JP3333832B2 - Multi-beam scanning optical system - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a laser beam scanning optical system for writing data on a digital copying machine, a laser beam printer, an optical disk or the like by using a light beam. The present invention relates to a multi-beam scanning optical system.

[0002]

2. Description of the Related Art FIGS. 3A and 3B are explanatory views of an example of a conventional laser scanning device used for a writing device of a digital copying machine. FIG. 3A shows two lines on a photosensitive member at the same time by two laser beams. FIG. 3B is a plan view of a multi-beam scanning optical system for performing writing, and FIG. 3B is a side view of the same. The multi-beam scanning optical system includes a multi-beam diode laser array 01 (see FIGS. 3A, 3B, and 4) as a semiconductor laser light source that simultaneously emits two laser beams.

As shown in FIG. 4, the multi-beam laser diode array 01 has an electrode substrate 02 on a lower surface and an LD chip (laser diode chip) 0 mounted thereon.
The LD chip 03 includes laser diodes LD ₁ and LD ₂ having two oscillation regions 06 and 07 separated by an insulating layer 05 on a chip substrate 04. The interval between the laser diodes LD ₁ and LD ₂ (the interval between the oscillation regions 06 and 07) is r ₁ .
Then, not shown LD drive circuit connected to the connection terminal Ta, electrodes from Tb 06a, when supplying a driving current through 07a, the respective laser diodes LD ₁ and LD
₂ forwards the _first and second laser beams L ₁ and L ₂ forward,
The back beams L ₁ ′ and L ₂ ′ are emitted backward. Generally, the diameter of the laser beams L ₁ and L ₂ when emitted is ₁ to 4 μm in a direction parallel to the heterointerface.
m, which is difficult to determine, the size of the light source is represented by the spread angle θ ₁ .

The laser array 01 includes a photodiode 08, which receives the back beams L ₁ ′ and L ₂ ′ and connects the light amount signal to a light amount control circuit (not shown). It is arranged to output to the connection terminal 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 an optical power only in the sub-scanning direction. Having a focal length of f ₂ , a mirror 013, a rotating polygon mirror 01
4, f-θ lens 015 and cylindrical lens 0
A multi-beam scanning optical system M comprising a photosensitive drum 018 is provided as a scanning surface rotatably provided around a central axis (that is, a photosensitive member surface).
18a is scanned. The collimating lens 010 and the cylindrical lens 012
The horizontal magnification in the sub-scanning direction of the first scanning optical system M ₁ is m ₁ , and the lateral magnification in the sub-scanning direction of the second scanning optical system M ₂ composed of the f-θ lens 015 and the cylindrical lens 016 is m _1. Magnification is m ₂ . The photosensitive drum 01
8 is provided with an optical sensor 019, and a beam position detection signal SOS (Sta.
The output timing of an image signal to each of the laser diodes LD ₁ and LD ₂ is set by rt of scan (see FIG. 3A).

FIGS. 5 and 6 show the multi-beam scanning optical system M.
Surface 018a when writing scan is performed using
Upper laser beam L₁, L_TwoFIG.
Here, two adjacent laser beams L₁, L_TwoScan with
The interval r between each scan line _ThreeThe scan line width (scan
) The natural number i divided by p is defined as “interlaced scanning cycle”.
Justify.

FIG. 5 shows a case where the number n of laser beams is 2 and the interlaced scanning period i is 1. The first and second laser beams L ₁ and L on the _second photoreceptor surface 018a spots a, b diameter of both the sub-scanning direction are equal in d _3. In this specification, the diameter of the laser beam and its spot is set to the maximum intensity (1 / e) of the light intensity.
² = 0.135 means the diameter of the portion. And
a ₁ and b ₁ are the positions of the spots a and b at the time of the first scan (in the figure, they are indicated as scan numbers (1)),
a ₂ , b ₂ are the positions at the time of the second scan,..., at, bt are the t-th (t =
1, 2, 3,...) Indicate the positions at the time of scanning.

In FIG. 5, at the time of the first scanning, that is, at the scanning number (1), after the _first and second scanning lines are simultaneously scanned by the _first and second laser beams L ₁ and L ₂ , the scanning number is changed.
In (2), the scanning of the third and fourth scanning lines by the _first and second laser beams L ₁ and L ₂ is performed simultaneously. In the same manner, scanning of two lines is repeated in the order of scanning numbers (3), (4), (5),.

As shown in FIG. 6, when the interlaced scanning period is 5, that is, when the interval r ₃ between the _two laser beams L ₁ and L ₂ is set to 5p (p is the scanning line pitch), FIG. the scan number (1), the second laser beam L ₂ is the second scanning line (2), after the scanning of the fourth scan line, the second laser beam L ₂ in scan number (3) or later sixth ,
,... Scan lines are simultaneously scanned, and at the same time, the first laser beam L ₁ scans the first, third, fifth,... Scan lines five lines before the second laser beam L _2. .

The outline of the conventional multi-beam scanning apparatus has been described with reference to FIGS.
In general, the interlaced scanning by the multi-beam is performed when the number n of the laser beams and the interlaced scanning period i are relatively prime, that is, a common positive integer in which the number of the laser beams and the interlaced scanning period are divisible by other than 1. And a multi-beam scanning device using three or more laser beams is also conventionally known.

Next, the conditions for establishing interlaced scanning will be described with reference to the case of four laser beams shown in FIG.
As shown in FIG. 8, i (i =
3) N (n = 4) spots sj (j = 1 to n) are arranged at twice the interval (that is, at the interlaced scanning period i), which is q (q = 4) times the scanning line interval p. Sub-scan interval q
It is assumed that scanning is performed with p and the number of scans t = to (to = 3) becomes one cycle, ie, the number of scans to in one cycle is three. In FIG. 8, the scan number is indicated by t, the first scan is t = 1, and the second scan is t =
The second and third scans are indicated by t = 3, fourth,. Then, the scanning of the first cycle is completed with the scanning number (number of times) t = 3, and the scanning of the second cycle is completed with the scanning of t = 4 to 6. The scanning lines in the first cycle are L ₁ , _{0 to} L ₁ ,
Indicated by _11, the scanning lines of the second period is indicated by L _{2, 0} ~L _{2, 11.}

Since the position of the spot sj (j = 1 to 4) needs to be on the scanning line, i and q are natural numbers. In order for interlaced scanning to be established, the following two conditions (a) and (b) are required. (B) All scanning lines are scanned. (B) The same scanning line must not be scanned twice.

As shown in FIG. 8, in the scan at t = 1 (ie, the first scan), four lines L ₁ , ₀ , L ₁ , ₃ , L ₁ , ₆ ,
L ₁ and ₉ are scanned. One cycle ends with the scanning at t = 1, 2, 3, and so, at t = 4, the first scanning in the next cycle starts. Therefore, at this time,
(B), in order to satisfy the condition of (b) is, want necessary position of the spot S ₁ in the case of t = 4 th scanning is located at the position indicated by the spot S ₅ shown by a dotted line in FIG. 8. That is, to
(= 3) times, that is, the movement distance to × qp of the spot when scanning is performed for the number of times of one cycle needs to be equal to the length n × ip of the spot train for one cycle. Therefore, toq = ni (...) (a) Each spot interval ip is to (= 3) during one cycle.
Since it is filled by the number of scans, ip = top
And i = to......... (B). From the above formulas (a) and (b), q = n.........

As can be seen from FIG. 8, the position (line) of the spot S _{1 at} the _first scan in the second cycle, ie, at t = 4, is the spot at the first scan in the previous cycle, ie, t = 1. ni from the position of the S ₁ (line)
It is a position where the line has advanced. The moving amount of one period of just not predetermined spot Sj spots S ₁ has a common multiple in the interlaced scanning period i and the spot number n.

By the way, the condition (b) is that each spot does not scan the same scanning line during the same period. To this end, n and i are mutually prime. is necessary. Next, this will be described with reference to FIG.
Referring to FIG. 9, when the number of the scanning line is represented by L (t, k) using the number of beams n and the skip period i, L (t, k) = (n · t + 1) + i (k−1) ... (D) where t = −i + 1,... −1, 0, 1,..., I−1; an integer with a scan number k = 1, 2,. In FIG. 9 and the equation (d), the scanning line number scanned by the spot Sk (k = 1, 2,...) At the scanning number t is represented by L (t, k), and t = 0, The scanning line number L (t, k) = 1 when k = 1.

In order not to scan the same scanning line, it is necessary that the numbers of the scanning lines scanned by two arbitrarily selected spots do not coincide within the spot length ni. Are defined as t ₁ and t _2, and arbitrary different spot numbers are defined as k ₁ and k ₂ , the following equation may be satisfied from the equation (d). _{L (t 1, k 1)} = (n · t 1 +1) + i (k 1 -1) ≠ (n · t 2 +1) + i (k 2 -1) = L (t 2, k 2) ∴ n · (t ₁ −t ₂ ) ≠ i (−k ₁ + k ₂ )... (e) where (t ₁ −t ₂ ) and (−k ₁ + k ₂ ) are arbitrary In particular, -n + 1 ≦ (−k ₁ + k ₂ ) ≦ n−1 −k ₁ + k ₂ ≠ 0 ………………………………… (f )

When the signs of (t ₁ −t ₂ ) and (−k ₁ + k ₂ ) are the same and are positive integers, if i and n are relatively prime, the least common multiple is i · n. From (f), the right side i (−k ₁ + k ₂ ) <i · n of the equation (e) is satisfied. Therefore, the number obtained by multiplying n by an arbitrary integer (t ₁ -t ₂ ) is not equal to i (−k ₁ + k ₂ ) which is an integer smaller than the least common multiple i · n of i and n. Therefore, equation (e) holds. Similarly,
The case where the sign is a negative integer also holds. On the other hand, when the signs are different, since n · i is a positive integer, equation (e) clearly holds.

From the above description, the following two conditions must be satisfied in order for interlaced scanning to be established. When the number of laser beams is n and the scanning line interval is p, (1) the amount of parallel movement in the sub-scanning direction for one main scan is n
Must be p. (2) Assuming that a natural number obtained by dividing an interval r ₃ between adjacent laser spots by p is a skip scanning period i, i must be a natural number relatively prime to n (the greatest common divisor is 1). FIG. 10 shows the jump period i and the number n of laser beams that satisfy the above two conditions. As shown in FIG. 10, when the number n of laser beams is determined, a skipping cycle i that can be taken is discretely given.

In general, the factors that determine the image quality of a reproduced image are the spot diameter of a laser beam applied to the surface of a photoreceptor, the width of one scanning line on the surface of the photoreceptor (ie, the scanning pitch), and the laser beam. There is power etc. For example, if the diameter of the spot in the sub-scanning direction is too large, the portion to be colored in the highlight portion becomes small, and the image reproduced when the gradation display by the halftone dot is performed by the background exposure becomes small. Will not be reproduced,
In the shadow area, white areas are crushed. On the other hand, if the diameter is too small, the colored portion becomes 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.

5 and 6, the diameter of the spot of the laser beam irradiated on the photosensitive member surface in the sub-scanning direction is d ₃ , and the width of one scanning line on the photosensitive member surface (ie, the scanning pitch) ) Is p, K = (d ₃ / p)
It is known that good gradation reproducibility can be obtained by setting the value in the range of 1.4 to 1.8 (Tanaka: Optical Fourth Society,
Proceedings of the 6th Color Optics Conference, P77, 198
9 years).

[0021]

By the way, in a laser beam scanning optical system using a multi-beam, a plurality of laser beams L ₁ and L ₂ pass through the same scanning optical system. Accordingly, the plurality of laser beams L _1, L spot a _two photosensitive member surface 018A, the sub-scanning direction between r ₃ and spot a between b, the sub-scanning direction of the diameter d ₃ of b is a respective light source If the distance in the sub-scanning direction between the plurality of laser diodes LD ₁ and LD ₂ of the laser array 1 and the diameter of the oscillation region of the laser diode in the sub-scanning direction (beam diameter at the time of emission) can be accurately determined, 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, the K = (d
It is easy to set the value of ( ₃ / p) in the range of 1.4 to 1.8.

However, it is difficult to accurately determine the beam diameter at the time of emission because the diameter is small, and the diameter d ₃ of the spots a and b in the sub-scanning direction is determined by the laser diode L.
It is determined from the divergence angle θ ₁ of the laser beams L ₁ and L ₂ emitted from D ₁ and LD ₂ . In addition, since the outer peripheral portion of the laser beam is removed by a component of the optical system such as a lens and a rotating polygon mirror while the laser beam passes through the scanning optical system (so-called vignetting of the laser beam occurs), a plurality of laser beams L _1, L ₂ of the spot a, the set the interval r ₃ of b in interlaced scanning period times the scanning pitch p and simultaneously K = the value of (d ₃ / p) 1.
It was difficult to set it in the range of 4-1.8. Therefore, conventionally, it has not been easy to improve the tone reproducibility and line image reproducibility in a multi-beam scanning optical system.

Therefore, the present inventor considered as follows.
That is, the interval r ₁ between each laser diode of the semiconductor laser array that emits a multi-beam, the spread angle θ ₁ and the wavelength λ of each laser beam emitted from each laser diode, and the components of the scanning optical system the values of the parameters of the focal length of, should the spot a, and a distance r ₃ and the sub-scanning direction of the diameter d ₃ of b determined. Therefore, if the relational expression between those parameters is obtained,
By determining the parameters so as to satisfy the relational expression, 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 a jump period times the scanning pitch p and at the same time, The value of K = (d ₃ / p) is 1.4
It is easy to set the value in the range of ~ 1.8. Then, the gradation reproducibility of the multi-beam scanning optical system can be easily improved.

As a result of the examination based on the above consideration, FIG.
In the apparatus shown in FIGS. 3A and 3B, a multi-beam scanning optical system in which an aperture is disposed at a position where the plurality of laser beams (L ₁ , L ₂ ) as the collimated light intersect with the optical axis of the scanning optical system. Succeeded in finding the following relational expression (1). However, [pi ... pi r ₁ ... laser diode LD _1, the spacing between the LD _2, θ ₁ ... laser diode LD _1, the sub-scanning direction spread angle of the laser beam L _1, L ₂ output from the LD ₂ lambda ... The wavelengths of the laser beams L ₁ and L ₂ output from the laser diodes LD ₁ and LD ₂ , and i. The interlaced scanning cycle (the spots a and b of the laser beams L ₁ and L ₂ on the photosensitive member surface 018a (FIG. 5, 6) a natural number obtained by dividing the interval r ₃ by the scanning pitch p, α: a value depending on the diameter of the aperture in the sub-scanning direction,
The focal length of the cylindrical lens 12 is f ₂ , the diameter in the sub-scanning direction of the collimated light or approximately collimated laser beams L ₁ and L ₂ incident on the aperture is D, and the reflection from the rotary polygon mirror (14). When the diameter of the laser beam (L ₁ , L ₂ ) converging on the surface in the sub-scanning direction is d ₂ , a value satisfying d ₂ = (4α / π) (λf ₂ / D); _1, L ₂ of the spot a on the photosensitive member surface 018A, the sub-scanning direction of the diameter d ₃ of the width of the scanning line b divided by (scanning pitch) p, i.e. K = d ₃ / p,

Next, the basis of the above equation (1) will be described. FIGS. 7A and 7B are views showing a scanning optical system in which an aperture 011 is added to the multi-beam scanning optical system M similar to FIGS. 3A and 3B. The aperture 011 is provided at a position where the laser beams L ₁ and L ₂ passing through the collimating lens 010 cross the optical axis. 7A and 7B, if the lateral magnification of the multi-beam scanning optical system M including the optical members denoted by reference numerals 010 to 016 is m, (2)
Expression is made elevational _{r 3 = mr 1 = m 1} m 2 r 1 .............................. (2) Further, if the interlaced scanning period and i, the following equation (3) holds. r ₃ = ip = mr ₁ (3) Assuming that the focal length of the collimating lens 010 is f ₁ and the diameter of the laser beam emitted from the collimating lens 010 is D, (4) The formula holds.

(Equation 1)

After the laser beams L ₁ and L ₂ cross the optical axis at the position where the aperture is provided, an image is formed on the mirror surface of the rotary polygon mirror 014 by the cylindrical lens 012 having a focal length f _2. 014, the diameter d ₂ of the spot of the laser beams L ₁ and L ₂ in the sub-scanning direction
Can be expressed by equation (5) from the Fresnel-Kirchhoff diffraction integral. d ₂ = (4α / π) (λf ₂ / D) …………………………… (5)

The value of α in the above equation (5) is a constant determined by the diameter of the aperture 011 in the sub-scanning direction. For example, the diameter da of the aperture 011 is the same as the diameter of a portion having an intensity half that of the highest intensity portion (beam center portion) of the collimated laser beam having the outer diameter D (hereinafter, referred to as such The diameter having the largest size is expressed as “１ ／ intensity diameter.” In the case of a beam having a Gaussian intensity distribution, the 1/2 intensity diameter is D / 1.70 = 0.
59D. ), The value of α is α = 1.94 as shown in FIG. Similarly, the inner diameter of the aperture 011 is 1 / e ² intensity diameter (that is, 1 / e ² of the highest intensity portion of the laser beam =
Diameter of the same size as the diameter of the part having the strength of 0.135)
Then, the value of α is α = 1.28. When the inside 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 = 1.

A collimating lens 0 having a focal length f ₁
10 and a focal length f ₂ of a cylindrical lens 012
, The lateral magnification m ₁ of the first scanning optical system M ₁ can be expressed by equation (6). m ₁ = f ₂ / f ₁ ─────────── (6) From the above equations (4), (5) and (6), the following equation (7) is obtained. d ₂ = (4α / π) (λf ₂ / D) = (4α / π) (λf ₂ / f ₁ θ ₁ ) = (4α / π) (λm ₁ / θ ₁ ) ... (7) second aperture scanning optical system M ₂ between the rotary polygon mirror 014 and the surface of the photosensitive body 018a is by setting a very large with respect to the laser beam diameter, (8) holds. d ₃ = m ₂ d ₂ ····················································································································· (8) From equations (7) and (8), d ₃ = (4α / π) λm ₁ m ₂ / θ ₁ = (4α / π) λm / θ ₁ (9)

As described above, since K = d ₃ / p,
From this and equation (9), equation (10) is obtained. Kp = (4α / π) λm / θ ₁ (10) The following equation (11) is obtained from the above equations (3) and (10). K / i = (4α / π) λ / r ₁ θ ₁ (11) The equation (1) is obtained by modifying the equation (11). In the above equation (1), by appropriately setting the value of K in the range of 1.4 to 1.8, the values of other parameters can be easily determined.

The present invention has been made in view of the above circumstances and research results, and has as its object to improve the gradation reproducibility of halftone images and line image reproducibility in a multi-beam scanning optical system using a plurality of laser beams. I do.

[0031]

Means for Solving the Problems Next, the present invention for solving the above-mentioned problems will be described. Elements of the present invention are described in order to facilitate correspondence with the elements of the embodiments described later. The sign of parentheses is added in parentheses. The reason why the present invention is described in correspondence with the reference numerals of the following embodiments is to facilitate understanding of the present invention, and not to limit the scope of the present invention to the embodiments. In order to solve the above problems,
A multi-beam scanning optical system according to a first invention of the present application has the following configuration. That is, a laser array (1) having a plurality of laser diodes (LD1, LD2) each driven by an independently modulated LD drive signal and having an oscillation position arranged at a distance of r1.
And a collimating lens (1 / e ² ) output from the plurality of laser diodes (LD1 and LD2) and having a (1 / e ² ) intensity spread angle θ1 and a plurality of laser beams (L1 and L2) having a wavelength λ and collimated. 10) and the laser beam (L1, L2) converted into the collimated light is rotated by a polygon mirror (1).
4) a first scanning optical system (M1) comprising a first sub-scanning direction power optical member (12) having an optical power in the sub-scanning direction converged on the mirror surface, the rotating polygon mirror (14) and the surface of the photoreceptor (18a) and the f-θ lens (1
5) and a sub-scanning direction in which the laser beams (L1, L2) emitted from the f-θ lens (15) are converged at a position separated by a predetermined interlaced scanning period i in the sub-scanning direction Y of the photoconductor surface (18a). A second scanning optical system (M2) comprising a second sub-scanning direction power optical member (16) having an optical power in Y, and a plurality of lasers converted to the collimated light in the multi-beam scanning optical system. When an aperture (11) is arranged at a position where the beams (L1, L2) intersect with the optical axis of the first scanning optical system (M1), and the number of the plurality of laser beams (L1, L2) is n, The interlaced scanning cycle i and the number n of laser beams are relatively prime and n
≧ 3 and i ≦ n, and the above parameters r1, λ, θ
A multi-beam scanning optical system in which 1, and i are determined to satisfy the following equation: K = (4α / π) × (iλ / r1θ1). Here, i ≧ 2 and 1.4 ≦ K ≦ 1.8, and α is a value depending on the diameter of the aperture (11) in the sub-scanning direction, and α is a value of the power optical member (12) in the first sub-scanning direction. The focal length is f
2. (1/1) of the laser beam (L1, L2) converted into collimated light incident on the aperture (11) in the sub-scanning direction.
e ² ) The intensity value diameter is D, and the diameter in the sub-scanning direction of the laser beam (L1, L2) converging on the mirror surface of the rotary polygon mirror (14) is d.
When 2, the value satisfies d2 = (4α / π) × (λf2 / D), and 1.28 ≦ α ≦ 1.94.

[0032]

According to the present invention having the above structure, (4α /
π) iλ / r1 θ1 is determined by setting the values of the parameters α, i, λ, r1 and θ1 so that the value of the parameters α, i, λ, r1 and θ1 is an appropriate value between 1.4 and 1.8. The value K obtained by dividing the diameter of the beam spot in the sub-scanning direction by the width (scanning pitch) of the scanning line is set to an appropriate value between 1.4 and 1.8. The multi-beam scanning optical system in which K is set to such a value has good tone reproducibility and line image reproducibility.

[0033]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1A is a schematic plan view of the scanning optical system of the embodiment,
FIG. 1B is a schematic view of the side view. In FIGS. 1A and 1B, components corresponding to the components in FIGS. 7A and 7B are denoted by the same reference numerals in FIGS. 7A and 7B except for the most significant digit of 0, and redundant detailed description is omitted. I do. In FIG. 1A,
1B is a power optical member in the second sub-scanning direction, and is the cylindrical lens 016 of FIGS. 7A and 7B.
Is replaced by a cylindrical mirror, but the other components employ the same components as those in FIGS. 7A and 7B.

In FIGS. 1A and 1B, reference numerals 10 to 13
The first scanning optical system M₁Is composed
And the lateral magnification in the sub-scanning direction is m₁It is. FIG. 1B
, The focal length of the collimating lens 10 is f₁,
Of the cylindrical lens (first sub-scanning direction optical member) 12
The focal length is f_Two, The focal length of the f-θ lens 15 is f_Three,
Let f be the focal length of the_FourAnd Soshi
Between the laser array 1 and the rotating polygon mirror 14.
Also, collimating lens 10, aperture 11, cylinder
A first lens unit composed of a lithographic lens 12 and a mirror 13
Scanning optical system M₁Is the horizontal magnification in the sub-scanning direction Y₁, And then times
F- is disposed between the polygon mirror 14 and the photoreceptor surface 18a.
Consists of a θ lens 15 and a cylindrical mirror 16
Second scanning optical system M_TwoIs the horizontal magnification in the sub-scanning direction_TwoWhen
And these lateral magnifications m ₁, M_TwoMaru which combined both optical systems
Let the lateral magnification of the chi-beam scanning optical system M be m.

The laser diodes LD ₁ and LD ₂
The distance between the laser beam emission positions is r ₁ , and the divergence angles of the laser beams L ₁ and L ₂ emitted from the laser diodes LD ₁ and LD _{2 in} the sub-scanning direction are θ.
_Set to ₁ . Then, these laser beams L ₁ and L ₂
The lateral through the first scanning optical system M ₁ magnification m _1, is configured to converge once rotary polygon mirror 14 to form a sub-scanning direction size d ₂ in. The rotating polygon mirror laser beam L ₁ reflected by 14, L ₂ is the lateral magnification m ₂ of diameter d ₃ of the spot a sub-scanning direction Y to the second through the scanning optical system M ₂ surface of the photosensitive member 18a, b is formed at a position separated by an interval r ₃ in the sub-scanning direction Y.

The 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 = 13.5 ゜ = 0.235 (radian) f ₁ = 25 mm f ₂ = 419.43 mm m ₁ = f ₂ / f ₁ = 16.78 α = 1.28 m ₂ = 0.5588 m = m ₁ · m ₂ = 9.377 p = 31.25 μm

When the parameters are set as described above, the values of the diameter d ₃ of the spots a and b on the photosensitive member surface 18a in the sub-scanning direction and the distance r ₃ between the spots a and b are set as follows. Try to calculate. r ₃ = r ₁ · m = 93.77 μm ∴i = r ₃ /p=93.77/31.25 = ₃ Also, D = f ₁ · θ ₁ = 25 × 0.235 = 5.9 (mm) ∴d ₂ = (4α / π) λf ₂ / D = 90 μm ∴d ₃ = d ₂ · m ₂ = 90 × 0.5588 = 50 μm ∴K = d ₃ / p = 50 μm / 31.25 μm = 1.6

Therefore, the multi-beam scanning optical system M shown in FIGS. 1A and 1B in which the parameters are set as described above is provided on the photosensitive member surface 18a as spots a and b of the laser beams L ₁ and L ₂ as shown in FIG. b is formed. In FIG. 2, the interlaced scanning cycle i = 3, and the spots a and b of the _two laser beams L ₁ and L _{2 on} the photosensitive member surface 18a.
Of the interval r ₃ = ip = is 3p.

[0039] In this Figure 2, after the scan number (1) and the second laser beam L ₂ was scanned in the second scan line, scan number (2) a second laser in the subsequent beam L ₂
Perform the scanning of the fourth, sixth,.
The laser beam L1 scans the _first , third, fifth,... Scanning lines three lines earlier. In such a scanning optical system having a scanning pitch p = 31.25 μm, 1 m
An image can be written on the photoreceptor surface 18a with a resolution of m / 31.25 μm = 32 dots / mm. In the scanning optical system shown in FIGS. 1A and 1B in which the values of the parameters are set as described above, the value of K (= d ₃ /p=1.6) is in the range of 1.4 to 1.8. , It is possible to obtain good image reproduction.

Next, the resolution described in FIGS. 1A, 1B and 2 is 32 dots / mm, and the value of K (= d ₃ / p) falls within the range of 1.4 to 1.8. A method for setting the parameters of the multi-beam scanning optical system 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) = 13.5 °, wavelength λ = 0.78
μm is used. The value of the distance r ₁ between the laser diode LD ₁ and LD ₂ are determined later.

When the resolution is 32 dots / mm, the scanning pitch p is as follows: p = 1000/32 = 31.25 (μm) Further, as described above, K =
The value of d ₃ / p is 1.4 ≦ K (= d ₃ /p)≦1.8. Therefore, if d ₃ /p=1.6, then d ₃ = 50 μm.

Here, an appropriate value, for example, m ₂ = 0.5588 is adopted as the lateral magnification m ₂ of the second scanning optical system M ₂ disposed between the rotary polygon mirror 14 and the photosensitive member surface 18a. Then, the diameter d ₂ of the laser beam L _1, L ₂ in the sub-scanning direction Y of the spots formed on the rotary polygon mirror 14 becomes _{d 2 = d 3 / m 2} = 89μm. Note that the scanning optical system M ₂ having the lateral magnification m ₂ = 0.5588 has parameters of its components, for example,
It can be obtained by defining the following (a) to (e). That is, (a) the focal length f ₃ of the f-θ lens 15 = 358.75 mm, and (b) the focal length f ₄ of the cylindrical mirror 16 = 10.
(C) a distance of 133.01 mm from the surface of the rotary polygon mirror 14 to the principal point of the f-θ lens 15, (d) a distance of 147.79 mm from the principal point of the cylindrical mirror 16 to the photosensitive member surface 18 a, (E) The distance between the principal points of the f-θ lens 15 and the cylindrical mirror 16 is 210.96 mm,

Next, an appropriate value, for example, f ₂ = 419.43 mm is adopted as the focal length f ₂ of the cylindrical lens 12, and the intensity of 1 / e ² of the peak intensity of the collimated light beam incident on the cylindrical lens 12 is adopted. The diameter in the sub-scanning direction of the collimated light in the sub-scanning direction Y
When an aperture having an inner diameter equal to the diameter of a portion having an intensity of 1 / e ² of the peak intensity (an aperture where α = 1.28) is used, d ₂ = (from the Fresnel-Kirchhoff diffraction integral equation 4 × 1.28 / π) × (λf ₂ / D). Here, the oscillation wavelength λ of the laser diodes LD ₁ and LD ₂ is D = 5.9 mm because λ = 0.78 μm. In addition, since D = f ₁ · θ ₁ and θ ₁ = 13.5 ° (= 0.235 radians) as described above, f ₁ = 25 mm.

From the values of f ₁ and f ₂ , m 1 = f ₂ / f ₁ = 16.78. Therefore, the lateral magnification m of the entire multi-beam scanning optical system M is as follows: m = m ₁ · m ₂ = 16.78 · 0.5588 = 9.377 Incidentally, in the case shown in FIG. 2, since the interlaced scanning cycle 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, each component of the multi-beam scanning optical system M By setting the parameters as described above, a laser scanning device with good image reproducibility can be obtained.

The following is a summary of how to determine the above parameters. That is, to obtain a scanning optical system having a resolution of 32 dots with good image reproducibility using a laser array of θ ₁ = 13.5 °, first determine the value of d ₃ , and then set an appropriate lateral magnification m ₂ . The second scanning optical system is employed. Then, the value of d ₂ is determined. Next, while appropriately selecting a cylindrical lens (power member in the first sub-scanning direction) 12 having an appropriate focal length f ₂ , an appropriate value of α determined by Fresnel-Kirchhoff diffraction integration, for example, α = 1 If .28 is selected, the diameter D of the collimated light in the sub-scanning direction is determined from Expression (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 . If f ₁ and f ₂ are determined, m ₁ is determined, and m is determined from m ₁ and m ₂ . And if m is determined, r
₁ is determined. Thus, the laser array 1 to be used
Is determined.

By the way, as described above, α = 1.28 ≦ α
≦ 1.94 means that the inner diameter of the aperture 11 in the sub-scanning direction is equal to or larger than a half intensity diameter of the collimated light in the sub-scanning direction (that is, D / 1.70 = 0.59D) and 1
/ E ² intensity diameter (that is, D) or less. When α is determined in this manner, a very excellent scanning optical system can be obtained for the following reasons. That is, since the light quantity distribution of the laser beam generally has a Gaussian distribution, the inner diameter of the aperture 11 is set to 1/2 of the collimated light.
As the intensity diameter becomes smaller, the light amount (vignetting light amount) blocked by the aperture 11 sharply increases. That is, the loss of the light amount increases, which is inconvenient.

The laser beam passing through the aperture 11 includes light directly passing through the inner diameter of the aperture 11 and light passing through the surface of the photoreceptor 18a. It is determined by the superposition of two lights, ie, the diffraction integral of Fresnel Kirchhoff. Therefore, when the inner diameter of the aperture 11 is made larger than １ ／, the influence of diffraction is reduced, so that the diameter of the spot easily changes as shown in FIG. It is difficult to adjust the diameter. 0.58 ≦ T ≦ 1, that is, 1.28
If the diameter of the aperture is determined in the range of ≦ α ≦ 1.94, the fluctuation of the spot diameter on the photosensitive material surface due to the fluctuation of the diameter of the beam incident on the aperture can be small, and the design of the scanning optical system becomes easy.

In the above, the spread angle θ _{1 of} the laser beams L ₁ and L ₂ emitted from the laser diodes LD ₁ and LD _{2 is} 13.
5 ° and a wavelength λ = 0.78 μm are set in advance,
This is a method of obtaining a multi-beam scanning optical system having good image reproducibility by determining r ₁ for setting K = d ₃ / p to a desired value later. Distance r ₁ = 1 between laser diodes LD ₁ and LD ₂
A case in which 0 μm and a wavelength λ = 0.78 μm are set in advance and θ ₁ is determined later will be described.

As described above, when the resolution is 32 dots / mm,
The scanning pitch p is p = 1000/32 = 31.25 (μm). Further, as described above, K =
The value of d3 / p is _{1.4 ≦ K (= d 3 /p)≦1.8} . Therefore, if d ₃ /p=1.6, then d ₃ = 50 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, the rotary polygon mirror 1
When the lateral magnification m ₂ of the second scanning optical system M ₂ disposed between the photoreceptor 4 and the photosensitive member surface 18 a is set to m ₂ = 0.5588, d ₂ becomes d ₂ = d ₃ / m ₂ = 89 μm. Next, assuming that a lens of f ₂ = 419.43 mm is adopted as the cylindrical lens 12, d ₂ = (1.6λf ₂ ) / D, as described above. Here, since d ₂ , λ, and f ₂ are known, D = 5.9 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. 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-described embodiments, and various modifications may be made without departing from the present invention described in the appended claims. It is possible to make design changes. For example, by using the above-described parameter setting method, K =
It is possible to easily obtain a multi-beam scanning optical system in which the value of d ₃ / p is in the range of 1.4 to 1.8. Further, the number of laser beams to be used can be an arbitrary number of 2 or more as described with reference to FIGS. Furthermore, a cylindrical mirror may be used as the first sub-scanning direction power optical member 12 instead of a cylindrical lens,
As the second optical power member 16 in the sub-scanning direction, a cylindrical lens, a hologram element, or the like can be used instead of the cylindrical mirror. And mirror 1
3 can be omitted.

[0052]

The multi-beam scanning optical system of the present invention described above.
According to the above, (4α / π) iλ / r ₁θ₁Is 1.4
Each of the above parameters is set to an appropriate value between ~ 1.8.
Α, i, λ, r₁, Θ1 to determine the
Scans the diameter of the laser beam spot on the body surface in the sub-scanning direction.
The value obtained by dividing by the width of the inspection line (scanning pitch) is 1.4 to 1.8.
Can be set to an appropriate value. Therefore,
According to the multi-beam scanning optical system of the present invention, a good image can be obtained.
Reproducibility can be obtained.

[Brief description of the drawings]

FIG. 1 is a schematic plan view and a schematic side view of an embodiment of a multi-beam scanning optical system according to the present invention.

FIG. 2 is a diagram showing a relationship between a laser beam diameter on a photosensitive member surface and a scanning pitch in the embodiment.

FIG. 3 is a plan view and a side view of a conventional example of a multi-beam scanning optical system.

FIG. 4 is an explanatory diagram of a laser array light source of the conventional multi-beam scanning optical system.

FIG. 5 is a diagram showing a relationship between a laser beam (spot) on a photosensitive member surface and a scanning interval in a conventional example.

FIG. 5 is a diagram showing the relationship between a laser beam (spot) on the surface of a photosensitive member and a scanning interval in another conventional example.

FIG. 7 is an explanatory view of an arrangement in which an aperture is provided in the conventional multi-beam scanning optical system shown in FIG. 3;

FIG. 8 is a diagram showing the relationship between the number of laser beams (spots) on a photosensitive member surface and a scanning interval in a conventional example.

FIG. 9 is an explanatory diagram of conditions for establishing a jump cycle.

FIG. 10 is a diagram showing a combination of the number n of laser beams satisfying the conditions of the interlaced scanning and the interlacing period i.

FIG. 11 is a diagram showing the relationship between the 1 / e ² intensity diameter D of the laser beam and α at the position where the aperture having the diameter da is disposed.

FIG. 12 is a diagram showing a relationship between a change in a 1 / e ² intensity diameter D of a laser beam and a laser spot diameter at a position where an aperture having a diameter da is provided.

[Explanation of symbols]

a, b: spot of the laser beam on the surface of the photoconductor, D: diameter of the collimated laser beam in the sub-scanning direction, d
₂ ... diameter in the sub-scanning direction of the laser beam on the reflecting surface of the rotating polygon mirror, d ₃ ... diameter in the sub-scanning direction of the laser beam on the surface of the photoreceptor, f ₂ ... focal length of the power optical member in the first sub-scanning direction,
i ... interlaced scanning period, K ... value obtained by dividing the sub-scanning direction of the diameter d ₃ of the laser beam on the photoreceptor surface by a 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 : interval between a plurality of laser diodes provided in the laser array, r ₃ : spot of the laser beam on the photosensitive member surface a,
distance between b, α: a value depending on the diameter of the aperture, determined by Kirchhoff's diffraction integral, θ ₁ : 1 / e ² intensity spread angle of the laser beam emitted from the laser diode, λ: wavelength of the laser beam, 1: laser array, 10
... Collimating lens, 11 aperture, 12 first sub-scanning direction power optical member (cylindrical lens), 1
4: rotating polygon mirror, 15: f-θ lens, 16: power optical member (cylindrical mirror) in the second sub-scanning direction, 18
a: Photoconductor surface,

Claims (1)

(57) [Claims] 1. A laser array having a plurality of laser diodes, each of which is driven by an independently modulated LD drive signal and whose oscillation position is arranged at a distance of r1, and a sub-scan output by the plurality of laser diodes Lens for converting a plurality of laser beams having a wavelength λ at a (1 / e ² ) intensity spread angle θ1 in the direction into collimated light, and optics in a sub-scanning direction for converging the collimated laser beam to the mirror surface of a rotary polygon mirror Scanning optical system comprising a first sub-scanning-direction power optical member having specific power, and f-θ disposed between the rotary polygon mirror and the surface of the photoreceptor.
A second sub-scanning direction having optical power in the sub-scanning direction Y in which the laser beam emitted from the lens and the f-θ lens is converged at a position separated by a predetermined jump scanning period i in the sub-scanning direction Y on the photoreceptor surface A second scanning optical system comprising: a power optical member; and a multi-beam scanning optical system comprising: a plurality of laser beams converted into the collimated light, wherein an aperture is disposed at a position where the plurality of laser beams intersect with an optical axis of the first scanning optical system. When the number of the plurality of laser beams is n,
The skip scanning period i and the number of laser beams n are relatively prime.
Where n ≧ 3 and i ≦ n, and a multi-beam scanning optical system in which the respective parameters r1, λ, θ1, and i satisfy the following equation: K = (4α / π) (iλ / r1θ1 Here, i ≧ 2 and 1.4 ≦ K ≦ 1.8, and α is a value dependent on the diameter of the aperture in the sub-scanning direction Y, and the focal length of the first sub-scanning direction power optical member is f2. D is the (1 / e ² ) intensity value diameter in the sub-scanning direction of the collimated laser beam incident on the aperture, and d2 is the diameter in the sub-scanning direction of the laser beam converging on the mirror surface of the rotary polygon mirror. Then, d2 = (4α / π) × (λf2 / D), and 1.28 ≦ α ≦ 1.94.