Image forming method and apparatus using rotated screen with pulse width modulation

Image forming apparatus and method for forming half tone images by pulse width modulating multi-valued image signals comprises first and second pattern signal generators which generate pattern signals each having the same period and a phase shifted from each other, first and second pulse width modulators for pulse width modulating said image signals using the first and second pattern signals, respectively, a selector for selecting either of the first and second pulse width modulated signals and a controller for controlling the selector to obtain a screen angle of 45.degree.. Further, image forming apparatus and method which realizes a screen angle .theta. wherein tan .theta. is represented by a rational number.

BACKGROUND OF THE INVENTION 
1. Field of the invention 
The present invention relates to an image forming apparatus for forming 
images by digitalizing multivalued images using pulse width modulation. 
2. Description of the prior art 
Both high resolution and excellent gradation capabilities are in high 
demand today for both personal- and business-grade laser printers and 
other hard copy imaging devices. An example of a conventional image 
forming apparatus common today is described below with reference to FIG. 
14. 
FIG. 14 is a block diagram of a conventional pulse width modulation circuit 
used for the image forming apparatus. A D/A converter 102 converts a 
raster scan digital image signal 101 to an analog image signal 103. A 1/2 
frequency divider 104 divides a pixel clock 119 of the digital image 
signal 101 in half, and outputs a screen clock 120. Pattern signal 
generator circuits 105, 106, and 107 output pattern signals 108, 109, and 
110, respectively, based on the screen clock 120. The period of each of 
the pattern signals 108, 109, and 110 is twice the pixel clock 119, and 
waveforms of these signals are different from each other. The comparators 
111, 112, and 113 compare the analog image signal 103 with each of the 
pattern signals 108, 109, and 110, and outputs pulse width modulated (PWM) 
signals 121, 122, and 123. A density gradient detection circuit 116 
detects the density gradient of the digital image signal 101 in the main 
scanning direction, and outputs a density gradient detection signal 117. A 
selector 114 selects one of the PWM signals 121, 122, and 123 based on the 
density gradient detection signal 117, and outputs a PWM signal 115. 
FIG. 15 is a timing chart of the conventional pulse width modulation 
circuit shown in FIG. 14. Digital image signal 101 is synchronized with 
rising edges of pixel clock 119. The frequency of screen clock 120 is 
one-half that of pixel clock 119. The voltage of analog image signal 103 
which is converted from digital image signal 101 is low level when digital 
image signal 101 is white data, and it is high level when digital image 
signal 101 is black data. The pattern signal 108 is a ramp wave with a 
slope rising to the right. The pattern signal 109 is a triangular wave. 
The pattern signal 110 is a ramp wave with a slope descending to the 
right. PWM signals 121, 122 and 123 have duties corresponding to 
individual voltage levels of analog image signal 103. The density gradient 
detection circuit 116 shown in FIG. 14 detects the direction and steepness 
of the image signal density gradient, and determines which PWM signal is 
to be selected by the selector 114. PWM signal 115 is an output selected 
by the selector 114 according to a selector control input. 
As thus described, this conventional pulse width modulation circuit is able 
to prevent a drop in the resolution of text images without jaggies 
appearing in the edge area with pulse width modulation of image signals 
containing text and other line images even though the pattern signal 
frequency is twice the pixel clock (see Japanese patent laid-open 
publication number H2-47973). 
However, the screen pattern of the image thus formed is a linear screen 
with longitudinal lines, and, accordingly, the screen pattern is hard on 
the eyes when viewing. 
Furthermore, the linear screen pattern affects differences in the tone upon 
forming halftone color images by overlaying at least cyan, magenta and 
yellow partial images since they are shifted in a different manner 
according to their relative positions on a print paper and, thereby, the 
rate of overlap among them is changed at individual positions. 
In order to avoid these disadvantages due to the linear screen pattern, 
there has been proposed a method in which a screen processing is performed 
by giving a different screen angle for each color so that differences in 
the relative position on the paper do not affect differences in the tone. 
SUMMARY OF THE INVENTION 
Therefore, an object of the present invention is to provide image forming 
method and apparatus which use pulse width modulation, can make the screen 
pattern visually inconspicuous, and can apply screen processing with the 
forty-five (45) degree screen angle necessary when forming color images. 
A further object is to provide image forming method and apparatus which use 
pulse width modulation and can apply the screen processing necessary when 
forming color images using a rational screen angle, 
To achieve these objects, according to the present invention, there is 
provided an image forming apparatus for forming half tone images by pulse 
width modulating multivalued image signals comprising a first pattern 
signal generator for generating a first pattern signal having a period 
other than those corresponding to twice a pitch of a line scanning 
multiplied with an integer; a second pattern signal generator for 
generating a second pattern signal with the same period as the first 
pattern signal but the phase shifted 180.degree. from the phase of the 
first pattern signal; a first pulse width modulation means for outputting 
a first pulse width modulation signal by pulse width modulating the image 
signal based on the first pattern signal; a second pulse width modulation 
means for outputting a second pulse width modulation signal by pulse width 
modulating the image signal based on the second pattern signal; a selector 
for selecting either of the first and second pulse width modulation 
signals; and a selector control means for controlling the selection by the 
selector for each scan line, wherein an image is formed at a screen pitch 
equal to an inverse of a root of the period of the selected pattern signal 
and a 45.degree. pseuedo-screen angle. 
According to one aspect of the present invention, an image forming 
apparatus comprises a clock signal generator for generating a first clock 
signal with a predetermined frequency, and a second clock signal with the 
same frequency as the first clock signal and a phase shifted 180.degree. 
from the phase of the first clock signal; a selector for selecting and 
outputting either the first or the second clock signal ; a pattern signal 
generator for generating a pattern signal based on the clock signal output 
from the selector; a pulse width modulation means for pulse width 
modulating the image signal based on the pattern signal and outputting a 
pulse width modulation signal; and a selector control means for 
controlling the selection made by the selector for each scan line, wherein 
an image is formed at a screen pitch equal to an inverse of a root of the 
predetermined period and a 45.degree. pseudo-screen angle. 
According to another aspect of the present invention, an image forming 
apparatus comprises a pattern signal generator for generating three or 
more pattern signals, each having the same predetermined frequency and a 
different phase; a plurality of pulse width modulation means for pulse 
width modulating the image signal based on the plural three or more 
pattern signals and outputting three or more pulse width modulation 
signals; a selector for selecting and outputting one of the three or more 
pulse width modulation signals; and a selector control means for 
controlling the selection made by the selector for each scan line, wherein 
an image is formed so as to have a screen angle .theta. where tan .theta. 
is a rational number. 
According to a further aspect of the present invention, an image forming 
apparatus comprises a clock generator for generating three or more clock 
signals, each having the same predetermined frequency and a different 
phase; a selector for selecting and outputting one of the three or more 
clock signals; a pattern signal generator for generating a pattern signal 
based on the selector output; a pulse width modulation means for pulse 
width modulating an image signal based on the pattern signal and 
outputting a pulse width modulation signal; and a selector control means 
for controlling the selection made by the selector for each scan line, 
wherein an image is formed so as to have a screen angle .theta. where tan 
.theta. is a rational number. 
The screen used to display an image thus formed can be made visually 
inconspicuous by means of the present invention because screen processing 
is possible at a 45.degree. pseudo-screen angle and desired screen pitch. 
In addition, screen processing at any desired frequency or period and at 
the 45.degree. screen angle required for color imaging is also possible. 
Furthermore, because screen processing at a screen angle of .theta. degrees 
where tan .theta. is a rational number is also possible, the screen 
processing required for color imaging can also be performed.

DESCRIPTION OF PREFERRED EMBODIMENTS 
The preferred embodiments of the present invention are described 
hereinbelow with reference to the accompanying figures, of which FIG. 1 is 
a simplified diagram of the recording section of a laser printer, which is 
one type of image forming apparatus according to the present invention. 
Referring to FIG. 1, the pulse width modulated laser beam emitted from a 
semiconductor laser 31 is collimated by a collimator lens 45. The laser 
beam is then reflected by a rotating polygonal mirror 46, f/.theta. 
corrected by a f/.theta. lens 47, and thus scans a photoconductive drum 
48. The photoconductive drum 48 rotates clockwise as indicated by an arrow 
in FIG. 1, thus forming an electrostatic latent image on the 
photoconductive drum 48. The image represented by this electrostatic 
latent image on the photoconductive drum 48 is then formed on a print 
paper by a well-known electrophotographic method. A pin photodiode 30 is 
provided near the point where each laser beam scan line starts to detect 
the line scanning timing of the laser beam. 
FIG. 2 is a block diagram of the image signal processing section of a laser 
printer according to a first embodiment of an image forming apparatus 
according to the present invention. 
Referring to FIG. 2, an 8-bit digital image signal 1 is converted to an 
analog image signal 3 by a D/A converter 2. The pixel rate of the digital 
image signal 1 is 20 MHz. A crystal oscillator 20 outputs a 56.5685-MHz 
rectangular wave 4. An active LOW beam detect (BD) 5 is input to an 
asynchronous clear (CLR) input of a binary counter 6. The beam detect 
signal 5 is the wave-shaped signal output from the photodiode 30 shown in 
FIG. 1, and is output at each laser beam scan. 
A rectangular wave 4 is input to the binary counter clock input. The binary 
counter 6 1/8-frequency divides the rectangular wave 4 to generate a 
pattern clock 7, which it then outputs from the output terminal QC 
thereof. 
The pattern clock 7 is a rectangular wave synchronized to the beam detect 
signal 5, and has a frequency of 7.0711 MHz. The pattern clock 7 is input 
directly to a first pattern signal generator 8, and is input through an 
inverter 21 to a second pattern signal generator 9. The pattern signal 
generators 8 and 9 generate triangular waves 10 and 11 based on the 
respectively input rectangular waves. 
The triangular waves 10 and 11 have the same frequency as the pattern clock 
7, but the phase of the triangular waves 10 and 11 is offset by 
180.degree.. Because the pixel rate of the digital image signal 1 is 20 
MHz, the frequency of the triangular waves 10 and 11 corresponds to 2.8284 
pixels. 
A comparator 12 compares the analog image signal 3 with one triangular wave 
10, and outputs a HIGH pulse width modulation signal 14 when the analog 
image signal 3 is greater than the triangular wave 10. The other 
comparator 13 compares the analog image signal 3 with the other triangular 
wave 11, and likewise outputs a HIGH pulse width modulation signal 15 when 
the analog image signal 3 is greater than the triangular wave 11. 
Both pulse width modulation signals 14 and 15 are input to a selector 16. 
When a select signal 19 is HIGH, the pulse width modulation signal 15 is 
selected and a laser modulation signal 22 is output. When the select 
signal 19 is LOW, the other pulse width modulation signal 14 is selected 
and the laser modulation signal 22 is output. The laser modulation signal 
22 is input to the laser drive circuit, which is not shown in the figures 
but well known to those in the art. The laser drive circuit drives the 
semiconductor laser when the laser modulation signal 22 is HIGH. 
The beam detect signal 5 and TOP signal 18, which identifies the top of a 
single plane of image, are input to the selector control circuit 17, which 
outputs the select signal 19. The TOP signal 18 is an active LOW pulse 
signal. The operation of the selector control circuit 17 is described in 
greater detail below. 
FIG. 3 is a timing chart of the image signal processing section shown in 
FIG. 2. The operation of the image signal processing section shown in FIG. 
2 is described below with reference to this timing chart. 
The beam detect signal 5 is a LOW pulse line synchronization signal output 
at each laser beam scan. The digital image signal 1 is synchronized to the 
beam detect signal 5. The pixel rate of the 8-bit digital image signal is 
20 MHz, which means that each 50 nsec corresponds to one pixel. The analog 
image signal 3 is an analog signal resulting from digital/analog 
conversion of the digital image signal 1 by the D/A converter 2. A high 
signal potential corresponds to black, and a low potential to white. The 
pattern clock 7 frequency corresponds to 2.8284 pixels. 
The triangular waves 10 and 11 are synchronized to the pattern clock 7. The 
phases of the two triangular waves are shifted 180.degree. relative to the 
other. The pulse width modulation signal 14 is HIGH when the analog image 
signal 3 potential is greater than the triangular wave 10 potential. 
Similarly, the pulse width modulation signal 15 is HIGH when the analog 
image signal 3 is greater than the triangular wave 11. 
FIG. 4 is a block diagram of the selector circuit 17 shown in FIG. 2. The 
single-chip microprocessor (CPU) 25 contains both a programmable counter 
and output port. The beam detect signal 5 is input to the interrupt input 
terminal and the programmable counter clock input terminal of the CPU 25. 
The TOP signal 18, which indicates the top of a single plane of image, is 
input to the trigger input terminal of the programmable counter in the CPU 
25. 
The programmable counter is reset to 0 based on the trigger input, and 
counts up (increments) according to the beam detect signal 5. The CPU 25 
performs an interrupt process according to the beam detect signal 5. 
This interrupt process is described below. 
The CPU 25 reads the current line value (count n) of the programmable 
counter, and computes the equation 
EQU RND(2.times.n/a)MOD2 
where a is the pixel equivalent of the period of each of the 10 triangular 
waves 10 and 11 (a=2.8284 in the present embodiment), RND is a rounding 
function for the decimal part, and MOD is a residue operator. The result 
is either 0 or 1. Based on the result, the CPU 25 sets the output port to 
either a HIGH or LOW level. The output signal 26 from the CPU 25 is LOW 
when the computed result is 0, and HIGH when 1. 
According to the above algorithm, it enables to obtain desirable screen 
pitch and angle as follows. 
If the period of the triangular wave is equal to 2 pixels (a=2), a screen 
processing with a screen pitch of .sqroot.2 pixels and a screen angle of 
45.degree. can be done by shifting the phase of the triangular wave for 
every one line by 180.degree.. Also, if a=4, it is possible to obtain a 
screen processing with a screen pitch of 2.sqroot.2 pixels and a screen 
angle of 45.degree. by shifting the phase of the triangular wave for every 
two lines by 180.degree.. Generally, if a=2.times.m pixels (m is an 
integer), it is possible to obtain a screen processing with a screen pitch 
of m.sqroot.2 a screen angle of 45.degree. by shifting the phase of the 
triangular wave for every m lines by 180.degree.. However, if the period 
of the triangular wave is not equal to 2.times.m pixels (a.noteq.2 m 
pixels), namely, the screen pitch is other than m.sqroot.2 pixels, it is 
impossible to realize a screen processing with a screen angle of 
45.degree. even by shifting the phase of the triangular wave for every 
predetermined number of lines by 180.degree.. 
The present preferred embodiment of this invention solves the above problem 
by introducing a round off calculation [RND(2.times.n/a)]. This enables to 
determine whether or not the phase of the triangular wave has to be 
shifted by 180.degree., approximately. Thus, a screen processing with an 
arbitrary screen pitch and a screen angle of 45.degree. can be realized 
artificially. 
Again, returning to FIG. 4, the beam detect signal 5 is input to the clock 
input of a D flip-flop 27. The CPU 25 output signal 26 is input to the D 
flip-flop 27 D input. A select signal 19, which is a Q output signal from 
the D flip-flop 27, is a signal obtained by synchronizing the D input 
signal 26 to the beam detect signal 5. 
The values obtained by the CPU 25 for the computations based on a given 
counter value n are shown in Table 1 below. 
TABLE 1 
______________________________________ 
n Result 
______________________________________ 
1 1 
2 1 
3 0 
4 1 
5 0 
6 0 
7 1 
8 0 
9 0 
10 1 
11 0 
12 0 
. . . 
. . . 
______________________________________ 
The image formed when the value of all digital image signals 1 in the first 
embodiment of the invention is 64 is shown in FIG. 5. As will be known 
from FIG. 5, the average screen angle is 45.degree., and the average 
screen pitch is one over the square root of the triangular wave period. 
As described hereinabove, screen processing with a 45.degree. screen angle 
and any desired pitch is possible by choosing the triangular wave 
frequency suitably. 
It is to be noted that the CPU 25 used in this embodiment may also execute 
operation other than the calculation described above, including laser 
printer sequence control. The pattern signal may also be a ramp signal 
rather than the triangular wave of the present embodiment. 
FIG. 6 is a block diagram of the image signal processing section of a laser 
printer according to a second embodiment of an image forming apparatus 
according to the present invention. 
Referring to FIG. 6, an 8-bit digital image signal 201 is converted to an 
analog image signal 203 by a D/A converter 202. The pixel rate of the 
digital image signal 201 is 20 MHz. The quartz oscillator 220 outputs a 
64-MHz rectangular wave 204. An active LOW beam detect (BD) signal 205 is 
input to an asynchronous clear (CLR) input of a binary counter 206. The 
beam detect signal 205 is the wave-shaped signal output from the 
photodiode 30 shown in FIG. 1, and is output at each laser beam scan. 
The rectangular wave 204 is input to the binary counter 206 clock input. 
The binary counter 206 1/8-frequency divides the rectangular wave 204 to 
generate a pattern clock 207, which it then outputs from an output 
terminal QC thereof. 
The pattern clock 207 is an 8-MHz rectangular wave synchronized to the beam 
detect signal 205, and is input directly and through an inverter 221 to a 
selector 216. 
When a select signal 219 is LOW, the selector 216 selects and outputs the 
pattern clock 207. A pattern signal generator 208 generates a triangular 
wave 210 based on a rectangular wave 222 output from the selector 216. The 
triangular wave 210 has the same frequency as the pattern clock 207 with a 
phase shift of 180.degree. depending on which input is selected by the 
selector 216. Because the pixel rate is 20 MHz, each triangular wave 210 
period corresponds to 2.5 pixels. 
A comparator 212 compares the analog image signal 203 with one triangular 
wave 210, and outputs a HIGH pulse width modulation signal 214 when the 
analog image signal 203 is greater than the triangular wave 210. The laser 
modulation signal 214 is input to the laser drive circuit (not shown in 
the figures). The laser drive circuit drives the semiconductor laser when 
the laser modulation signal 214 is HIGH. 
The beam detect signal 205 and TOP signal 218 indicating the top of one 
image, are input to the selector control circuit 217, which outputs the 
select signal 219. The TOP signal 218 is an active LOW pulse signal. The 
operation of the selector control circuit 217 is described in greater 
detail below. 
As in the first embodiment described above, the CPU computes the equation 
EQU RND(2.times.n/a)MOD2 
where n is a current scan line of the image being processed, a is the pixel 
equivalent of the triangular wave 210 period (a=2.5 in the present 
embodiment), RND is a rounding function for the decimal part, and MOD is a 
residue operator. 
The values returned for the computations based on a given counter value n 
are shown in Table 2 below. 
TABLE 2 
______________________________________ 
n Result 
______________________________________ 
1 1 
2 0 
3 0 
4 1 
5 0 
6 1 
7 0 
8 0 
9 1 
10 0 
. . . 
. . . 
______________________________________ 
As shown in Table 2, the calculated result is repeated every five scan 
lines. In general, when a is a rational number, the calculated result is 
repeated on a regular cycle of scan lines. 
FIG. 7 is a block diagram of the selector control circuit 217. A 5-bit 
shift register 230 has a parallel load function, and sets a parallel data 
A-E to the internal flip-flop asynchronously to the clock input when the 
LOAD input level is LOW. The parallel load data ABCDE of the shift 
register 230 is set to 01001. BD signal 205 is input to the shift register 
230 clock input. The TOP signal 218 is input to the shift register 230 
LOAD input. The select signal 219 output from one serial output port of 
the shift register 230 is input to another input port of the shift 
register 230 in a feedback loop. 
With this construction, the select signal 219 varies as shown in Table 2 
with the beam detect (BD) signal 205. It is to be noted that the selector 
control circuit shown in FIG. 7 may be formed by a memory device and a 
quinary counter that generates the memory address. 
The image formed when the value of all digital image signals 201 in the 
second embodiment of the invention is 64 is shown in FIG. 8. As will be 
known from FIG. 8, the average screen angle is 45.degree., and the average 
screen pitch is one over the square root of the triangular wave period. 
As described hereinabove, screen processing with a 45.degree. screen angle 
and any desired pitch is possible by controlling the triangular wave 
frequency according to this second embodiment. 
As thus described, this second embodiment of an image forming apparatus can 
make the imaging screen visually inconspicuous with a 45.degree. screen 
angle, and can apply the 45.degree. screen angle screen processing 
required for color imaging at any desired screen pitch. 
FIG. 9 is a block diagram of the image signal processing section of a laser 
printer according to a third embodiment of an image forming apparatus 
according to the present invention. 
Referring to FIG. 9, an 8-bit digital image signal j is converted to an 
analog image signal 1 by a D/A converter 321. The pixel rate of the 
digital image signal j is 5 MHz. A crystal oscillator 322 outputs an 
80-MHz rectangular wave m. An active LOW beam detect (BD) signal n is 
input to an asynchronous clear (CLR) input of a binary counter 323. A beam 
detect signal n is the wave-shaped signal output from the photodiode 30 
shown in FIG. 1, and is output at each laser beam scan. 
The rectangular wave m is a clock input of the binary counter 323. The 
binary counter 323 1/8-frequency divides the rectangular wave m to 
generate a clock p, which it then outputs from an output terminal QC 
thereof. 
The clock p is a 10-MHz rectangular wave synchronized to the beam detect 
signal n, and is input to a pattern clock generator 324. 
The pattern clock generator 324 outputs plural pattern clocks q1-q5 with a 
1-MHz frequency based on the clock p. The phase of each pattern clock is 
shifted by 144.degree. . The pattern clock period corresponds to 5 pixels. 
The phase of the pattern clock q2 is delayed 144.degree. relative to the 
pattern clock q1 phase. Similarly, the pattern clock q3 is delayed 
144.degree. relative to the pattern clock q2, the pattern clock q4 to the 
pattern clock q3, and the pattern clock q5 to the pattern clock q4. A 
pattern clock generator 324 uses the beam detect signal n to synchronize 
the pattern clocks q1-q5 to the beam detect signal. 
The pattern clocks q1-q5 are input to the pattern signal generators 
325-329, respectively, which then output triangular waves r1-r5 based on 
and with the same frequency as the respective pattern clock. 
Comparators 330-334 compare the analog image signal 1 with the triangular 
waves r1-r5, and output a HIGH pulse width modulation signal s1-s5 when 
the analog image signal 1 is greater than the respective triangular wave. 
The pulse width modulation signals s1-s5 are input to the selector 335, 
which selects one of the input pulse width modulation signals based on the 
selector control signal t, and outputs the laser modulation signal u. The 
laser modulation signal u is input to a laser drive circuit, which is not 
shown in the figures. When the laser modulation signal u is HIGH, the 
laser drive circuit drives the semiconductor laser. 
A quinary counter 336 counts the beam detect signal n, and outputs a value 
from 0-4 over output buses v1-v3 to a selector control circuit 337. Based 
on the v1-v3 values input from the quinary counter 336, the selector 
control circuit 337 outputs a selector control signal t causing the 
selector 335 to output the appropriate pulse width modulation signal. The 
pulse width modulation signals s1-s5 selected by the selector 335 for the 
quinary counter 336 output values v1-v3 are shown in Table 3 below. 
TABLE 3 
______________________________________ 
Counter value Selected signal 
______________________________________ 
0 S1 
1 S2 
2 S3 
3 S4 
4 S5 
______________________________________ 
FIG. 10 is a block diagram of the pattern clock generator 324 shown in FIG. 
9. 
Referring to FIG. 10, a serial-in, parallel-out shift register 324a has a 
parallel load function. A value [0000011111] is set in the parallel load 
input of the shift register 324a, and parallel loading occurs when the 
beam detect signal n is ACTIVE. The last output of the shift register 324a 
is input back through the serial input terminal. 
The output p of the 10-MHz counter 323 is input to the shift clock input of 
the shift register 324a. The first output of the shift register 324a is 
output as pattern clock q1. Similarly, the fifth output is output as 
pattern clock q2, the ninth output as pattern clock q3, the third output 
as pattern clock q4, and the seventh output as pattern clock q5. 
The pattern clocks q1-q5 are rectangular waves with a 1-MHz frequency. The 
phase of each pattern clock is shifted by 144.degree.. 
FIG. 11 is a block diagram of the image signal processing section of a 
laser printer according to a fourth embodiment of an image forming 
apparatus according to the present invention. 
Referring to FIG. 11, an 8-bit digital image signal J is converted to an 
analog image signal L by a D/A converter 441. The pixel rate of the 
digital image signal J is 5 MHz. A crystal oscillator 442 outputs an 
80-MHz rectangular wave M. An active LOW beam detect (BD) beam detect 
signal N is input to an asynchronous clear (CLR) input of a binary counter 
443. The beam detect signal N is the wave-shaped signal output from the 
photodiode 30 shown in FIG. 1, and is output at each laser beam scan. 
The rectangular wave M is input to the binary counter 443 clock input. The 
binary counter 443 1/8-frequency divides the rectangular wave M to 
generate a clock signal P, which it then outputs from the output terminal 
QC thereof. 
The clock P is a 10-MHz rectangular wave synchronized to the beam detect 
signal N, and is input to a pattern clock generator 444. The pattern clock 
generator 444 is the same as the pattern clock generator 324 of the third 
embodiment described above. 
The pattern clock generator 444 outputs plural pattern clocks Q1-Q5 with a 
1-MHz frequency based on the clock P. The phase of each pattern clock is 
shifted by 144.degree.. The pattern clock frequency corresponds to 5 
pixels. The phase of pattern clock Q2 is delayed by 144.degree. relative 
to the pattern clock Q1 phase. Similarly, pattern clock Q3 is delayed 
144.degree. relative to pattern clock Q2, pattern clock Q4 to pattern 
clock Q3, and pattern clock Q5 to pattern clock Q4. The pattern clock 
generator 444 uses the beam detect signal N to synchronize the pattern 
clocks Q1-Q5 to the beam detect signal N. 
The pattern clocks Q1-Q5 are input to a selector 445, which selects one of 
the input pattern clocks based on a selector control signal T, and outputs 
a pattern clock U. Based on the selected pattern clock U, a pattern signal 
generator 446 outputs a triangular wave R with the same frequency as the 
pattern clock. 
A comparator 447 compares the analog image signal L with the triangular 
wave R, and outputs a HIGH pulse width modulation signal S when the analog 
image signal L is greater than the triangular wave R. The pulse width 
modulation signal S is input to the laser drive circuit, which is not 
shown in the figures. When the pulse width modulation signal S is HIGH, 
the laser drive circuit drives the semiconductor laser. 
A quinary counter 448 counts the beam detect signal N, and outputs a value 
from 0-4 over output buses V1-V3 to a selector control circuit 449. Based 
on the V1-V3 values input from the quinary counter 448, the selector 
control circuit 449 outputs a selector control signal T causing the 
selector 445 to select the appropriate pattern clock. The pattern clocks 
Q1-Q5 selected by the selector 445 for the quinary counter 448 output 
values V1-V3 are shown in Table 4 below. 
TABLE 4 
______________________________________ 
Counter value Selected signal 
______________________________________ 
0 Q1 
1 Q2 
2 Q3 
3 Q4 
4 Q5 
______________________________________ 
FIG. 12 is an illustration of the formed image when the value of all 
digital image signals in an image forming apparatus according to the third 
or fourth embodiment of the invention is 50. As will be understood from 
FIG. 12, the image forming apparatus of these embodiments uses a 
63.435.degree. screen angle in screen processing. The present embodiment 
is shown for tan 63.435.degree.=2, but screen processing is possible by 
changing the phase of the pattern signal for the screen angle .theta. 
where tan .theta. is a rational number. 
For example, where tan.sup.-1 (1/2)=26.565.degree., the pattern signal 
period is equivalent to (1.sup.2 +2.sup.2)=5 pixels, and screen processing 
is thus made possible for a 26.565.degree. screen angle by delaying the 
triangular wave phase for every line equivalent to 3 pixels. 
Where tan.sup.-1 (1/3)=18.345.degree., the pattern signal frequency is 
equivalent to (1.sup.2 +3.sup.2)=10 pixels, and screen processing is thus 
made possible for an 18.345.degree. screen angle by delaying the 
triangular wave phase for every line equivalent to 7 pixels. 
FIG. 13 shows an example of the screen processing with a screen angle 
.theta. where tan .theta. is a rational number 2/3. In this case, the 
screen dot period in a line scanning direction is 13 pixels (=2.sup.2 
+3.sup.2), as is easily understood from the geometric relation shown in 
FIG. 13. Generally, in the screen processing with a screen angle .theta. 
where tan .theta. is a rational number represented by m/n (m and n are 
integers), the screen dot period is equal to (m.sup.2 +n.sup.2) pixels. 
Accordingly, the period of the triangular wave is to be set equal to 
(m.sup.2 +n.sup.2) pixels. 
Also, it is to be noted that a position of one screen dot on a scanning 
line is equivalent to that on the scanning line locating (m.sup.2 
+n.sup.2) lines after when counted from that line. Accordingly, triangular 
waves equal to a number (m.sup.2 +n.sup.2) which have phases different 
from each other are needed. Further, the phase of each triangular wave has 
to be shifted for every line by 360.degree..times.i/(m.sup.2 +n.sup.2) 
wherein i is an integer since the position of a screen dot on a scanning 
line is shifted by the same pixel number between scanning lines. 
As described hereinabove, by controlling the screen angle, the screen can 
be made visually inconspicuous, the screen processing required for color 
imaging can be applied, and screen processing at the various screen angles 
required for different color imaging effects can be applied. 
The invention being thus described, it will be obvious that the same may be 
varied in many ways. Such variations are not to be regarded as a departure 
from the spirit and scope of the invention, and all such modifications as 
would be obvious to one skilled in the art are intended to be included 
within the scope of the following claims.