JP2671890B2 - Optical scanning device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [0001] BACKGROUND OF THE INVENTION 1. Field of the Invention
The present invention relates to an optical scanning device used for a computer or the like. Learn more
Relates to a scanning lens system. [0002] 2. Description of the Related Art A laser beam or the like is deflected and scanned at high speed.
Laser beam printers that record image information
It has excellent features such as high resolution and low noise, and is compact.
As the price becomes lower, the demand for them will increase rapidly.
I have. Therefore, the important component is optical writing.
It is necessary to reduce the size and cost of optical scanning devices.
The demand is great. The optical scanning device is roughly divided into a light source and a deflector.
It consists of a scanning lens system, but the scanning lens system is simple
Reduction is effective for downsizing and price reduction. The scanning lens system is adapted to the turning characteristics of the deflector.
Distortion such that the light spot moves at a constant speed on the scanning surface,
For example, if the deflector is a rotating polygon mirror and the light beam is
When it is deflected, the deflection angle θ is proportional to the image height Y.
It has a distortion and a light spot everywhere on the scanning plane.
Must have the ability to form a uniform image at the desired diameter
No. Furthermore, in the case of a rotary polygon mirror deflector,
Troublesome to compensate for variations in tilt (faulting error)
A correction function is also required. Resolution that combines these functions
High-performance, high-performance scanning lenses have traditionally been large and complex.
It had to be crude and expensive. Therefore, JP-A-54-98627 and JP-A-5-98627
No. 5-7727, JP-A-58-5706, etc.
As described above, it has been attempted to use a single scanning lens. Toko
However, in JP-A-54-98627, it has a sinusoidal vibration characteristic.
For the deflector that is
Aberration correction can be performed widely for various values of parameters.
However, it is still widely used because of its high speed.
For the constant angular velocity characteristics of a rotating polygon mirror deflector
Although it is aspherical to correspond to
Therefore, it can be used only under extremely limited conditions.
Flexible for various requirements such as size, light source, required dot diameter, etc.
Can not correspond to. In Japanese Patent Laid-Open No. 55-7727, plano-convex lens is used.
The fθ lens is composed of two lenses, but it is good in terms of field curvature.
It is hard to say that it has good imaging performance. In addition,
58-5706 Meniscus lens with positive power
The fθ lens is composed of
There is a problem, in order to eliminate this problem
We have to add a double-sided cylindrical lens. further,
All of the above 3 examples are new in order to add the trouble correction function.
I have to add a lens, and eventually a single lens
Is gone. In addition, the deflection angle can be increased by increasing the optical axis length.
It is possible to keep the aberration within the allowable range by narrowing it.
However, it is not preferable because the entire optical system becomes large. By the way, when considering downsizing and cost reduction,
The material of the lens is also an important issue. Conventional scanning lens
Glass is used as the material, but the performance of the diffraction limit is
Since it is a required optical system and the required accuracy is high, polishing etc.
Manufacturing cost is high. So polymethylmethacrylate
(PMMA), polycarbonate, polystyrene, etc.
If the plastic of the
Since it is possible to mass-produce it, it can be manufactured at extremely low cost.
There are few types of optical plastic materials, and
There is no one with a higher refractive index than lath. Therefore, the number of lenses
It is more difficult to reduce or downsize the optical system than glass. [0007] These points are taken into consideration, and the refractive index of the material
Without using a single lens, the aberration can be corrected well even if the optical axis is short.
A lens shape with a large degree of freedom is desired.
I understand. [0008] SUMMARY OF THE INVENTION The present invention is as described above.
It was made in view of the problems, and its purpose is small and low.
Cost and high performance optical scanning device, especially scanning lens
To provide. [0009] [MEANS FOR SOLVING THE PROBLEMS]
The bright optical scanning device includes a light source that emits a thin light beam and the light beam.
And a deflector that deflects and scans in a predetermined direction.
And a scanning lens for forming an image of the formed light flux on the scanned surface
And the scanning lens is made of a plastic material
It is composed of a single lens, and has a unique turning characteristic of the deflector.
Distortion in which the deflected light flux moves at a constant speed on the scanned surface
It has characteristics and at any position on the scanned plane
To correct the field curvature aberration in the meridional direction of the light flux,
The shape of both sides in the plane is connected to the scanning position by the non-circular amount of both sides.
Independently defined shape to constrain the two degrees of freedom of the image point
It is formed in a non-circular shape, and further field curvature aberration in the sagittal direction
To correct at least one of the both sides.
Curvature in the meridian plane along a non-circular curve
The index is set so that it changes independently of the meridional curvature.
It is characterized by becoming. [0010] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The principle of the present invention is shown in FIGS.
3 and FIG. 4 will be described below. The scanning lens is
As described above, the deflector causes constant angular velocity or sinusoidal vibration.
Image of the light beam deflected by the rotation characteristics such as
Images are formed without surface curvature, and the image points scan at a constant speed on the scanned plane.
It has a function of giving distortion as described above. For example a deflector
If is a rotating polygon mirror, as shown in Figure 1,
The emitted light beam is a mirror surface S_MAccording to the rotation of the polygon mirror 5
Is reflected at a deflection angle θ. The scanning lens 1 uses this light
A point T where the coordinate value Y is proportional to the deflection angle θ on the plane to be scanned
_IIs set to image. The scanning lens of the present invention is
Based on the principle described below, S shown in FIG.₁, S_TwoBoth
The aspherical surface is highly utilized and the aberration is small.
It is a single lens that is capable of wide-angle deflection without it. The first component original of the lens surface shape according to the present invention
The theory is that the light flux is
Only the parameters of the position and direction of the chief ray and the imaging distance are displayed.
However, one point on the lens surface is only for the chief ray passing through it.
Tilt and curvature to change the direction or imaging distance
Is defined. This is aberration correction
The spherical surface and coma are ignored in the image plane.
Completely corrects bending and distortion, including higher-order terms
It means that The above assumption is the laser beam
Generally, it is sufficiently established in a scanning optical system such as a printer. Further, the scanning lens system is designed to deviate at an arbitrary deflection angle.
The chief ray of the directed light beam is always on the same plane (
It is called the meridian plane.)
The points for which the slope and curvature are specified on the surface are the meridional surface and the lens.
It can be seen that it is sufficient only on the curve where the surfaces intersect. Therefore
The second construction principle of the present invention is to create a curve on the meridian plane,
The slope and curvature in the meridian plane at any point on the curve
Has achieved the purpose of the scanning lens mentioned above, and
A section including the chief ray at any point above and perpendicular to the meridian plane
A surface can be formed if a curvature (called a spherical section) is given.
That is to say. However, the inclination and the curvature in the meridian direction are continuous.
To connect continuously to form the lens surface position in the meridian plane
Although not independently defined, the spherical section curvature is
It can be treated independently. Therefore, the lens surface shape in the meridian plane
Optical to which the above-mentioned first and second constitutional principles are applied
It is obvious that the system is also included in the scope of the present invention. The present invention will be described below with reference to the perspective view of FIG.
The principle of lens construction will be specifically described. Light in Figure 2
Bunch {L_i-1｝ Is the surface S_iLuminous flux ｛L_i} Is converted to
You. Luminous flux {L_iＴ's T_iThe imaging distance measured from is the meridional luminous flux
In g_miG_siAnd Generally g_miAnd g_siIs
Not good. As mentioned above, the luminous flux is very thin, so
｛L_iWhen dealing with｝, the principal ray L_ciAnd meridian, each missing ball
Imaging distance g_mi, G_siJust think about it. Well, surface S
_iRay L after passing through_ciDirection is surface S_iT_iIn
Normal direction e_iCan be controlled with. Surface S_iThrough
Imaging distance after passing g_mi, G_siIs the surface S_iT_iAt noon
Radius of curvature R_miAnd radius of curvature R of spherical section_siControl with
Can be. Therefore, run one light beam deflected at an angle
Function to form an image at a position where constant velocity scanning can be realized on the inspection plane
Is the position of one point on the lens surface and its derivative (normal direction and curve
It was possible to have it by holding it, so connect it
Each on the lens surface corresponding to the light beam deflected at an arbitrary angle
If the point has the above function, the desired scanning lens shape
The situation is fixed. This is the above-mentioned first configuration principle
is there. Now, as described above, the chief ray L_ciEtc. is meridian
Since it does not leave the surface, surface S_iNormal direction vector e_iAlso
Fig. 2 shows the degrees of freedom that are in the meridian plane and represent the inclination of the plane.
Angle α between the optical axis and the normal vector_iOne degree of freedom is sufficient. Ma
Face S_iThe meridional cross-section curvature of is the inclination of the surface α_iIs the differential amount of
, Surface inclination α_iIs the surface S_iIs the derivative of the position on the meridian of
Therefore, after all, specify the tilt and curvature of the surface in the meridian direction.
Is to solve the differential equation and create a two-dimensional curve on the meridian plane.
It turns out that it has the same meaning as doing. Also, lack of ball
The cross-section curvature is determined without affecting the above curve.
Therefore, for each point on the curve after the curve is created,
Each is decided. This is the second configuration principle. According to the above-mentioned construction principle, the scanning lens is practically used.
It can be realized, but it is actually a single lens with both aspherical surfaces.
What is possible is explained by using the principle diagram of FIG. Figure
In 3, the paper surface represents the meridian surface. First, consider the meridian plane. Restrained now
Ino is the chief ray L_ciAnd the scanned plane S_IIntersection T_ICoordinate value of
Y_IAnd T_IAre two degrees of freedom that are imaging points. example
For example, the scanning position Y of the light beam deflected at an arbitrary angle θ_ITo
The slope α of the surface to constrain₁Is specified at all positions on the surface,
According to that, the shape that connects the surfaces smoothly is the boundary condition (example
For example, the intersection P with the optical axis₁Coordinate value X₁And the slope there is 0
Is specified), S₁It is decided in one way like
And the radius of curvature R on that surface_m1Cannot be specified,
The light flux is a point T not on the plane to be scanned_I’.
On the contrary, the radius of curvature R of the surface for restraining the image formation point_m1On the surface
If all positions are specified, the surface inclination α₁Specify
I can not do such a thing. Of the parameters that rays have like this
To constrain one degree of freedom with an arbitrary value of the deflection angle θ
Requires one surface, so now the two degrees of freedom above
At least two lens surfaces are required for restraint. Next, let us consider the spherical light flux.
Inoculation position g_siThis is one degree of freedom
Is the state of constraint in the meridian plane, that is, the shape of the curve
The curvature on the meridian in the direction perpendicular to it.
Because it can be controlled by kicking, a new surface is added to the above two surfaces.
No need to add. Therefore, two lens surfaces are required, and a single lens
I understand that it is good. Also, both surfaces are all positions on the lens surface.
Since it is a surface whose inclination and curvature are specified by
Must be aspheric. Now, here, the single-lens aspherical lens having the above-mentioned structure is used.
Consider the symmetry of the Z's plane. Created in the meridian plane
The two curved lines around an axis such as the optical axis
And the degree of freedom of the radius of curvature in the sagittal direction is lost. Follow
If it has rotational symmetry, it cannot control the image formation of the spherical ray.
Spherical field curvature aberration occurs. For plane symmetry, the luminous flux
Is always on the meridian, so obviously
The deflection angle is 0, and the deflection angle is 0.
Is the same condition as the luminous flux of θ and the luminous flux of −θ.
It is also symmetrical about a plane perpendicular to the implied meridian plane. This
As described above, the scanning lens of the present invention is paired except that it has two planes of symmetry.
Spherical aspheric curvature of field due to lack of name, meridional field bay
It is possible to completely correct bending aberration and distortion characteristic aberration.
You. Hereinafter, a single-lens double aspherical lens for scanning according to the present invention will be described.
A concrete method to realize the shape is explained using the principle diagram of FIG.
I do. First, a method of creating two curves on the meridian plane will be described.
As shown in FIG. 4, the lens surface S₁, S_TwoAre the optical axis and
Intersection P of₁, P_TwoThe distance s along the curve from₁, S_TwoToso
Angle α from the direction perpendicular to the optical axis at the point₁, Α_TwoWith
It is regulated by the relationship. Re-express this in Cartesian coordinates
And surface S₁, S_TwoAbout P₁, P_TwoThe origin
Assuming that the optical axis is the x-axis and the lens height direction is the y-axis,
Point T₁, T_TwoCoordinate value (x₁, Y₁), (X_Two, Y_Two)
Is Becomes Now, as shown in FIG. 4, the emission point on the optical axis
P_M, Deflection angle θ, meridional imaging distance g _m0Luminous flux L emitted at
_i(I = 0, 1, 2) is the surface S₁, S_TwoAnd T respectively₁,
T_TwoAnd the image plane S_IAnd T_IAnd then light as follows
The output position and the output direction of the bundle are shown. Ie     Vector P_MT₁= (A₀cos θ, a₀sin θ)     Vector T₁T_Two= (A₁cos θ₁, A₁sin θ₁) (2)     Vector T_TwoT_I= (A_Twocos θ_Two, A_Twosin θ_Two) And Further surface S₁, S_TwoT₁, T_TwoMeridian section at
R is the radius of curvature_m1, R_m2And the luminous flux L₁,
L_TwoThe meridional imaging distance of g_m1, G_m2And According to the above description method, the above-mentioned lens
The constitution principle of the shape can be formulated. Following the formulation
The following six items will be described separately.   Surface S₁, S_TwoAt the intersection of
Control the direction of the light flux.   Surface S₁, S_TwoAt the intersection of
To control the image forming distance of the light flux.   The coordinates of the intersections of the light beams on the surfaces are equal.   Each point on the surface is smoothly continuous.   The light flux forms an image on the scanning plane.   The imaging point is scanned at a constant speed on the scanning plane. The relationship between the inclination of the refracting surface and the direction of the light beam is
The well-known law of refraction is S₁, S_TwoPlane and L₁, L_Twoof
By applying about the intersection     sin (α₁−θ) = nsin (α)₁−θ₁): S₁Surface (3)     nsin (α_Two−θ₁) = Sin (α)_Two−θ_Two): S_TwoSurface (4) Can be expressed as Here, n is the refractive index of the lens medium. The relationship between the curvature of the surface and the image forming distance of the light beam is
A meridian when a thin light beam is obliquely incident on a surface with a certain curvature
The relational expression of the imaging distance is S₁Surface, S_TwoApply to the surface     ncos^Two(Α₁−θ₁) / G_m1      = cos^Two(Α₁−θ) / (g_m0-A₀) +             ｛Ncos (α₁−θ₁) -Cos (α₁-Θ)｝ / R_m1  (5)                                                           S₁surface     cos^Two(Α_Two−θ_Two) / G_m2           = Ncos^Two(Α_Two−θ₁) / (G_m1-A₁) +             ｛Cos (α_Two−θ_Two) -Ncos (α_Two−θ₁)｝ / R_m2(6)                                                           S_Twosurface Is obtained. [Mathematical formula-see original document] is calculated by the above equation (1).
Calculated based on the Cartesian coordinate value of the surface position and the equation (2) above.
Given that the orthogonal coordinate values of the refraction points of theThere is a relationship. Where X₁Is the surface S₁X seat at the intersection of
Standard value, X_TwoIs the surface S_TwoIs the x-coordinate value of the intersection of the and the optical axis. As for the condition that the surfaces are continuous,
By the fact that the integration in equations (7) to (10) is possible,
is there. The condition that the surface is smooth is determined by the inclination α of the surface.₁, Α
_TwoIs differentiable     dα₁/ Ds₁= -1 / R_m1                                  (11)     dα_Two/ Ds_Two= -1 / R_m2                                  (12) There is a relationship. The image points are scanned at a constant speed on the scanning plane of
The case is the intersection of the image plane and the light flux (X_I, Y_I)But     X_I= A_Twocos θ_Two+ A₁cos θ₁+ A₀cos θ (13)     Y_I= A_Twosin θ_Two+ A₁sin θ₁+ A₀sin θ (14) And the scanning point position Y_IIs the turning of the deflector
Characteristic     θ = F (τ) (15) Using     Y_I= K ・ F^-1(Θ) (16) Becomes Where F^-1Is the inverse function of F, τ is the parameter of time
And K are appropriate proportional constants. For example,
If the angular velocity deflection is     F (τ) = ωτω: angular velocity (17) Because     Y_I= K · θ / ω = f · θ f = K / ω: constant (18) Can be written. In addition, X in equation (13)_IIs the light at the x coordinate of the scanning plane
Shows the axial length. The conditions for forming an image on the scanning plane of (6) are as follows:
Meridional luminous flux image formation distance g in the formula_m2Is in equations (13) and (14)
Represented a_TwoSatisfied if equal to. That is     g_m2= A_Two                                                  (19) As described above, the principle of forming the lens shape according to the present invention is
(3), (4), (5), (6), (7), (8),
(9), (10), (11), (12), (13),
Formulated by 14 equations (14), (16), and (19)
However, by actually calculating these below
Stated that the lens surface shape can be directly expressed in some way
You. Among the variables appearing in the equation, the deflection angle θ and the initial meridional imaging distance
Separation g_m0Is given at the time of emission and is known. Also the optical axis
Long X_I, Surface S₁, S_TwoPosition X with the optical axis of₁, X_Two,
The constant velocity scanning constant K is a constant value that does not depend on the deflection angle θ.
Therefore the unknown remains₁, Θ_Two, Α₁, Α_Two, S₁,
s_Two, G_m1, G_m2, A₀, A₁, A_Two, R_m1, R_m2, Y
_I14 of the above, and the above-mentioned 14 expressions are all independent
Therefore, the simultaneous equations can be solved and the above 14 variables are, for example, deflection angles.
It can be expressed as a function of θ. Thus, for example, surface S₁Express
When doing₁And the distance s along the plane from the optical axis₁connection of
May be made to correspond using the deflection angle θ as a parameter. By the way, the above 14-system simultaneous equations are non-linear
Since it has the form and includes a differential term and an integral term, it can be solved directly.
Cannot be used and a numerical solution must be used. Numerical solution
However, the present invention is not limited thereto.
However, here, as an example, in the differential vector field,
This equation is actually solved numerically by the numerical integration method.
It is shown that the lens shape can be determined. Solving with a differential vector field means that all equations are
Expressed in differential form, all current variable values are known
Calculate the increment (differential variable) of each variable and move to the next variable
The value of is calculated. Organize the above formula 14
Expressed in differential form, equations (3) and (4) are     (Dα₁−dθ) cos (α₁−θ)                     = N (dα₁−dθ₁) Cos (α₁−θ₁) (20)     n (dα_Two−dθ₁) Cos (α_Two−θ₁)                     = (Dα_Two−dθ_Two) Cos (α_Two−θ_Two) (21) Combining equations (5) and (6) with equations (11) and (12)     ｛Ncos^Two(Α₁−θ₁) / G_m1} Ds₁           = ｛Cos^Two(Α₁−θ) / (g_m0-A₀)｝ Ds₁−           ｛Ncos (α₁−θ₁) -Cos (α₁−θ)｝ dα₁  (22)     ｛Cos^Two(Α_Two−θ_Two) / A_Two} Ds_Two           = ｛Ncos^Two(Α_Two−θ₁) / (G_m1-A₁)｝ Ds_Two−           ｛Cos (α_Two−θ_Two) -Ncos (α_Two−θ₁)｝ Dα_Two(23) However, g_m1Erases by making simultaneous equations (22) and (23)
I do. Equations (7) to (10) are     da₀cos θ-a₀sinθdθ = -sinα₁ds₁        (24)     da₀sin θ + a₀cosθdθ = cosα₁ds₁          (25)     da₁cos θ₁-A₁sin θ₁dθ₁+ Da₀cos θ                         -A₀sinθdθ = -sinα_Twods_Two  (26)     da₁sin θ₁+ A₁cos θ₁dθ₁+ Da₀sin θ                         + A₀cosθdθ = cosα_Twods_Two    (27) Equations (13) and (14) are     0 = da_Twocos θ_Two-A_Twosin θ_Twodθ_Two+ Da₁cos θ₁−         a₁sin θ₁dθ₁+ Da₀cos θ-a₀sin θd θ (28)     dY_I= Da_Twosin θ_Two+ A_Twocos θ_Twodθ_Two+ Da₁sin θ₁+         a₁cos θ₁dθ₁+ Da₀sin θ + a₀cos θd θ (29) Equation (16) is     dY_I= K ｛F^-1(Θ)} dθ (30) Becomes Equation (19) may be simply substituted. (20) ~
The unknown differential variable in equation (30) is dθ.₁, D
θ_Two, Dα₁, Dα_Two, Ds₁, Ds_Two, Da₀, Da
₁, Da_Two, DY_IAnd above (20) to (30)
The formulas (22) and (23) are combined into one formula.
Everything is linear except that it is a quadratic equation
It is easy to solve, for example by the known differential variable dθ     dθ₁     = Fθ₁(Θ₁, Θ_Two, Α₁, Α_Two, S₁, S_Two, A₀, A₁, A_Two) Dθ                                                                 (31) Can be expressed as From this, for example, θ₁Is And the deflection angle θ can be expressed as a parameter.
Where θ⁰ ₁Is the initial value. The actual calculation
θ₁, Θ_Two, Α₁, Α_Two, S₁, S_TwoFor 0, a
₀, A₁, A_TwoAbout X₁, X_Two, X_IThe value of the
Using     a⁰ ₀= X₁     a⁰ ₁= X_Two-X₁                                            (33)     a⁰ _Two= X_I-X_Two Can be calculated by numerical integration. The lens shape of the present invention is as described above.
The meridional curve of the shape is embodied, but it is embodied
Constants n and X that appeared in the process₁, X_Two, X_I, G_m0, K is
The degree of freedom that the lens shape of the present invention can take is as it is. You
That is, an appropriate set of constants {X₁ ^*, X_Two ^*,
X_I ^*, G_m0 ^*, K^*} One lens shape for one
That is, the present invention naturally applies to all of these.
Includes The meridional initial image formation position g_m0 ^*To infinity
Set, that is, the meridional light before entering the scanning lens
If the bundle is a parallel light beam, the beam diameter etc. can be easily controlled.
The optical system is easy to handle. The scanning lens of the present invention is as described above.
As a matter of course, it is also applicable to a parallel light flux. Now, the sphere cutoff for controlling the sphere cut image forming distance
Radius of curvature R_s1, R_s2The method of determining will be described. (5),
The meridional image forming distance when a thin light beam is obliquely incident on the formula (6).
The relational expression of     n / g_s1= 1 / (g_s0-A₀) +                 ｛Ncos (α₁−θ₁) -Cos (α₁-Θ)｝ / R_s1                                                       : S₁Surface (34)     1 / g_s2= N / (g_s1-A₁) +                 ｛Cos (α_Two−θ_Two) -Ncos (α_Two−θ₁)｝ / R_s2                                                       : S_TwoSurface (35) Holds. Article with an image forming point in the direction of the spheroid on the plane to be scanned
The matter is     g_s2= A_Two                                                  (36) It is. Missing ball according to formulas (34), (35) and (36)
Radius of curvature R_s1, R_s2Is determined, but the formula
In a₀, A₁, A_Two, Α₁, Α_Two, Θ, θ₁, Θ_TwoIs
The meridional curve has already been determined by the above method
Known for g_s0Is given, the unknown is g
_s1, G_s2, R_s1, R_s2Are four. Therefore 3 equations
There is a redundant degree of freedom for one of the unknowns
It is understood that can be set appropriately. For example, simple surface shape
R_s1Is always infinity and the right-hand side of (34)
If the second term is set to 0, the first surface is a surface that has no curvature in the sagittal direction.
become. Note that the initial spherical lack imaging distance g_s0Is given arbitrarily
If the deflector is a rotating polygon mirror, g_s0= 0 If so, the reflection point of the mirror surface and the scanning point become a conjugate image point.
A tilt correction function can be added. [0037] BEST MODE FOR CARRYING OUT THE INVENTION Lens-shaped constituent elements according to the present invention
An example in which the lens surface shape is calculated based on
The results are shown in Table 9 and FIGS. 5 to 12. As described above, the lens shape of the present invention is
Refractive index n of glass medium, initial imaging distance g₀, The first of the lens
Position where the surface and the second surface intersect the optical axis₁, X_Two, Optical axis length
X_I, 6 parameters of scanning speed constant K
Can be changed vertically, and a set of values for one parameter
There is one lens shape for. So at first glance
There are a large number of examples that seem to be completely different shapes
Exist and it is impossible to list them all,
Here, only representative examples are shown. The calculation conditions common to the following embodiments are: -Refractive index of lens medium n = 1.486 .Optical axis length from deflection point to scanned plane X_I= 200 mm ・ The deflector is deflected at a constant angular velocity by a rotating polygon mirror deflector. ・ Initial meridional imaging distance g_m0Is infinite. That is, the scanning lens
The light beam before entering the lens is a parallel light beam. -Spherical section curvature is given only to the second surface. ・ Initial sphere missing image distance g_s0Is 0. Therefore, the reflection of the rotating polygon mirror
The point and scanning point are conjugate image points, and the surface tilt correction function is added.
Have been. It is. The lens shape according to the present invention has a simple numerical value.
Or numerical expression, the result is obtained as a numerical example.
You. Therefore, for convenience, the curve shape on the meridian plane is well known.
Formula using the aspherical coefficient of x = (y^Two/ R) / [1 + √ ｛1- (y / R)^Two｝] +
By^Four+ Cy⁶+ Dy⁸+ Ey^Ten : Where x is the optical axis and the origin is at the intersection of the plane and the optical axis.
X-coordinate value when , The radius of curvature of the spherical section of the second surface
R_s2about R_s2= R_s2 ⁰+ Ay^Two+ By^Four+ Cy⁶+ Dy⁸+ Ey
^Ten Expressed by The error from the true shape when approximated in this way is
It is about 0.001% to 0.01%. In Table 1, Table 2 and Table 3, the first surface S₁Meridian plane
Coefficient R indicating the upper curve shape_m1, B₁, C₁, D₁, E₁
In Table 4, Table 5, and Table 6_TwoOn the meridian plane of
Coefficient R indicating the shape_m2, B_Two, C_Two, D_Two, E_TwoThe table
7, Table 8 and Table 9 show the changes in the radius of curvature in the spherical section direction.
Number R_s ⁰, A_s, B_s, C_s, D_s, E_sThe parameter
TA θ_e, X₁, X_TwoThe value calculated by changing is shown.
Where the effective deflection angle θ_eIs the scanning speed factor of the above formula (18).
It is a parameter used instead of several K, and the effective scan width is 20
If set to 0 mm, θ_e= 200 / K (rad) It is. X₁, X_TwoIs the first surface S as described above.₁, Second
Surface S_TwoIs the position of the point that intersects the optical axis. In addition,
Parameter set θ under common calculation conditions_e, X ₁, X
_TwoAre the same lens. In addition, some of the examples shown in the table
For the thing, an outline of the curved shape on the meridian plane and an optical path diagram
Both are shown in FIGS. 5 to 12. Dashi curve is the optical axis
Since it is symmetric with respect to, the opposite side of the optical axis is omitted.
The examples presented here all follow the principles of construction of the present invention.
Therefore, spherical aberration field curvature aberration and meridional field curvature aberration are completely removed.
The distortion characteristic is that the scanning point moves at a constant speed.
Is fully defined. However, perfection is an ideal state.
Therefore, for the actual lens shape, numerical calculation when calculating the shape
Due to errors or manufacturing errors, field curvature aberration and distortion characteristics
Some sexual aberration occurs. Of course there are those aberrations
There is a certain range of tolerance, and within that range, the scanning lens
Therefore, the present invention excludes them as well.
Not. [0044] [Table 1] [0045] [Table 2][0046] [Table 3] [0047] [Table 4][0048] [Table 5][0049] [Table 6] [0050] [Table 7] [0051] [Table 8][0052] [Table 9]FIG. 13 shows an example of the lens shape according to the present invention.
Overall image of optical system of laser beam printer using example
The perspective view showing is shown. Light emitted from the semiconductor laser 2
The bundle becomes a parallel light beam by the collimator lens 3 and
The cull lens 4 converges the light only in the direction of the sphere and rotates.
A linear image is formed near the mirror surface of the polygonal mirror deflector 6. Luminous flux
The polygonal mirror 5 is rotated to deflect the angular velocity in the meridian plane.
After passing through the scanning lens 1 according to the present invention,
An image is formed on the ram 7. Regarding the direction of ball loss,
The Lamb surface serves as a conjugate image forming point and forms a plane tilt correction system.
I have. The image point is formed by the scanning lens 1 of the present invention.
Scanning is performed at a constant speed in the axial direction of the frame 7 and the image is combined on a straight line without curvature
Image. The photosensitive drum is only one pitch per scan
By rotating and repeating it on the photosensitive drum
A latent image is formed. [0054] As described above, the optical scanning of the present invention
The device has a scanning lens so that the light flux moves at a constant speed on the scanned plane.
It has a moving distortion characteristic and is placed on the scanned plane.
The field curvature aberration of the luminous flux is zero or almost zero
Single lens made of plastic material with aspherical surfaces on both sides
Since it is a single lens, there is almost no aberration even with a single lens.
And a good image spot can be obtained, and the optical axis is long due to wide-angle deflection.
A scanning lens having a short length can be constructed. Also, the lens medium
As a quality, polymethylmethacrylate (PMMA),
Refraction compared to glass such as carbonate and polystyrene
Same as above, even if low-rate plastic material is used
It does not hinder the design for some reason and is injection molded.
Since it can be mass-produced by
Can be manufactured at low cost. Therefore, small size, low price, and high performance
The ability to provide a high-performance optical scanning device.
Have.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a principle diagram showing a schematic configuration of an optical scanning device of the present invention. FIG. 2 is a principle diagram for explaining the principle of configuring the lens shape of the present invention. FIG. 3 is a principle diagram for explaining that the scanning lens of the present invention can be realized by a single-lens bi-aspherical lens. FIG. 4 is a principle diagram for explaining a method of calculating the shape of a scanning lens according to the present invention. FIG. 5 is a view showing one embodiment of a lens shape according to the present invention. FIG. 6 is a view showing another embodiment of the lens shape of the present invention. FIG. 7 is a view showing another embodiment of the lens shape of the present invention. FIG. 8 is a view showing another embodiment of the lens shape of the present invention. FIG. 9 is a view showing another embodiment of the lens shape of the present invention. FIG. 10 is a view showing another embodiment of the lens shape of the present invention. FIG. 11 is a view showing another embodiment of the lens shape of the present invention. FIG. 12 is a view showing another embodiment of the lens shape of the present invention. FIG. 13 is a perspective view showing an embodiment of the entire optical scanning device of the present invention. [Description of Signs] 1 ... Scanning lens 2 ... Semiconductor laser 5 ... Polygon mirror 6 ... Rotating polygon mirror deflector 7 ... Scanning surface (photosensitive drum)

Claims (1)

(57) [Claims] The scanning lens includes a light source that emits a thin light beam, a deflector that deflects and scans the light beam in a predetermined direction, and a scanning lens that forms an image of the light beam deflected by the deflector on a scanning plane. Is a single-lens lens made of a plastic material , has a distortion characteristic that a light beam deflected by the peculiar rotation characteristic of the deflector moves at a constant speed on the scanned plane, and has a distortion characteristic on the scanned plane. In order to correct the field curvature aberration in the meridional direction of the light flux at any position, the shapes of both surfaces in the meridian plane are independent so that the non-arc amount of both surfaces constrains the two degrees of freedom between the scanning position and the image formation point. Is formed in a non-arc shape of the shape defined in, further, so as to correct the field curvature aberration in the sagittal direction, at a position along the non-arc curve in at least one of the meridional planes of the both surfaces. The curvature in the sagittal direction changes independently of the curvature in the meridian direction Optical scanning apparatus characterized by comprising stipulated in so that.