CN101650475B - Two-piece fθ mirror of MEMS laser scanning device - Google Patents

Abstract

The invention discloses a two-piece type f theta lens of a micro electro mechanical laser scanning device, wherein the first lens is a lens with a crescent positive diopter shape and a convex surface at the side of a micro electro mechanical reflector, the second lens is a lens with a crescent positive diopter shape and a concave surface at the side of the micro electro mechanical reflector, the first lens is provided with two optical surfaces, at least one optical surface in the main scanning direction is an aspheric surface, the second lens is provided with two optical surfaces, at least one optical surface in the main scanning direction is an aspheric surface, scanning light with the nonlinear relation of the angle reflected by the micro electro mechanical reflector and the time is mainly converted into scanning light spots with the linear relation of the distance and the time, the scanning light spots are corrected and condensed on a target object, and the first lens and the second lens both meet specific optical conditions so as to achieve the purposes of linear scanning effect and high-resolution scanning.

Description

The two-chip type f theta lens of MEMS laser scanning device

Technical field

The present invention relates to a kind of two-chip type f theta lens of MEMS laser scanning device, be particularly related in order to correction and be the mems mirror of simple harmonic characteristic motion and produce the angle variable quantity that becomes sine relation in time, to reach the two-chip type f theta lens that laser scanning apparatus is required the linear sweep effect.

Background technology

The present employed laser scanning device of laser printer (LBP:Laser Beam Print) (LSU:Laser Scanning Unit), utilize the scanning motion (laser beam scanning) of polygonal mirror (polygon mirror) to control laser beam of high speed rotating, as U.S. Pat 7079171, US6377293, US6295116, or as described in the patent I198966 of Taiwan.The following summary of its principle: utilize semiconductor laser give off laser beam (laser beam), earlier via collimating mirror (collimator), form parallel beam again via aperture (aperture), and parallel beam passes through cylindrical mirror (cylindrical lens) afterwards again, can be at the width on the Y-axis of secondary scan direction (sub scanning direction) along the parallel focusing of parallel direction of the X-axis of main scanning direction (main scanningdirection) and form linear image (line image), be projected to again on the polygonal mirror of high speed rotating, and evenly being provided with polygonal mirror on the polygonal mirror continuously, it just is positioned at or approaches the focal position of above-mentioned linear image (line image).Projecting direction by polygonal mirror control laser beam, when continuous a plurality of catoptrons during at high speed rotating can be incident upon on the catoptron laser beam along the parallel direction of main scanning direction (X-axis) with identical tarnsition velocity (angular velocity) deflective reflector to f θ linear sweep eyeglass, and f θ linear sweep eyeglass is arranged at the polygonal mirror side, can be single-piece lens structure (single-element scanning lens) or is two formula lens structures.The function of this f θ linear sweep eyeglass is to make the laser beam of injecting the f Theta lens via the mirror reflects on the polygonal mirror can be focused into elliptical spot and be incident upon light receiving surface (photoreceptor drum, be imaging surface) on, and reach the requirement of linear sweep (scanning linearity).Yet can there be following point in existing laser scanning apparatus (LSU) in the use:

(1), the manufacture difficulty height and the price of rotary multi mirror be not low, increases the cost of manufacture of LSU relatively.

(2), polygonal mirror must possess high speed rotating (as 40000 rev/mins) function, precision requirement is high again, so that the minute surface Y-axis width of reflecting surface as thin as a wafer on the general polygonal mirror, make and all need set up cylindrical mirror (cylindrical lens) among the existing LSU, so that increase member cost and assembling operation flow process so that laser beam can be focused into line (becoming a bit on the Y-axis) through cylindrical mirror and be incident upon on the catoptron of polygonal mirror again.

(3), existing polygonal mirror must high speed rotating (as 40000 rev/mins), cause Rotation Noise and improve relatively, and polygonal mirror must expend the long period from starting to working speed, increases the stand-by period after the start.

(4), in the package assembly of existing LSU, the laser beam central shaft that is projected to the polygonal mirror catoptron is not the central rotating shaft over against polygonal mirror, so that when the f Theta lens that design matches, need consider simultaneously polygonal mirror from axle deviation (offaxis deviation) problem, increase the design of f Theta lens relatively and make to go up trouble.

In recent years since,, developed the mems mirror (MEMS mirror) of a kind of swing type (oscillatory) at present on the market, control laser beam flying in order to replace existing polygonal mirror in order to improve the problem of existing LSU package assembly.Mems mirror is torque oscillation device (torsion oscillators), has reflector layer on its top layer, can be by vibration swing reflector layer, the light reflection is scanned, to can be applicable to laser scanning device (the laser scanning unit of imaging system (imaging system), scanner (scanner) or laser printer (laser printer) future, be called for short LSU), its scan efficiency (Scanning efficiency) can be higher than traditional polygonal rotating mirror.As U.S. Pat 6,844,951, US6,956,597, produce at least one drive signal, the resonant frequency of a plurality of mems mirrors of its driving frequency convergence, and scan the path with generation with the drive mems mirror, similarly also have U.S. Pat 7,064,876, US7,184,187, US7,190,499, US2006/0113393; Or as Taiwan patent TW M253133, it between collimating mirror and the f Theta lens, utilizes mems mirror to replace existing rotary multi mirror, with the projecting direction of control laser beam in the LSU modular structure; Or as Jap.P. JP2006-201350 etc.This mems mirror has that assembly is little, and velocity of rotation is fast, advantage of low manufacturing cost.Yet because mems mirror, after receiving driven, will do simple harmonic motion, and the mode of this simple harmonic motion (harmonicmotion) is that time and angular velocity are sine relation, and be projeced into mems mirror, its after reflection reflection angle θ and the pass of time t be:

θ(t)＝θ _s·sin(2π·f·t)　　　　　　　　　　　(1)

Wherein: f is the sweep frequency of mems mirror; θ _sFor laser beam behind mems mirror, the scanning angle of monolateral maximum.

Therefore, Δ t under the identical time interval, pairing reflection angle become sine function (Sinusoidal) to change with the time, and promptly when identical time interval Δ t, reflection angle is changed to:

Δ θ (t)=θ _s(sin (2 π ft ₁)-sin (2 π ft ₂)), and be nonlinear relationship with the time, promptly when the light of this reflection is incident upon object with different angles, the spot distance that is produced in the identical time interval is at interval and inequality and increasing or decreasing in time.

For example, when the pendulum angle of mems mirror is positioned at sinusoidal wave crest and trough, angle variable quantity is increasing or decreasing in time, different with the mode of motion that existing polygonal mirror becomes constant angular velocity to rotate, if use existing f Theta lens on the laser scanning apparatus with mems mirror (LSU), can't revise the angle variable quantity that mems mirror produces, and cause the laser light velocity that is incident upon on the imaging surface will produce speed scanning phenomenon such as non-and produce the imaging deviation that is positioned on the imaging surface.Therefore, for the laser scanning device that mems mirror constituted, abbreviate MEMS laser scanning device (MEMSLSU) as, its characteristic is that laser beam is via after the mems mirror scanning, form the not equal angular scanning ray of constant duration, therefore development can be used in MEMS laser scanning device the f Theta lens to revise scanning ray, making can correct imaging on object, will become urgently required.

Summary of the invention

The object of the present invention is to provide a kind of two-chip type f theta lens of MEMS laser scanning device, this two-chip type f theta lens is started at successively from mems mirror, crescent and convex surface is at first eyeglass of mems mirror side and positive diopter is crescent and concave surface is constituted at second eyeglass of mems mirror side by positive diopter, the scanning ray that mems mirror reflected can be projected correct imaging on the object, and reach the desired linear sweep effect of laser scanning apparatus.

Another object of the present invention is to provide a kind of two-chip type f theta lens of MEMS laser scanning device, in order to dwindling the area that is incident upon luminous point on the object (spot), and reaches the effect that improves resolution.

Another purpose of the present invention is to provide a kind of two-chip type f theta lens of MEMS laser scanning device, the modifying factor that can distort scanning ray departs from optical axis, increase and cause in the skew of main scanning direction and sub scanning direction, make the luminous point that images in photosensitive drums be deformed into similar oval-shaped problem, and make each imaging luminous point size be able to homogenising, improve the effect of separating picture element amount (resolution quality) and reach.

Therefore, the two-chip type f theta lens of MEMS laser scanning device of the present invention is applicable to that comprising at least one swings with the mems mirror of light source institute emitted laser bundle reflection the becoming scanning ray of emission of lasering beam, with imaging on object with resonance; For laser printer, this object often is a photosensitive drums (drum), that is, treat that the luminous point of imaging gives off laser beam via light source, via scanning about mems mirror, the mems mirror reflection lasering beam forms scanning ray, scanning ray via two-chip type f theta lens angle correction of the present invention and position after, on photosensitive drums, form luminous point (spot), because photosensitive drums scribbles photosensitizer, can respond to carbon dust it is gathered on the paper, so data can be printed.

Two-chip type f theta lens of the present invention comprises first eyeglass and second eyeglass of starting at successively from mems mirror, wherein first eyeglass has first optical surface and second optical surface, it is aspheric surface that first optical surface and second optical surface have an optical surface at least at main scanning direction, mainly will carry out the mems mirror of simple harmonic motion, the speed scanning phenomenon such as non-of successively decreasing by originally increasing in time or increasing progressively at imaging surface glazing dot spacing, speed scanning such as be modified to, make speed such as the projection work scanning of laser beam at imaging surface.Second eyeglass has the 3rd optical surface and the 4th optical surface, it is aspheric surface that the 3rd optical surface and the 4th optical surface have an optical surface at least at main scanning direction, mainly scanning light in order to homogenising, to be formed into kine bias at main scanning direction and sub scanning direction because of the skew optical axis causes on photosensitive drums poor, and the scanning ray correction of first eyeglass is concentrated on the object.

Description of drawings

Fig. 1 is the synoptic diagram of the optical path of two-chip type f theta lens of the present invention;

Fig. 2 is the graph of a relation of mems mirror scanning angle θ and time t;

Fig. 3 is optical path figure and the symbol description figure by the scanning ray of first eyeglass and second eyeglass;

Fig. 4 is for after scanning ray is incident upon on the photosensitive drums, the synoptic diagram that spot areas changes with the difference of launching position;

Fig. 5 is the graph of a relation of the Gaussian distribution and the light intensity of light beam;

Fig. 6 is the optical path figure of the present invention by the scanning ray embodiment of first eyeglass and second eyeglass;

Fig. 7 is the luminous point synoptic diagram of first embodiment;

Fig. 8 is the luminous point synoptic diagram of second embodiment;

Fig. 9 is the luminous point synoptic diagram of the 3rd embodiment;

Figure 10 is the luminous point synoptic diagram of the 4th embodiment; And

Figure 11 is the luminous point synoptic diagram of the 5th embodiment.

[primary clustering symbol description]

10: mems mirror; 11: LASER Light Source;

111: light beam;

113a, 113b, 113c, 114a, 114b, 115a, 115b: scan light;

131: the first eyeglasses; 132: the second eyeglasses;

14a, 14b: photoelectric sensor; 15: photosensitive drums;

16: cylindrical mirror; 2,2a, 2b, 2c: luminous point;

3: the effective scanning window.

Embodiment

With reference to Fig. 1, be the optical path synoptic diagram of the two-chip type f theta lens of MEMS laser scanning device of the present invention.The two-chip type f theta lens of MEMS laser scanning device of the present invention comprises first eyeglass 131 with the first optical surface 131a and second optical surface 131b and second eyeglass 132 with the 3rd optical surface 132a and the 4th optical surface 132b, to be applicable to micro electronmechanical laser scanning apparatus.Among the figure, MEMS laser scanning device mainly comprises LASER Light Source 11, mems mirror 10, cylindrical mirror 16, two photoelectric sensor 14a, 14b, and in order to the object of sensitization.In the drawings, object is to implement with photosensitive drums (drum) 15.The light beam 111 that LASER Light Source 11 is produced projects on the mems mirror 10 by behind the cylindrical mirror 16.And the mode that mems mirror 10 swings with resonance is reflected into light beam 111 and scans light 113a, 113b, 113c, 114a, 114b, 115a, 115b.Wherein scan light 113a, 113b, 113c, 114a, 114b, 115a, 115b is referred to as sub scanning direction (subscanning direction) in the projection of directions X, projection in the Y direction is referred to as main scanning direction (main scanningdirection), and mems mirror 10 scanning angles are θ _c

With reference to Fig. 1 and Fig. 2, wherein Fig. 2 is the graph of a relation of mems mirror scanning angle θ and time t.Because mems mirror 10 is done simple harmonic motion, its movement angle is sinusoidal variations in time, and the ejaculation angle and the time that therefore scan light are nonlinear relationship.Crest a-a ' as shown and trough b-b ', its pendulum angle are significantly less than wave band a-b and a '-b ', and the unequal phenomenon of this angular velocity causes scanning ray to produce the imaging deviation easily on photosensitive drums 15.Therefore, photoelectric sensor 14a, 14b are arranged within mems mirror 10 maximum scans angle ± θ c, and its angle is ± θ p that laser beam is begun to be reflected by mems mirror 10 by the crest place of Fig. 2, is equivalent to the scanning ray 115a of Fig. 1 this moment; When photoelectric sensor 14a detected scanning light beam, expression mems mirror 10 swung to+θ p angle, was equivalent to the scanning ray 114a of Fig. 1 this moment; When mems mirror 10 scanning angles change as during a point of Fig. 2, are equivalent to scanning ray 113b position at this moment; LASER Light Source 11 will be driven and give off laser beam 111 this moment, and when being scanned up to the b point of Fig. 2, be equivalent to scanning ray 113c position this moment till (quite ± θ n angle is interior to give off laser beam 111 by LASER Light Source 11); When mems mirror 10 produces reversals of vibrations, as being driven by LASER Light Source 11 when the wave band a '-b ' and beginning to give off laser beam 111; So finish one-period.

With reference to Fig. 1 and Fig. 3, wherein Fig. 3 is the optical path figure by the scanning ray of first eyeglass and second eyeglass.Wherein, ± θ n is the effective scanning angle, when the rotational angle of mems mirror 10 enter ± during θ n, LASER Light Source 11 begins to give off laser beam 111, be reflected into via mems mirror 10 and scan light, reflected by the first optical surface 131a and the second optical surface 131b of first eyeglass 131, it is the scanning ray of linear relationship with the time with the time that the distance that mems mirror 10 is reflected becomes the scanning ray of nonlinear relationship to convert distance to.After scanning ray is by first eyeglass 131 and second eyeglass 132, optical property by the first optical surface 131a, the second optical surface 131b, the 3rd optical surface 132a, the 4th optical surface 132b, scanning ray is focused on the photosensitive drums 15, and on photosensitive drums 15, form a luminous point (Spot) 2 that is listed as.On photosensitive drums 15, two farthest the spacing of luminous point 2 be called effective scanning window 3.Wherein, d ₁Spacing, d for mems mirror 10 to first optical surface 131a ₂Be spacing, the d of first optical surface 131a to the second optical surface 131b ₃Be spacing, the d of the second optical surface 131b to the, three optical surface 132a ₄Be spacing, the d of the 3rd optical surface 132a to the four optical surface 132b ₅Be spacing, the R of the 4th optical surface 132b to photosensitive drums 15 ₁Be radius-of-curvature (Curvature), the R of the first optical surface 131a ₂Be the radius-of-curvature of the second optical surface 131b, radius-of-curvature and the R that R3 is the 3rd optical surface 132a ₄It is the radius-of-curvature of the 4th optical surface 132b.

With reference to Fig. 4, for after scanning ray is incident upon on the photosensitive drums, the synoptic diagram that spot areas (spot area) changes with the difference of launching position.When scanning when being incident upon photosensitive drums 15 after light 113a sees through first eyeglass 131 and second eyeglass 132 along optical axis direction, because of the angle that is incident in first eyeglass 131 and second eyeglass 132 is zero, so in the deviation ratio that main scanning direction produced is zero, therefore the luminous point 2a that images on the photosensitive drums 15 is similar circle.When scanning ray 113b and 113c see through first eyeglass 131 and second eyeglass, 132 backs and when being incident upon photosensitive drums 15, non-vanishing because of being incident in first eyeglass 131 and second eyeglass 132 and the formed angle of optical axis, so non-vanishing in the deviation ratio that main scanning direction produced, be big and cause projected length than the formed luminous point of scanning ray 113a at main scanning direction; This situation is also identical at sub scanning direction, departs from the formed luminous point of scanning ray of scanning ray 113a, also will be bigger; So the luminous point 2b, the 2c that image on the photosensitive drums 15 are similar ellipse, and the area of 2b, 2c is greater than 2a.Wherein, S _A0With S _B0Be the luminous point that scans light on mems mirror 10 reflectings surface length, G at main scanning direction (Y direction) and sub scanning direction (directions X) _aWith G _bFor the Gaussian beam (Gaussian Beams) that scans light is 13.5% to be in the beam radius of Y direction and directions X in light intensity, as shown in Figure 5, only shown the beam radius of Y direction among Fig. 5.

Vertical the above, the scanning ray that two-chip type f theta lens of the present invention can be reflected mems mirror 10, with the scanning ray of Gaussian beam distort (distortion) revise, and the relation of time-angular velocity is changed into the relation of time-distance.Scanning ray is exaggerated through the f Theta lens at the light beam of main scanning direction (Y direction) with sub scanning direction (directions X), produces luminous point on imaging surface, so that the resolution that meets demand to be provided.

For reaching above-mentioned effect, two-chip type f theta lens of the present invention is at the first optical surface 131a of first eyeglass 131 or the 3rd optical surface 132a or the 4th optical surface 132b of the second optical surface 132a and second eyeglass 132, at main scanning direction or sub scanning direction, can use the design of sphere curved surface or non-spherical surface, if use the non-spherical surface design, its non-spherical surface satisfies following surface equation formula:

1: horizontal picture surface equation formula (Anamorphic equation)

$Z=\frac{\left(\mathrm{Cx}\right)X^2+\left(\mathrm{Cy}\right){\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="H2008102104692E00021.png,H2008102104692E00031.png"\; state="\{\{state\}\}">Y</figure-callout>}}^2}{1+\sqrt{1-(1+\mathrm{Kx}){\left(\mathrm{Cx}\right)}^2{X}^2-(1+\mathrm{Ky}){\left(\mathrm{Cy}\right)}^2{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="H2008102104692E00021.png,H2008102104692E00031.png"\; state="\{\{state\}\}">Y</figure-callout>}}^2}}+A_R{[(1-A_P)X^2+(1+A_P)Y^2]}^2+$

$B_R{[(1-B_P)X^2+(1+B_P)Y^2]}^3+C_R{[(1-C_P)X^2+(1+C_P)Y^2]}^4+$

$D_R{[(1-D_P)X^2+(1+D_P)Y^2]}^5---\left(2\right)$

Wherein, Z be on the eyeglass any point with the distance (SAG) of optical axis direction to the initial point section; C _xWith C _yBe respectively the curvature (curvature) of directions X and Y direction; K _xWith K _yBe respectively the circular cone coefficient (Conic coefficient) of directions X and Y direction; A _R, B _R, C _RWith D _RBe respectively the circular cone deformation coefficient (deformationfrom the conic) with ten powers four times, six times, for eight times of rotation symmetry (rotationallysymmetric portion); A _P, B _P, C _PWith D _PBe respectively the circular cone deformation coefficient (deformation from the conic) of four times, six times, eight times, ten times powers of non-rotating symmetry (non-rotationallysymmetric components); Work as C _x=C _y, K _x=K _yAnd A _p=B _p=C _p=D _p, then be reduced to single aspheric surface at=0 o'clock.

2: ring is as surface equation formula (Toric equation)

$Z=\mathrm{Zy}+\frac{\left(\mathrm{Cxy}\right){\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="H2008102104692E00021.png,H2008102104692E00031.png"\; state="\{\{state\}\}">X</figure-callout>}}^2}{1+\sqrt{1-{\left(\mathrm{Cxy}\right)}^2{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="H2008102104692E00021.png,H2008102104692E00031.png"\; state="\{\{state\}\}">X</figure-callout>}}^2}}$

$\mathrm{Cxy}=\frac{1}{(1/\mathrm{Cx})-\mathrm{Zy}}$

$\mathrm{Zy}=\frac{\left(\mathrm{Cy}\right){\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="H2008102104692E00021.png,H2008102104692E00031.png"\; state="\{\{state\}\}">Y</figure-callout>}}^2}{1+\sqrt{1-(1+\mathrm{Ky}){\left(\mathrm{Cy}\right)}^2{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="H2008102104692E00021.png,H2008102104692E00031.png"\; state="\{\{state\}\}">Y</figure-callout>}}^2}}+B_4{Y}^4+B_6{\mathrm{<figure-callout\; id="6"\; label="Y"\; filenames="H2008102104692E00021.png"\; state="\{\{state\}\}">Y</figure-callout>}}^6+B_8{Y}^8+B_{10}{Y}^{10}---\left(3\right)$

Wherein, Z be on the eyeglass any point with the distance (SAG) of optical axis direction to the initial point section; C _yWith C _xBe respectively the curvature (curvature) of Y direction and directions X; K _yCircular cone coefficient (Coniccoefficient) for the Y direction; B ₄, B ₆, B ₈With B ₁₀Be respectively the coefficient (4th～10thorder coefficients deformation from the conic) of four times, six times, eight times, ten times powers; Work as C _x=C _yAnd K _y=A _p=B _p=C _p=D _p, then be reduced to single sphere at=0 o'clock.

Sweep velocity such as on the imaging surface on the object, keep for making scanning ray, for example, in two identical time intervals, the spacing of keeping two luminous points equates, two-chip type f theta lens of the present invention can be with scanning ray 113a to the light between the scanning ray 113b, carry out the correction of scanning ray emergence angle by first eyeglass 131 and second eyeglass 132, make two scanning rays in the identical time interval, after the shooting angle correction, the distance of two luminous points that form on the photosensitive drums 15 of imaging equates.Further, after laser beam 111 is via mems mirror 10 reflections, its Gaussian beam radius G _aWith G _bBigger, if after the distance of this scanning ray through mems mirror 10 and photosensitive drums 15, Gaussian beam radius G _aWith G _bTo be bigger, do not meet practical resolution requirement; The scanning ray 113a that two-chip type f theta lens of the present invention further can reflect mems mirror 10 is to the formation of the light between scanning ray 113b G _aWith G _bLess Gaussian beam makes on the photosensitive drums 15 of the image formation by rays after the focusing and produces less luminous point; Moreover two-chip type f theta lens of the present invention more can be with the luminous point size homogenising (being limited in the scope that meets resolution requirement) that is imaged on the photosensitive drums 15, to obtain best parsing effect.

Two-chip type f theta lens of the present invention comprises, start at successively from mems mirror 10, be first eyeglass 131 and second eyeglass 132, first eyeglass 131 be the crescent and convex surface of positive diopter the eyeglass of mems mirror 10 sides and second eyeglass 132 for positive diopter crescent and concave surface at the eyeglass of mems mirror 10 sides, wherein first eyeglass 131 has the first optical surface 131a and the second optical surface 131b, the scanning ray luminous point that the angle and time of mems mirror 10 reflection is nonlinear relationship convert to apart from the time be the scanning ray luminous point of linear relationship; Wherein second eyeglass 132 has the 3rd optical surface 132a and the 4th optical surface 132b, and the scanning ray correction of first eyeglass 131 is concentrated on the object; By of scanning ray on photosensitive drums 15 imaging of this two-chip type f theta lens with mems mirror 10 reflections; Wherein, the first optical surface 131a, the second optical surface 131b, the 3rd optical surface 132a and the 4th optical surface 132b have at least one to be optical surface that aspheric surface constituted at main scanning direction, and the first optical surface 131a, the second optical surface 131b, the 3rd optical surface 132a and the 4th optical surface 132b can have at least one to be optical surface that aspheric surface constituted or the optical surface that all uses sphere and constituted at sub scanning direction at sub scanning direction.Further, on first eyeglass 131 and second eyeglass 132 constitute, on optical effect, two-chip type f theta lens of the present invention, further satisfy the condition of formula (4)～formula (5) at main scanning direction:

$0.1<\frac{{\mathrm{<figure-callout\; id="3"\; label="d"\; filenames="H2008102104692E00021.png,H2008102104692E00031.png"\; state="\{\{state\}\}">d</figure-callout>}}_3+d_4+d_5}{f_{\left(1\right)Y}}<0.8---\left(4\right)$

$0.2<\frac{d_5}{f_{\left(2\right)Y}}<0.8---\left(5\right)$

Or, satisfy formula (6) at main scanning direction

$0.3<|f_{\mathrm{sY}}\&CenterDot;(\frac{(n_{d1}-1)}{f_{\left(1\right)y}}+\frac{(n_{d2}-1)}{f_{\left(2\right)y}})|<0.6---\left(6\right)$

And satisfy formula (7) at sub scanning direction

$0.8<|(\frac{1}{R_{1x}}-\frac{1}{R_{2x}})+(\frac{1}{R_{3x}}-\frac{1}{R_{4x}})f_{\mathrm{sX}}|<1.6---\left(7\right)$

Wherein, f _{(1) Y}Be focal length, the f of first eyeglass 131 at main scanning direction _{(2) Y}Be focal length, the d of second eyeglass 132 at main scanning direction ₃Distance, the d of first eyeglass, 131 object side optical surface to the second eyeglasses, 132 mems mirrors, 10 side optical surfaces during for θ=0 ° ₄Thickness, the d of second eyeglass 132 during for θ=0 ° ₅Second eyeglass, 132 object side optical surfaces are to distance, the f of object during for θ=0 ° _SxBe compound focal length (combination focal length), the f of two-chip type f theta lens at sub scanning direction _SYBe compound focal length, the R of two-chip type f theta lens at main scanning direction _IxBe the radius-of-curvature of i optical surface at sub scanning direction; R _IyBe the radius-of-curvature of i optical surface at main scanning direction; n _D1With n _D2It is the refractive index (refraction index) of first eyeglass 131 and second eyeglass 132.

Moreover the formed luminous point homogeneity of two-chip type f theta lens of the present invention can be represented with the maximal value of the beam size of scanning ray on photosensitive drums 15 and the ratio delta of minimum value, promptly satisfies formula (8):

$0.4<\mathrm{\&delta;}=\frac{\min (S_b\&CenterDot;S_a)}{\max (S_b\&CenterDot;S_a)}---\left(8\right)$

Further, the formed resolution of two-chip type f theta lens of the present invention can be used η _MaxFor the luminous point that scans light on mems mirror 10 reflectings surface through the scanning peaked ratio of luminous point and η on photosensitive drums 15 _MinFor the luminous point that scans light on mems mirror 10 reflectings surface is expression through the ratio of scanning luminous point minimum value on photosensitive drums 15, can satisfy formula (9) and (10),

${\mathrm{\&eta;}}_{\max }=\frac{\max (S_b\&CenterDot;S_a)}{({\mathrm{<figure-callout\; id="0"\; label="S\; b"\; filenames="H2008102104692E00021.png,H2008102104692E00081.png"\; state="\{\{state\}\}">S</figure-callout>}}_b\&CenterDot;S_{a0})}<0.10---\left(9\right)$

${\mathrm{\&eta;}}_{\min }=\frac{\min (S_b\&CenterDot;S_a)}{({\mathrm{<figure-callout\; id="0"\; label="S\; b"\; filenames="H2008102104692E00021.png,H2008102104692E00081.png"\; state="\{\{state\}\}">S</figure-callout>}}_b\&CenterDot;S_{a0})}<0.10---\left(10\right)$

Wherein, S _aWith S _bIs that ratio, the η of smallest spot and maximum luminous point is ratio, the S that scans luminous point on the luminous point of light and the photosensitive drums 15 on mems mirror 10 reflectings surface on the photosensitive drums 15 for scanning any luminous point that light forms on the photosensitive drums 15 at length, the δ of Y direction and directions X _A0With S _B0For scanning the length of the luminous point of light on mems mirror 10 reflectings surface at main scanning direction and sub scanning direction.

For making the present invention clear and definite more full and accurate, enumerate preferred embodiment and cooperate following diagram, details are as follows with structure of the present invention and technical characterictic thereof:

The following embodiment that is disclosed of the present invention explains at the main composition assembly of the two-chip type f theta lens of MEMS laser scanning device of the present invention, though therefore the following embodiment that is disclosed of the present invention is applied in the MEMS laser scanning device, but with regard to generally having MEMS laser scanning device, except disclosed two-chip type f theta lens, other structure still belongs to general technique known, therefore the personage who generally is familiar with this technology in the art understands, the constituent components of the two-chip type f theta lens of disclosed MEMS laser scanning device is not restricted to the following example structure that discloses, just each constituent components of the two-chip type f theta lens of this MEMS laser scanning device is to carry out many changes, revise, even the equivalence change, for example: the radius-of-curvature design of first eyeglass 131 and second eyeglass 132 or the design of face type, material is selected for use, spacing adjustment etc. does not limit.

＜the first embodiment 〉

First eyeglass 131 of the two-chip type f theta lens of present embodiment and second eyeglass 132, wherein first eyeglass 131 be crescent and convex surface at the eyeglass of mems mirror 10 sides, wherein second eyeglass 132 be crescent and concave surface at the eyeglass of mems mirror 10 sides, the 3rd optical surface 132a and the 4th optical surface 132b of the first optical surface 131a of first eyeglass 131 and the second optical surface 131b, second eyeglass 132 are aspheric surface, and use formula (2) is carried out the aspheric surface design.Its optical characteristics and aspheric surface parameter such as table one and table two.

The f θ optical characteristics of table one, first embodiment

^*The expression aspheric surface

The optical surface aspheric surface parameter of table two, first embodiment

Two-chip type f theta lens through being constituted thus, f _{(1) Y}=231.883, f _{(2) Y}=248.128, f _SX=23.211, f _SY=128.531 (mm), scanning ray can be converted to distance is the scanning ray luminous point of linear relationship with the time, and with luminous point S on the mems mirror 10 _A0=12.90 (μ m), S _B0=4618.85 (μ m) scanning becomes scanning ray, in photosensitive drums 15 enterprising line focusings, forms less luminous point 6, and satisfies the condition of formula (4)～formula (10), as table three; On the photosensitive drums 15 with the Gaussian beam diameter (μ m) of central shaft Z axle, as table four at the luminous point of Y direction distance center axle Y distance (mm); And the luminous point distribution plan of present embodiment as shown in Figure 7.Among the figure, the unit circle diameter is 0.05mm.

Table three, first embodiment table that satisfies condition

The maximal value of luminous point Gaussian beam diameter on table four, the first embodiment photosensitive drums

＜the second embodiment 〉

First eyeglass 131 of the two-chip type f theta lens of present embodiment and second eyeglass 132, wherein first eyeglass 131 be crescent and convex surface at the eyeglass of mems mirror 10 sides, wherein second eyeglass 132 be crescent and concave surface at the eyeglass of mems mirror 10 sides, the 3rd optical surface 132a and the 4th optical surface 132b of the first optical surface 131a of first eyeglass 131 and the second optical surface 131b, second eyeglass 132 are aspheric surface, and use formula (2) is carried out the aspheric surface design.Its optical characteristics and aspheric surface parameter such as table five and table six.

The f θ optical characteristics of table five, second embodiment

^*The expression aspheric surface

The optical surface aspheric surface parameter of table six, second embodiment

Two-chip type f theta lens through being constituted thus, f _{(1) Y}=230.847, f _{(2) Y}=248.37, f _SX=25.189, f _SY=128.63 (mm), scanning ray can be converted to distance is the scanning ray luminous point of linear relationship with the time, and with luminous point S on the mems mirror 10 _A0=12.90 (μ m), S _B0=4618.85 (μ m) scanning becomes scanning ray, in photosensitive drums 15 enterprising line focusings, forms less luminous point 8, and satisfies the condition of formula (4)～formula (10), as table seven; On the photosensitive drums 15 with the Gaussian beam diameter (μ m) of central shaft Z axle, as table eight at the luminous point of Y direction distance center axle Y distance (mm); And the luminous point distribution plan of present embodiment as shown in Figure 8.Among the figure, the unit circle diameter is 0.05mm.

Table seven, second embodiment table that satisfies condition

The maximal value of luminous point Gaussian beam diameter on table eight, the second embodiment photosensitive drums

＜the three embodiment 〉

First eyeglass 131 of the two-chip type f theta lens of present embodiment and second eyeglass 132, wherein first eyeglass 131 be crescent and convex surface at the eyeglass of mems mirror 10 sides, wherein second eyeglass 132 be crescent and concave surface at the eyeglass of mems mirror 10 sides, the 3rd optical surface 132a of the first optical surface 131a of first eyeglass 131 and the second optical surface 131b, second eyeglass 132 is an aspheric surface, and use formula (3) is carried out the aspheric surface design; The 4th optical surface 132b of second eyeglass 132 uses formula (2) to carry out the aspheric surface design.Its optical characteristics and aspheric surface parameter such as table nine and table ten.

The f θ optical characteristics of table nine, the 3rd embodiment

The optical surface aspheric surface parameter of table ten, the 3rd embodiment

Two-chip type f theta lens through being constituted thus, f _{(1) Y}=128.339, f _{(2) Y}=257.258, f _SX=26.0, f _SY=128.339 (mm), scanning ray can be converted to distance is the scanning ray luminous point of linear relationship with the time, and with luminous point S on the mems mirror 10 _A0=12.90 (μ m), S _B0=4618.85 (μ m) scanning becomes scanning ray, in photosensitive drums 15 enterprising line focusings, forms less luminous point 10, and satisfies the condition of formula (4)～formula (10), as table ten one; On the photosensitive drums 15 with the Gaussian beam diameter (μ m) of central shaft Z axle, as table ten two at the luminous point of Y direction distance center axle Y distance (mm); The luminous point distribution plan of present embodiment as shown in Figure 9.Among the figure, the unit circle diameter is 0.05mm.

Table ten the one, the 3rd embodiment table that satisfies condition

The maximal value of luminous point Gaussian beam diameter on table ten the two, the 3rd embodiment photosensitive drums

＜the four embodiment 〉

First eyeglass 131 of the two-chip type f theta lens of present embodiment and second eyeglass 132, wherein first eyeglass 131 be crescent and convex surface at the eyeglass of mems mirror 10 sides, wherein second eyeglass 132 be crescent and concave surface at the eyeglass of mems mirror 10 sides, the 3rd optical surface 132a and the 4th optical surface 132b of the first optical surface 131a of first eyeglass 131 and the second optical surface 131b, second eyeglass 132 are aspheric surface, and use formula (2) is carried out the aspheric surface design.Its optical characteristics and aspheric surface parameter such as table ten three and table ten four.

The f θ optical characteristics of table ten the three, the 4th embodiment

^*The expression aspheric surface

The optical surface aspheric surface parameter of table ten the four, the 4th embodiment

Two-chip type f theta lens through being constituted thus, f _{(1) Y}=233.066, f _{(2) Y}=244.281, f _SX=27.931, f _SY=128.819 (mm), scanning ray can be converted to distance is the scanning ray luminous point of linear relationship with the time, and with luminous point S on the mems mirror 10 _A0=12.90 (μ m), S _B0=4618.85 (μ m) scanning becomes scanning ray, in photosensitive drums 15 enterprising line focusings, forms less luminous point 12, and satisfies the condition of formula (4)～formula (10), as table ten five; On the photosensitive drums 15 with the Gaussian beam diameter (μ m) of central shaft Z axle, as table ten six at the luminous point of Y direction distance center axle Y distance (mm); And the luminous point distribution plan of present embodiment as shown in figure 10.Among the figure, the unit circle diameter is 0.05mm.

Table ten the five, the 4th embodiment table that satisfies condition

The maximal value of luminous point Gaussian beam diameter on table ten the six, the 4th embodiment photosensitive drums

＜the five embodiment 〉

First eyeglass 131 of the two-chip type f theta lens of present embodiment and second eyeglass 132, wherein first eyeglass 131 be crescent and convex surface at the eyeglass of mems mirror 10 sides, wherein second eyeglass 132 be crescent and concave surface at the eyeglass of mems mirror 10 sides, the 3rd optical surface 132a and the 4th optical surface 132b of the first optical surface 131a of first eyeglass 131 and the second optical surface 131b, second eyeglass 132 are aspheric surface, and use formula (2) is carried out the aspheric surface design.Its optical characteristics and aspheric surface parameter such as table ten seven and table ten eight.

The f θ optical characteristics of table ten the seven, the 5th embodiment

^*The expression aspheric surface

The optical surface aspheric surface parameter of table ten the eight, the 5th embodiment

Two-chip type f theta lens through being constituted thus, f _{(1) Y}=223.383, f _{(2) Y}=247.789, f _SX=33.301, f _SY=128.847 (mm), scanning ray can be converted to distance is the scanning ray luminous point of linear relationship with the time, and with luminous point S on the mems mirror 10 _A0=12.90 (μ m), S _B0=4618.85 (μ m) scanning becomes scanning ray, in photosensitive drums 15 enterprising line focusings, forms less luminous point 12, and satisfies the condition of formula (4)～formula (10), as table ten nine; On the photosensitive drums 15 with the Gaussian beam diameter (μ m) of central shaft Z axle, as table two ten at the luminous point of Y direction distance center axle Y distance (mm); And the luminous point distribution plan of present embodiment as shown in figure 11.Among the figure, the unit circle diameter is 0.05mm.

Table ten the nine, the 5th embodiment table that satisfies condition

The maximal value of luminous point Gaussian beam diameter on table two the ten, the 5th embodiment photosensitive drums

By aforesaid embodiment explanation, the present invention can reach following effect at least:

(1) setting by two-chip type f theta lens of the present invention, the speed scanning phenomenon such as non-that the mems mirror that carries out simple harmonic motion can be successively decreased by increasing in time originally or increases progressively at imaging surface glazing dot spacing, speed scanning such as be modified to, make laser beam in the scanning of the speed such as projection work of imaging surface, make to image in that formed two adjacent luminous point spacings equate on the object.

(2) by the setting of two-chip type f theta lens of the present invention, can distort and revise scanning ray at main scanning direction and sub scanning direction, the luminous point on the object that focuses on imaging is dwindled.

(3) by the setting of two-chip type f theta lens of the present invention, can distort and revise scanning ray at main scanning direction and sub scanning direction, make the luminous point size homogenising that is imaged on the object.

The above only is a most preferred embodiment of the present invention, only is illustrative for the purpose of the present invention, and nonrestrictive; It will be appreciated by those skilled in the art that in the spirit and scope that limit in claim of the present invention and can carry out many changes, revise it, even the equivalence change, but all will fall within the scope of protection of the present invention.

Claims (5)

1. A two-piece fθ eyeglass of a MEMS laser scanning device, the two-piece fθ eyeglass is suitable for a MEMS laser scanning device, the MEMS laser scanning device at least includes a light source for emitting light beams, and is used to resonate left and right The light beam emitted by the light source is reflected into a micro-electromechanical mirror for scanning light, and an object for photosensitive; the two-piece fθ lens includes, counting from the micro-electromechanical mirror in sequence, a crescent with a positive diopter and a convex surface a first lens on the side of the MEMS mirror and a second lens of positive diopter crescent shape and concave on the side of the MEMS mirror, wherein the first lens has a first optical surface and a second optical surface, At least one optical surface of the first optical surface and the second optical surface in the main scanning direction is an aspherical surface, and the scanning light spot reflected by the micro-electromechanical mirror with a nonlinear relationship between the angle and time is converted into a distance and time It is a scanning light spot with a linear relationship; wherein the second lens has a third optical surface and a fourth optical surface, and at least one optical surface of the third optical surface and the fourth optical surface is an aspheric surface in the main scanning direction, The scanning light of the first mirror is corrected and focused on the target; the scanning light reflected by the micro-electromechanical mirror is imaged on the target through the two-piece fθ mirror. 2. The two-piece fθ eyeglass of the MEMS laser scanning device according to claim 1, is characterized in that the following conditions are further satisfied in the main scanning direction: $\mathrm{<span\; class="notranslate">\; 0.1</span>}<span\; class="notranslate">\; <</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; Y</span>}}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0.8</span>}<span\; class="notranslate">\; ;</span>$ $\mathrm{<span\; class="notranslate">\; 0.2</span>}<span\; class="notranslate">\; <</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; Y</span>}}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0.8</span>}<span\; class="notranslate">\; ;</span>$ Wherein, f _(1)Y is the focal length of the first mirror in the main scanning direction, f _(2)Y is the focal length of the second mirror in the main scanning direction, and _d3 is the focal length of the first lens when θ=0°. The distance from the optical surface on the target object side of the lens to the optical surface on the MEMS mirror side of the second lens, _d4 is the thickness of the second lens when θ=0°, and _d5 is the second lens when θ=0° The distance from the optical surface on the target side to the target. 3. The two-piece fθ eyeglass of the MEMS laser scanning device according to claim 1, is characterized in that further satisfying the following conditions: in the main scanning direction to meet the $\mathrm{<span\; class="notranslate">\; 0.3</span>}<span\; class="notranslate">\; <</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; s\; Y</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}}}<span\; class="notranslate">\; +</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0.6</span>}<span\; class="notranslate">\; ;</span>$ Satisfied in the sub-scanning direction $\mathrm{<span\; class="notranslate">\; 0.8</span>}<span\; class="notranslate">\; <</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; sX</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 1.6</span>}<span\; class="notranslate">\; ;</span>$ Wherein, f _(1)Y and f _(2)Y are the focal lengths of the first lens and the second lens in the main scanning direction, f _sX is the composite focal length of the two-piece fθ lens in the sub-scanning direction, f _sY is the composite focal length of the two-piece fθ lens in the main scanning direction, R _ix is the curvature radius of the i-th optical surface in the sub-scanning direction, n _d1 and n _d2 are the refractive indices of the first lens and the second lens, respectively . 4. The two-piece fθ eyeglass of MEMS laser scanning device according to claim 1, is characterized in that the ratio of maximum light spot and minimum light spot size satisfies: $\mathrm{<span\; class="notranslate">\; 0.4</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ;</span>$ Wherein, S _a and S _b are the lengths of any light spot formed by the scanning light on the target in the main scanning direction and the sub-scanning direction, and δ is the ratio of the smallest light spot to the largest light spot on the target. 5. The two-piece fθ mirror of the MEMS laser scanning device according to claim 1, characterized in that the ratio of the light spot of the scanning light on the reflective surface of the MEMS mirror to the maximum light spot on the target and the ratios to the minimum light spot respectively satisfy ${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0.10</span>}<span\; class="notranslate">\; ;</span>$ ${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0.10</span>}<span\; class="notranslate">\; ;</span>$ Wherein, S _a0 and S _b0 are the lengths of the scanning light spots on the reflection surface of the micro-electromechanical mirror in the main scanning direction and the sub-scanning direction, and S _a and S _b are any one formed by scanning light on the target object. The length of the light spot in the main scanning direction and the sub-scanning direction, η _max is the ratio of the maximum light spot on the target to the light spot of the scanning light on the reflective surface of the micro-electromechanical mirror, and η _min is the target object The ratio of the upper minimum light spot to the light spot of the scanning light on the reflective surface of the MEMS mirror.

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