JP2012163810A - Method for designing optical element and optical element designed by using the method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for designing an optical element, the method capable of easily providing, by an analytical calculation, an optimal change in the tilt of a marginal line of an optical element in an imaging optical system used in a scanning optical system and having fθ characteristics.SOLUTION: In a method for designing an optical element used in a scanning optical system, the optical element has an optical surface on which the angle defined by a light beam passing through the optical surface and the normal line to a marginal line surface varies on the marginal line cross-section of the optical surface according to the position in the main scanning direction independently of the curvature in the marginal line direction. The method comprises: a calculation process for calculating wavefront aberration sensitivity of the optical surface for every optical surface at a plurality of positions in the main scanning direction; an equation formulating process for formulating an equation at a plurality of positions in the main scanning direction to correct remaining irradiation displacement in the sub-scanning direction; a corrective equation formulating process for formulating an equation at a plurality of positions in the main scanning direction to correct remaining wavefront aberration; and a tilt angle calculating process for calculating change in tilt angle for correcting wavefront aberration from the equation formulated in the corrective equation formulating process.

Description

  The present invention relates to an optical element (fθ lens) constituting an imaging optical system used in a scanning optical system of an image forming apparatus such as a laser beam printer having an electrophotographic process, a digital copying machine, or a multifunction printer (multifunction printer). The present invention relates to a (scanning lens) design method. In particular, the present invention relates to a method for designing an optical element of a scanning optical system.

  Conventionally, in a scanning optical system used in an image forming apparatus such as a laser beam printer or a digital copying machine, a light beam emitted from a light source is deflected and scanned by a deflecting means such as a polygon mirror. Then, the image is scanned on the surface to be scanned through an imaging optical system including one or a plurality of fθ lenses.

  In many cases, an optical element used in an imaging optical system is manufactured from a resin by injection molding. By forming the lens surface of the optical element with a complex surface shape by injection molding, various aberrations that occur when an image is formed on the surface to be scanned are corrected well, and high imaging performance is obtained. As an image forming apparatus, in a tandem type image forming apparatus that forms a latent image corresponding to a plurality of colors on independent image carriers, a single optical element is shared by scanning light beams directed toward a plurality of image carriers, and the entire system is used. The size is reduced.

  Many of the tandem type image forming apparatuses employ a so-called oblique incidence optical system in which light beams from respective light sources directed to a plurality of image carriers are incident on the deflecting unit at an angle in the sub-scanning direction. Thereby, in the optical element, the light beam passing through the position off the optical axis is imaged on the image bearing pair. In addition, a scanning optical system called an overfield scanning optical system (OFS) that scans by entering a light beam having a main scanning width wider than the deflection surface of the deflecting unit is used. In this OFS, it is necessary to cause the light beam to enter the deflecting means from an angle close to the front of the angle of view to be deflected and scanned. In order to separate incident and outgoing light, the light beam incident on the optical element has an angle in the sub scanning direction. Is incident.

  In OFS, a polygon polygon mirror having eight or more deflection surfaces is often used, and the polygon polygon mirror has a narrow angle of view that can be deflected and scanned, but can perform a number of scans in one rotation. For this reason, it is mainly used for high-speed copying machines.

  In addition, the image forming apparatus uses a so-called double-pass scanning optical system in which the light beam deflected by the polygon mirror passes through the optical element, is folded back by the mirror, passes again through the same optical element, and travels toward the surface to be scanned. Yes. This double-pass scanning optical system can be used in a compact and higher-performance scanning optical system because the optical path can be shortened and the number of optical elements can be reduced by passing one optical element twice. The scanning optical system introduced above has various merits, but the scanning light beam passes through a position deviated from the optical axis of the optical element. Therefore, compared with the conventional imaging optical system that passes on the bus of the optical element. It is known that the design of optical elements is more difficult.

  In particular, there are problems such as “scanning curve” in which the scanning trajectory in the main scanning direction on the image carrier is not a straight line, and “spot rotation” that affects the size of the imaging spot of the scanning light beam. If the scanning line curve remains, not only the printed straight line in the main scanning direction is curved, but also causes a registration error in the color image forming apparatus. Further, spot rotation leads to degradation of resolution and a significant decrease in effective depth because the spot diameter becomes larger than the diffraction limit due to aberration. The above two problems are caused by the fact that the scanning light flux passes through a position off the optical axis of the optical element, so that the lens surface inclination angle at the optical element passage position of the light flux varies depending on the scanning field angle.

  Many recent scanning optical systems use an optical element in which the number of optical elements is reduced in order to reduce the size, or the curvature in the sub-line direction is changed in the main scanning direction in order to obtain high optical performance. For this reason, it is very difficult to suppress scanning line curvature and spot rotation while maintaining field curvature and magnification uniformity in the sub-scanning direction. In order to solve this problem, the angle formed between the ray passing through the lens surface and the normal of the ray surface within the ray cross section of the optical surface of the optical element is independent of the curvature of the ray surface and in the main scanning direction. There has been proposed a technique for designing to change in accordance with the position (subordinate tilt change) (Patent Document 1).

JP 2002-214559 A

  Patent Document 1 does not disclose a method for searching for an optimum tilt change of a child line. When designing the tilt change of the slave line, the actual situation is that optimization is performed on the workstation so that the scan coefficient and the wavefront aberration can be corrected using the change coefficient as a variable. In general, the starting point is important when optimizing the imaging optical system. If the starting point is far from the best solution, there is a problem that even if optimization is performed, it converges to the local minimum and does not reach the best solution.

  The present invention provides an optical element design method capable of easily obtaining the optimum change in the tilt of a child line of an optical element constituting an imaging optical system having an fθ characteristic used in a scanning optical system by analytical calculation. With the goal.

An optical element design method of the present invention is an optical element design method used in an imaging optical system that forms an image on a surface to be scanned with a light beam deflected and scanned by a deflection means.
In the optical element, the angle between the ray passing through the optical surface and the normal of the child surface changes within the sub-line cross section of the optical surface according to the position in the main scanning direction independently of the curvature of the child wire. An optical surface to
Within the sub-line cross section of the optical surface, the ratio of the incident beam deviation per unit inclination angle of the sub-line surface normal at any point on the optical axis to the irradiation position deviation in the sub-scanning direction is sensitive to the irradiation position deviation. Degree and
When the ratio of the amount of change in wavefront aberration per rate of change in which the tilt angle changes according to the position in the main scanning direction is defined as wavefront aberration sensitivity, the wavefront aberration sensitivity is set for each optical surface and in the main scanning direction. A calculation step of calculating at a plurality of positions;
An equation creating step for formulating equations at a plurality of positions in the main scanning direction so that the sum of products of the irradiation position deviation sensitivity and the inclination angle in each optical surface corrects the remaining irradiation position deviation in the sub-scanning direction;
A correction equation creating step for creating an equation at a plurality of positions in the main scanning direction so that the sum of products of wavefront aberration sensitivity and inclination angle change rate on each optical surface corrects the remaining wavefront aberration, and the correction equation creating step An inclination angle calculating step for obtaining a change in inclination angle for correcting wavefront aberration from the equation established in
It is characterized by having.

  According to the present invention, an optical element design method capable of easily obtaining the optimum change in the tilt of a child line of an optical element constituting an imaging optical system having an fθ characteristic used in a scanning optical system by analytical calculation Is obtained.

4 is a flowchart of a method for designing an optical element according to the present invention. It is explanatory drawing which showed a mode that the spot rotation has occurred It is explanatory drawing which shows the wavefront aberration when spot rotation has occurred FIG. 3 is an explanatory diagram of a main part of the scanning optical system of Example 1. FIG. 6 is an explanatory diagram for explaining a light ray passage region in the fθ lens of the scanning optical system of Example 1. It is explanatory drawing which shows the initial scanning line curve and 45 degree asphalt in the flowchart of Example 1. FIG. It is explanatory drawing which shows the scanning line curve and the 45-degree ass transition in the flowchart of Example 1. It is explanatory drawing which shows the scanning line curve and the 45-degree ass transition in the flowchart of Example 1. It is explanatory drawing which shows the scanning line curve and the 45-degree ass transition in the flowchart of Example 1. FIG. 6 is an explanatory diagram showing spots after design completion in the scanning optical system of Example 1. 2 is an explanatory diagram illustrating an image forming apparatus equipped with the scanning optical system of Example 1. FIG.

  Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. The optical element design method of the present invention is an optical element design method used in an imaging optical system that forms an image on a surface to be scanned with a light beam deflected and scanned by a deflecting unit in an optical scanning device. The optical element is an optical element in which the angle formed between the ray passing through the optical surface and the normal of the child surface in the subsection of the optical surface changes according to the position Y in the main scanning direction or independently of the curvature of the child wire. Has a surface. In the cross section of the optical surface, the inclination angle of the normal of the child plane at an arbitrary point on the optical axis is φ, and the ratio dPo / of the incident light flux per unit inclination angle φo to the irradiation position deviation Po in the sub-scanning direction. Let φφo be the irradiation position deviation sensitivity A.

  When the wavefront aberration sensitivity B is the ratio of the change amount of the wavefront aberration per rate of change dφ / dY (unit tilt) at which the inclination angle φ changes according to the position Y in the main scanning direction, the wavefront aberration sensitivity B is And a calculation step for calculating at a plurality of positions Y in the main scanning direction for each optical surface. The wavefront aberration at the time of calculating the wavefront aberration sensitivity in the calculation step and obtaining the correction coefficient is ass in the 45 ° direction. A plurality of positions in the main scanning direction so that the sum (Pz, Equation 3.1) of the product of the irradiation position deviation sensitivity A and the inclination angle φ on each optical surface corrects the remaining irradiation position deviation P in the sub-scanning direction. And an equation creation step for establishing an equation.

  The sum of the products of the wavefront aberration sensitivity B and the change rate dφ / dY of the tilt angle φ on each optical surface (conditional expression 3.2) at a plurality of positions Y in the main scanning direction so as to correct the remaining wavefront aberration. A correction equation creating step for establishing an equation. An inclination angle calculating step for obtaining a change in the inclination angle φ for correcting the wavefront aberration from the equation established in the correction equation creating step. There is an optimization step for introducing the change in the inclination angle φ of the child surface normal obtained in the inclination angle calculation step into the optical surface shape and optimizing the outer shape of the optical surface of the optical element including other aberrations.

[Example 1]
Hereinafter, a method for designing an optical element according to Example 1 of the present invention will be described with reference to the drawings and equations. As an optical element, an fθ lens used in an imaging optical system of a scanning optical system is targeted. FIG. 1 is a flowchart of an optical element designing method in Embodiment 1 of the present invention. Here, the tilt φ as the tilt angle of the lens surface is X in the optical axis direction, Y in the main scanning direction, and Z in the sub scanning direction. If the initial tilt is M ₀ , and the coefficient when changing according to the value of the nth power of the position Y in the main scanning direction on the optical surface is Mn, the tilt φ is expressed by the following formula 1.1. .

  Further, the tilt change rate dφ / dY can be expressed as the following equations 1.1 and 1.2 as a first-order derivative with respect to the position Y of the tilt φ.

In this embodiment, the expression of tilt φ is a polynomial of Y, and the coefficient M is defined as an even value starting from 0. However, the change of the tilt φ in this embodiment can also be defined by other expressions.
In addition, the scanning line curvature in this embodiment is a difference between the irradiation position in the sub-scanning direction at each off-axis evaluation image height and the irradiation position at the on-axis image height. The wavefront aberration is a wavefront aberration amount difference (hereinafter referred to as 45 ° ass) in the azimuth 45 degree direction as an index for quantifying the spot rotation. Here, the wavefront aberration amount difference in the azimuth 45 degree direction will be described. Spot rotation occurs when the balance of azimuth ± 45 ° wavefront aberrations is lost.

  FIGS. 2A and 2B show spot shapes in the case where spot rotation occurs in the imaging spot of the scanning light beam. When the imaging spot is in a state as shown in FIG. 2B, the spot diameter is enlarged in both the main scanning direction and the sub-scanning direction, and the effective depth is remarkably reduced.

  FIGS. 3A and 3B illustrate wavefront aberrations on the pupil of an fθ lens normalized to a unit circle in a state where spot rotation occurs as shown in FIG. 2B. As shown in FIG. 3 (a), the wavefront is a “twisted” wavefront aberration that appears as if diagonally tilted with respect to the scanning direction. In order to quantify this aberration, the main scanning direction is azimuth 0 degrees. Suppose that the azimuth is 90 degrees in the sub-scanning direction, and azimuth in the direction of ± 45 degrees in the middle is considered.

  FIG. 3B is a cross-sectional view of the azimuth 45-degree direction and the −45-degree direction of FIG. As shown in FIG. 3B, the wavefront aberrations of the two marginal rays in the azimuth are Wa (u) and Wa (l), respectively, and the halo component of the wavefront aberration is Wa (u) -Wa (l). To do. Each halo component of wavefront aberration in ± 45 degrees azimuth

, Azimuth 45 degree wavefront aberration amount difference:

And will be referred to as 45 ° ass.

  In the present embodiment, the 45 ° ass are defined as described above, but other expression formulas representing so-called wavefront twists can also be defined. It can be said that spot rotation has not occurred if the 45 ° asphalt is zero. First, in step 1 of FIG. 1, a slight angle tilt is given to the lens surface for setting the tilt change, the irradiation position change in the sub-scanning direction at a plurality of evaluation image heights is calculated, and the irradiation position change per unit tilt, for example, An irradiation position shift sensitivity A per minute of tilt is obtained.

  Similarly, a minute tilt change is given, and the difference in wavefront aberration, for example, 45 ° ass sensitivity (wavefront aberration sensitivity B) when the tilt (tilt angle) φ changes by 1 minute is obtained. Step 1 is a calculation step for calculating the irradiation position deviation sensitivity A and the wavefront aberration sensitivity B. Step 2 is an equation creation process for establishing an equation (correcting irradiation position and wavefront aberration) to correct the scanning line curvature and 45 ° ass (45 ° ass) from the sensitivities A and B obtained in Step 1. is there.

The equation creation process established in step 2 is as follows. First, with respect to a light beam directed to an image height as shown in equation 3.1, the tilt (tilt angle) φ at the passing position of the surface where the tilt change is set and the irradiation position deviation sensitivity in the sub-scanning direction The product of degree A is summed up at each lens surface. The sum of these is an expression that achieves a desired value Pz at a plurality of image heights for correcting the existing sub-scanning irradiation position deviation. Further, the product of the tilt change at the passing position of the lens surface where the tilt change is set as shown in Equation 3.2 and 45 ° ass sensitivity (wavefront aberration sensitivity) B is summed for each lens surface. This summation is the correction equation creation step that makes the desired value P _45AS (formula 3.4) to correct the existing 45 ° ass (45 ° direction ass).

  The wavefront aberration sensitivity B is calculated and corrected. Therefore, for each evaluation image height, the following two equations are obtained for the scanning line curvature and 45 ° assemble.

  In step 3, the above-described two types of tilt (tilt angle) φ are expanded as shown in equations 3.3 and 3.4 according to equation 1, and a coefficient of tilt change M for correcting these scanning line curvature and 45 ° astigmatism is obtained. It is to obtain as a variable. Step 3 is a tilt angle calculation step for obtaining a change in the tilt angle φ.

  In this simultaneous linear equation, there are two equations for one image height, and there are n variables M per surface in the k tilt change surfaces, so that there are a total of k × n. Since the tilt change coefficient M of the lens surface does not change depending on the image height, in order to determine the variable M of this equation, it is only necessary to increase the image height to be evaluated and increase the number of equations. Furthermore, by combining the number of equations and the number of tilt change coefficients, it is possible to uniquely determine the coefficient M of each tilt change, and by setting the equation more than the number of coefficients, a constraint condition is imposed on the obtained solution. May be added.

  In step 4, the tilt change coefficient M obtained in step 3 is actually substituted (introduced into the surface shape) to simulate the imaging optical system, and the field curvature and other performance due to the change in tilt φ ( This is an optimization process for taking other aberrations. This is because, unless the tilt change surface is the final surface of the final lens in the scanning optical system, the light passing position on the subsequent lens surface changes due to the tilt change. This is because of changes. Here, when the target performance is sufficiently reached when the aspheric coefficient obtained in step 3 is applied, such as when the amount of tilt change corrected in step 3 is small, the step 4 may be omitted. You may proceed to the performance check process in step 5.

  A specific example of the optical element design method described above will be described. 4A and 4B are diagrams illustrating a scanning optical apparatus including an optical element (fθ lens) designed using the design method of the present embodiment. 4A is a main scanning sectional view, and FIG. 4B is a sub-scanning sectional view. A light beam emitted from the light source device 101 using a semiconductor laser is converted into a substantially parallel light beam by the collimator lens 102 and converted into light focused in the sub-scanning direction by the cylinder lens 103 having power only in the sub-scanning direction.

  The light beam that has passed through the cylinder lens 103 forms a long focal line in the main scanning direction on the deflecting surface of the optical deflector 104, and is then deflected and scanned toward the optical element (scanning lens) 105 constituting the imaging optical system. . Hereinafter, the optical element 105 is also referred to as a scanning lens. The light beam that has once passed through the scanning lens 105 is returned to the optical path by the folding mirror 106, passes through the scanning lens 105 again, and forms a scanning image on the photosensitive drum 107 that is the surface to be scanned. The focal line formed on the deflecting surface of the optical deflector 104 and the image on the scanned surface 107 have a conjugate relationship in the sub-scanning direction, and form a so-called surface deflection correcting optical system for the optical deflector. .

  In the scanning lens 105, the surface 105b on the folding mirror 106 side has no power in the sub-scanning direction, and is formed as a continuous surface over the entire optical surface. Further, the surface on the optical deflector 104 side is a composite multi-step surface in which the lower step surface 105a has a minus power in the sub-scan section and the upper step surface 105c has a plus power. In order to correct the scanning line curvature and wavefront aberration while maintaining the field curvature and magnification uniformity in the sub-scanning direction on the surfaces 105a and 105c, the curvature changes in the main scanning direction and the tilt changes around the generatrix. It is composed of the surface to be.

  On the surface of the scanning lens 105, the scanning trajectory of the scanning light incident on the scanning lens 105 from the optical deflector 104 and the scanning light emitted from the lens 105 toward the scanned surface 107 is as shown in FIG. A light beam incident from the optical deflector 104 passes through the lower surface 105a, and a light beam that passes through the scanning lens 105 for the second time passes through the upper surface 105c.

  As in this embodiment, by passing the light beam twice through one scanning lens, it becomes a compact optical system, and various aberrations are corrected by using more optical surfaces than a single scanning lens system. Can do. Tables 1 and 2 show the optical arrangement of the present example and numerical examples of the lens. The generatrix shape of each optical surface of the scanning lens 105 is constituted by an aspheric shape that can be expressed as a function up to the 16th order. When the intersection of the scanning lens 105 and the optical axis is the origin, the optical axis direction is the X axis, and the axis perpendicular to the optical axis in the main scanning section is the Y axis, the generatrix direction corresponding to the main scanning direction is

It is expressed by the following formula.
Also, a child line at a position Y away from the optical axis in the main scanning direction is

It is expressed by the following formula.
(However, D, E, and M are sub-wire change coefficients and sub-surface aspheric coefficients)
In the present embodiment, an infrared light source that emits a light beam having a wavelength λ = 790 nm is used as the light source means 101, and both the field curvature in the main scanning direction and the sub-scanning direction are corrected well over the entire effective scanning area. In the present embodiment, the surface shape of the scanning lens 105 is defined by the above formula that can set the tilt change according to the Y position on the lens, but the aspherical surface in the present embodiment can also be defined by another expression. is there. Further, the angle formed between the ray passing through the optical surface and the normal of the child surface in the sub-line cross section of the optical surface may change independently of the curvature of the child wire and according to the position in the main scanning direction.

  In the scanning lens 105 of this embodiment, the light beam passes through a position away from the optical axis on the upper optical surface 105C. The R1 surface (105a) and R4 surface (105c) of the scanning lens 105 have negative and positive refracting powers in the sub-scan section in order to reduce the sub-scan magnification of the imaging optical system. Since the effective portion cannot be formed, each surface is formed by another mirror piece.

  For this reason, there is a discontinuous portion at the joint between the R1 surface (105a) and the R4 surface (105c), and it is necessary to jump up the light beam passage position on the R4 surface so that no light rays are applied to the joint portion. there were. Further, it is necessary to radiate light emitted from the R4 surface upward so that the light beam emitted from the scanning lens 105 and directed to the surface to be scanned 101 does not interfere with the polygon mirror 104 or its axis.

  However, if the light beam emitted from the R4 surface goes too far, the position of the scanned surface 107 and the relative position limit of the imaging optical system are exceeded, so the R4 surface passing position is raised as much as possible, and the light beam is emitted from there. The surface is refracted downward. In this imaging optical system, the light beam passes through a position away from the optical axis of the surface on the R4 surface of the scanning lens 105, and a change in the child line tilt is introduced together with the R1 surface of the scanning lens. Table 1 shows the surface arrangement and aspherical coefficients before the application of the design method in the present embodiment, and FIG. 6 shows the scanning line curve and 45 ° distribution at the initial stage of design.

Next, the specific contents of each step will be described along the flow of FIG.
・ Step 1 Sensitivity calculation:
Table 2 shows the irradiation position deviation sensitivity A per unit tilt calculated in accordance with Step 1 of the flowchart, that is, the irradiation position deviation sensitivity A per 1 minute of the tilt angle, and 45 ° when the tilt φ changes per minute by 1 minute. Indicates asthma sensitivity.

  The irradiation position deviation sensitivity per unit tilt is given to M0,1 in the sub-line definition formula of the scanning lens 105, and the irradiation position deviation sensitivity per one minute of tilt is calculated from the irradiation position change on the image plane. It is what I have sought. M0,1 in the sub-line definition formula of the scanning lens 105 is constant regardless of the Y (main scanning direction) position on the lens, and expresses a uniform tilt in which the sag amount changes linearly according to Z (sub scanning direction). It is a coefficient. Further, the 45 ° ass sensitivity per unit tilt change gives a minute value to Mn, 1 in the lens sub-line definition formula, and 45 ° when the tilt φ changes by 1 minute per 1 mm from the change in 45 ° ass. This is a measure of asthma sensitivity.

  Mn, 1 in the sub-line definition formula of the scanning lens is a coefficient that expresses a tilt change in which the tilt changes in accordance with Z (sub-scanning direction) in proportion to the n-th power of the Y (main scanning direction) coordinate value on the lens. . It is desirable that the off-axis tilt change -45 ° ass sensitivity is obtained by calculating the minute change from the original shape as much as possible.

・ Step 2 Set up simultaneous equations:
From these sensitivities, the equation described in Step 3 is established. In this embodiment, six coefficients M2, 1, M4, 1, M6, 1, M8, 1, M10, 1, M12, and 1 are given to the R1 surface Upper and Lower, respectively. The R4 surface also gives six coefficients M2, 1, M4, 1, M6, 1, M8, 1, M10, 1, M12, 1 to Upper and Lower, respectively. The image heights for which the equations are established are a total of 12 positions of ± 110, ± 105, ± 100, ± 80, ± 60, and ± 40 mm image heights, so that 24 equations can be established. Since the number of coefficients is 24, these coefficients can be uniquely determined mathematically.

Step 3 Solve the equation:
Table 3 shows the results of solving the above 24 equations. From the table, it can be seen that both the irradiation position and the 45 ° asperity are sufficiently small at the image height based on the equation. Since the solution is obtained by focusing calculation, each coefficient is not exactly 0, but it does not need to be obtained exactly because it changes in a later step.

Step 4 Various aberration correction (optimization of other aberrations):
FIG. 7 shows the result of the simulation performed by substituting the sub-line tilt change coefficient obtained above. From FIG. 7, although the correction was attempted, the scanning line curvature and 45 ° asperity were not corrected as intended, and field curvature occurred. This is because the light beam passing position on the downstream lens surface has changed due to the change in the tilt of the upstream surface. After that, in accordance with step 4 of the flowchart, the field curvature and other performance due to the change in tilt are corrected by optimization.

-Step 5 Performance check:
When optimization is carried out to some extent, various performances including scanning line curvature, 45 ° angle and field curvature are checked according to step 5. Table 4 shows the surface arrangement and aspherical coefficients at the end of optimization, and FIG. 8 is a graph showing the field curvature, scan line curvature, and 45 ° angle before and after the end of step 4. Although the scanning line curvature is almost corrected, 45 ° asphalt still remains large outside the shaft. Since the scanning line curvature is within 100 μm, the 45 ° angle is within 0.1λ, and the field curvature is within 2 mm, the process from step 1 is repeated again using the current lens according to the flowchart.

  FIG. 9 shows a simulation result of the sub-scanning irradiation position and 45 ° asper based on a solution obtained by solving the second equation, and various performances after the second optimization. The scanning line curvature is within 100 μm, the 45 ° angle is within 0.1λ, and the field curvature is within 2 mm. Each surface arrangement and aspheric coefficient at this time are shown in Table 5, and a spot image calculated by simulation is shown in FIG. By correcting the 45 ° angle within 0.05λ, the rotation of the spot is almost corrected.

  As described above, according to the present embodiment, it is suitable for an optical element of an optical scanning device used in an image forming apparatus, and a compact and highly functional optical element is designed by analytically searching for an optimum tilt change. be able to. Thereby, it is possible to form a good image with a compact optical scanning device and with various aberrations corrected well.

  An image forming apparatus using an optical element designed by the design method of this embodiment will be described below. FIG. 11 is a schematic diagram of a main part of a sub-scan section showing an embodiment of the image forming apparatus of the present invention. In FIG. 11, reference numeral 1104 denotes an image forming apparatus. Code data Dc is input to the image forming apparatus 1104 from an external device 1117 such as a personal computer. The code data Dc is converted into image data (dot data) Di by a printer controller 1111 in the image forming apparatus 1104.

  This image data Di is input to an optical scanning unit (scanning optical system) 1100 having the configuration shown in the present embodiment. The light scanning unit 1100 emits a light beam 103 modulated according to the image data Di, and the light beam 1103 scans the photosensitive surface of the photosensitive drum 1101 in the main scanning direction.

  The photosensitive drum 1101 serving as an electrostatic latent image carrier (photoconductor) is rotated clockwise by a motor 1115. With this rotation, the photosensitive surface of the photosensitive drum 1101 moves in the sub-scanning direction orthogonal to the main scanning direction with respect to the light beam 1103. Above the photosensitive drum 1101, a charging roller 1102 for uniformly charging the surface of the photosensitive drum 1101 is provided so as to contact the surface. The surface of the photosensitive drum 1101 charged by the charging roller 1102 is irradiated with a light beam 1103 scanned by the light scanning unit 1100.

  As described above, the light beam 1103 is modulated based on the image data Di, and an electrostatic latent image is formed on the surface of the photosensitive drum 1101 by irradiating the light beam 1103. This electrostatic latent image is developed as a toner image by a developing device 1107 disposed so as to be in contact with the photosensitive drum 1101 further downstream in the rotation direction of the photosensitive drum 1101 than the irradiation position of the light beam 1103.

  The toner image developed by the developing device 1107 is transferred onto a sheet 1112 as a transfer material by a transfer roller 1108 disposed below the photosensitive drum 1101 so as to face the photosensitive drum 1101. The paper 1112 is stored in a paper cassette 1109 in front of the photosensitive drum 1101 (on the right side in FIG. 11), but can be fed manually. A paper feed roller 1110 is disposed at the end of the paper cassette 1109 and feeds the paper 1112 in the paper cassette 1109 into the transport path.

  As described above, the sheet 112 on which the unfixed toner image has been transferred is further conveyed to a fixing device behind the photosensitive drum 1101 (left side in the drawing). The fixing device includes a fixing roller 1113 having a fixing heater (not shown) therein and a pressure roller 1114 disposed so as to be in pressure contact with the fixing roller 1113. Then, the sheet 1112 conveyed from the transfer roller 1110 is heated while being pressed at the pressure contact portion between the fixing roller 1113 and the pressure roller 1114 to fix the unfixed toner image on the sheet 1112. Further, a paper discharge roller 1116 is disposed behind the fixing roller 1113, and the fixed paper 1112 is discharged out of the image forming apparatus.

  Although not shown in FIG. 11, the print controller 1111 controls not only the conversion of the image data but also the various parts in the image forming apparatus 1104 including the motor 1115 and the polygon motor in the optical scanning unit 1100. Do.

  As described above, according to this embodiment, the lens (optical element) designed by the optical element design method is suitable for an optical scanning device, particularly an optical scanning device used in an image forming apparatus. By searching for the optimal tilt change analytically, it is possible to design a high-performance lens, and there is a possibility of downsizing by reducing the number of lenses, which is compact and has various aberrations corrected well. An optical scanning device can be configured.

  As mentioned above, although preferable embodiment of this invention was described, this invention is not limited to these embodiment, A various deformation | transformation and change are possible within the range of the summary.

DESCRIPTION OF SYMBOLS 101 Light source 102 Collimator lens 103 Cylindrical lens 104 Polygon mirror 105 f (theta) lens 106 Folding mirror 107 Scanned surface 105a R1 surface (lower stage) 105b R2 / 3 surface 105c R4 surface (upper stage)

Claims (5)

In a method for designing an optical element used in an image forming optical system that forms an image of a light beam deflected and scanned by a deflecting unit on a surface to be scanned,
In the optical element, the angle between the ray passing through the optical surface and the normal of the child surface changes within the sub-line cross section of the optical surface according to the position in the main scanning direction independently of the curvature of the child wire. An optical surface to
Within the sub-line cross section of the optical surface, the ratio of the incident beam deviation per unit inclination angle of the sub-line surface normal at any point on the optical axis to the irradiation position deviation in the sub-scanning direction is sensitive to the irradiation position deviation. Degree and
When the ratio of the amount of change in wavefront aberration per rate of change in which the tilt angle changes according to the position in the main scanning direction is defined as wavefront aberration sensitivity, the wavefront aberration sensitivity is set for each optical surface and in the main scanning direction. A calculation step of calculating at a plurality of positions;
An equation creating step for formulating equations at a plurality of positions in the main scanning direction so that the sum of products of the irradiation position deviation sensitivity and the inclination angle in each optical surface corrects the remaining irradiation position deviation in the sub-scanning direction;
A correction equation creating step for creating an equation at a plurality of positions in the main scanning direction so that the sum of products of wavefront aberration sensitivity and inclination angle change rate on each optical surface corrects the remaining wavefront aberration, and the correction equation creating step An inclination angle calculating step for obtaining a change in inclination angle for correcting wavefront aberration from the equation established in
A method for designing an optical element, comprising:   It has an optimization step of introducing a change in the inclination angle of the sub-plane normal obtained in the inclination angle calculation step into the optical surface shape and optimizing the outer shape of the optical surface of the optical element including other aberrations The method of designing an optical element according to claim 1.   3. The method of designing an optical element according to claim 1, wherein the wavefront aberration when calculating the wavefront aberration sensitivity in the calculation step to obtain a correction coefficient is 45 ° angle.   An optical element characterized by being designed by the optical element design method according to claim 1.   An imaging optical system comprising the optical element according to claim 4.