Scanning optical apparatus

Abstract

In a scanning optical apparatus, an illumination optical system has a diffractive power φdM and a refractive power φnM in a main scanning direction, and a ratio φnM/φdM in the main scanning direction for a focal length fi in a range of 10-22 mm satisfies: g2(fi)≤φnM/φdM≤g1(fi), where A(z)=(1.897×10⁷)z²+6744Z+0.5255, B(z)=(2.964×10⁷)z²+5645Z+0.6494, C(z)=(3.270×10⁷)z²+3589Z+0.5250, D(z)=(5.016×10⁷)z²+4571Z+0.8139, g1(fi)=fi{D(z)−B(z)}/12−5D(z)/6+11B(z)/6, g2(fi)=fi{C(z)−D(z)}/12−5C(z)/6+11A(z)/6 g2(fi)=fi{C(z)−A(z)}/12−5C(z)/6+11A(z)/6.

Description

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application
where s′ is a distance from an image-space principal point in the main scanning direction to an image point, and fm is a focal length in the main scanning direction.

The illumination optical system has at least one rotation-symmetric diffractive surface and at least one anamorphic refractive surface, the illumination optical system having a focal length fi [mm] in the main scanning direction, which satisfies:
10≤fi≤22   (2)

A ratio mM/mS of a lateral magnification mM in the main scanning direction to a lateral magnification mS in the sub-scanning direction, of an entire optical system which includes the illumination optical system and the scan lens, satisfies:
mM/mS≥1.38   (3)

Furthermore, a holding member provided to retain a distance between the light source and the illumination optical system has a coefficient Z of linear expansion [1/K] which satisfies:
3.05×10⁻⁵≤Z≤9.50×10⁻⁵   (4)

The illumination optical system has a refractive power ϕnM in the main scanning direction and a diffractive power ϕdM in the main scanning direction, and a ratio ϕnM/ϕdM of the refractive power ϕnM to the diffractive power ϕdM in the main scanning direction satisfies:
g2(fi)≤ϕnM/ϕdM≤g1(fi)   (5)
where A(Z)=(1.897×10⁷)Z²+6744Z+0.5255, B(Z)=(2.964×10⁷)Z²+5645Z+0.6494, C(Z)=(3.270×10⁷)Z²+3589Z+0.5250, D(Z)=(5.016×10⁷)Z²+4571Z+0.8139, g1(fi)=fi{D(Z)−B(Z)}/12−5D(Z)/6+11B(Z)/6,

In other words, the holding member is made of a material which has a relatively great coefficient Z of linear expansion. In order to reduce variation in the amount of image plane shift which would result from change in temperature, it is preferable that the coefficient Z of linear expansion be made smaller if possible; that is, the following range may be preferable:
3.05×10⁻⁵≤Z≤7.40×10⁻⁵   (6)

The holding member is not necessarily composed of a single part, but may be an assembly of several parts. For example, the holding member may be a combination of parts made of metal and parts made of resin material. In this case, the resultant of coefficients of linear expansion of these parts which hold the light source and the illumination optical system to thereby retain the distance between them may be considered to be the coefficient Z.

The semiconductor laser 1 is a device configured to generate a slightly divergent laser beam (a beam of light). A light-emitting element of the semiconductor laser 1 is configured to give off and interrupt light emissions in accordance with an image formed on the target surface 9A of the photoconductor drum 9 under control of a controller (not shown).

The aperture stop 2 is a member having an opening which determines a size in the sub-scanning direction of a laser beam emitted from the semiconductor laser 1.

The diffraction lens 3 is disposed between the semiconductor laser 1 and the polygon mirror 5 and configured to convert the beam of light emitted from the semiconductor laser 1 and passed through the aperture stop 2 into a beam of light slightly converging in a main scanning direction (the direction of the beam of light sweeping laterally with respect to the direction of travel thereof in FIG. 1; the direction of deflection thereof effected by the polygon mirror 5) and focused near a specular surface 5A of the polygon mirror 5 in a sub-scanning direction (the direction perpendicular to the main scanning direction and to the drawing sheet of FIG. 1).

As shown in FIG. 2, the diffraction lens 3 in this embodiment has an incident-side surface 3A (surface at a light beam incident side on which the beam of light strikes) configured as a rotation-symmetric diffractive surface and an exit-side surface 3B (surface at a light beam exit side from which the beam of light goes out) configured as an anamorphic refractive surface. In view of the costs, it may be preferable that the diffraction lens 3 is a single lens made of plastic (resin). However, the illumination optical system consistent with the present invention is not limited to this specific configuration; for example, the illumination optical system may comprise a lens made of glass, and the number of lenses (surfaces) is also not limited to one but may be more as long as the illumination optical system is provided with at least one refractive surface and at least one diffractive surface. In order to reduce aberration such as a spherical aberration of the illumination optical system, it may be preferable that the illumination optical system be configured to have the rotation-symmetric diffractive surface provided at a lens surface closest to the light source, and to have the anamorphic refractive surface provided at a lens surface from which the beam of light exits the illumination optical system.

The diffraction lens 3 has a focal length fi [mm] in the main scanning direction, which satisfies:
10≤fi≤22   (2)

As the focal length fi is not less than 10 [mm], the lateral magnification can be moderately restricted so that the magnification will not become too great. As the focal length fi is not greater than 22 [mm], the apparatus can be designed to be compact in size, and the loss of the efficiency of use of light in the semiconductor laser 1 can be suppressed.

Also in this embodiment, a ratio mM/mS of a lateral magnification mM in the main scanning direction to a lateral magnification mS in the sub-scanning direction, of an entire optical system which includes the illumination optical system (diffraction lens 3) and the scan lens (f-theta lens 6) and other components, if any, provided between the illumination optical system and the scan lens, satisfies:
mM/mS≥1.38   (3)

As shown in Examples which will be described later, the ratio of magnification mM/mS in the main scanning direction not less than 1.38 serves to reduce the amount of image plane shift caused by the change in ambient temperature.

The diffraction lens 3 has a diffractive power ϕdM in the main scanning direction and a refractive power ϕnM in the main scanning direction, and a ratio ϕnM/ϕdM of the refractive power ϕnM to the diffractive power ϕdM of the diffraction lens 3 in the main scanning direction satisfies:
g2(fi)≤ϕnM/ϕdM≤g1(fi)   (5)
where A(Z)=(1.897×10⁷)Z²+6744Z+0.5255, B(Z)=(2.964×10⁷)Z²+5645Z+0.6494, C(Z)=(3.270×10⁷)Z²+3589Z+0.5250, D(Z)=(5.016×10⁷)Z²+4571Z+0.8139, g1(fi)=fi{D(Z)−B(Z)}/12−5D(Z)/6+11B(Z)/6,

In the present embodiment, the lateral magnification β(=1−s′/fm) in the main scanning direction of the f-theta lens 6 is in the following range:
0.2≤1−s′/fm≤0.5   (1)

As the lateral magnification β is not less than 0.2, the scanning optical apparatus 10 can be designed to be compact in size. As the lateral magnification 3 is not greater than 0.5, the jitter caused by vibrations of the specular surfaces 5A of the polygon mirror 5 can be reduced low.

Although the illustrative embodiment of the present invention has been described above, the present invention is not limited to the above-described embodiments. Various modifications and changes may be made to the specific structures and arrangement without departing from the scope of the present invention.

For example, the diffraction lens 3 in the present embodiment is configured to have its incident-side surface 3A configured as a diffractive surface and its exit-side surface 3B configured as a refractive surface, but may be configured vice versa, i.e., it may have a refractive surface provided at its incident side and a diffractive surface provided at its exit side.

The number of specular surfaces 5A of the polygon mirror 5 may be six, for example. As a deflector, a vibration mirror may be used instead of the polygon mirror 5.

EXAMPLES

Inventors named in the present application and their colleagues have investigated the influence, on the image plane shift associated with the change in ambient temperature, of adjustments made to the diffraction lens 3 (illumination optical system) by varying the ratio ϕnM/ϕdM of the refractive power ϕnM in the main scanning direction to the diffractive power ϕdM in the main scanning direction (hereinafter referred to as “main scanning direction power ratio”).

To be more specific, the amount of image plane shift is calculated, as in EXAMPLES 1-5, using an optical system in which a single lens having a diffractive surface and an anamorphic refractive surface is adopted as an illumination optical system, by varying any of (1) magnification ratio mM/mS, (2) main scanning direction power ratio ϕnM/ϕdM, and (3) focal length fi in the main scanning direction of the diffraction lens. For example, the conditions and particulars of the optical system in EXAMPLE 1 are as follows:

Example 1

Wavelength of semiconductor laser: 792.6 [nm]

Range of temperature −5 to 55 [° C.]

Rate of change in wavelength of semiconductor laser: 0.238 [nm/° C.]

Focal length fi in main scanning direction of diffraction lens: 22 [mm]

Coefficient Z of linear expansion of member provided to retain distance between semiconductor laser and diffraction lens: 3.05×10⁻⁵ [1/K]

Lateral magnification mM in main scanning direction of entire optical system: 6.69

Lateral magnification mS in sub-scanning direction of entire optical system: 4.85

Ratio of magnifications mM/mS: 1.38

Refractive power ϕnM in main scanning direction of diffraction lens: 0.021

Diffractive power ϕdM in main scanning direction of diffraction lens: 0.026

Main scanning direction power ratio ϕnM/ϕdM: 0.800

Refractive power ϕnS in sub-scanning direction of diffraction lens: 0.03267

Diffractive power ϕdS in sub-scanning direction of diffraction lens: 0.02564

Sub-scanning direction power ratio ϕnS/ϕdS: 1.27

Phase function of diffractive surface:

$\varphi =\sum _{n=1}^{10}{C}_n{r}^{2n}$ $C_1=-0.0128$

TABLE 1
Optical System in EXAMPLE 1
		RADIUS OF CURVATURE
		MAIN	SUB-
SURFACE		SCANNING	SCANNING		REFRACTIVE	OPTICAL
No.	SURFACE	DIRECTION	DIRECTION	DISTANCE	INDEX	ELEMENT
1		∞	∞	0.970	1
2		∞	∞	0.250	1.511	GLASS COVER
3		∞	∞	21.84	1
4	DIFFRACTIVE	∞	∞	2.000	1.527	DIFFRACTION
	SURFACE					LENS
5	ANAMORPHIC	−25.686	−16.124	56.78	1
	SURFACE
6		∞	∞	42.35	1
7	ANAMORPHIC	67.257	−12.543	13.00	1.527	fθ LENS
	SURFACE
8	ANAMORPHIC	152.98	−9.618	98.8	1
	SURFACE

Temperature dependence of the amounts of image plane shift in the main scanning direction and in the sub-scanning direction in Example 1 is shown in FIG. 4. FIG. 4 represents focal positions shifted in the main scanning direction and the sub-scanning direction at temperatures of −5° C. and 55° C. from the image plane position at an ambient temperature (25° C.).

From the values (amounts) of image plane shift varying according to temperature as shown in FIG. 4, values of which the absolute values are relatively large are selected for each of the amounts of image plane shift in the main scanning direction and in the sub-scanning direction, and a graph is created which shows a relationship between the main scanning direction power ratios ϕnM/ϕdM and the maximum absolute values of image plane shift. For example, in FIG. 4, the maximum of the absolute value of image plane shift in the main scanning direction is 0.3 [mm] at −5° C., while the maximum of the absolute value of image plane shift in the sub-scanning direction is 3.4 [mm] at 55° C. In the graph of FIG. 5, these values of image plane shift 0.3 [mm] (solid lines connecting black diamond marks) and 3.4 [mm] (solid lines connecting white diamond marks) are plotted at ϕnM/ϕdM=0.80.

Other values (amounts of image plane shift in the main scanning direction and in the sub-scanning direction) obtained similarly by varying the parameters of the focal lengths fi, the magnification ratios mM/mS and the main scanning direction power ratios ϕnM/ϕdM are plotted in FIG. 5 from which it is shown that the higher the magnification ratio mM/mS is, the smaller the maximum absolute value of image plane shift (of the amounts of image plane shift) shows. The same tendency is observed when the coefficient Z of linear expansion takes some different value. Therefore, for the coefficients Z of linear expansion=6.50×10⁻⁵ [1/K] and 9.50×10⁻⁵ [1/K], the values at the smallest magnification ratio mM/mS=1.38 only are selected among the simulation results and shown in FIGS. 6 and 7, respectively.

From observations of simulation results as shown in FIGS. 5-7, the range in which the amount of image plane shift in the main scanning direction is not greater than 1 [mm] and the amount of image plane shift in the sub-scanning direction is not greater than 4 [mm] is three-dimensionally shown in FIG. 8. It has been confirmed that if the amount of image plane shift in the main scanning direction is not greater than 1 [mm], then the amount of image plane shift in the sub-scanning direction is always not greater than 4 [mm].

In FIG. 8, ridge lines A(Z), B(Z), C(Z) and D(Z) are quadric curves obtained by approximation from the dots plotted for three values of the coefficient Z of linear expansion: 3.05×10⁻⁵, 6.50×10⁻⁵ and 9.50×10⁻⁵.

By making use of the ridge lines A(Z), B(Z), C(Z) and D(Z), the range of the main scanning direction power ratio ϕnM/ϕdM in which the following inequality is satisfied is depicted in FIG. 8.
g2(fi)≤ϕnM/ϕdM≤g1(fi)
where A(Z)=(1.897×10⁷)Z²+6744Z+0.5255, B(Z)=(2.964×10⁷)Z²+5645Z+0.6494, C(Z)=(3.270×10⁷)Z²+3589Z+0.5250, D(Z)=(5.016×10⁷)Z²+4571Z+0.8139, g1(fi)=fi{D(Z)−B(Z)}/12−5D(Z)/6+11B(Z)/6, g2(fi)=fi{C(Z)−D(Z)}/12−5C(Z)/6+11A(Z)/6 g2(fi)=fi{C(Z)−A(Z)}/12−5C(Z)/6+11A(Z)/6, and the focal length fi in the main scanning direction is in the range of 10≤fi≤22 [mm].

If the main scanning direction power ratio ϕnM/ϕdM falls within the range shown in FIG. 8, the amount of image plane shift with a coefficient Z of linear expansion of the holding member falling within the range of 3.05×10⁻⁵≤Z≤9.50×10⁻⁵ and a focal length fi of the illumination optical system falling within the range of 10-22 [mm] can be restricted within the range of not greater than 1 [mm] in the main scanning direction and 4 [mm] in the sub-scanning direction. Accordingly, proper temperature compensation in the scanning optical apparatus can be achieved.

Besides Example 1 described above, several other examples in which proper temperature compensation can be achieved under the above conditions will be described below.

Example 2

The scanning optical apparatus in Example 2 is configured such that the coefficient Z of linear expansion is 6.50×10⁻⁵ [1/K] and the focal length fi is 22 [mm]. The other conditions for simulation are as follows:

Wavelength of semiconductor laser: 792.6 [nm]

Range of temperature −5 to 55 [° C.]

Rate of change in wavelength of semiconductor laser: 0.238 [nm/° C.]

Focal length fi in main scanning direction of diffraction lens: 22 [mm]

Coefficient Z of linear expansion of member provided to retain distance between semiconductor laser and diffraction lens: 6.50×10⁻⁵ [1/K]

Lateral magnification mM in main scanning direction of entire optical system: 6.70

Lateral magnification mS in sub-scanning direction of entire optical system: 4.85

Ratio of magnifications mM/mS: 1.38

Refractive power ϕnM in main scanning direction of diffraction lens: 0.024

Diffractive power ϕdM in main scanning direction of diffraction lens: 0.022

Main scanning direction power ratio ϕnM/ϕdM: 1.100

Refractive power ϕnS in sub-scanning direction of diffraction lens: 0.03621

Diffractive power ϕdS in sub-scanning direction of diffraction lens: 0.02198

Sub-scanning direction power ratio ϕnS/ϕdS: 1.65

Phase function of diffractive surface:

$\varphi =\sum _{n=1}^{10}{C}_n{r}^{2n}$ $C_1=-0.0110$

TABLE 2
Optical System in EXAMPLE 2
		RADIUS OF CURVATURE
		MAIN	SUB-
SURFACE		SCANNING	SCANNING		REFRACTIVE	OPTICAL
No.	SURFACE	DIRECTION	DIRECTION	DISTANCE	INDEX	ELEMENT
1		∞	∞	0.970	1
2		∞	∞	0.250	1.511	GLASS COVER
3		∞	∞	21.73	1
4	DIFFRACTIVE	∞	∞	2.000	1.527	DIFFRACTION
	SURFACE					LENS
5	ANAMORPHIC	−21.791	−14.548	57.35	1
	SURFACE
6		∞	∞	42.35	1
7	ANAMORPHIC	67.257	−12.543	13.00	1.527	fθ LENS
	SURFACE
8	ANAMORPHIC	152.98	−9.618	98.8	1
	SURFACE

In this Example 2, the amount of image plane shift is 0.3 [mm] in the main scanning direction and 3.5 [mm] in the sub-scanning direction.

Example 3

The scanning optical apparatus in Example 3 is configured such that the coefficient Z of linear expansion is 6.50×10⁻⁵ [1/K] and the focal length fi is 10 [mm]. The other conditions for simulation are as follows:

Wavelength of semiconductor laser: 792.6 [nm]

Range of temperature −5 to 55 [° C.]

Rate of change in wavelength of semiconductor laser: 0.238 [nm/° C.]

Focal length fi in main scanning direction of diffraction lens: 10 [mm]

Coefficient Z of linear expansion of member provided to retain distance between semiconductor laser and diffraction lens: 6.50×10⁻⁵ [1/K]

Lateral magnification mM in main scanning direction of entire optical system: 15.11

Lateral magnification mS in sub-scanning direction of entire optical system: 10.95

Ratio of magnifications mM/mS: 1.38

Refractive power ϕnM in main scanning direction of diffraction lens: 0.054

Diffractive power ϕdM in main scanning direction of diffraction lens: 0.049

Main scanning direction power ratio ϕnM/ϕdM: 1.100

Refractive power ϕnS in sub-scanning direction of diffraction lens: 0.06649

Diffractive power ϕdS in sub-scanning direction of diffraction lens: 0.04929

Sub-scanning direction power ratio ϕnS/ϕdS: 1.35

Phase function of diffractive surface:

$\varphi =\sum _{n=1}^{10}{C}_n{r}^{2n}$ $C_1=-0.0246$

TABLE 3
Optical System in EXAMPLE 3
		RADIUS OF CURVATURE
		MAIN	SUB-
SURFACE		SCANNING	SCANNING		REFRACTIVE	OPTICAL
No.	SURFACE	DIRECTION	DIRECTION	DISTANCE	INDEX	ELEMENT
1		∞	∞	0.970	1
2		∞	∞	0.250	1.511	GLASS COVER
3		∞	∞	8.47	1
4	DIFFRACTIVE	∞	∞	2.000	1.527	DIFFRACTION
	SURFACE					LENS
5	ANAMORPHIC	−9.716	−7.924	56.33	1
	SURFACE
6		∞	∞	42.35	1
7	ANAMORPHIC	67.257	−12.543	13.00	1.527	fθ LENS
	SURFACE
8	ANAMORPHIC	152.98	−9.618	98.8	1
	SURFACE

In this Example 3, the amount of image plane shift is 0.7 [mm] in the main scanning direction and 3.7 [mm] in the sub-scanning direction.

Example 4

The scanning optical apparatus in Example 4 is configured such that the coefficient Z of linear expansion is 9.50×10⁻⁵ [1/K] and the focal length fi is 22 [mm]. The other conditions for simulation are as follows:

Wavelength of semiconductor laser: 792.6 [nm]

Range of temperature −5 to 55 [° C.]

Rate of change in wavelength of semiconductor laser: 0.238 [nm/° C.]

Focal length fi in main scanning direction of diffraction lens: 22 [Mm]

Coefficient Z of linear expansion of member provided to retain distance between semiconductor laser and diffraction lens: 9.50×10⁻⁵ [1/K]

Lateral magnification mM in main scanning direction of entire optical system: 6.71

Lateral magnification mS in sub-scanning direction of entire optical system: 4.86

Ratio of magnifications mM/mS: 1.38

Refractive power ϕnM in main scanning direction of diffraction lens: 0.028

Diffractive power ϕdM in main scanning direction of diffraction lens: 0.018

Main scanning direction power ratio ϕnM/ϕdM: 1.500

Refractive power ϕnS in sub-scanning direction of diffraction lens: 0.03958

Diffractive power ϕdS in sub-scanning direction of diffraction lens: 0.01845

Sub-scanning direction power ratio (ϕnS/ϕdS: 2.15

Phase function of diffractive surface:

TABLE 4
Optical System in EXAMPLE 4
		RADIUS OF CURVATURE
		MAIN	SUB-
SURFACE		SCANNING	SCANNING		REFRACTIVE	OPTICAL
No.	SURFACE	DIRECTION	DIRECTION	DISTANCE	INDEX	ELEMENT
1		∞	∞	0.970	1
2		∞	∞	0.250	1.511	GLASS COVER
3		∞	∞	21.63	1
4	DIFFRACTIVE	∞	∞	2.000	1.527	DIFFRACTION
	SURFACE					LENS
5	ANAMORPHIC	−19.035	−13.312	57.99	1
	SURFACE
6		∞	∞	42.35	1
7	ANAMORPHIC	67.257	−12.543	13.00	1.527	fθ LENS
	SURFACE
8	ANAMORPHIC	152.98	−9.618	98.8	1
	SURFACE

$\varphi =\sum _{n=1}^{10}{C}_n{r}^{2n}$ $C_1=-0.0092$

In this Example 4, the amount of image plane shift is 0.5 [mm] in the main scanning direction and 3.6 [mm] in the sub-scanning direction.

Example 5

The scanning optical apparatus in Example 5 is configured such that the coefficient Z of linear expansion is 7.40×10⁻⁵ [1/K] and the focal length fi is 22 [mm]. The other conditions for simulation are as follows:

Wavelength of semiconductor laser: 792.6 [nm]

Range of temperature −5 to 55 [° C.]

Rate of change in wavelength of semiconductor laser: 0.238 [nm/° C.]

Focal length fi in main scanning direction of diffraction lens: 22 [nm]

Coefficient Z of linear expansion of member provided to retain distance between semiconductor laser and diffraction lens: 7.40×10⁻⁵ [1/K]

Lateral magnification mM in main scanning direction of entire optical system: 6.70

Lateral magnification mS in sub-scanning direction of entire optical system: 4.85

Ratio of magnifications mM/mS: 1.38

Refractive power ϕnM in main scanning direction of diffraction lens: 0.025

Diffractive power ϕdM in main scanning direction of diffraction lens: 0.021

Main scanning direction power ratio ϕnM/ϕdM: 1.200

Refractive power ϕnS in sub-scanning direction of diffraction lens: 0.03717

Diffractive power ϕdS in sub-scanning direction of diffraction lens: 0.02098

Sub-scanning direction power ratio ϕnS/ϕdS: 1.77

Phase function of diffractive surface:

$\varphi =\sum _{n=1}^{10}{C}_n{r}^{2n}$ $C_1=-0.0105$

TABLE 5
Optical System in EXAMPLE 5
		RADIUS OF CURVATURE
		MAIN	SUB-
SURFACE		SCANNING	SCANNING		REFRACTIVE	OPTICAL
No.	SURFACE	DIRECTION	DIRECTION	DISTANCE	INDEX	ELEMENT
1		∞	∞	0.970	1
2		∞	∞	0.250	1.511	GLASS COVER
3		∞	∞	21.70	1
4	DIFFRACTIVE	∞	∞	2.000	1.527	DIFFRACTION
	SURFACE					LENS
5	ANAMORPHIC	−20.928	−14.173	57.53	1
	SURFACE
6		∞	∞	42.35	1
7	ANAMORPHIC	67.257	−12.543	13.00	1.527	fθ LENS
	SURFACE
8	ANAMORPHIC	152.98	−9.618	98.8	1
	SURFACE

In this Example 5, the amount of image plane shift is 0.4 [mm] in the main scanning direction and 3.5 [mm] in the sub-scanning direction.

Example 6

The scanning optical apparatus in Example 6 is assumed to include a two-lens illumination optical system configuration with a collimating lens having a rotation-symmetric diffractive surface and a cylinder lens having an anamorphic refractive surface, wherein the coefficient Z of linear expansion is 6.50×10⁻⁵ [1/K] and the focal length fi is 22 [mm]. The other conditions for simulation are as follows:

Wavelength of semiconductor laser: 792.6 [nm]

Range of temperature −5 to 55 [° C.]

Rate of change in wavelength of semiconductor laser: 0.238 [nm/° C.]

Focal length fi in main scanning direction of diffraction lens: 22 [nm]

Coefficient Z of linear expansion of member provided to retain distance between semiconductor laser and diffraction lens: 6.50×10⁻⁵ [1/K]

Lateral magnification mM in main scanning direction of entire optical system: 6.63

Lateral magnification mS in sub-scanning direction of entire optical system: 4.81

Ratio of magnifications mM/mS: 1.38

Refractive power ϕnM in main scanning direction of diffraction lens: 0.024

Diffractive power ϕdM in main scanning direction of diffraction lens: 0.022

Main scanning direction power ratio ϕnM/ϕdM: 1.100

Refractive power ϕnS in sub-scanning direction of diffraction lens: 0.03791

Diffractive power ϕdS in sub-scanning direction of diffraction lens: 0.02198

Sub-scanning direction power ratio ϕnS/ϕdS: 1.72

Phase function of diffractive surface:

$\varphi =\sum _{n=1}^{10}{C}_n{r}^{2n}$ $C_1=-0.0110$

TABLE 6
Optical System in EXAMPLE 6
		RADIUS OF CURVATURE
		MAIN	SUB-
SURFACE		SCANNING	SCANNING		REFRACTIVE	OPTICAL
No.	SURFACE	DIRECTION	DIRECTION	DISTANCE	INDEX	ELEMENT
1		∞	∞	0.970	1
2		∞	∞	0.250	1.511	GLASS COVER
3		∞	∞	21.74	1
4	DIFFRACTIVE	∞	∞	2.000	1.527	COLLIMATING
	SURFACE					LENS
5		−21.791	−21.791	1.000	1
6	CYLINDRICAL	∞	38.372	2.000	1.527	CYLINDER
	SURFACE					LENS
7		∞	∞	53.26	1
8		∞	∞	42.35	1
9	ANAMORPHIC	67.257	−12.543	13.00	1.527	fθ LENS
	SURFACE
10	ANAMORPHIC	152.98	−9.618	98.8	1
	SURFACE

In this Example 6, the amount of image plane shift is 0.3 [mm] in the main scanning direction and 3.1 [mm] in the sub-scanning direction.

Claims

1. A scanning optical apparatus comprising:

a light source;

a deflector configured to deflect a beam of light from the light source in a main scanning direction;

an illumination optical system disposed between the light source and the deflector and configured to convert the beam of light emitted from the light source into a beam of light slightly converging in the main scanning direction and focused near the deflector in a sub-scanning direction; and

a holding member provided to retain a distance between the light source and the illumination optical system; and

a scan lens configured to cause the beam of light deflected by the deflector to be focused into a dot-like image on a target surface to be scanned,

wherein the scan lens satisfies:

0.2≤1−s′/fm≤0.5

2. The scanning optical apparatus according to claim 1, wherein the illumination optical system is configured to have comprises at least one lens having a first lens surface closest to the light source and a second lens surface from which the beam of light exits the illumination optical system, the rotation-symmetric diffractive surface being provided at a the first lens surface closest to the light source, and to have the anamorphic refractive surface being provided at a the second lens surface from which the beam of light exits the illumination optical system.

3. The scanning optical apparatus according to claim 1, wherein the coefficient z of linear expansion is in the following range:

3.05×10⁻⁵≤Z≤7.40×10⁻⁵.

4. The scanning optical apparatus according to claim 1, wherein the illumination optical system is a single plastic lens.

5. The scanning optical apparatus according to claim 1, wherein with a change in temperature of ±30° C. from a reference temperature of 25° C., an amount of image plane shift in the main scanning direction is not greater than 1 [mm] and an amount of image plane shift in the sub-scanning direction is not greater than 4 [mm].