The present invention provides a laser scanning apparatus for modulating a laser beam with a modulator into plural independent modulated beams and scanning a plane with the plural beams. In order to prevent a change of the intensity of each beam spot on the scanned plane depending on the exit angle of the beam from the laser, there is provided a converging lens of a focal length f1 between the laser and modulator in such a manner, when the distance from the beam exit of the laser to the converging lens is selected equal to f1+.DELTA.S and the distance from the lens to the modulating point of the modulator is selected approximately equal to f1, as to satisfy the following relation: EQU .vertline..DELTA.S.vertline.<.pi..multidot.Bi.sub.2 /4.lambda. wherein Bi is the diameter of the laser beam and .lambda. is the wave-length of said laser beam.

BACKGROUND OF THE INVENTION 
The present invention relates to a high-speed recording apparatus in which 
a laser beam is modulated into plural independent modulated beams. 
In a laser beam recording apparatus utilizing an acousto-optical modulator, 
a high-speed recording can be achieved by converting a single beam from a 
light source into plural independent beams by simultaneously applying 
ultrasonic waves of plural frequencies to the acousto-optical element and 
scanning a recording medium simultaneously with said plural beams 
modulated independently. 
In a scanning system for single beam scanning by applying an ultrasonic 
wave of a single frequency to the acousto-optical element, the primary 
diffraction intensity is maximized when the incident beam angle to the 
acousto-optical element is so selected that the primary diffraction light 
satifies the optimum Bragg angle. 
In constrast to the above-mentioned case with a single frequency wherein 
the beam incident angle to the acousto-optical element can be determined 
so as to maximize the primary diffraction intensity, the incident angle in 
case of plural frequencies is determined in the following manner. 
FIG. 1 shows the change of the primary diffraction intensity as a function 
of incident angle .theta., in case the acousto-optical element receives 
two different frequencies. 
The curves A and B respectively correspond to the frequencies .nu.A and 
.nu.B, having respective maximum points. Consequently, if the incident 
angle is selected corresponding to the maximum value of either one curve, 
the diffraction intensity for the other curve becomes inevitably lower. 
The two beams having such unbalanced diffraction intensities will provide 
different energy densities on the recording medium, thus giving rise to a 
difference in the density or in the spot diameter. In order to prevent 
such difference the incident angle is selected at .theta..sub.o, shown in 
FIG. 1, corresponding to the crossing point of said curves A and B, 
whereby the diffraction intensities corresponding to two frequencies are 
selected mutually equal, thus giving equal recording densities or spot 
diameters. 
As the above-mentioned incident beam angle .theta..sub.o selected to obtain 
equal intensities in the diffracted beams does not correspond to the 
maximum diffraction intensity for each frequency, an eventual aberration 
of the actual incident angle from said selected angle .theta..sub.o will 
result in a difference among the diffraction intensities, leading to a 
difference in the recording density or in the spot diameter as explained 
in the foregoing. 
An example of the scanning apparatus utilizing an acousto-optical element 
as the modulator and performing the scanning with plural independent beams 
is disclosed in Japanese Patent Laid-Open Sho53-101228, the optical system 
of which, from the laser to the modulator, is schematically there is shown 
in FIG. 2, wherein shown a laser 1, lenses 2, 3 for compressing the beam 
diameter, and an acousto-optical modulator 4. The beam compressing lenses 
2 and 3 constitute an afocal lens system for reducing the diameter Bi of 
the incident laser beam from the laser 1 to an emergent beam diameter Bo. 
In response to a change of the laser beam angle from the laser by 
.DELTA..theta..sub.i, the beam emerging from the beam compressor and 
entering the acousto-optical modulator shows an angular change: 
EQU .DELTA..theta..sub.o =Bi/Bo.times.66.theta..sub.i ( 1) 
Thus, in such optical system as explained in the foregoing, the angular 
change .DELTA..theta..sub.i in the beam emerging from the laser is 
amplified by Bi/Bo in the angular change .DELTA..theta..sub.o of the beam 
entering the acousto-optical modulator. 
SUMMARY OF THE INVENTION 
The object of the present invention is to provide a high-speed scanning 
apparatus which avoids variations in the recording density or in the 
recording spots even when the emerging beam angle of the laser is changed 
by a change in the circumferential temperature or by vibration. 
According to the present invention, the above-mentioned object is achieved 
by maintaining a substantially constant incident beam angle to the 
modulator even when the emerging beam angle from the laser is changed. 
More specifically, in the high-speed scanning apparatus of the present 
invention, there is provided a converging lens of focal length f1 between 
the laser and the multiplex modulator in such a manner, when the distance 
from the beam exit of said laser to said converging lens is selected equal 
to f1+.DELTA.S and the distance from said lens to the beam modulating 
point of said multiplex modulator is selected approximately equal to f1, 
as to satisfy the following relation: 
EQU }.DELTA.S.vertline.&lt;.pi..multidot.Bi.sup.2 /4.lambda. 
wherein Bi is the diameter of the laser beam entering the converging lens 
and .lambda. is the wavelength of said laser beam. 
Furthermore, in a preferred embodiment of the present invention, the 
above-mentioned .DELTA.S is selected equal to zero, while said converging 
lens constitutes a telecentric system having the pupil at the beam exit of 
said laser.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
In the scanning apparatus of the present invention, as schematically shown 
from the light source to the modulator in FIG. 3, a laser 5, a lens 6 and 
an acousto-optical modulator 7 are arranged in such a manner that the 
distance from the beam exit 5a of said laser 5 to the converging lens and 
the distance from the optimum deflecting point 7a of said modulator 7 to 
said lens 6 are both equal to the focal length f1 thereof. 
In such arrangement, in case the emerging beam from the laser 5 is shifted 
from the normal position Lo by an angle .DELTA..theta.i to the position 
Li, the resulting incident beam Li' to the modulator 7 is displaced, in 
comparison with the normal incident beam Lo', by an amount 
f.multidot..DELTA..theta.i in a direction perpendicular to the optical 
axis of the lens 6, but the incident angle of said beam Li' with respect 
to the acousto-optical modulator 7 is the same as that of the beam Lo' 
with respect to the modulator 7. 
The above-mentioned optical system constitutes a so-called telecentric 
system having the pupil at the beam exit of the laser whereby the 
principal ray of the beam being parallel to the optical axis after 
emerging from the lens 6, so that the direction of the beam emerging from 
the lens 6 remains unchanged even when the incident beam angle to the lens 
6 is changed. 
In practice, however, it is not necessary to have such complete telecentric 
system as will be clarified in the following description. 
FIG. 4 illustrates a recording apparatus utilizing the scanning apparatus 
of the present invention, wherein there are shown a laser 5, a converging 
lens 6 of a focal length f1, an acousto-optical modulator 7 capable of 
generating plural primary diffraction lights in response to ultrasonic 
waves of plural frequencies, a converging lens 8 of a focal length f2, a 
converging lens 9 of a focal length f3, a rotary deflecting mirror 10, an 
imaging lens 11 of a focal length f4, and a photosensitive medium 12. 
In the arrangement shown in FIG. 4, the distance from the beam exit 5a of 
the laser to the lens 6 is assumed as f1+.DELTA.S, while the distance from 
said lens 6 to the modulator 7 is selected equal to f1, wherein said 
distances being measured from the principal point of the lens. 
In such arrangement, in case the beam from the exit 5a, which is distanced 
by f1+.DELTA.S from the lens 6, is inclined by an angle .DELTA..theta.i, 
the incident beam angle .DELTA..theta..sub.o to the modulator 7 is 
represented by: 
EQU .DELTA..theta.o=.DELTA.S.multidot..DELTA..theta.i/f1 (2) 
When .DELTA.S=0, the above-explained system is reduced to the telecentric 
system shown in FIG. 3 wherein .DELTA..theta.o is constantly equal to 
zero. 
FIG. 5 shows the effect of the present invention, wherein the line g.sub.1 
represents the case of using a beam compressor between the laser and the 
modulator as shown in FIG. 2 corresponding to the relation (1), while the 
line g.sub.2 represents the case of using a converging lens 6 as shown in 
FIG. 4 corresponding to the relation (2). 
In FIG. 5 there is shown the change .DELTA..theta.o in the incident beam 
angle to the modulator 7 in the ordinate as a function of the change 
.DELTA..theta.i in the emergent beam angle from the laser. If the amount 
.DELTA.S is selected to satisfy the following relation: 
EQU .vertline..DELTA.S.vertline.&lt;(Bi/Bo).multidot.f1 (3) 
the system of the present invention is advantageous as the value 
.DELTA..theta..sub.o according to the present invention is smaller than 
that obtainable with the beam compressor. 
In general, in comparison with the change .DELTA..theta..sub.o of incident 
beam angle to the acousto-optical modulator said change in the present 
invention can be made smaller by a factor (Bi/Bo)/(.DELTA.S/f1), wherein 
Bi is the beam diameter emerging from the laser while Bo is the spot 
diameter at the optimum deflecting point in the acousto-optical modulator 
in the present invention. 
The optimum value of said spot diameter Bo is determined in response to the 
frequency of the ultrasonic wave to be applied to said modulator. 
Also the optimum value of the focal length f1 of the lens 6 is determined 
according to the following equation: 
EQU f1=.pi./4.lambda..multidot.Bi.multidot.Bo (4) 
By substituting this equation (4) into the equation (3) there is obtained: 
EQU .vertline..DELTA.S.vertline.&lt;.pi./4.lambda..multidot.B.sub.i.sup.2 (5) 
wherein .lambda. is the wavelength of the laser beam. 
FIG. 6 is a developed view of the optical system of FIG. 4 shown in a 
cross-section perpendicular thereto, wherein shown is the separation of 
two beams by a pitch P on the photosensitive medium in response to two 
ultrasonic frequencies applied to the acousto-optical modulator. 
When two ultasonic frequencies are applied to the modulator with the 
propagating direction of said ultrasonic waves at an angle .theta.o to the 
optical axis of the optical system, there are generated two primary 
diffraction beams 13, 14 separated by an angle .theta..sub.o ', which 
provides focused spots, on the photosensitive medium, separated by a 
distance P defined by the following equation: 
EQU .DELTA.P=.beta..multidot.f2.multidot..DELTA..theta..sub.o '(6) 
wherein .beta. is the synthesized imaging magnification of the system 
composed of the converging lens 9 and imaging lens 10 by which the focal 
point of the converging lens 8 and the photosensitive medium 12 are 
maintained mutually conjugate. In case the lens 8 and lens 9 constitute an 
afocal system (called the beam relay lens system), said value .beta. is 
defined by f4/f3. 
In the following there will be given a numerical example of the scanning 
apparatus emboyding the present invention. 
In case of using a He-Ne laser with a wavelength .lambda.=6328 A, with an 
emerging beam diameter (1/e.sup.2) Bi of 1.2 mm and with a spot diameter 
of (1/e.sup.2) Bo of 0.15 mm in the modulator, the optimum focal length f1 
of the lens 6 is determined as 223.4 mm from the relation (4), so that 
.vertline..DELTA.S.vertline. should be smaller than 1787 mm according to 
the relation (5). 
Tab. 1 shows the relative intensities of diffracted beams 13, 14 in 
response to an aberration .DELTA..theta..sub.o in the incident beam angle 
to the modulator: 
TABLE 1 
______________________________________ 
Aberration .DELTA..theta..sub..omicron. 
-1 mrad 0 1 mrad 
Beam 13 1.06 1 0.82 
Relative 
intensity Beam 14 0.66 1 1.32 
______________________________________ 
The above-mentioned fluctuation in the diffraction intensities results in a 
fluctuation in the amount of light exposed to the photosensitive medium, 
appearing as a change in the image intensity or in the spot size. 
As explained in the foregoing, if the distance between the laser 5 and the 
lens 6 is selected to satisfy the condition 
.vertline..DELTA.S.vertline.&lt;1787 mm, the diffraction intensities of the 
acousto-optical modulator are superior to those obtainable with the 
conventional beam compressor. 
However, in the foregoing example, the change in the diffraction intensity 
is limited by the values shown in Tab. 1. Thus, inserting f1=223.4 mm and 
.DELTA..theta..sub.o .times.10.sup.-3 rad. into the relation (2) there is 
obtained: 
EQU .DELTA.S.multidot..DELTA..theta.i&lt;223.4.times.10.sup.-3 mm. rad. (7) 
as graphically represented in FIG. 7. 
Also, as already explained, the condition for being superior to the 
conventional beam compressor is: 
EQU .DELTA.S&lt;1787 mm. (8) 
Further, as the distance from the beam exit of the laser to the lens 6 must 
be positive, there should be satisfied: 
EQU .DELTA.S&gt;-f1=-223.4 (9) 
The relations (7), (8) and (9) are satisfied in the hatched areas in FIG. 
7. 
FIG. 8 schematically shows the basic structure of a computer output printer 
utilizing the high-speed scanning apparatus of the present invention. In 
said apparatus the laser beam emitted by a laser 21 is introduced through 
a converging lens system 22 as explained in the foregoing to a multiplex 
acousto-optical modulator 23, which performs beam modulation in response 
to signals received from an unrepresented computer. The plural modulated 
beams emerging from said modulator 23 are expanded by an afocal optical 
system 24 and enter a rotary polygonal mirror 26 having one or plural 
mirror faces and rotated by a drive mechanism 25. Said beams, put into 
horizontal sweeping motion by said rotary polygonal mirror 26, are focused 
as spots on a photosensitive drum 28 through an imaging lens 27 of 
f-.theta. characteristic. In an ordinary imaging lens, the image position 
r on the image plane is related to the incident angle .theta. of the light 
by an equation r=f.multidot..theta. wherein f is the focal length of said 
lens. Consequently, when the incident angle to the imaging lens 27 is 
changed linearly in time by the constant-speed rotation of the mirror 26 
as in the present embodiment, the displacing speed of the focused spot on 
the photosensitive drum constituting the image plane is not constant but 
shows a non-linear change, thus giving a higher displacing speed as the 
incident angle increases. Thus, when the laser is activated at regular 
intervals, the spot obtained on the photosensitive drum 28 are spaced 
closer in the central portion and wider in the edge portions of the drum. 
In order to prevent such phenomenon said imaging lens 27 is designed to 
have a characteristic r=f.multidot..theta., and such imaging lens is 
called an f-.theta. lens. 
Also in case of focusing a parallel beam by an imaging lens into a spot, 
the minimum diameter d.sub.min thereof is given by: 
EQU d.sub.min =f.lambda./A 
wherein f is the focal length of the imaging lens, .lambda. is the 
wavelength of the beam and A is the entrance aperture of said imaging 
lens, so that the spot diameter can be reduced by increasing the aperture 
A for given values of f and .lambda.. The aforementioned afocal lens 
system 24 is employed for this reason. 
The laser beams modulated and deflected as explained in the foregoing are 
directed to the photosensitive drum 28 and converted by a known 
electrophotographic process into a visible image, which is then 
transferred onto plain paper and fixed thereon as a hard copy. As an 
example of the electrophotographic process applicable to the present 
embodiment, there is employed, as disclosed in the Japanese Patent 
Publication Sho 42-23910 assigned to the assignee of the present 
application, a photosensitive drum 28 essentially composed of a conductive 
substrate, a photoconductive layer and an insulating layer is at first 
surfacially charged uniformly with a positive or negative primary corona 
discharger 29 to capture the charge of a polarity opposite to said 
charging polarity at the interface between said photoconductive layer and 
insulating layer or in the photoconductive layer. Subsequently the surface 
of said charged insulating layer is exposed to the aforementioned laser 
beams simultaneously with an AC corona discharge or a corona discharge of 
a polarity opposite to that of said primary charging by a secondary corona 
discharger 30 to form a pattern of surface potential difference on said 
insulating layer corresponding to the intensity pattern of said laser 
beams, and is then illuminated uniformly by a flush exposure lamp 31 to 
form an electrostatic latent image of an elevated contrast on said 
insulating layer. Said latent image is rendered visible by a development 
with a developer principally composed of charged colored particles in a 
developing station 32, and the visible image thus obtained is transferred 
by a transfer charger 34 onto a fan-hold paper 33 (hereinafter referred to 
as transfer paper) maintained in contact with the photosensitive drum 28 
by means to be explained later, and fixed thereon by fixing means to 
obtain an electrophotographic printed image. On the other hand, after said 
image transfer, the surface of said insulating layer is cleaned by a 
cleaning station 35 to remove the remaining charged particles, thereby 
preparing the photosensitive drum 28 for repeated use. In another example 
of the electrophotographic process, there is employed, as disclosed in the 
Japanese Patent Laid-Open Sho 42-19748 assigned to the assignee of the 
present application, a photosensitive drum essentially composed of a 
conductive substrate, a photoconductive layer and an insulating layer, 
which is at first surfacially charged uniformly with a positive or 
negative primary corona discharge to capture a charge of a polarity 
opposite to said charging polarity at the interface between said 
photoconductive layer and insulating layer or in the photoconductive 
layer. Subsequently said insulating layer is subjected to an AC corona 
discharge to attenuate the charge present on the surface of said 
insulating layer, and is then exposed to the aforementioned laser beams as 
information signals thereby forming an electrostatic latent image on said 
insulating layer corresponding to the intensity of said laser beams. The 
latent image thus formed is processed in the same manner as explained in 
the foregoing. In FIG. 8, 36 is a charger for preliminary charge 
elimination for maintaining the photosensitive drum 28 at a uniform and 
constant surface potential, while 37 is a pre-exposure lamp for realizing 
a uniform and constant characteristic in the photosensitive layer, whereby 
said means functioning in cooperation to eliminate various hystereses, 
such as retentive potential, remaining on the photosensitive drum 28 after 
passing the cleaning station 35 and thus to contribute to obtaining a 
stable image. 
Also there has been proposed, in Japanese Patent Application Sho 51-111562, 
a process for stabilizing an electrostatic latent image for constantly 
obtaining a stable and satisfactory image in the electrophotographic 
processes applicable in the present embodiment. 38 is an electrostatic 
potential meter provided for conducting such stabilizing process and for 
measuring the electrostatic potentials of a dark area and a lighted area 
exposed to the laser beams on the photosensitive drum 28. Also 39 is a 
carrier eliminating device for preventing the carrier particles present in 
the developer in the developing station 32 from being carried over by the 
photosensitive drum 28 to the transfer paper or to the cleaning station 
35. 
33 is unprinted paper ordinarily used for computer output such as having 
perforations along the lateral edges thereof. For assisting the 
transportation of said paper there are provided a holding rod 40 for 
facilitating the smooth advancement of the paper, a light source 41 such 
as a light-emitting diode and a photodetector 42 such a photodiode which 
constitute a paper end detector, a known tractor 43 having pins engaging 
with said perforations and rotated by an unrepresented tractor shaft for 
transporting said paper, a paper guide roller 44, a separating claw 45 for 
separating from the photosensitive drum 28 said paper which is pressed 
against said drum by the transfer rollers 46, 47 and by a transfer charger 
34 and remains in such contact state even after the function of said 
rollers and said transfer charger is terminated, and transfer rollers 46, 
47 actuated simultaneously in a same direction to press said paper against 
the photosensitive drum 28. 
Also there are provided a guide roller 48 also functioning to absorb an 
excessive tension eventually applied to the paper during the 
transportation thereof, a hollow preliminary heating roller 49 having a 
heater in the center thereof and a heating roller 50 for fixing the 
transferred toner particles and constituting the fixing station in 
combination with a back-up roller 51. 
Said fixing roller 50 is of a hollow tubular shape and is provided with a 
heat source such as a heater in the center thereof, while said back-up 
roller 51 functions to press the paper having the toner particles thereon 
against said fixing roller 50 to facilitate the heat transmission 
therefrom to the toner particles and to the paper and to apply a high 
pressure to said toner particles. 52 and 53 are eject rollers for ejecting 
the paper 54 after said fixing step.