JP2508871B2 - Multi-beam scanning optical system - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION A. Object of the Invention 1) Field of Industrial Application The present invention relates to a digital copying machine, a laser beam printer,
The present invention relates to a laser beam scanning optical system for writing on an optical disc or the like with a light beam, and particularly to a multi-beam scanning optical system for simultaneously writing with a plurality of laser beams.

2) Prior Art FIGS. 3A and 3B are explanatory views of an example of a conventional laser scanning device used in a writing device of a digital copying machine. FIG. 3A shows that two laser beams are simultaneously applied to a photosensitive member. A plan view of a multi-beam scanning optical system for writing lines is shown in FIG. 3B. This multi-beam scanning optical system has 2
Multi-beam diode laser array 01 (3A, 3A, 3) as a semiconductor laser light source that simultaneously emits two laser beams
B, see Fig. 4).

As shown in FIG. 4, the multi-beam laser diode array 01 is mounted on the lower surface of the electrode substrate 02 and the electrode substrate 02.
And an LD chip (laser diode chip) 03,
LD chip 03 is a laser diode having two oscillation regions 06 and 07 separated by an insulating layer 05 on a chip substrate 04.
It has LD ₁ and LD ₂ . Laser diode LD
The interval between ₁ and LD ₂ (the interval between the oscillation regions 06 and 07) is r ₁ . Then, when a drive current is supplied from the connection terminals Ta and Tb connected to an LD drive circuit (not shown) via the electrodes 06a and 07a, the laser diodes LD ₁ and LD ₂ cause the first and second laser beams L ₁ to pass. , L ₂ forward, and back beam L ₁ ′,
It is designed to emit L ₂ ′ backward. Generally,
The laser beams L ₁ and L ₂ have a diameter of 2 to 4 μm when emitted.
The size of the light source is represented by a spread angle θ ₁ . Further, the laser array 01
Is provided with a photodiode 08. The photodiode 08 receives the back beams L ₁ ′ and L ₂ ′ and outputs a light amount signal thereof to a connection terminal connected to a light amount control circuit (not shown).
It is arranged to output to Tc.

As shown in FIGS. 3A and 3B, the optical paths of the laser beams L ₁ and L ₂ emitted from the oscillation regions 06 and 07 have a collimating lens 010 with a focal length f ₁ and have optical power only in the sub-scanning direction. A cylindrical lens 012 with a focal length f ₂ , a mirror 013,
A multi-beam scanning optical system M including a rotary polygon mirror 014, an f-θ lens 015, and a cylindrical lens 016 is provided, and the surface of the photosensitive drum 018 as a scanning surface rotatably provided around the central axis ( That is, the surface of the photoconductor) 018a is scanned. The lateral magnification in the sub-scanning direction of the first scanning optical system M ₁ composed of the collimator lens 010 and the cylindrical lens 012 is m ₁
And the f-θ lens 015 and the cylindrical lens 0
The lateral magnification of the second scanning optical system M ₂ composed of 16 in the sub-scanning direction is m ₂ . An optical sensor 019 is provided at the end of the photosensitive drum 018, and each of the laser diodes LD ₁ , LD is detected by a beam position detection signal SOS (Start of scan, see FIG. 3A) output from the optical sensor 019. The output timing of the image signal to ₂ is set.

FIGS. 5 and 6 are views showing spots of the laser beams L ₁ and L ₂ on the surface 018a of the photoconductor when the writing scanning is performed using the multi-beam scanning optical system M. Here, the natural number i obtained by dividing the interval r ₃ between the scanning lines scanned by the two adjacent laser beams L ₁ and L ₂ by the scanning line width (scanning pitch) p is defined as the “interlaced scanning period”. To do.

FIG. 5 shows a case where the number of laser beams is 2 and the interlaced scanning period i is 1. The spots a and b of the first and second laser beams L ₁ and L _{2 on} the photoconductor surface 018a are equal in the sub-scanning direction with a diameter d ₃ . In addition,
In this specification the diameter of the laser beam and its spot is
It means the diameter of the part where the intensity of light is (1 / e ² ) = 0.135 of the maximum intensity. Then, a ₁ and b ₁ are the positions at the time of the first scanning of the spots a and b (displayed as the scanning number (1) in the figure), and a ₂ and b ₂ are the positions at the second scanning. Position, ..., an, b
n indicates the position at the n-th (n = 1, 2, 3, ...) Scan.

In FIG. 5, during the first scan, that is, scan number (1)
First and second laser beam at L _1, after the scanning of the first and second scan lines by L ₂ is performed at the same time, the first and second laser in scanning number (2) beams L _1, L ₂ of the third, Scanning of four scanning lines is performed simultaneously. Similarly, scan number (3)
The scanning of two lines is repeated in the order of (4), (5), ....

Further, as shown in FIG. 6, in the case of the interlaced scanning period 5, that is, the interval r ₃ between the _two laser beams L ₁ and L ₂ is 5p.
When (p is a scan pitch), the second laser beam L ₂ scans the scan lines 2 and 4 at scan numbers (1) and (2) in FIG. The second laser beam L ₂ scans the 6th, 8th, 10th, ... Scanning lines, and at the same time, the first laser beam L ₁ changes to the second laser beam.
The scanning of the 1st, 3rd, 5th, ... Scanning lines 5 lines before L ₂ is simultaneously performed.

The outline of the conventional multi-beam scanning device has been described above with reference to two beams as an example in FIGS. 5 and 6. In the interlaced scanning by such a multi-beam, the number of laser beams and the interlaced scanning period are generally mutually different. It is possible as long as it is a prime number, that is, if the number of laser beams and the interlaced scanning period do not have a common positive integer that is divisible by other than 1, and a multi-beam scanning device using three or more laser beams is also conventionally known. is there.

By the way, generally, the factors that determine the image quality of a reproduced image are the spot diameter of the laser beam applied to the surface of the photoconductor, the width of one scanning line on the surface of the photoconductor (that is,
Scanning pitch), laser power, and the like.

For example, an image reproduced when gradation display is performed by halftone dots by background exposure is such that if the diameter of the spot in the sub-scanning direction is too large, the colored portion becomes small in the highlight portion and becomes an image. It will not be reproduced and the shadow part will be crushed.
On the other hand, if the diameter is too small, the colored portion will become too large in the highlight portion. That is, the image quality of the reproduced image depends on the spot diameter of the laser beam on the surface of the photoconductor.

In FIGS. 5 and 6, the diameter of the spot of the laser beam irradiated on the surface of the photoconductor in the sub-scanning direction is d ₃ , and the width of one scanning line on the surface of the photoconductor (that is, the scanning pitch) is p. , It is known that good gradation reproducibility can be obtained by setting the value of k = (d ₃ / p) in the range of 1.5 to 1.8 (Tanaka: Optics Society of Japan, 6th Color Optics). See Conference Papers, P77, 1989).

3) Problem to be Solved by the Invention In a laser beam scanning optical system using multiple beams, a plurality of laser beams L ₁ and L ₂ pass through the same scanning optical system. Therefore, the distance r _{3 in} the sub-scanning direction between the spots a and b of the plurality of laser beams L ₁ and L _{2 on} the photosensitive member surface 018a and the diameter d _{3 of the} spots a and b in the sub-scanning direction.
However, the diameter in the sub-scanning direction (beam diameter at the time of emission) of the oscillation region of the laser diode is accurately obtained with the space in the sub-scanning direction between the plurality of laser diodes LD ₁ and LD ₂ of the laser array 1 which is the light source. If possible, the interval r ₃ between the spots a and b of the plurality of laser beams L ₁ and L ₂ is set to an integral multiple of the scanning pitch p, and at the same time, k = (d ₃ / p)
It is easy to set the value of to within the range of 1.5 to 1.8.

However, since the beam diameter at the time of emission is as small as 2 to 4 μm, it is difficult to accurately obtain it, and the spots a, b
The diameter d _{3 in} the sub-scanning direction is determined by the divergence angle θ _{1 of} the laser beams L ₁ and L ₂ emitted from the laser diodes LD ₁ and LD ₂ . Further, while the laser beam is passing through the scanning optical system, the outer peripheral portion of the laser beam may be removed by the components of the optical system, such as a rotating polygon mirror (so-called laser beam vignetting occurs). The interval r ₃ between the spots a and b of the plurality of laser beams L ₁ and L ₂ is set to be an interlaced scanning period times the scanning pitch p, and at the same time, the value of k = (d ₃ / p) is in the range of 1.5 to 1.8. Was difficult to set. Therefore, conventionally, it has not been easy to improve gradation reproducibility in a multi-beam scanning optical system.

Therefore, the present inventor considered as follows. That is,
The spacing r ₁ between the laser diodes of the semiconductor laser array that emits multiple beams, the divergence angle θ ₁ and the wavelength λ of each laser beam emitted from each laser diode, and the focus of the components of the scanning optical system. The distance r ₃ between the spots a and b and the system d _{3 in the} sub-scanning direction should be determined by the values of parameters such as maintenance. Therefore, if the relational expression between these parameters is obtained, by defining each of the parameters so as to satisfy the relational expression, the distance r ₃ between the spots a and b of the plurality of laser beams L ₁ and L ₂ is set. It becomes easy to set the interlacing period times the scanning pitch p and simultaneously set the value of k = (d ₃ / p) in the range of 1.5 to 1.8. Then, the gradation reproducibility of the multi-beam scanning optical system should be easily improved.

As a result of the examination based on the above consideration, in the device as shown in FIGS. 3A and 3B, the position where the plurality of laser beams (L ₁ , L ₂ ) that are the collimated light intersect with the optical axis of the scanning optical system. We succeeded in obtaining the following relational expression (1) for the multi-beam scanning optical system in which the aperture is arranged.

However, r ₁ ... laser diode LD _1, the spacing between the LD _2, θ _{1 ...} laser diode LD _1, the laser beam L ₁ output from the LD _2, L ₂ in the sub-scanning direction divergence angle lambda ... laser diode LD ₁ , LD ₂ output from the laser beams L ₁ and L ₂ , wavelengths, i ... interlaced scanning period (between spots a and b (see FIGS. 5 and 6) of the laser beams L ₁ and L ₂ on the photoconductor surface 018a) Is a natural number obtained by dividing the interval r ₃ by the scanning pitch p, and α is a value depending on the diameter of the aperture in the sub-scanning direction, and the focal length of the cylindrical lens 12 is f ₂ , which is collimated light incident on the aperture. The diameter of the laser beams L ₁ and L _{2 in} the sub-scanning direction is D, and the rotating polygon mirror (14)
When the diameter of the laser beam (L ₁ , L ₂ ) converging on the reflection surface of the sub scanning direction is d ₂ , a value satisfying d ₂ = (αλf ₂ ) / D, k ... Laser beam L ₁ , L ₂ is a value obtained by dividing the diameter d ₃ of the spots a and b on the surface 018a of the photoconductor in the sub-scanning direction by the width (scanning pitch) p of the scanning line, that is, k = d ₃ / p. ) Is explained.

FIG. 7 is a diagram showing a scanning optical system in which an aperture 011 is added to a multi-beam scanning optical system M similar to FIGS. 3A and 3B in FIGS. 7A and 7B. The aperture 011 is arranged at a position where the laser beams L ₁ and L ₂ that have passed through the collimator lens 010 intersect the optical axis.

In FIGS. 7A and 7B, if the lateral magnification of the multi-beam scanning optical system M composed of the optical members denoted by reference numerals 010 to 016 is m, the equation (2) is established. R ₃ = mr ₁ = m ₁ m ₂ r ₁ (2) If the interlaced scanning period is i, the following equation (3) is established.

r ₃ = ip = mr ₁ (3) If the focal length of the collimation lens 010 is f ₁ and the diameter of the laser beam emitted from the collimating lens 010 is D, then equation (4) holds.

_{D = f 1 × 2sin (θ} 1/2) = f 1 θ 1 ...... (4) After crosses the optical axis at the laser beam L _1, L ₂ is the aperture disposed position, the focal length f ₂ of the cylindrical lens 012
Since the image is formed on the mirror surface of the rotating polygon mirror 014 by the above, the diameter d ₂ of the spots of the laser beams L ₁ and L ₂ formed on the mirror surface of the rotating polygon mirror 014 in the sub-scanning direction is given by the Fresnel Kirchhoff diffraction integration ( It can be expressed by equation (5).

It should be noted that the value of α in the equation (5) is the same as the aperture 011
Is a constant determined by the diameter in the sub-scanning direction. For example, the diameter of the aperture 011 is the maximum intensity portion (beam center portion) of the laser beam having the collimated outer diameter D.
The diameter of the same size as the diameter of the part with 1/2 strength (hereinafter,
The diameter of such a size is expressed as "1/2 strength diameter". This 1/2 intensity diameter is D / 1.70 = 0.59D for a beam having a Gaussian intensity distribution. )If it is,
The value of α is 2.5. Similarly, the inner diameter of the aperture 011 is 1 / e ² intensity diameter (that is, 1 / e ² = 0.13 of the highest intensity part of the laser beam).
If the diameter is the same as the diameter of the part with the strength of 5,)
The value of α is α = 1.6. Further, when the inner diameter of the aperture 011 is much larger than the diameter D of the collimated laser beam or when the aperture 011 is not used, the value of α is α = 4 / π 2.

In addition, a _first lens including a collimator lens 010 having a focal length f ₁ and a cylindrical lens 012 having a focal length f ₂ .
The lateral magnification m ₁ of the scanning optical system M ₁ can be expressed by equation (6).

m ₁ = f ₂ / f ₁ (6) The following expression (7) is obtained from the expressions (4), (5) and (6).

If the diaphragm of the second scanning optical system M ₂ between the rotary polygon mirror 014 and the photosensitive member surface 018a is set to be very large with respect to the laser beam diameter, the formula (8) is established.

d ₃ = m ₂ d ₂ (8) From equations (7) and (8), d ₃ = αλm ₁ m ₂ / θ ₁ = αλm / θ ₁ (9) As described above, k = d _Since it is ₃ / p, the equation (10) is obtained from this and the equation (9).

kp = αλm / θ ₁ (10) The following formula (11) is obtained from the formulas (3) and (10).

k / i = αλ / r ₁ θ ₁ (11) The formula (1) is obtained by modifying the formula (11).

In the equation (1), by appropriately setting the value of k within the range of 1.5 to 1.8, it becomes possible to easily set the values of other parameters.

SUMMARY OF THE INVENTION In view of the above circumstances and examination results, it is an object of the present invention to improve gradation reproducibility in a multi-beam scanning optical system using a plurality of laser beams.

B. Configuration of the Invention 1) Means for Solving the Problems In order to solve the problems, the multi-beam scanning optical system of the first invention of the present application is characterized by having the following structure. That is, a laser array having a plurality of laser diodes which are respectively driven by LD drive signals which are independently modulated and whose oscillation positions are arranged at a distance r _1; and a spread angle θ ₁ output by the plurality of laser diodes.
And a first sub-scanning direction power optical member having optical power in the sub-scanning direction for converging the laser beams converted into the collimated light on the mirror surface of the rotating polygon mirror. A first scanning optical system, and f- disposed between the rotary polygon mirror and the surface of the photoconductor.
Second sub-scan having optical power in the sub-scanning direction Y for converging the laser beam emitted from the θ lens and the f-θ lens in the sub-scanning direction Y on the surface of the photoconductor at a position separated by a predetermined interlaced scanning cycle i. A second scanning optical system including a directional power optical member, and a plurality of laser beams converted into the collimated light in the first scanning optical system.
A multi-beam scanning optical system in which an aperture is arranged at a position intersecting the optical axis of the scanning optical system, and the parameters r ₁ , λ, θ ₁ , and i are determined so as to satisfy the following equation.

However, 1.5 ≦ k ≦ 1.8, α is a value depending on the diameter of the aperture in the sub-scanning direction Y, the focal length of the first sub-scanning direction power optical member is f ₂ , and the collimated light incident on the aperture is D ₂ = (αλf ₂ ) / D, where D is the diameter of the laser beam in the sub-scanning direction and D ₂ is the diameter of the laser beam that converges on the mirror surface of the rotating polygon mirror. It is a value.

The multi-beam scanning optical system of the second invention of the present application is the multi-beam scanning optical system of the first invention,
The feature is that α = 2.5.

2) Operation According to the first and second inventions of the present application having the above-mentioned configuration,
By setting the values of the parameters α, i, λ, r ₁ , θ _{1 so that} the value of α i λ / r ₁ θ ₁ is an appropriate value between 1.5 and 1.8, The value k obtained by dividing the diameter of the spot in the sub-scanning direction by the width of the scanning line (scanning pitch) is set to an appropriate value between 1.5 and 1.8. The multi-beam scanning optical system in which k is set to such a value has good gradation reproducibility.

3) Example Hereinafter, an example of the present invention will be described with reference to the drawings.

FIG. 1A is a schematic plan view of the scanning optical system of the embodiment, FIG.
The figure is a schematic view of the same side view. In this Figure 1A, 1B,
The components corresponding to the components of FIGS. 7A and 7B include
Reference numerals other than the most significant digit 0 of the reference numerals in FIGS. 7A and 7B are given and redundant detailed description is omitted. Component 1 of Figures 1A and 1B
6 is a second sub-scanning direction power optical member,
Although a cylindrical mirror is used instead of the cylindrical lens 016 in the figure, the other components adopt the same components as in FIGS. 7A and 7B.

In FIGS. 1A and 1B, the first scanning optical system M ₁ is composed of the optical members denoted by reference numerals 10 to 13, and the lateral magnification in the sub-scanning direction is m ₁ .

In FIG. 1B, the focal length of the collimating lens 10 is
f ₁ , cylindrical lens (first sub-scanning direction optical member)
The focal length of 12 is f ₂ , the focal length of the f-θ lens 15 is f ₃ , and the focal length of the cylindrical mirror 16 is f ₄ . And
The lateral magnification in the sub-scanning direction Y of the first scanning optical system M _{1 including} the collimator lens 10, the aperture 11, the cylindrical lens 12 and the mirror 13 arranged between the laser array 1 and the rotary polygon mirror 14 is m. ₁ , and a second scanning optical system M _{2 including} an f-θ lens 15 and a cylindrical mirror 16 arranged between the rotary polygon mirror 14 and the photosensitive member surface 18a.
Let m _{2 be} the horizontal magnification in the sub-scanning direction, and these horizontal magnifications m ₁ and m ₂
Let m be the lateral magnification of the multi-beam scanning optical system M that is a combination of both optical systems. Further, the respective spacings of the laser beam emitting position of the laser diode LD ₁ and LD ₂ r _1, each of the spread angle of the laser beams L ₁ and L ₂ emitted from the laser diode LD ₁ and LD ₂ and theta _1. Then, these laser beams L ₁ and L ₂ pass through the first scanning optical system M ₁ having the lateral magnification m ₁ and once enter the rotary polygon mirror 14 in the sub-scanning direction.
It is configured to form d ₂ and converge. And
The laser beams L ₁ and L ₂ reflected by the rotary polygon mirror 14 pass through the second scanning optical system M ₂ having the lateral magnification m ₂ to form spots a and b having a diameter d _{3 in} the sub-scanning direction Y on the photoconductor surface 18a. , R in the sub-scanning direction Y
It is configured to form at a position separated by only ₃ .

The respective parameters of the embodiment of the multi-beam scanning optical system shown in FIGS. 1A and 1B are set as follows.

λ = 0.78 μm r ₁ ＝ 10 μm θ ₁ ＝ 20 ° ＝ 0.35 (radian) f ₁ ＝ 25mm f ₂ ＝ 419.43mm m ₁ ＝ f ₂ / f ₁ ＝ 16.78 α ＝ 2.5 m ₂ ＝ 0.5588 m ＝ m ₁・ m ₂ = 9.377 p = 31.25 μm When each of the above parameters is set as described above, the diameter d ₃ of the spots a and b on the photoconductor surface 18a in the sub-scanning direction
Then, the value of the interval r ₃ between the spots a and b will be calculated next.

_{r 3 = r 1 · m =} 93.77μm ∴i = r 3 /p=93.77/31.25=3 _{Also, D = = f 1 · θ} 1 = 25 × 0.35 8.76mm ∴d 2 = αλf 2 /D=92.2μm ∴d ₃ ＝ d ₂ · m ₂ ＝ 92.2 × 0.5588 ＝ 51.5μm ∴k ＝ d ₃ /p＝51.5μm/31.25μm = 1.65 Therefore, the multi-parameter shown in Fig. 1A and 1B with each parameter set as described above. The beam scanning optical system M forms spots a and b of the laser beams L ₁ and L _{2 on} the surface 18a of the photoreceptor as shown in FIG. In FIG. 2, the interlaced scanning period i = 3, and the distance r ₃ = ip = 3p between the spots a and b of the _two laser beams L ₁ and L _{2 on} the photosensitive member surface 18a.

In FIG. 2, the second scan number (1) is used.
After the laser beam L ₂ is subjected to scanning of the second scan lines, scanning signals (2) a second laser in the subsequent beam L ₂ is a 4,6,
--- Simultaneously with scanning the scanning line, the first laser beam
In L ₁ , the scanning of the _first , third, fifth, ... Scanning lines three lines before is simultaneously performed.

In the scanning optical system having such a scanning pitch p = 31.25 μm, an image can be written on the surface 18a of the photoconductor with a resolving power of 1 mm / 31.25 μm = 32 dots / mm.

Then, the scanning optical system shown in FIGS. 1A and 1B in which the values of the parameters are set as described above is the k (= d ₃ /p=1.6)
Since the value of 5) falls within the range of 1.5 to 1.8, it is possible to obtain good gradation reproduction.

Next, the resolution described in FIGS. 1A, 1B, and 2 is 32.
A method of setting the parameters of the multi-beam scanning optical system so that the value of k (= d ₃ / p) in dot / mm falls within the range of 1.5 to 1.8 will be described.

Here, the multi-beam as a laser array 1 of the scanning optical system, the laser diode LD _1, the spread angle theta ₁ of the laser beam L ₁ emitted from the LD _2, L ₂ in the sub-scanning direction (heterointerface direction parallel to) = 20 °, wavelength λ = 0.78 μm. The value of the distance r ₁ between the laser diodes LD ₁ and LD ₂ will be determined later.

 When the resolution is 32 dots / mm, the scanning pitch p is p = 1000/32 = 31.25 (μm).

Further, as described above, the value of k = d ₃ / p suitable for gradation reproduction is 1.5 ≦ k (= d ₃ /p)≦1.8. Therefore, if d ₃ /p=1.65, then d ₃ = 51.5 μm.

Here, if an appropriate value is adopted as the lateral magnification m ₂ of the second scanning optical system M ₂ arranged between the rotary polygon mirror 14 and the photosensitive member surface 18a, for example, m ₂ = 0.5588, then the rotary polygon mirror Laser beam formed on 14
The diameter d ₂ of the spots of L ₁ and L ₂ in the sub-scanning direction Y is d ₂ = d ₃ / m ₂ = 92.2 μm. A scanning optical system in which the lateral magnification is m ₂ = 0.5588
M ₂ can be obtained by defining the parameters of its constituent elements, for example, as in the following (a) to (e). That is, (a) the focal length of the f-θ lens 15 f ₃ = 358.75 mm, (b) the focal length of the cylindrical mirror 16 f ₄ = 109.88.
mm, (c) Distance from the surface of the rotating polygon mirror 14 to the principal point of the f-θ lens 15 133.01 mm, (d) From the principal point of the cylindrical mirror 16 to the photoconductor surface
Distance to 18a is 147.79 mm, (e) Distance between principal points of f-θ lens 15 and cylindrical mirror 16 is 210.96 mm, and then, an appropriate value as focal length f ₂ of cylindrical lens 12, for example, f ₂ = 419.43. mm is used, and the diameter in the sub-scanning direction Y of the portion having the intensity of 1 / e ² of the peak intensity of the collimated light beam incident on the cylindrical lens 12 is defined as the diameter D of the collimated light in the sub-scanning direction. When an aperture having an inner diameter equal to the diameter of the portion having the intensity (α = 2.5) is used, d ₂ = (2.5λf ₂ ) / D is obtained from the Fresnelkirchhoff diffraction integral equation. Here, the oscillation wavelength λ of the laser diodes LD ₁ and LD ₂ is λ = 0.78 μm, and therefore D = 8.76 mm. Further, since D = f ₁ · θ ₁ and θ ₁ = 20 ° (= 0.35 radian) as described above, f ₁ = 25 mm.

From the values of f ₁ and f ₂ described above, m ₁ = f ₂ / f ₁ = 16.78. Therefore, the lateral magnification m of the entire multi-beam scanning optical system M is m = m ₁ · m ₂ = 16.78 · 0.5588 = 9.377. By the way, in the case shown in FIG. 2, since the interlaced scanning period i = 3 and the scanning pitch p = 31.25 μm, r ₃ = i · p = 93.75 μm. Therefore, the distance r ₁ between the laser diodes LD ₁ and LD _{2 of} the laser array 1 is r ₁ = r ₃ /m=93.75/9.377 = 10 μm, that is, the parameters of the respective components of the multi-beam scanning optical system M are set as described above. By setting in this way, it is possible to obtain a laser scanning device having good gradation reproducibility.

The method of defining the above parameters is summarized as follows. That is, when a scanning optical system having a resolution of 32 dots with good gradation reproducibility is obtained by using a laser array with θ ₁ = 20 °, first, the value of d ₃ is determined, and then the appropriate lateral magnification m ₂ is set. The second scanning optical system is adopted. Then, the value of d ₂ is determined. Next, the cylindrical lens (first optical power member in the sub-scanning direction) 12 having an appropriate focal length f ₂ is appropriately selected, and an appropriate value, for example, 2.5 is selected as the value of α determined by the Fresnel Kirchhoff diffraction integral. Then, the diameter D of the collimated light in the sub-scanning direction is determined from equation (5). Then, the focal length f ₁ of the collimating lens can be determined from the diameter D of the collimated light and θ ₁ . f ₁ and
If f ₂ is determined, m ₁ is determined, and m is determined from m ₁ and m ₂ . Then, when m is determined, r ₁ is determined. In this way, the specifications of the laser array 1 to be used are determined.

By the way, setting α = 2.5 as described above means that the inner diameter of the aperture 11 in the sub-scanning direction is set to 1/2 the intensity diameter of the collimated light in the sub-scanning direction (that is, D / 1.70 = 0.59D). However, if α is set in this way, an extremely excellent scanning optical system can be obtained for the following reason. That is, since the light amount distribution of the laser beam generally has a Gaussian distribution, when the inner diameter of the aperture 11 is made smaller than the 1/2 intensity diameter of the collimated light, the light amount blocked by the aperture 11 (vignetting light amount) Increases rapidly. That is, the loss of the light amount becomes large, which is not convenient.

The laser light passing through the aperture 11 includes light that directly passes through the inner diameter of the aperture 11 and light that passes through after being diffracted. However, the diameter of the spot of the laser beam on the photoreceptor surface 18a is It is defined by the superposition, ie the Kirchhoff diffraction integral. Therefore, as the inner diameter of the aperture 11 is made larger than 1/2, the influence of diffraction decreases, so that the diameter of the spot is likely to fluctuate as the laser beam diameter fluctuates, and the diameter of the spot can be adjusted. It becomes difficult.

When the scanning optical system is designed by always setting the system in the sub-scanning direction of the aperture 11 to the 1/2 intensity diameter of the collimated light, the variation of the spot diameter d ₃ due to the variation of the beam diameter is reduced, and the scanning optical system is reduced. The design of is also easy.

The above is the spread angle θ ₁ = 20 ° and the wavelength λ = 0.78 μ of the laser beams L ₁ and L ₂ emitted from the laser diodes LD ₁ and LD _2.
A method for obtaining a multi-beam scanning optical system with good gradation reproducibility by presetting m and then determining r ₁ for setting k = d ₃ / p to a desired value later. In Although,
Next, the laser diodes LD ₁ and LD of the laser array used
_A case will be described in which the distance r ₁ between the _{two is} 10 μm and the wavelength λ is 0.78 μm, and θ ₁ is determined later.

Similar to the above, when the resolution is 32 dots / mm, the scanning pitch p
Is p = 1000/32 = 31.25 (μm).

Further, as described above, the value of k = d ₃ / p suitable for gradation reproduction is 1.5 ≦ k (= d ₃ /p)≦1.8. Therefore, if d ₃ /p=1.65, then d ₃ = 51.5 μm. Then, r ₃ = i · p = 93.75 μm. Therefore, m = r ₃ / r ₁ = 93.75 / 10 = 9.375.

Next, in the same manner as described above, when the lateral magnification m ₂ of the second scanning optical system M ₂ arranged between the rotary polygon mirror 14 and the photosensitive member surface 18a is set to m ₂ = 0.5588, d ₂ Is d ₂ = d ₃ / m ₂ = 92.2 μm. Next, if a lens with f ₂ = 419.43 mm is adopted as the cylindrical lens 12, then d ₂ = (2.5λf ₂ ) / D, similarly to the above. Here, since d ₂ , λ, f ₂ are known, D = 8.76 mm. By the way, since m ₁ = m / m ₂ = f ₂ / f ₁ and m, m ₂ and f ₂ are known, f ₁ is determined. Further, since D = f ₁ · θ ₁ , θ ₁ is determined.

Although the embodiments of the present invention have been described in detail above, the present invention is not limited to the above embodiments, and various small design changes can be made without departing from the present invention described in the claims. It is possible to do.

For example, a multi-beam scanning optical system in which the value of k = d ₃ / p is in the range of 1.5 to 1.8 while setting the parameters of the respective components to various values by utilizing the above-described parameter setting method. It can be easily obtained.
Further, the number of laser beams used can be any number of 2 or more. Furthermore, it is possible to adopt an arbitrary value around 2.5 as the value of α. Furthermore, the first
A cylindrical mirror may be used as the sub-scanning direction power optical member 12 instead of the cylindrical lens, and a cylindrical lens, a hologram element, or the like may be used instead of the cylindrical mirror as the second sub-scanning direction power optical member 16. It is possible. Then, the mirror 13 can be omitted.

C. Effects of the Invention According to the above-described multi-beam scanning optical system of the present invention, each of the parameters α, i, and i, so that the value of αiλ / r ₁ θ ₁ becomes an appropriate value between 1.5 and 1.8. By determining the values of λ, r ₁ and θ _1, the value obtained by dividing the system of the spot of the laser beam on the surface of the photoconductor in the sub-scanning direction by the width (scanning pitch) of the scanning line is set to an appropriate value between 1.5 and 1.8. Can be set to a value.

 Therefore, good gradation reproducibility can be obtained.

[Brief description of drawings]

FIGS. 1A and 1B are a schematic plan view and a schematic side view, respectively, of an embodiment of a multi-beam scanning optical system according to the present invention, and FIG. 3A and 3B are a plan view and a side view of a conventional example of a multi-beam scanning optical system, respectively.
FIG. 5 is an explanatory view of a laser array light source of a multi-beam scanning optical system of the conventional example, and FIGS. 5 and 6 are views showing the relationship between the laser beam diameter on the photosensitive member surface and the scanning pitch of the conventional example, FIGS. 7A and 7B are explanatory views of a multi-beam scanning optical system of the same conventional example in which an aperture is arranged. a, b ... laser beam spot on the surface of the photoconductor, D ...
The diameter of the laser beam in the sub-scanning direction that is collimated light,
d ₂ …… diameter of the laser beam on the reflecting surface of the rotary polygon mirror in the sub-scanning direction, d ₃ …… diameter of the laser beam on the photoconductor surface in the sub-scanning direction, f ₂ …… of the first sub-scanning direction power optical member Focal length,
i: interlaced scanning cycle, k: value obtained by dividing the diameter d ₃ of the laser beam on the surface of the photoconductor in the sub-scanning direction by the scanning pitch p,
L ₁ , L ₂ ...... laser beam, LD ₁ , LD ₂ ...... laser diode, M ₁ ...... first scanning optical system, M ₂ ...... second scanning optical system, M
...... Multi-beam scanning optical system, p …… scanning pitch, r ₁ …
… Spacing between multiple laser diodes provided in the laser array, r ₃ …… Spot of laser beam on photoreceptor surface
Interval between a and b, α: A value that depends on the diameter of the aperture and is determined by Kirchhoff's diffraction integral, θ ₁ ...... 1 / e ² intensity divergence angle of the laser beam emitted from the laser diode, λ ...... Laser beam wavelength, 1 ... Laser array, 10 ... Collimating lens, 11 ...
Aperture, 12 ... 1st sub-scanning direction power optical member (cylindrical lens), 14 ... rotating polygon mirror, 15 ... f-
θ lens, 16 ... Power optical member (cylindrical mirror) in second sub-scanning direction, 18a ... Photoreceptor surface,

Claims (2)

(57) [Claims] _1. A laser array (1) having a plurality of laser diodes (LD ₁ , LD ₂ ) which are respectively driven by LD drive signals which are independently modulated and whose oscillation positions are arranged at a distance r _1. A collimator that collimates a plurality of laser beams (L ₁ , L ₂ ) having a wavelength λ with a 1 / e ² intensity spread angle θ ₁ in the sub-scanning direction output from the plurality of laser diodes (LD ₁ , LD ₂ ). A first sub-scanning direction power optical member having optical power in the sub-scanning direction for converging the lens (10) and the laser beam (L ₁ , L ₂ ) converted into the collimated light onto the mirror surface of the rotating polygon mirror (14) ( A first scanning optical system (M ₁ ) composed of 12), an f-θ lens (15) arranged between the rotary polygon mirror (14) and the surface of the photoconductor (18a), and this f-θ lens the laser beam emitted from the _{(15) (L 1, L} 2) of the photosensitive member surface (18a) Given in the scanning direction Y interlaced scanning period i
A second scanning optical system (M ₂ ) comprising a second sub-scanning direction power optical member (16) having optical power in the sub-scanning direction Y, which converges at a position separated by a distance, and a multi-beam scanning optical system comprising: At the plurality of laser beams (L ₁ ,
An aperture (11) is arranged at a position where L ₂ ) intersects the optical axis of the first operation optical system (M ₁ ) so that the parameters r ₁ , λ, θ ₁ and i satisfy the following equations. Defined multi-beam scanning optics. However, 1.5 ≦ k ≦ 1.8, α is a value that depends on the diameter of the aperture (11) in the sub-scanning direction, and the focal length of the first sub-scanning direction power optical member (12) is f ₂ , and the aperture is Laser beam (L ₁ , L ₂ ) that is collimated light incident on (11)
The 1 / e ² intensity value diameter in the sub-scanning direction of D is D, and the rotating polygon mirror (1
This is a value that satisfies d ₂ = (αλf ₂ ) / D, where d ₂ is the diameter in the sub-scanning direction of the laser beam (L ₁ , L ₂ ) that converges on the mirror surface of 4). 2. The multi-beam scanning optical system according to claim 1, wherein α = 2.5.