488E10 1.2564E09 5.1622E09 1.7553E09 9.0267E10 2.2488E10 5.3905E10 1.2070E09 1.5444E08 1.6295E09 4.6931E10 4 5.2367E11 5.1995E11 7.6783E12 4.7064E11 4.5120E11 5.2367E11 2.6093E11 6.6033E11 7.2859E11 8.4037E12 2.1480E11 5 2.2805E14 4.1177E14 3.3774E13 2.7946E14 6.7343E15 2.2805E14 4.3864E14 4.0818E14 1.2705E13 3.3682E14 2.4752E14 6 1.0407E14 9.2574E15 3.7464E15 2.8415E15 5.4244E15 1.0407E14 5.5246E15 8.4130E15 8.2037E15 4.4053E15 4.0918E15 7 5.8454E18 7.2279E18 1.1523E17 1.3909E17 1.3898E17 5.8454E18 2.8512E18 5.1735E18 1.3458E17 4.0877E19 1.7566E18 8 8.3698E19 5.7025E19 5.1872E19 2.8562E19 5.6903E19 8.3698E19 6.6173E19 6.0555E19 4.9957E19 5.7716E19 4.4034E19 9 4.5831E22 6.2562E22 3.2746E22 1.1693E21 1.1152E21 4.5831E22 7.3067E23 9.2862E23 2.1908E21 1.3129E23 2.0835E22 10 1.8764E23 9.3699E24 2.5403E23 2.5273E23 4.5096E23 1.8764E23 3.1675E23 6.2309E23 6.6453E23 2.5877E23 2.0037E23 THE SECOND SURFACE OF THE SECOND LENS IS FLAT IN ALL EXAMPLES AND COMPARISONS

    TABLE-US-00005 TABLE 5 DISTANCE TO NEXT SURFACE AND EFFECTIVE LENGTH OF SECOND LENS (UNIT: mm) EXAM- EXAM- EXAM- EXAM- EXAM- EXAM- EXAM- COMPAR- COMPAR- COMPAR- COMPA- PLE 1 PLE 2 PLE 3 PLE 4 PLE 5 PLE 6 PLE 7 ISON 1 ISON 2 ISON 3 RISON 4 DEFLECTOR 56.36 56.36 56.36 56.36 56.36 56.36 56.36 56.36 56.36 56.36 56.36 SURFACE L1S1 14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5 L1S2 56.19 66.87 98.78 62.03 65.02 71.14 108.82 49.91 50.60 120.07 112.21 L2S1 4 4 4 4 4 4 4 4 4 4 4 L2S2 242.149 231.466 199.556 236.307 233.324 227.200 189.520 248.427 247.739 178.265 186.128 EFFECTIVE 135.93 144.7 167.86 140.76 143.25 148.17 178.53 131.07 131.4 188.14 181.26 LENGTH L1, L2 DNOTE THE FIRST AND SECOND LENSES AND S1, S2 DENOTE THE FIRST AND SECOND SURFACES

    TABLE-US-00006 TABLE 6 COMPAR- COMPAR- COMPAR- COMPAR- COMPAR- DEGREE EXAMPLE 1a EXAMPLE 2a EXAMPLE 3a EXAMPLE 4a EXAMPLE 5a EXAMPLE 6a ISON 1a ISON 2a ISON 3a ISON 4a ISON 5a FIRST LENS, FIRST SURFACE, COEFFICIENT A 2 7.0703E03 7.0017E03 6.2933E03 7.9183E03 7.6016E03 6.2446E03 7.8374E03 7.8678E03 7.1050E03 5.4559E03 6.2871E03 4 1.3998E07 1.2375E07 2.7567E08 6.3231E07 4.0234E07 4.7887E09 5.6946E07 1.1310E05 1.9470E07 5.5783E08 2.4841E08 6 1.5329E10 2.7531E10 5.1939E10 5.7412E10 8.0881E10 6.9993E10 3.9054E11 6.0058E10 2.0047E10 5.3934E10 7.0834E10 8 7.3311E14 1.7035E13 4.6555E13 6.4399E13 2.7790E13 2.2690E13 2.7605E13 2.8864E13 1.7560E13 2.2400E13 4.3117E13 10 2.1724E17 6.7149E17 2.2543E16 2.4719E16 1.3923E16 1.3368E16 4.8814E17 8.8488E17 1.8639E16 6.7708E17 1.8462E16 FIRST LENS, FIRST SURFACE, COEFFICIENT B 0 2.7000E02 2.7000E02 2.7000E02 2.7000E02 2.7000E02 2.7000E02 2.7000E02 2.7000E02 2.7000E02 2.7000E02 2.7000E02 1 3.1544E04 7.1382E04 2.7748E04 1.4886E04 1.3640E04 1.1169E03 3.2787E04 1.5775E04 1.1670E03 2.5707E03 6.6672E04 2 1.6417E05 2.1122E05 1.2755E05 1.8311E05 1.7791E05 2.2198E07 1.6980E05 2.8963E05 2.5124E05 1.5056E05 1.2938E05 3 2.0740E07 3.3016E07 1.3246E07 1.0446E07 8.3799E08 1.7990E07 2.3307E07 1.6566E07 8.6956E08 5.3227E08 5.7119E07 4 4.3706E09 2.4880E09 1.0058E08 2.0328E08 1.7234E08 1.5101E08 7.8965E09 2.5262E08 3.9678E08 1.0312E08 5.5017E09 5 1.1317E10 1.0899E10 2.5668E10 6.6091E11 6.4106E11 2.0666E10 2.5297E10 3.0580E10 9.1927E11 2.1181E10 3.8877E10 6 1.6077E11 3.4501E11 4.0109E11 5.8621E12 7.9498E12 3.9660E11 3.9587E12 2.9516E11 6.7736E11 2.9177E11 6.9778E11 7 4.4539E13 3.2319E13 1.0794E13 2.1390E14 1.8102E14 1.6622E13 4.9572E13 1.0628E13 8.8275E13 2.4110E13 3.3624E13 8 3.9085E15 2.5076E14 1.7676E14 1.5928E15 2.8199E15 2.2303E14 1.1323E14 2.9724E14 2.6674E14 1.8580E14 3.4213E14 FIRST LENS, SECOND SURFACE, COEFFICIENT A 1 5.3293E05 1.5223E04 3.9543E04 1.9570E04 1.3363E04 3.6141E04 7.4886E05 1.3614E04 2.0513E03 1.2161E04 3.1680E04 2 1.0319E02 1.0123E02 9.1893E03 1.0989E02 1.0653E02 8.1101E03 1.1172E02 1.1184E02 1.0028E02 8.3384E03 9.1384E03 3 8.9241E08 1.1707E07 1.7512E07 9.5713E08 1.3178E07 2.3660E07 2.0038E08 1.2819E07 1.1488E07 1.7646E07 2.6298E07 4 3.0127E07 3.4072E07 3.2127E07 6.8882E07 5.4540E07 3.1973E07 5.6438E07 9.3632E07 7.0543E08 3.1940E07 3.4977E07 5 1.4092E10 5.2023E11 5.1080E11 1.1148E10 2.0441E10 1.7618E10 5.1481E12 7.2175E11 1.1081E10 2.2444E10 2.3290E10 6 8.7146E11 1.4169E10 2.4783E10 3.3582E10 3.9331E10 3.2080E10 7.7607E11 3.9198E10 9.5582E11 2.5431E10 3.2395E10 7 6.8854E14 1.5956E14 1.3059E13 4.5660E16 1.0072E13 5.0161E15 2.1762E14 1.9422E13 3.7048E13 1.0896E13 3.6734E14 8 2.5287E14 1.0785E13 2.3504E13 2.7478E13 2.1192E13 1.6792E13 6.4321E14 1.9829E14 5.1716E14 1.3366E13 2.2430E13 9 7.2146E18 1.5520E17 7.9370E17 2.7071E17 7.8128E18 3.3488E17 1.1532E17 7.0971E17 2.6409E16 1.3091E17 2.5826E17 10 4.3592E17 2.7904E18 1.8814E17 3.5056E17 1.5527E17 1.9479E18 4.1519E17 1.9218E17 1.3357E17 2.4849E17 1.2706E17 FIRST LENS, SECOND SURFACE, COEFFICIENT B 0 9.6497E03 1.0325E02 1.1391E02 1.2202E02 1.3360E02 1.4149E02 9.1361E03 6.7261E03 9.8368E03 1.4174E02 1.5018E02 1 1.9267E04 4.1711E04 1.5407E04 9.0160E05 8.1598E05 5.9724E04 1.8891E04 1.0645E04 6.8694E04 1.3703E03 3.5125E04 2 7.8860E06 8.6702E06 4.7038E06 9.1473E06 9.2153E06 2.1055E05 7.8551E06 1.3673E05 6.9734E06 1.1913E05 5.0803E06 3 9.7706E08 1.5529E07 1.0505E07 3.9600E08 3.1575E08 2.3801E07 1.1639E07 4.8299E08 1.0213E07 4.4418E07 6.1011E08 4 1.7524E09 3.8488E09 5.7011E10 2.9230E08 2.1886E09 3.3521E09 1.9107E10 5.2573E09 3.5221E09 4.8765E09 2.0708E09 5 6.3375E12 1.3274E11 7.8341E11 1.1188E11 5.8357E12 3.9870E11 1.1200E10 4.3755E11 7.1991E11 4.8127E11 1.7535E10 6 2.5226E12 6.2518E12 4.1924E12 2.5517E12 2.3761E12 4.4023E12 6.5171E13 4.1811E12 5.5173E12 6.1316E12 1.2313E11 7 7.3343E14 1.3141E13 4.4143E14 5.2314E15 6.0079E15 1.3764E13 7.6620E14 2.0753E14 1.5620E13 2.6503E13 1.0172E13 8 2.6122E15 2.4158E15 4.8586E15 2.1243E16 3.4290E16 3.6765E15 1.0372E15 3.5321E15 5.6533E15 2.3351E15 5.3014E15 9 5.5719E17 1.6798E17 1.4156E17 6.7930E18 3.3501E18 3.7587E17 8.1610E17 6.8239E17 1.0675E16 3.9763E18 4.9783E17 10 5.8774E19 2.4462E18 1.4088E18 6.9834E19 4.3519E19 2.1384E18 1.2050E18 4.1273E18 1.4000E18 1.9040E18 8.8674E19 SECOND LENS, FIRST SURFACE, COEFFICIENT A 1 9.5456E05 2.1943E04 7.1181E04 1.4059E04 5.1148E05 6.0050E04 1.8342E04 1.4759E04 3.4989E03 2.5256E04 5.6424E04 2 1.1814E03 1.0504E03 6.7169E04 1.1260E03 1.0440E03 6.4142E04 1.4207E03 1.4074E03 7.1026E04 5.2816E04 6.3927E04 3 3.5702E08 5.8543E08 9.3120E08 6.3279E08 6.1305E08 9.8447E08 1.6315E08 9.8911E08 2.8715E07 4.8938E08 9.8565E08 4 2.7041E07 2.1163E07 1.0497E07 2.5119E07 2.2643E07 8.8182E08 3.5484E07 3.1303E07 2.3815E07 6.1352E08 8.3485E08 5 1.3215E11 1.1655E11 1.5767E11 2.4140E11 2.5672E11 1.6579E11 9.3436E13 2.6165E11 2.7828E11 7.9279E12 1.6751E11 6 2.4478E11 2.0503E11 9.4096E12 2.9538E11 2.5657E11 6.4643E12 3.8938E11 2.8765E11 2.6126E11 2.4239E12 5.5957E12 7 1.9023E15 1.2379E15 1.2360E15 4.3042E15 4.5824E15 1.3128E15 7.4230E16 2.3590E15 4.0352E17 4.6492E16 1.2320E15 8 1.2258E15 1.6458E15 7.5029E16 2.8906E15 2.4281E15 4.1980E16 2.9300E15 1.9359E15 2.2885E15 2.4133E17 2.9824E16 9 7.8447E20 4.5230E20 2.0297E20 2.4544E19 2.6826E19 2.7406E20 8.9311E20 4.4274E20 4.7395E19 2.7278E21 2.1547E20 10 1.2626E20 6.7428E20 2.6358E20 1.2962E19 1.0470E19 1.1943E20 1.0589E19 6.2654E20 1.4973E19 2.7751E21 5.7531E21 SECOND LENS, FIRST SURFACE, COEFFICIENT B 0 1.1846E02 1.1165E02 1.0089E02 1.1125E02 1.0803E02 9.7416E03 1.2364E02 1.2682E02 1.1657E02 9.7085E03 9.6438E03 1 6.2456E06 8.9631E06 1.5014E06 2.9029E06 2.5473E06 6.2745E06 6.6336E06 4.2328E06 1.9812E05 1.1657E05 3.4775E06 2 3.3486E07 2.9232E07 1.1536E07 2.7762E07 2.5733E07 1.1905E07 3.7025E07 5.2896E07 4.0110E07 1.2936E07 8.5312E08 3 6.5147E10 1.0953E09 2.2150E11 5.5790E10 4.8959E10 5.1004E10 4.6442E10 1.1091E09 3.8579E09 9.1865E10 6.9569E10 4 6.1682E11 4.6556E11 1.8227E11 1.6199E11 1.5033E11 1.3903E11 6.8626E11 3.6316E11 5.8360E11 1.2512E11 1.1052E11 5 2.0425E13 5.6389E14 1.3140E14 6.0417E14 5.7907E14 3.8858E14 2.1745E13 2.0701E14 1.2332E13 5.3129E14 1.6268E14 6 9.1796E15 7.7121E15 3.1269E15 4.7728E15 4.7951E15 2.8209E15 8.7123E15 4.2422E15 1.3784E14 3.1924E15 2.7734E15 7 2.4441E17 7.0651E18 2.7327E18 2.0768E18 3.3475E18 1.9329E18 1.9732E17 2.2306E17 4.1172E17 2.8271E18 6.2746E18 8 5.4180E20 2.7267E19 2.7643E19 8.0916E19 8.6161E19 2.9382E19 6.5774E20 2.4169E18 8.1329E19 3.5280E19 3.2775E19 9 2.0002E22 2.9626E22 1.5319E22 1.3361E22 4.4744E23 2.0550E23 8.9096E22 8.9375E22 6.8796E21 9.6139E23 4.4534E22 10 5.4116E23 1.2232E23 9.6644E24 6.4261E23 5.6779E23 1.2330E23 2.8658E23 4.5315E22 4.4232E23 1.4803E23 1.3731E23

    TABLE-US-00007 TABLE 7 EXAM- EXAM- EXAM- EXAM- EXAM- EXAM- COMPAR- COMPAR- COMPAR- COMPAR- COMPAR- PLE 1a PLE 2a PLE 3a PLE 4a PLE 5a PLE 6a ISON 1a ISON 2a ISON 3a ISON 4a ISON 5a DEFLECTOR 56.36 56.36 56.36 56.36 56.36 56.36 56.36 56.36 56.36 56.36 56.36 SURFACE L1S1 14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5 L1S2 68.64 80.35 116.44 74.93 78.18 126.29 61.83 62.68 70.13 138.92 129.95 L2S1 4 4 4 4 4 4 4 4 4 4 4 L2S2 261.503 249.786 218.705 255.206 251.964 203.849 268.310 267.459 260.013 191.216 200.195 EFFECTIVE 134.7 140.1 171.6 140.1 142.7 179.0 129.4 129.8 138.3 188.8 181.5 LENGTH

    TABLE-US-00008 TABLE 8 DEGREE EXAMPLE 1b EXAMPLE 2b EXAMPLE 3b EXAMPLE 4b EXAMPLE 5b FIRST LENS, FIRST SURFACE, COEFFICIENT A 2 5.7230E03 4.7568E03 5.5770E03 4.9925E03 4.4385E03 4 1.1213E06 3.8792E07 3.0858E07 6.1012E07 3.2632E07 6 3.6955E10 1.4117E10 3.4918E10 3.5997E10 6.6447E11 8 1.2006E13 2.0478E14 6.4221E16 7.8773E15 3.9094E14 10 1.4577E17 8.5618E19 3.5734E19 3.3476E18 3.4039E18 FIRST LENS, FIRST SURFACE, COEFFICIENT B 0 2.7000E02 2.7000E02 2.7000E02 2.7000E02 2.7000E02 1 6.7389E05 1.2596E03 5.7083E05 2.3942E04 4.7516E04 2 1.3558E05 1.0027E05 1.5776E05 3.5475E05 1.2733E05 3 1.0812E07 2.9616E07 1.2844E07 1.0141E07 1.7142E07 4 1.3360E08 6.2733E10 5.4361E08 7.7861E08 3.9718E08 5 7.5221E12 1.0850E10 1.0615E10 2.7623E10 2.1380E10 6 1.9824E11 1.1985E12 7.5905E12 1.0513E11 6.0629E12 7 1.7050E15 5.1228E14 1.5117E14 4.9164E14 1.7186E13 8 5.8621E15 8.0571E16 4.0254E15 4.3625E15 6.7231E15 FIRST LENS, SECOND SURFACE, COEFFICIENT A 1 1.7792E04 7.0752E05 4.3839E05 6.5303E05 7.8164E05 2 1.0319602 8.6479E03 9.9325E03 9.2166E03 8.2643E03 3 5.0791E07 1.5164E07 4.0974E08 7.1894E08 1.1882E07 4 7.4525E07 4.6364E08 1.2797E07 3.2530E07 8.0137E09 5 2.7677E10 1.4445E10 3.1469E11 3.7476E11 9.1712E11 6 1.2641E12 1.6030E11 2.0150E10 2.5741E10 2.1885E12 7 3.7864E14 5.5746E14 2.9676E15 1.8995E15 2.8939E14 8 5.3564E14 2.4525E14 7.1139E14 7.2791E14 1.6778E14 9 1.7897E18 6.3562E18 3.8814E18 3.4267E18 1.5860E18 10 4.2874E17 1.0871E17 4.3371E18 4.7542E18 1.0998E17 FIRST LENS, SECOND SURFACE, COEFFICIENT B 0 6.6198E03 9.3733E03 1.1593E02 9.9915E03 1.2811E02 1 3.4332E05 7.4286E04 3.1277E05 1.4599E04 2.7290E04 2 7.2203E06 8.5774E08 6.8274E06 1.7141E05 6.4777E06 3 3.1161E08 4.5871E08 5.6385E08 6.1816E08 2.6184E08 4 2.6501E09 4.0945E09 1.5180E08 1.8077E08 1.5486E08 5 7.3148E12 2.6994E11 3.1564E12 1.6826E11 2.9902E11 6 3.9106E12 3.2906E13 1.2414E11 2.2308E11 3.7678E12 7 4.3386E15 2.5731E14 4.7316E14 2.5134E14 1.6184E14 8 2.4103E15 4.0979E16 5.2011E15 1.0499E14 3.1748E15 9 5.0622E18 1.0574E17 9.5083E18 5.1969E18 1.1790E17 10 6.7143E19 3.1192E19 1.2085E19 4.2798E19 2.0365E19 SECOND LENS, FIRST SURFACE, COEFFICIENT A 1 1.6742E04 8.6342E05 1.4269E04 1.4279E04 1.5846E04 2 2.0159E03 1.1718E03 1.7485E03 1.5127E03 1.0672E03 3 2.8122E07 5.8570E08 2.5092E08 3.9967E08 4.8509E08 4 4.8320E07 1.7804E07 4.3230E07 3.4999E07 1.4325E07 5 9.8581E11 1.3967E11 6.1858E12 8.6816E12 9.3935E12 6 4.3024E11 1.1966E11 4.6372E11 3.3917E11 8.2518E12 7 1.4602E14 1.4026E15 6.2229E16 7.8287E16 8.1974E16 8 1.7598E15 5.0770E16 3.1007E15 2.0583E15 2.9717E16 9 8.6826E19 4.8696E20 5.6334E21 1.3004E20 2.4186E20 10 2.4221E21 8.6343E21 9.8773E20 5.9762E20 3.9970E21 SECOND LENS, FIRST SURFACE, COEFFICIENT B 0 1.4903E02 1.2125E02 1.3181E02 1.3144E02 1.1542E02 1 1.1436E06 1.4261E05 1.6351E06 5.1589E06 4.9807E06 2 4.4295E07 2.0490E07 2.0220E07 3.0207E07 1.9230E07 3 8.3231E10 2.7955E09 2.9579E10 5.8052E10 9.0595E10 4 7.0535E11 4.4067E11 5.6113E10 5.5379E10 5.5758E11 5 7.2202E14 3.3640E13 2.0550E14 1.0110E13 1.5809E13 6 7.5491E15 7.4997E15 1.5144E13 1.4234E13 8.6425E15 7 8.1358E18 2.7727E17 1.4903E17 1.0331E18 2.3513E17 8 3.1961E19 5.9749E19 2.0426E17 1.9370E17 4.5428E19 9 1.3403E21 1.0915E21 1.6778E21 5.4242E22 1.3656E21 10 5.2911E23 2.0677E23 1.1752E21 1.1445E21 5.4759E24

    TABLE-US-00009 TABLE 9 EXAM- EXAM- EXAM- EXAM- EXAM- PLE 1b PLE 2b PLE 3b PLE 4b PLE 5b DEFLECTOR 56.36 56.36 56.36 56.36 56.36 SURFACE L1S1 14.5 14.5 14.5 14.5 14.5 L1S2 47.28 87.16 55.51 61.20 96.33 L2S1 4 4 4 4 4 L2S2 282.859 242.980 274.628 268.940 233.811 EFFECTIVE 136.2 170.0 143.6 148.8 177.8 LENGTH

    [0041] FIG. 2 to FIG. 10 are graphs of sub image plane shift (deviation in the optical axis x direction of the focal point in the sub scanning z direction according to the location in the main scanning y direction) when the scanning optical apparatus experiences a temperature change of 15 C. The image height in the horizontal direction corresponds to the coordinate in the main scanning y direction.

    [0042] As illustrated in FIG. 2, the sub image plane shift in Example 1 falls within the proper range of equal to or less than 2.6 mm in any image height. As illustrated in FIG. 3, the sub image plane shift in Comparison 1 and Comparison 2 exceeds the proper range when <1.3 and 1/2<1.2. Example 2 to Example 7 in FIG. 4 and FIG. 5 demonstrate that the sub image plane shift falls within the proper range when 1.3 and 1/21.2. The effective length in the main scanning direction of the second lens 3 is equal to or less than 180 mm (see Table 5).

    [0043] The above results show that the sub image plane shift falls within the proper range so that an increase of the spot size and the wobbling can be prevented when the following conditions are met.


    1.21/20.9Condition 1


    1.30.8Condition 2

    [0044] A comparison of Example 1 to Example 7 with Comparison 3 and Comparison 4 shows that the effective length in the main scanning direction of the second lens 3 falls within the proper range when the conditions of 0.8 and 1/20.9 are met, but the effective length in the main scanning direction of the second lens 3 exceeds 180 mm when >0.9 and 1/2>0.8 (see Table. 5).

    [0045] As described above, when the above-described Condition 1 and Condition 2 are met, it is possible to bring the sub image plane shift within the proper range to prevent an increase of the spot size and the wobbling while reducing the effective length in the main scanning direction of the second lens 3 to achieve a reduction in size.

    [0046] Example 1a to Example 6a and Comparison 1a to Comparison 5a are samples in which the conjugation length is extended to 405 mm. These samples (see Table 7 for the effective length in the main scanning direction of the second lens and FIG. 6 to FIG. 9 for the graphs) show that when the above-described Condition 1 and Condition 2 are met, it is similarly possible to bring the sub image plane shift within the proper range to prevent an increase of the spot size and the wobbling while reducing the effective length in the main scanning direction of the second lens 3 to 180 mm or less to achieve a reduction in size.

    [0047] As seen in Comparison 3a, the sub image plane shift exceeds the proper range when L>405 mm.

    [0048] That is, when the condition of L<405 mm is met, the sub image plane shift falls within the proper range, and it is thus possible to prevent an increase of the spot size and the wobbling.

    [0049] Example 1b to Example 5b are samples in which the conjugation length is 350 mm. These samples (see Table 9 for the effective length in the main scanning direction of the second lens and FIG. 10 for the graph) show that when the above-described Condition 1 and Condition 2 are met, the sub image plane shift and the effective length of the second lens 3 similarly fall within the respective proper ranges.

    [0050] As described above, when Condition 3 of 350 mmL405 mm is met in addition to the above-described Condition 1 and Condition 2, the sub image plane shift falls within the proper range, and it is thus possible to prevent an increase of the spot size and the wobbling.

    [0051] The example in FIG. 4 of JP 2012-163977A has a magnification of 1.46. When the optical system is proportionally enlarged so that the maximum image height becomes the same as that of the present examples, i.e. 164.5 mm, the conjugation length and the image plane shift due to a temperature change of 15 C. become 275 mm and 3.6 mm respectively. Thus, the image plane shift is too large.

    [0052] It is effective that the scanning optical apparatus of the embodiment, such as the above-described Example 1 to Example 7, Example 1a to Example 6a and Example 1b to Example 5b, further has the following configurations.

    [0053] As illustrated in FIG. 11, beams 10a, 10b emitted from respective light sources may be reflected on different faces of the same deflector 1 and focused on different scanning surfaces 4a, 4b by means of respective first lenses 2a, 2b and respective second lenses 3a, 3b. This simultaneous multi-face deflection can further reduce the size of a print head of the scanning optical apparatus and reduce the cost by means of commonality of components.

    [0054] As illustrated in FIG. 12, a beam 11 deflected by the deflector 1 may be reflected on one or more turn-back mirrors 5, 6 and thereafter focused on the scanning surface 4. Such turn-back mirrors provide compatibility to various arrangements of the scanning optical apparatuses according to need. Suitably applying such turn-back mirrors to the simultaneous multi-face deflection in FIG. 11 enables further reduction in size of the print head and further cost reduction by means of commonality of components as well as retaining compatibility to various arrangements.

    [0055] In the embodiment, the two lenses 2, 3 of the f lens are configured such that the first lens 2 has negative power in the sub scanning z direction while the second lens 3 has positive power in the sub scanning z direction. This configuration enables disposing the second lens 3 near the deflector and thereby reducing the size of the second lens 3. Further, the powers 1 and 2 in the sub scanning z direction of the first lens 2 and the second lens 3 and the magnification in the sub scanning z direction of the imaging optical system satisfy 1.21/20.9 (Condition 1) and 1.30.8 (Condition 2). This configuration enables reducing the sub scanning image plane shift due to temperature change and preventing an increase of the spot size and the wobbling.

    [0056] In the embodiment, the long conjugation length L ensures compatibility to various arrangements of the apparatus according to need. In an apparatus that includes two or more scanning optical systems for scanning respectively different photoreceptor drums for example, folding the beam by means of mirrors as illustrated in FIG. 12 after deflecting it by means of the deflector 1 allows various arrangements of the photoreceptor drums and a print head in which the scanning optical system is housed. Further, the size of a print head dominantly depends on the length of the second lens 3 in the main scanning y direction. To reduce the size of a print head, it is desirable that the effective length of the second lens 3 in the main scanning direction is equal to or less than 180 mm. This is achievable in the embodiment.

    [0057] When the conjugation length L satisfies 350 mmL405 mm, it is possible to satisfy all conditions of the extended conjugation length L, the effective length in the main scanning direction being 180 mm or less, and the above-described Condition 1 and Condition 2.

    [0058] Although embodiments of the present invention have been described and illustrated in detail, the disclosed embodiments are made for purposes of illustration and example only and not limitation. The scope of the present invention should be interpreted by terms of the appended claims.

    [0059] The entire disclosure of Japanese patent application No. 2016-237404, filed on Dec. 7, 2016, is incorporated herein by reference in its entirety.