Laser printer using multiple sets of lasers with multiple wavelengths

A color printer for imaging on an image plane includes: (a) a plurality of light sources, each of the light sources being adapted to provide a spatially coherent, composite beam of light, each of the composite beams including a plurality of spectral components; (b) a single beam shaping optics accepting the composite beams, the beam shaping optics having optical elements adapted to shape said composite beams by a different amount in a scan direction and a cross scan direction, so as to form for each of the composite beams (i) a first beam waist in the cross scan direction of the composite beam and (ii) a second waist in the scan section of the composite beam, the first and second beam waists being spaced from one another; (c) a deflector adapted to move said plurality of composite beams across the image plane, the deflector being located closer to the first beam waists than to the second beam waists; and (d) scan optics located between the deflector and the image plane, the scan optics being adapted to (i) geometrically conjugate said deflector to the photosensitive medium in the cross scan direction of each composite light beam for each of the spectral components, and (ii) re-image the first and second waists onto the image plane.

FIELD OF THE INVENTION 
This invention relates to laser printers utilizing multiple sets of lasers 
to expose a photosensitive medium, and in particular, to color laser 
printers where each set of lasers has at least two lasers of different 
wavelengths. 
BACKGROUND OF THE INVENTION 
Laser printers utilizing multiple lasers as light sources are known. Such 
laser printers are used primarily for one of two reasons as described 
below. 
First, multiple lasers of the same wavelength are used to increase the 
printing speed of a laser printer by simultaneously scanning across and 
exposing a photosensitive medium with several laser beams. More 
specifically, these laser beams form several adjacent laser spots that are 
scanned simultaneously across a photosensitive medium during a sweep of a 
single polygon facet. Thus, several lines of the photosensitive medium are 
exposed simultaneously, enabling a faster laser printer. 
Light intensity distribution of each laser spot at the photosensitive 
medium is approximately gaussian. The diameters of the exposed pixels are 
equal to the diameters of the laser spots at their 50% intensity level. 
One major problem with simultaneous, multiple spot printing is achieving 
sufficient overlap of the adjacent exposed pixels on the photosensitive 
medium to provide uniform exposed areas without image artifacts. Unless 
these pixels, and thus, the exposed scan lines have sufficient overlap of 
their light intensity profiles, the presence of individual scan lines on 
prints will be apparent and objectionable. Therefore, a printer that 
utilizes multiple lasers to simultaneously expose a photosensitive medium 
must have means for appropriate overlap of the exposed pixels and for 
producing appropriate spot sizes. The following patents describe different 
approaches for producing proper laser spot overlaps, and thus proper pixel 
exposure and proper scan line overlap at the photosensitive medium. 
U.S. Pat. No. 4,253,102 discloses a printer that produces a desired scan 
line pitch (i.e., spacing between the scan lines) by utilizing an inclined 
semiconductor laser array having a plurality of laser light emitters. More 
specifically, these laser light emitters are arranged in a line that is 
tilted with respect to the line scan direction. In such arrays, all laser 
light emitters operate at the same wavelength. The pitch of the laser 
light emitters on this array is P.sub.o (as shown in FIG. 2 of this 
patent). Scanning across the photosensitive medium with the laser beams 
produced by the array that is tilted by an angle .theta. (See FIG. 3 of 
this patent ) results in the pitch of the laser spots at the 
photosensitive medium that is P'=P.sub.o cos(.theta.). 
U.S. Pat. No. 4,393,387 also discloses a printer with a semiconductor laser 
array having a plurality of laser light emitters. This printer produces 
the desired pitch of the laser spots at the photosensitive medium, and 
thus the desired line pitch, by utilizing a prism that changes the 
apparent pitch of the laser light emitters. The pitch of the laser spots 
at the photosensitive medium in the cross scan direction can also be 
adjusted to a desired value by using reflectors as shown in U.S. Pat. No. 
4,445,126. 
Another method of adjusting the pitch of the laser spots is disclosed in 
U.S. Pat. No. 5,463,418 in which the centroids of the laser spot's 
intensity distributions are shifted closer to each other by using an 
aperture stop. This aperture stop is placed in the path of the laser beams 
and is located in front of a polygon. The frame of the aperture stop 
blocks off a portion of a laser beam's cross section, thereby creating non 
uniform laser spots and causing loss of light. U.S. Pat. No. 4,637,679 
uses polarizing beam combiners to combine multiple laser light beams so 
they overlap in the primary scanning direction, but are separated by the 
required amount in the cross scan direction. Polarizing beam combiners 
absorb some of the light and thus cause loss of light. 
It is also possible to write with more widely spaced scan lines as long as 
the scan lines in between are exposed in later scans. This method is 
called interleaving and is described in U.S. Pat. Nos. 4,806,951 and 
4,900,130. 
The above described laser printers are not color printers. They are not 
capable of producing color prints because all lasers operate at the same 
wavelength. In addition, in the above described laser printers, off-axis 
laser beams enter the post-polygon optics causing these laser printers to 
suffer from bowed scan lines. The problem of bowed scan lines is described 
later on in the specification. 
A second reason for utilizing multiple lasers in printers is to print color 
images. This is done by exposing the photosensitive medium, which is 
sensitive to two or more wavelengths of light, by modulated laser beams of 
different wavelengths. This type of a laser printer is known and such 
printers are described in U.S. Pat. Nos. 4,728,965; 5,018,805; 5,471,236; 
5,305,023; and 5,295,143. These laser printers are slow because they 
expose each pixel on the photosensitive medium with a laser beam of 
different wavelength and scan one line at a time. 
SUMMARY OF THE INVENTION 
The object of this invention is to simultaneously expose multiple lines of 
a photosensitive medium with laser beams, each of which laser beams being 
capable of creating laser spots of two or more wavelengths on a given 
pixel of a photosensitive medium, thus exposing these pixels with light 
containing different color wavelengths. 
According to the present invention a color printer for imaging on an image 
plane comprises: 
(a) a plurality of light sources, each of the light sources being adapted 
to provide a spatially coherent, composite beam of light, each of the 
composite beams including a plurality of spectral components; 
(b) a single beam shaping optics accepting the composite beams, the beam 
shaping optics having optical elements adapted to shape said composite 
beams by a different amount in a scan direction and a cross scan 
direction, so as to form for each of the composite beams (i) a first beam 
waist in the cross scan direction of the composite beam and (ii) a second 
waist in the scan direction of the composite beam, the first and second 
beam waists being spaced from one another; 
(c) a deflector adapted to move said plurality of composite beams across 
the image plane, the deflector being located closer to the first beam 
waists than to the second beam waists; and 
(d) scan optics located between the deflector and the image plane, the scan 
optics being adapted to (i) geometrically conjugate said deflector to the 
photosensitive medium in the cross scan direction of each composite light 
beam for each of the spectral components, and (ii) re-image the first and 
second waists onto the image plane.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
In the following discussion and throughout this specification the term 
"page direction" means the cross scan direction. It is the direction 
perpendicular to the scan line produced by a rotation of a polygon or 
other deflector. The term "line direction" means the direction along the 
scan line produced by the rotation of the polygon or other deflectors. 
These directions must be understood in the context of the local coordinate 
system of an optical component; the coordinate system will be tilted by 
fold mirrors. The optical axis of the printer is the Z axis, the page 
direction is the X direction, and the line direction is the Y direction. 
A printer 10 illustrated in FIG. 1a utilizes a plurality of laser beams 12, 
14, 16 produced by multiple sets 20 of lasers 22, 24, 26. Each set 20 of 
lasers 22, 24, 26 provides a plurality of laser beams of at least three 
different wavelengths (red R, green G and blue B, for example). The 
plurality of laser beams 12, 14, 16 from each set 20 of lasers 22, 24, 26 
are combined (as described below) into a composite beam, therefore 
producing multiple composite beams, one for each set of lasers. These 
multiple composite beams are scanned simultaneously across a 
photosensitive medium that is sensitive to these three different 
wavelengths, exposing multiple lines of the photosensitive medium with 
image data. Thus, the photosensitive medium is moved in a page direction 
at a faster rate than if only one line of the photosensitive medium was 
exposed at a time, producing color prints faster. It is preferred that the 
scanning of multiple composite beams be done by a single deflector and 
that a single f-.theta. lens be used to focus all of these composite beams 
on the photosensitive medium. If is preferred that these composite beams 
be held in a close proximity to one another because the image quality 
deteriorates when the composite beams are located further away from an 
optical axis of the f-.theta. lens. Two embodiments of a holder that 
provides the required proximity are described in detail in this 
specification. 
More specifically, the printer 10 of FIGS. 1a, 1b and 1c includes a digital 
image store 11. This digital image store contains three values for each 
pixel of each of the scan lines that are being scanned, each of the three 
values representing the intensity required at one of three wavelengths to 
produce a correct color on an associated photosensitive medium. As stated 
earlier in the specification, the printer utilizes a plurality of red, 
green and blue wavelength laser beams 12, 14, 16 produced by multiple sets 
20 of lasers 22, 24, 26. These laser beams 12, 14 and 16 are propagated to 
a plurality of light intensity modulators. In this embodiment the 
acousto-optical modulators 32, 34, and 36 are used for modulating the 
intensity of laser beams 12, 14 and 16 according to image information. 
Acousto-optical modulators are well known devices. Other means for 
modulating the laser beams may also be employed. 
Each of these acousto-optical modulators 32, 34, 36 modulates its 
associated laser beam by changing its intensity according to the image 
data provided. This will be discussed in more detail in the "Lateral Color 
Correction" section of this specification. All three laser beams are 
modulated simultaneously. 
Two examples of how to couple laser beams 12, 14, 16 from the laser sources 
to the modulators are illustrated in FIGS. 2 and 3. FIG. 2 shows that a 
laser beam 12 is directed to the modulator 32 through a monochromatic 
focusing lens 31 to form a beam waist at the modulator. A similar 
arrangement is used for the laser beams 14 and 16. FIG. 3 shows that, 
alternatively, the laser beams 12, 14, 16 may be coupled to a single mode 
fiber through a fiber optic connector 23, 25, 27. The fiber optic 
connector comprises of a first focusing lens 23a, 25a, 27a, a fiber 23b, 
25b, 27b, and a fiber holder 23c, 25c, 27c with a mechanical motion 
capability to precisely locate and maintain the position of the fiber with 
respect to the laser beam 12, so as to maximize the amount of light 
coupled into the fiber. The beam waist formed on the end of the fiber 23b, 
25b, 27b is re-imaged by a second lens 23d, 25d, 27d to form an 
appropriate beam waist at the modulator 32, 34, 36. More specifically, the 
fiber 23b, 25b, 27b circularizes the laser beam and a circular beam waist 
is then formed at the modulator 32, 34, 36. 
Modulated laser beams (red, green, blue) from each set 20 of lasers are 
optically combined into a plurality composite beams 42 (each composite 
beam having red, green and blue components) by optical combiners such as 
conventional fiber optic multiplexers 40, as shown in FIGS. 1a and 1b. The 
fiber optic multiplexers 40 have appropriate fiber connectors (similar to 
fiber optic connectors 23, 25, 27) to couple the laser beams exiting the 
modulators to the input fibers 40a, 40b, 40c of the fiber optic 
multiplexer 40. (FIG. 1b) Thus, the output end of each of the fiber optic 
multiplexers 40 produces a beam waist of different size in each of the 
three colors at the output end of each of the beam combining fibers 40d 
(see FIG. 4). The output end of each fiber 40d becomes a source of one of 
the composite beams 42 and corresponds to one scan line on the 
photosensitive media. Because printer 10 comprises several composite laser 
beam sources that are placed in close proximity to one another, several 
adjacent lines of image data are exposed simultaneously, making this color 
printer faster than the prior art color printers described above. 
More specifically, the beam combining fibers 40d are single mode optical 
fibers. The beam waists formed at the output end of each of the beam 
combining fibers 40d are coplanar. In one embodiment the radii of these 
waists at the exp(-2) power level in this embodiment are: 0.00189 mm at 
.lambda.=532 nm (green color G), 0.00172 mm at .lambda.=457.9 nm (blue 
color B) and 0.00237 mm at .lambda.685 nm (red color R). The shapes of the 
beam waists formed at the output end of each of the beam combining fibers 
40d are circular. 
An advantage of using multiplexers and the holder is that once the beam 
combining fibers are rigidly held, one has the ability to rotate the 
output ends of the beam combining fibers together as a unit. Another 
advantage is the ability to replace, when needed, only one of the lasers 
instead of replacing a light source containing a multiplicity of laser 
beams. This makes the optical alignment much simpler because only the 
optics dedicated to a specific laser will need to be re-aligned. 
The composite beams (of red, blue and green components) exit the 
multiplexers 40 (at the output ends of the beam combining fibers 40d. It 
is preferred that the composite beams be located very close to one 
another. This proximity is provided by a holder 43. Two embodiments of the 
holder 43 are described later on in the specification. 
The cores of the beam combining fibers contain almost all of the laser 
power. Thus, it is the cores at the output ends of these fibers that must 
be located in close proximity to one another. The positioning of the cores 
at the output ends of the beam combining fibers 40d in close proximity to 
one another is a problem because the cores of the fibers have a very small 
diameter d.sub.1 compared with the outside fiber cladding diameter 
d.sub.2, thus limiting how close the cores can be located with respect to 
one another. The core diameters d.sub.1 are typically less than 4 microns 
while the cladding diameters d.sub.2 are typically about 125 microns. 
Thus, even if the fibers touch each other, the core centers are separated 
from one another by about 65 microns. It is preferable to reduce this 
distance. 
A solution for this large separation of the cores is to chemically etch 
away, or otherwise reduce, the outside cladding of each beam combining 
fiber in such a way that a tapered profile is fashioned near the output 
ends of the beam combining fibers. Such fibers 40d are shown in FIG. 5a. 
However, if one etches the cladding too close to the core, intensity 
profiles of the exiting composite beams will be adversely affected. This 
effect can be minimized if the outside fiber cladding diameter d.sub.2 is 
not reduced to less than three core diameters d.sub.1. Thus, if the 
tapered ends have outside diameters are about 20 microns, and the etching 
is uniform about the core, and the fiber ends are abutting one another, 
the centers of the fiber cores are separated by a distance of only 20 
microns. 
It is noted that the distance between the fiber cores should be constant or 
nearly constant (less than 10% variation) in order to achieve uniform 
exposure at the photosensitive medium. If some of the fibers are etched 
more than other fibers, and the claddings of the fibers abut one another, 
the fiber cores will not be separated by a constant distance. This is 
shown in FIG. 5b. The irregular spacing of the fiber cores creates 
excessive or insufficient pixel overlap on the photosensitive medium, 
making it difficult to achieve uniform exposure at the photosensitive 
medium. Thus, care should be taken to ensure that the reduction in fiber 
cladding is uniform among the fibers. 
According to the first embodiment of the present invention the holder 43 is 
a V-block shown in FIG. 6. More specifically, V-block has a plurality of 
V-shaped grooves 43a and the output ends of the beam combining fibers 40d 
are held in a close proximity by these grooves 43a. The V-block may be 
made of a silicon or quartz, for example. FIG. 6 shows an end view of 
output ends of the beam combining fibers which have had their cladding 
reduced, so that their outer diameters d.sub.2 are three times size of the 
core diameters d.sub.1. The V-block ensures that the cores of the beam 
combining fibers are centered on their outer diameters. It is noted that 
it is important to keep the cores centered on the cladding diameters in 
order to achieve the uniform spacing of the exposed pixels on the 
photosensitive medium. 
The cores at the output ends of the beam combining fibers are used as the 
light sources of the composite beams 42. Thus, even a small separation 
(such as 10 micrometer separation) between the centers of these fiber 
cores may result in an undesirably large separation between the exposed 
pixels, introducing undesirable artifacts into an image. Therefore, some 
device or a method of operation is required to provide for properly 
overlapped exposed pixels on the photosensitive medium. One way to do this 
is to (i) place the output ends of the beam combining fibers into the V- 
block as described above and (ii) rotate the V-block as shown in FIG. 7 to 
achieve the desired pitch between the light sources--i.e., the desired 
spacing between the cores at the output ends of the beam combining fibers. 
Because of the tilt of the V-holder, the light sources appear to be spaced 
closer together, such that the intensity distributions of the laser spots 
produced at the photosensitive medium overlap sufficiently in the cross 
scan direction. More specifically, the pitch P of the fiber cores, 
produces an apparent pitch P', when the array of fiber cores is tilted by 
an angle q. The following equation relates these parameters: 
EQU P'=P cos (q) 
Tilting the array of fiber cores by a large angle makes it possible to 
avoid reducing the thickness of the cladding at the ends of the beam 
combining fibers 42. For example, if the cladding is 125 microns in 
diameter, a core diameter is 5 microns, and the desired pitch is 5 
microns, a tilt angle of 87.71 degrees would provide the needed pitch of 
laser spots on the photosensitive medium. However, such large tilt angles 
result in sensitivity to pitch changes caused by errors in the tilt angle, 
because even a relatively small change in the tilt angle q will result in 
a relatively large change in the pitch of the exposed pixels. 
Proper spot overlap in the line scan direction can be achieved through 
electronic timing of the pixel exposure. 
In a second embodiment the holder 43 is a waveguide with a set of input 
ports, a set of output ports and a set of channels 43b connecting the 
input ports to the output ports. According to this embodiment the output 
fibers 40d are coupled into the input ports of the waveguide channels 43b. 
The channels 43b are made so that the spacings 43c between the channels 
43b are reduced as the composite beams propagate down their length as 
shown in FIG. 8. The cross sectional size (i.e., width and height) of each 
of the waveguide channels 43b is maintained along its length so that the 
composite beams exiting from the output ports of the waveguide channels 
have substantially the same sizes as the entering composite beams. In this 
embodiment the output ports of the channels serve as the light sources of 
the closely spaced composite beams. 
The problems associated with uneven etching of fiber cladding can be 
avoided if the ends of the beam combining fibers are coupled into the 
input ports waveguide channels as shown in FIG. 8. This coupling requires 
no etching of claddings. Custom made waveguides such as the one shown in 
FIG. 8 are commercially available from Photonic Integration Research, 
Inc., Columbus, Ohio. In order to minimize power loss at the coupling 
interface, it is important to use a single mode waveguide whose 
fundamental mode closely matches the mode field size of the beam combining 
fiber. Also, if a direct coupling method is being used, the ends of the 
beam combining fibers must be positioned laterally with the waveguide 
channels so as to satisfy tight tolerance requirements (for example, 
.DELTA.X and .DELTA.Y tolerances should be within less than 10% of final 
core diameter). The optical axis of each beam combining fiber needs to be 
aligned with the waveguide channel's axis in order to achieve maximum 
coupled optical power. Methods for proper coupling of optical fibers to 
waveguide channels are well known. 
In order to avoid cross-talk, the channels of the waveguide must be 
separated even at the output end of the waveguide. Thus, it may be 
difficult to have the exiting beams close enough together even if one 
utilizes the improved waveguide shown in FIG. 8. Therefore, it may be 
necessary to use another, additional method to provide the adjacent 
exposed scan lines with sufficient overlap at the photosensitive medium. 
This may be accomplished, for example, by tilting the waveguide in a way 
similar to tilting the V-block, so that the line of laser spots exposing 
the medium has the desired pitch. Similar results may also be accomplished 
by using interleave printing. The waveguide has the same advantage as the 
fibers mounted in a V-block. That is, the waveguide can be tilted 
independently of the laser sources and the rest of the optical system. An 
advantage of the waveguide over fibers mounted in the V-block is that the 
waveguide channel dimensions and pitch are controlled easier than the 
position of the fiber cores within their reduced size cladding. 
Another way to have overlapping spots (at approximately 50% of their 
intensity profiles) is to use interleave printing in which the 
photosensitive medium is exposed with separated scan lines and the 
unexposed area between these lines is exposed in later passes of the 
separated light beams. The scan lines must be spaced by some multiple of 
the desired pitch. Also, interleave printing can be combined with printing 
that utilizes a tilted line of scanning laser spots. 
Typically, scanning is performed with a single light beam that is scanned 
in a plane that contains the optical axis of the post-polygon scan optics 
(such as an f-.theta. lens, for example). For purposes of this 
specification this plane is a YZ plane. The present printer utilizes a 
plurality of composite beams. These composite beams are displaced with 
respect to one another and should produce a plurality of essentially 
parallel scan lines at the photosensitive medium (FIG. 1c). Because only 
one of these composite beams can be scanned in a plane containing the 
optical axis, most of the composite beams are not contained within this YZ 
plane and enter the scan optics off-axis. We found that there are a series 
of problems associated with off-axis light beams being scanned by the scan 
optics, the severity of the problems increasing with the amount of 
displacement of the off-axis light beams. These problems are described 
below. 
First, an off-axis light beams follow a curved scan trajectory giving rise 
to the bowed scan lines on the photosensitive medium. (See FIG. 9a). 
Second, off-axis beams have different and generally increased amount of 
astigmatism (in comparison to the on-axis beam) which can cause a 
variation in the pixel dimensions and pixel shape as the off-axis beams 
are scanned across the photosensitive medium (see FIG. 9b). Third, 
off-axis light beams have a more imperfect conjugate relationship between 
the polygon facet and photosensitive medium in the cross scan direction 
due to field curvature of the scan optics. These problems and their 
solutions are described below in more detail. 
As stated above, the first problem with scanning multiple composite beams 
simultaneously is that these composite beams will not be in the plane 
containing the optical axis of the scan optics, and this can produce bowed 
scan lines. The amount of bow increases with larger spacing between the 
composite beams. Therefore, it is highly desirable to have the composite 
beam be as closely spaced as possible, so that they are near the optical 
axis of the scan optics. The amount of bow can be further minimized by 
using the scan optics, which has distortion, such that the scan position 
(i.e., laser spot location at the photosensitive medium) is proportional 
to the sine of the angle of the composite beam entering the scan optics 
(such as f-.theta. lens, for example). In addition, the use of cross scan 
optics which makes the polygon facet optically conjugate (as described in 
the Pyramid Error Correction section of the specification) to the 
photosensitive medium also greatly reduces the amount of bow. This 
conjugation provides that each of the composite beams that are imaged on 
or near the polygon facet 61 pass through one point (for all the three 
colors) at the photosensitive medium. These points form three lines when 
the polygon rotates. The fact that the composite beams are off-axis with 
respect to the scan optics makes this conjugate imperfect, but the error 
is small enough to ignore when the composite beams are only off-axis by 
several (.congruent.3 to 6) beam radii. There are other errors associated 
with such off-axis beams, but they are not a problem unless the 
displacement of the beams relative to the optical axis is large. In this 
application we are concerned with displacements of the order of several 
beam diameters at most, so these errors will not be discussed. Another 
reason for maintaining good conjugacy between the polygon facet and the 
photosensitive medium is to compensate for pyramidal errors in the 
polygon's facets. Thus, a proper optical conjugate relationship will 
compensate for polygon pyramidal errors and for the bowed lines produced 
by the scan optics processing the off-axis composite beams. 
As stated above, the off-axis composite beams also suffer from astigmatism. 
This leads primarily to a growth of the laser spots at the photosensitive 
medium during the rotation of the polygon. That is, pixel sizes grow as 
the polygon rotates. A certain amount of pixel growth can be tolerated. 
Thus, the pixel size increase is held in check as long as the composite 
beams are not too far off axis, and the polygon scan angle is not too 
large. The amount of tolerable pixel size increase depends on the image 
quality requirements for a specific printer. For example, in printer 10 
the pixel growth is limited to 25%. 
The third problem, i.e., the problem of having imperfect imaging in the 
cross scan direction between the polygon facet and the photosensitive 
medium during the rotation of the polygon is potentially the most serious. 
The motion of the polygon facet causes a focus variation of the facet on 
the image in the cross scan section of the compound beams. This phenomena 
is called cross scan field curvature. Fortunately, some of this polygon 
induced cross scan field curvature can be compensated by the field 
curvature of the scan optics (for example, field curvature of the 
f-.theta. lens), but inevitably there is an imperfect cancellation across 
the scan line. This can lead to banding in those sections of the image 
where the net field curvature is excessive. Care must be taken to design a 
proper scan optics to ensure that its field curvature does not add to the 
field curvature produced by the polygon. 
After going through the beam combining fibers 40d and the holder 43 the 
closely located composite beams 42 are directed first towards an 
apochromatic focusing lens 50, and then to a single set of beam shaping 
optics 52 (FIG. 1b). The focusing lens 50 re-images the three circular 
beam waists (red R, green G, blue B) produced at the output end 40d of 
each of the beam combining fibers to a second set of larger size beam 
waists, and thereby decreases the divergence of the three composite beams. 
The focusing lens 50 is apochromatic to insure that a plurality of three 
larger size (i.e., imaged) circular beam waists are located in a common 
plane. The plurality of three larger size circular beam waists produced by 
the focusing lens 50 comprise a plurality of composite beam waists that 
constitutes the input to the beam shaping optics 52. 
The beam shaping optics 52 includes two cylindrical mirrors 54 and 56. The 
first cylindrical mirror 54 has power only in the page direction. The 
second cylindrical mirror 56 has power only in the line direction. In one 
embodiment, the first cylindrical mirror 54 has concave radius of -119.146 
mm in the x-z plane and is tilted in the x-z plane to deviate the 
composite beams by six degrees. The cylindrical mirror 56 has concave 
radius of -261.747 millimeters in the y-z plane and is tilted in the y-z 
plane to restore the composite beam's direction to the direction that it 
had prior to impinging on the cylindrical mirror 54. The cylindrical 
mirror 54 shapes each of the composite beams 42 so as to form a plurality 
of composite beam waists in the page direction. Each of the composite beam 
waists includes three (essentially coplanar) waists W.sub.1, one for each 
of the three wavelengths. These waists are located in the plane 57 at or 
near the polygon facet 61. (See FIGS. 1b and 10 ). The cylindrical mirror 
56 also shapes the composite beam 42 so as to form a plurality of 
composite waists (each having three coplanar waists, one for each of the 
three wavelengths) in the line direction. These sets of three (R, G, B) 
waists W.sub.2 are located in the plane 73 (FIG. 11) approximately one 
meter away, behind the first vertex VI of the f-.theta. lens 70 (see FIG. 
12). This f-.theta. lens is described in detail in the "F-.theta. Lens" 
section of the specification. The sizes and locations of these waists, for 
each of the three wavelengths, are provided in the "Beam Shaping and 
Pyramid Correction" section of the specification. The printer of the 
present embodiment is convenient for use with any beam shaping optics 
producing waists at the locations given in the "Beam Shaping and Pyramid 
Correction" section of the specification. 
As stated above, after being shaped by the shaping optics 52, the composite 
beams 42 are directed towards the polygon facet 61. This facet 61 is 
located at or near plane 57. Although a rotating polygon deflector may be 
used in the invention, other deflectors or scanning means may also be 
employed, so long as they are capable of deflecting the composite beams by 
a sufficient amount at the high speed required by the printer. 
At the center of a scan line (here defined as 0.degree. polygon rotation), 
the composite beam's angle of incidence on the polygon facet 61 is 30 
degrees. The composite beams 42 striking the polygon facet 61 and the 
composite beam 42 reflected from the polygon facet 61 form a plane which 
is normal to the direction of the polygon's axis of rotation 63. In other 
words, the angle of incidence has no component in the page direction. 
Upon reflection from the polygon facet 61, the deflected composite beams 42 
enter the f-.theta. scan lens 70 as they are being scanned in a plane 
which is perpendicular to the axis of rotation 63 of the polygon. As 
described above, each of the composite beams 42 (also referred to as input 
beams when discussed in conjunction with the f-.theta. lens) comprises 
three coherent coaxial laser beams having perspective wavelengths of 458 
nm, 532 nm, and 685 nm, and has beam characteristics determined by the 
fiber optic multiplexer 40, focusing lens 50, and the beam shaping mirrors 
54 and 56. The f-.theta. lens 70, illustrated in FIG. 12, includes means 
for correcting the primary and secondary axial color aberration. The 
f-.theta. lens 70 itself is uncorrected for lateral color. Thus, red, blue 
and green spots are separated as shown schematically in FIG. 13. The 
overall printer 10 is corrected for lateral color by modulating the red, 
green and blue color laser beams at three different data rates as later 
described. The f-.theta. lens 70 is corrected so that residual lateral 
color errors (after a linear electronic correction is applied) are 
insignificant. The detail description as the f-.theta. lens 70 is provided 
in the "F-.theta. Lens" section of this specification. 
After passing through the f-.theta. lens 70, the deflected composite beams 
42 reflect off a conjugating cylindrical mirror 80 before they impinge on 
the photosensitive medium 100. (See FIGS. 14a, 14c, 14d). The cylindrical 
mirror 80 has optical power in X-Z plane (page direction) only (FIG. 14e). 
The cylindrical mirror 80 corrects for pyramid error of the polygon's 
facets. This is discussed in more detail in the "Beam Shaping and Pyramid 
Correction" section of the specification. 
A plano fold mirror 84 can be placed between the f-.theta. lens 70 and the 
cylindrical mirror 80 or between the cylindrical mirror 80 and an image 
surface 99 in order to place the image surface 99 in a desirable location, 
where it (at least in line scan direction) coincides with the 
photosensitive medium 100. Such a fold mirror 84 has no effect on the 
performance of the printer. In the preferred embodiment of the present 
invention, the image surface 99 is a plane. 
As stated above, each of the fiber optic multiplexers 40 produces a beam 
waist of different size in each of the three colors at the output end of 
the fiber 40d. Because the f-.theta. lens 70 is designed to work with the 
composite beams 42 after they have passed through a common apochromatic 
focusing lens and a common apochromatic beam shaping optics 52, the sizes 
of the red, green and blue spots at the image surface 99 will be different 
for the three wavelengths. The spots at the image surface 99 will maintain 
the same relative sizes as the red, green and blue waists located at the 
output end of each of the beam combining fibers 40d. 
This variation in spot size between wavelengths does not significantly 
impact the perceived image quality. 
In the actual embodiment, the radii of the laser spots produced by the 
printer 10 at the image surface 99 at the exp(-2) power level are: 0.035 
mm at .lambda.=532 nm, 0.032 mm at .lambda.=457.9 nm, and 0.044 mm at 
.lambda.=685 nm. As stated above, the image surface 99 of the f-.theta. 
lens 70 coincides with the location of the photosensitive medium 100. In 
this embodiment the photosensitive medium 100 is a conventional 
photographic paper. The paper rests on a support 100' which moves the 
paper in a predetermined direction. Writing with spots of this size onto 
photosensitive medium 100 over a scan line 12 inches long will produce 
sufficient resolution when the resulting prints are examined at a normal 
viewing distance. These spots (red, blue, green) refer to the images 
produced by the composite beams on an instantaneous basis. These spots are 
produced in a series and their location changes with the rotation of the 
polygon. Each pixel on the page receives up to three spots, one for each 
color. 
Beam Shaping 
As discussed in the previous section, the cylindrical mirrors 54 and 56 of 
the beam shaping optics 52 direct the composite beams 42 containing all 
three colors toward the polygon facet 61 and cause the composite beams 42 
to converge in both the line and page direction (as shown in FIGS. 10 and 
11). By "beam shaping optics" we mean beam shaping optics that shape a 
light beam differentially in the line direction and in the page direction. 
In this embodiment of the printer 10, each of the composite beams 42 
converges to a spot near the facet 61 in the X-Z or page direction (see 
FIG. 10), and toward a spot approximately one meter behind the front-most 
vertex V.sub.1 of the f-.theta. lens 70 in the Y-Z or line direction (see 
FIG. 11). Thus, the beam shaping optics 52 adjusts the spot sizes and 
converges the composite beams 42 by different amounts in the page and line 
direction. The beam convergence is much faster in the page direction (see 
FIG. 11) than the line direction (see FIG. 12). 
More specifically, in one embodiment the focusing lens 50 and the beam 
shaping optics 52 produce shaped composite beams which converge in such a 
manner as to produce 1.) green, page direction waists W.sub.1 at a plane 
located 22.904 mm in front of the first vertex V.sub.1 of the f-.theta. 
lens 70 (i.e., these beam waists are located between the polygon facet 61 
and the f-.theta. lens) and 2.) green, line direction waists W.sub.2 995.7 
mm behind the first vertex V.sub.1 of the f-.theta. lens 70 (the line 
direction beam waists are located between the f-.theta. lens 70 and the 
image surface 99). The size of the waists may be adjusted by the beam 
shaping optics depending on the spot size desired at the image surface. 
For example, the exp(-2)power radius of the green waists in the line 
direction may be 0.114 mm and the exp(-2) power radius of the green waists 
in the page direction may be 0.0396 mm. 
Similarly, the focusing lens 50 and the beam shaping optics 52 produce 
shaped composite beams 42 which converge in such a manner as to produce 
1.) blue, page direction waists W.sub.1 at a plane located 22.893 mm in 
front of the first vertex V.sub.1 of the f-.theta. lens 70 and 2.) blue, 
line direction waists W.sub.2 at a plane located 995.8 mm behind the first 
vertex of the f-.theta. lens. For example, the exp(-2)power radius of the 
blue waists in the line direction may be 0.104 mm and the exp(-2)power 
radius of the blue waists in the page direction may be 0.030 mm. 
Similarly, the focusing lens 50 and the beam shaping optics 52 produce 
shaped composite beams which converge in such a manner as to produce 1.) 
red, page direction waists W.sub.1 at a plane located 22.790 mm in front 
of the first vertex V.sub.1 of the f-.theta. lens 70 and 2.) red, line 
direction waists W.sub.2 at a plane located 995.9 mm behind the first 
vertex of the f-.theta. lens. For example, the exp(-2)power radius of the 
red waists in the line direction may be 0.144 mm and the exp(-2) power 
radius of the red waists in the page direction may be 0.0495 mm. 
Polygon 
The f-.theta. lens 70 of the preferred embodiment is designed to work with 
a variety of rotating polygons. It is particularly suitable for use with 
10 facet polygons having an inscribed radius between 32.85 mm and 40.709 
mm. These polygons are rotated by .+-.13.5 degrees to produce a scan line 
12 inches long at the image surface 99. 
The f-.theta. lens 70 also works well with 24 facet polygons having an 
inscribed radius between 38.66 mm and 44 mm. These polygons are rotated by 
.+-.5.625 degrees to produce scan lines 5 inches long at the image surface 
99. 
F-.theta. Lens 
The lens 70 is arranged in the optical path of the printer 10 as shown in 
FIGS. 14a-14d. 
As shown in FIG. 12, the optical axis O. A. of the f-.theta. lens 70 
extends in a direction referred to herein as the Z direction. When the 
polygon rotates (for line scanning) each of the composite beams 42 are 
scanned in the Y-direction. (See FIGS. 15a-15c). The cross scan (also 
referred to as the page direction) is in the X-direction. The performance 
of the f-.theta. lens 70 is shown in FIG. 16. 
The f-.theta. lens 70, described herein, is particularly suitable for use 
in the laser printer 10. Due to the lateral color present in the f-.theta. 
lens 70, the printer 10 simultaneously produces three spatially separated 
scanning spots at the image surface 99. Each of the three spots contains 
energy in one of the three laser wavelengths. This separation is 
compensated for in a manner described in the "Lateral Color Correction" 
section of this specification. To summarize, the spots are properly 
superimposed on a photosensitive medium when the data rates at which the 
different color laser beams are modulated are linearly adjusted to 
compensate for the lateral color of the f-.theta. lens 70. 
Ideally, the lateral color should be completely corrected with no residual 
errors by using three different data rates to move data between the 
digital image store and the laser modulator control circuitry. The spots 
should ideally travel in a straight line, at uniform velocities (as the 
polygon is rotated with uniform angular velocity), and should not 
significantly change their size and shape as they travel down the line. If 
necessary, the variation in the spot velocities can be compensated for by 
adjusting the data rate as the spots move across the scan line. The spots 
should have approximately circular shapes, with energy distributions which 
are approximately gaussian. The spot diameter at the exp (-2) level should 
be about 60-105 .mu.m (in green light) in order to achieve sufficient 
resolution at the photosensitive medium, the smaller size being necessary 
to achieve overprinting of fine text on a picture. It is preferred that 
this spot diameter be 64-88 .mu.m. 
A further requirement of an f-.theta. scan lens 70 of the preferred 
embodiment is that it be readily manufacturable at a reasonable cost. This 
requires that the lens have spherical surfaces on relatively low cost 
glass. 
The f-.theta. lens 70 satisfies all of the above requirements. In FIGS. 12 
and 14a there is shown the f-.theta. lens 70 which is constructed in 
accordance with the present invention. In the present embodiment of the 
present invention, the f-.theta. lens includes four lens components 
arranged along an optical axis. They are: a first lens component 72 of 
negative optical power, a second lens component 74 of positive optical 
power, a third lens component 76 of negative optical power, and a fourth 
lens component 78 of positive optical power. 
The lens components satisfy the following relationships: 
EQU -1.6&lt;f.sub.1 /f&lt;-0.9; 
EQU 0.38&lt;f.sub.2 /f&lt;0.5; 
EQU -0.65&lt;f.sub.3 /f&lt;-0.50; 
EQU 0.73&lt;f.sub.4 /f&lt;0.9, 
where f.sub.1 is the focal length of the first lens component, f.sub.2 is 
the focal length of the second lens component, f.sub.3 is the focal length 
of the third lens component, f.sub.4 is the focal length of the fourth 
lens component, and f is the focal length of the f-.theta. lens 70. The 
lens component 72 is a meniscus negative element, concave toward the 
polygon side. Lens component 74 is a meniscus positive lens element, also 
concave toward the polygon. Lens component 76 is a meniscus negative lens 
element, concave toward the image surface 99. Lens component 78 is a 
meniscus positive lens element, also concave toward the image surface 99. 
In the exemplary f-.theta. lens 70, the lens elements are formed of Schott 
glass with the lens element 72 being an PK-51A type, the lens element 74 
being LAK-21 glass, the lens element 76 being an SFL-56 glass, and the 
lens element 78 being an F-2 type glass. The f-.theta. lens 70 is 
apochromatic, that is, it is corrected for both the primary and the 
secondary axial color at a wavelength of 458 nm, 532 nm and 685 nm. 
In this embodiment, the first lens component 72 is a single lens element 
satisfying the following equations: 
EQU Vd.sub.1 &gt;65; 
and 
EQU P.sub.g,F;1 &gt;0.53, 
where Vd.sub.1 is the V-number of the first lens component material and 
P.sub.g,F;1 is its relative partial dispersion. 
The details of the elements in lens 70 are shown in TABLE 1A. In this 
table, the radii of curvature (r1-r8) and thicknesses of the lens elements 
are in millimeters. 
TABLE 1A 
______________________________________ 
V 
SURF RADIUS THICKNESS INDEX NUMBER 
______________________________________ 
Entrance Pupil 24.00 Polygon facet 
1 -33.0678 10.634 1.529 77.0 
2 -44.642 0.925 AIR 
3 -341.050 7.654 1.641 60.1 
4 -85.6131 0.836 AIR 
5 423.736 12.550 1.785 26.1 
6 129.480 6.034 AIR 
7 139.081 19.689 1.620 36.4 
8 403.727 
______________________________________ 
The following tables 1B-1D show the f-.theta. compliance and the relative 
spot velocity achieved in the green, red and blue light for the f-.theta. 
lens when it is used with a 10 facet polygon having an inscribed radius of 
32.85 mm. 
TABLE 1B 
__________________________________________________________________________ 
F-Theta compliance and instantaneous spot velocity data: 
= 532 
CFG 
ROT IDEAL 
ACTUAL 
DELTA 
PERCENT 
REL -LOG10 
NBR 
ANGLE 
RAYHT 
RAYHT 
RAYHT 
ERROR VEL REL VEL 
__________________________________________________________________________ 
1 0.000 
0.000 
0.000 
0.000 
0.000 1.0000 
0.0000 
2 4.500 
-51.265 
-50.089 
1.175 
-2.293 
1.0104 
-0.0045 
3 9.000 
-102.530 
-101.282 
1.248 
-1.217 
1.0440 
-0.0187 
4 13.500 
-153.794 
-154.644 
-0.850 
0.553 1.0948 
-0.0393 
5 -4.500 
51.265 
50.149 
-1.116 
-2.176 
1.0129 
-0.0056 
6 -9.000 
102.530 
101.526 
-1.004 
-0.979 
1.0492 
-0.0208 
7 -13.500 
153.794 
155.209 
1.415 
0.920 1.1023 
-0.0423 
__________________________________________________________________________ 
TABLE 1C 
__________________________________________________________________________ 
= 457.9 
CFG 
ROT IDEAL 
ACTUAL 
DELTA 
PERCENT 
REL -LOG10 
NBR 
ANGLE 
RAYHT 
RAYHT 
RAYHT 
ERROR VEL REL VEL 
__________________________________________________________________________ 
1 0.000 
0.000 
0.000 
0.000 
0.000 1.0000 
0.0000 
2 4.500 
-51.237 
-50.059 
1.179 
-2.300 
1.0105 
-0.0045 
3 9.000 
-102.474 
-101.224 
1.251 
-1.221 
1.0441 
-0.0188 
4 13.500 
-153.712 
-154.561 
-0.849 
0.552 1.0949 
-0.0394 
5 -4.500 
51.237 
50.119 
-1.118 
-2.183 
1.0130 
-0.0056 
6 -9.000 
102.474 
101.470 
-1.005 
-0.981 
1.0494 
-0.0209 
7 -13.500 
153.712 
155.132 
1.420 
0.924 1.1025 
-0.0424 
__________________________________________________________________________ 
TABLE 1D 
__________________________________________________________________________ 
= 685 
CFG 
ROT IDEAL 
ACTUAL 
DELTA 
PERCENT -LOG10 
NBR 
ANGLE 
RAYHT 
RAYHT 
RAYHT 
ERROR VEL REL VEL 
__________________________________________________________________________ 
1 0.000 
0.000 
0.000 
0.000 
0.000 1.0000 
0.0000 
2 4.500 
-51.321 
-50.145 
1.177 
-2.293 
1.0104 
-0.0394 
3 9.000 
-102.643 
-101.393 
1.250 
-1.218 
1.0440 
-0.0187 
4 13.500 
-153.964 
-154.816 
-0.851 
0.553 1.0950 
-0.0045 
5 -4.500 
51.321 
50.205 
-1.117 
-2.176 
1.0129 
-0.0056 
6 -9.000 
102.643 
101.637 
-1.005 
-0.980 
1.0491 
-0.0208 
7 -13.500 
153.964 
155.381 
1.417 
0.920 1.1025 
-0.0424 
__________________________________________________________________________ 
If necessary, the variation in the spot velocities can be compensated for 
by adjusting the rate at which data in the digital image store (described 
in the "Lateral Color Correction" section) is moved to the circuitry 
controlling the laser modulators. The adjustment amount is the same for 
each of the modulators. 
The following Table 2 shows how the spots grow as the polygon is rotated 
and the spot moves across the scan line. This data is for a 10 facet 
polygon having an inscribed radius of 32.85 mm. A polygon rotation of 
.+-.13.5 degrees corresponds to a scan position of approximately .+-.6 
inches at the image surface 99. 
TABLE 2 
__________________________________________________________________________ 
##STR1## 
##STR2## 
= 532, .omega. = .00189; = 457.9, .omega. = .00172; = 685, .omega. = 
.00237. 
Effects of beam truncation are not included in this computation. 
POLYGON 
ROTATION 
13.500.degree. 
9.000.degree. 
4.500.degree. 
0.000.degree. 
-4.500.degree. 
-9.000.degree. 
-13.500.degree. 
__________________________________________________________________________ 
= 532 .omega.y 
0.0390 
0.0371 
0.0359 
0.0355 
0.0359 
0.0371 
0.0390 
.omega.x 
0.0359 
0.0355 
0.0353 
0.0352 
0.0353 
0.0356 
0.0358 
= 457 .omega.y 
0.0360 
0.0340 
0.0328 
0.0325 
0.0328 
0.0340 
0.0357 
.omega.x 
0.0329 
0.0324 
0.0322 
0.0322 
0.0323 
0.0325 
0.0328 
= 685 .omega.y 
0.0490 
0.0467 
0.0452 
0.0450 
0.0452 
0.0467 
0.0489 
.omega.x 
0.0477 
0.0443 
0.0441 
0.0441 
0.0442 
0.0444 
0.0446 
__________________________________________________________________________ 
where 
##STR3## 
Pyramid Error Correction 
Printers utilizing rotating polygon deflectors are subject to an image 
defect known as banding, which is most easily seen in areas of the image 
where it is free of subject detail, i.e., a blank wall or a cloud free sky 
scene. Light and dark bands, which are not part of the desired image, will 
appear in these areas. These bands are caused by repetitive non uniform 
spacing of the scan lines. The banding is caused by a facet, or facets on 
the polygon which are tilted slightly out of position. Thus, every time 
the facet which is out of position comes around, it will cause a laser 
beam to move ever so slightly out of the nominal laser beam plane, i.e., 
the plane formed by a rotating laser beam in the absence of any pyramid 
error. After going through an f-.theta. lens, this misplaced laser beam 
will land in a slightly different position on the image surface, 
generating what is known as a "cross scan" error, since the position error 
is in a direction which is perpendicular to the scan line. An f-.theta. 
lens must function with the other optical elements in the printer to 
produce an image which is free from banding when a "good" polygon is used, 
that is, a polygon in which pyramidal angle errors on the polygon facets 
do not exceed .+-.10 arc seconds, as measured with respect to the axis of 
rotation of the polygon. 
In an embodiment of the present invention, the pyramid error is corrected 
by keeping the polygon facet 61 conjugate with the image surface 99 in the 
page meridional (X-Z plane). (Conjugate points are defined herein as any 
pair of points such that all rays from one are imaged on the other within 
the limits of validity of gaussian optics). This conjugation is achieved 
by the conjugating cylindrical mirror 80 working in conjunction with 
f-.theta. lens 70. Thus, there is a focal point (beam waist) at both the 
polygon facet 61 and at the photosensitive medium 100, and the polygon 
facet is thereby conjugated to the photosensitive medium 100. As a result, 
if the polygon facet 61 is tilted slightly in the X-Z plane, that is, 
around the "object" point, the path of the rays through the printer 10 is 
slightly different from that shown in the figure, but the rays all go to 
the same "image" point, and the cross scan error is zero. 
The conjugation condition described above imposes requirements on the beam 
shaping optics. Conjugation of the polygon facet 61 and the image surface 
99 in the page direction implies that in the page direction, a beam waist 
(for each wavelength) is located at (or adjacent to) both locations (i.e., 
at or near the polygon facet 61, and at or near the image surface 99). 
Hence, for each of the composite beams the beam shaping optics 52 must 
produce a beam waist W.sub.1 in the page direction at the plane 57 located 
at or near the polygon facet 61. This is achieved in the current design as 
is discussed in the "Beam Shaping" section and is shown in FIG. 10. It is 
preferred that the beam waist in the page direction be located less than 
##EQU1## 
from the polygon facet 61 (where f is the focal length of the f-.theta. 
lens). 
The degree of convergence (of the composite beams 42) in the line direction 
is not similarly constrained. In the present embodiment, the beam shaping 
optics 52 converges the composite beams 42 in the line direction to form a 
plurality of beam waists behind the rear focal point of the f-.theta. lens 
70. It is preferred that the beam waists W.sub.2 in the line direction at 
a distance be at least 1/3 behind the first vertex V.sub.1 of the 
f-.theta. lens 70 (see FIG. 11). In the printer 10 the distance between 
the rear focal point of the f-.theta. lens and the waist location is 
approximately equal to the focal length of the f-.theta. lens 70. More 
specifically, the f-.theta. lens 70 has a focal length of 426.4 mm and the 
line direction waists formed by the beam shaping optics 52 are located 
488.9 mm behind the rear focal point. This arrangement has been found to 
allow superior correction of the f-.theta. lens and other post-polygon 
optics, as well as providing a compact system. 
The conjugating cylindrical mirror 80 (see FIG. 14e) is located between the 
f-.theta. lens 70 and the photosensitive medium 100. As stated above, it 
corrects for the pyramid error of the polygon facets by conjugating, in 
the X-Z plane, the polygon facet 61 with the image surface 99. This 
cylindrical mirror 80 has a concave radius (in the page direction) of 
190.500 mm and is located 153.053 mm behind the last vertex of the 
f-.theta. lens. The cylindrical mirror 80 is tilted by 7 degrees and 
deviates the composite beams 42 by 14 degrees. The image surface 99 is 
located 162.96 mm behind the cylindrical mirror 80, the distance being 
measured along the deviated beam. As mentioned above, various plano fold 
mirrors 84 may be placed behind the polygon and the f-.theta. lens without 
affecting performance. 
FIGS. 15a, 15b, 15c show the position of the composite beams 42 on the 
photosensitive medium 100 (located at the image surface 99) for polygon 
rotations of +13.5, 0, and -13.5 degrees respectively. This represents 
scan angles of +27, 0, and -27 degrees, respectively. 
More specifically, in Table 3, the computed cross scan image displacements 
for the chief (central) rays of the light beam (at wavelengths of 532 nm, 
457 nm and 685 nm) are tabulated. It will be seen that the cross scan 
displacements are certainly well within acceptable limits. 
Table 3 shows the cross scan displacement due to 10 arc seconds of pyramid 
error on polygon facet. The displacement units are micrometers. 
TABLE 3 
______________________________________ 
CROSS SCAN DISPLACEMENT 
POLYGON FIELD 
ROTATION ANGLE = 532 nm = 457 nm 
= 685 nm 
______________________________________ 
4.5.degree. 
9.0.degree. 
-0.0204568 -0.0103607 
-0.0299763 
9.0.degree. 
18.0.degree. 
-0.0210595 -0.0113009 
-0.0301466 
13.5.degree. 
27.0.degree. 
-0.0327880 -0.0235740 
-0.0411589 
-4.5.degree. 
-9.0.degree. 
-0.0189723 -0.0079102 
-0.0294039 
-9.0.degree. 
-18.0.degree. 
-0.0209200 -0.0091726 
-0.0318579 
-13.5.degree. 
-27.0.degree. 
-0.0465809 -0.0344084 
-0.0576246 
none 0.0.degree. 
-0.0202603 -0.0097542 
-0.0302057 
______________________________________ 
Axial Color Aberration 
There are two kinds of color aberrations in any lens system: axial color 
and lateral color. Axial color causes light of different wavelengths to 
come to a focus at different distances from the rear surface of the lens 
system. Since axial color is a focus-related phenomenon, it is caused not 
only by aberrations in a lens system itself but also by the vergence of 
the input light beam to the lens system. 
In the printer 10, the line direction vergence of the green, blue, and red 
laser beams cannot be adjusted independently because the beam shaping 
optics 52 is common to the three (combined) laser beams. This makes the 
correction of the axial color more difficult. For the printer 10, the 
axial color must be corrected when the three laser beams have essentially 
the same vergence. This is what has been done in the f-.theta. lens 70, as 
is shown in the OPD plots in FIG. 16, which correspond to f-.theta. lens 
performance at the center of the line scan. The construction of the 
f-.theta. lens 70 is disclosed in the "F-.theta. Lens" section of the 
application. 
The axial color in the page direction must be corrected in order to prevent 
color banding due to pyramid errors. Otherwise, the pyramid error will 
only be corrected in a single color. In the printer 10 the axial color is 
corrected in both meridians, all the elements are spherical, a costly 
cemented cylindrical doublet is unnecessary, and the pyramid error is 
corrected with the conjugating cylindrical mirror 80. 
Lateral Color Correction 
As stated previously, the lateral color aberration of the f-.theta. lens 70 
is uncorrected. Lateral color is the variation in image height of focused 
spots having different wavelengths, or colors, taken in a specified image 
surface (see FIG. 12b). 
For example, in normal photographic objectives for use in color 
photography, lateral color is typically measured by 
EQU Y'(at .lambda..sub.1 =486.1 nm)-Y'(at .lambda..sub.2 =656.3 nm); 
this is the difference in image height taken in the gaussian focal plane 
for .lambda.=546.1 nm, between the blue point image and the red point 
image. Lateral color, as opposed to axial color, only occurs away from the 
optical axis, out in the field of the lens. Usually, the farther away from 
the axial image point, the greater the amount of lateral color. Thus, the 
largest amount of lateral color often occurs near the edge of the field of 
view of the lens. In the printer 10, the lateral color is exhibited as a 
separation of red, blue and green spots along the scan line at the 
photosensitive medium (FIG. 12b). 
The lateral color in the printer 10 is corrected by modulating the three 
color laser beams at three different data rates. To understand this, 
consider the following hypothetical example. Suppose that the lateral 
color in an f-.theta. lens is such that for a given amount of polygon 
rotation the green laser beam intercepts the image surface at a location 
100 pixels high whereas the red laser beam intercepts the image surface at 
a location 101 pixels high and the blue laser beam intercepts the image 
surface at a location 99 pixels high (see FIG. 17). For example, if the 
printer worked at 512 dots per inch, the blue and green spots would be 
separated by a distance d.sub.1 =1/512 inch and the red and green spots 
would be separated by a distance d.sub.2 =1/512 inch. According to one 
embodiment of the invention, the rate at which data is moved from a 
digital image store to the circuitry controlling the laser modulators is 
determined by three data clocks C.sub.1 -C.sub.3 shown in FIG. 1b. One 
clock controls the data rate for the green channel, a second clock 
controls the data rate for the blue channel, an a third clock controls the 
data rate for the red channel. If these three clocks are run at the same 
rate, then, at any instant in time, the three laser intensities correspond 
to the required green, blue and red intensity values for the same pixel. 
Due to the spot separation (d.sub.1 ', d.sub.2 ') produced at the image 
surface 99 by the lateral color in the f-.theta. lens, the image recorded 
on the photosensitive medium will show color fringing at an image location 
of 100 pixels high. More specifically, there will be color fringing of two 
pixels between red and blue, one pixel between green and red and one pixel 
between green and blue. 
Now suppose that the blue data clock is run at a frequency (i.e., data 
rate) f.sub.B which is 99% of the green clock frequency f.sub.G and that 
the red clock is run at a frequency f.sub.R which is 101% of the green 
clock frequency. At the given amount of polygon rotation, the green laser 
beam will intercept the image surface at a location 100 pixels high and 
the modulation of the laser beam is appropriate to produce the exposure of 
the 100th pixel. Likewise, at this same polygon rotation, the red laser 
beam still intercepts the image surface at a location 101 pixels high. 
However, since the red clock is being run at 101% of the frequency of the 
green clock, the red laser beam is now correctly data modulated to give 
the proper exposure for the 101st pixel. Similarly the blue laser beam 
remains 99 pixels high, but the blue laser light is data modulated to give 
the proper exposure for the 99th pixel. That is, at any given time (or at 
any given polygon rotation position) the laser printer 5 may produce three 
color spots at each scan line, but the image information contained in each 
one of the three color beams is different--i.e., it corresponds to 
different pixels on the scan line. So at same time T.sub.1, pixel 98 will 
receive the red beam R, at time T.sub.1 +.DELTA. the pixel 98 will receive 
the green laser beam G, and in time T.sub.1 +2.DELTA. it will receive the 
blue laser beam B (FIG. 18). This way, when the printer is operating in 
locations other than the center of the line scan, each pixel can receive 
red, green and blue image modulated light, albeit at a different time. 
Therefore, there will be no color fringing at the 100th pixel. Thus, in 
the printer 10, the data rates f.sub.B, f.sub.G and f.sub.R are not the 
same. More specifically, the data rates are f.sub.B =k.sub.1 
.times.f.sub.G, f.sub.R =k.sub.2 .times.f.sub.G, where k.sub.1 and k.sub.2 
are constants chosen to compensate for spot separation during the line 
scan. 
In any laser printer, there is a detection procedure to determine a 
specific starting location for each line on the photosensitive medium. In 
a printer 10, this is done by utilizing a "split" (dual) detector and the 
(unmodulated) red light beam to generate the initial start up pulse. More 
specifically, the split detector detects the presence of the laser beam 
and from its location (with respect to the beginning of the line), 
determines the time delays needed for starting of the modulation of each 
of the three color laser beams, so that the appropriate pixel at the 
beginning of the line scan is exposed with the laser beam carrying the 
proper data information. 
A potential problem remains that the same clock rates which produced good 
results for an image height of 100 pixels might still produce color 
fringing at other image heights. However, in the printer 10, these 
residual lateral color errors have been corrected in the f-.theta. lens 70 
so that the worst residual error (due to the lateral color aberration) 
over the entire scan line is less than 20% of the size of a green pixel. 
This is shown in tables 2 and 4. Table 2 shows the spot size across the 
scan line. Table 4 shows the residual lateral color when the laser beams 
are modulated at the rates shown at the bottom of the table. Both of these 
tables are for a 10 facet polygon with an inscribed radius of 32.85 mm. 
Similar results hold for the other 10 facet polygon sizes. The results for 
the 24 facet polygons are much better. 
TABLE 4 
______________________________________ 
Difference in line direction image position (in millimeters) for red, 
green and blue colors with red, green and blue pixel clocks in drive 
electronics adjusted in the ratio of 1.0011: 1.0000: 0.99946 
( = 457) - ( = 532) 
( = 685) - ( = 532) 
ROT Residual Error 
Residual Error 
ANGLE (Blue-Green) (Red-Green) 
______________________________________ 
4.500 0.003 0.001 
9.000 0.003 0.003 
13.500 0.001 -0.002 
-4.500 -0.003 -0.001 
-9.000 -0.001 -0.002 
-13.500 0.006 0.002 
______________________________________ 
Green = 532 nm; Blue = 457.9 nm; Red = 685 nm 
In a laser printer of a type which can incorporate the f-.theta. lens of 
the present invention, the system parameters can be as follows: 
Wavelengths: 532, 457.9, and 685 nm 
Scan length: 12 inches 
Polygon Duty Cycle: 0.75 
Polygon inscribed radius: 32.85 through 40.709 
Number of polygon facets: 10 
Total Scan angle: 54 degrees. (.+-.27 degrees with respect to the optical 
axis; .+-.13.5 degrees of polygon rotation) 
Light beam input angle onto polygon facet: 60 degrees from optical axis of 
f-.theta. lens (30 degree angle of incidence on polygon facet) 
Desired gaussian beam radius at the exp(-2) power point: 0.035 mm at 
.lambda.=532 nm. 
In a laser printer of a type which incorporates the f-.theta. lens 70 of 
the present invention, the system parameters can also be as follows: 
Wavelengths: 532, 457.9, and 685 nm 
Scan length: 5 inches 
Polygon Duty Cycle: 0.75 
Polygon inscribed radius: 38.66 through 44.00 
Number of polygon facets: 24 
Total Scan angle: 22.5 degrees. (.+-.11.25 degrees with respect to the 
optical axis; .+-.5.625 degrees of polygon rotation) 
Light beam input angle onto polygon facet: 60 degrees from optical axis of 
f-.theta. lens (30 degree angle of incidence on polygon facet) 
Desired gaussian beam radius at the exp(-2)power point: 0.051 mm at 532 nm. 
As stated above, the f-.theta. lens 70 itself is not corrected for lateral 
color. Correction of the lateral color in the scanner requires running the 
green, blue, and red clocks modulating the lasers in the ratio 1:000: 
0.99946: 1.0011. 
As disclosed in the "Axial Color Aberration" section of this specification, 
the f-.theta. scan lens 70 by itself is corrected for primary and 
secondary axial color. This is a requirement for this type of scanner 
because the beam shaping optics 52 is common to all composite beams. In 
the X-Z direction, the f-.theta. scan lens conjugates the polygon facet to 
the image surface (in all three wavelengths), this requires the use of an 
auxiliary cylindrical mirror having power in only the X-Z direction. 
Assuming the "object" is at the polygon facet, the axial color in the X-Z 
direction for the f-.theta. lens 70 is zero; it is also zero for the 
cylindrical mirror and, hence, the conjugation holds at all three 
wavelengths. 
It is an advantage of the printer of the present invention that it enables 
color printing much faster than prior art color printers. 
The invention has been described in detail with particular reference to the 
embodiment thereof, but it will be understood that variations and 
modifications can be effected within the spirit and scope of the 
invention. For example, other laser sources producing light beams in 
wavelengths other than 458 nm, 532 nm or 685 nm may be also utilized as 
long as the photosensitive medium is sensitive to these wavelengths. Thus, 
this invention can be used in a printer printing on a photographic paper, 
or on a "false sensitive paper". Printers utilizing such "false sensitive 
paper" are well known. Changing the wavelengths will change the ratios 
between the corresponding data rates. 
The term printer, for purposes of this specification means any image 
producing apparatus. Such an apparatus may be a printer, a copier or a fax 
machine, for example. 
TS LIST 
printer 10 
light beam 12, 14, 16 
3 laser sources 22, 24, 26 
3 modulators 21, 34, 36 
beam combiner 40 
beam combining fiber 40d 
composite light beam 42 
holder 43 
grooves 43a 
waveguide channels 43b 
channel spacing 43c 
focusing lens 50 
beam shaping optics 52 
cylindrical mirrors 54, 56 
1st waist plane 57 
light deflector (polygon) 60 
Polygon Facet 61 
axis of rotation 63 
f-.theta. lens 70 
four lens components 72, 74, 76, 78 
cylindrical mirror 80 
flat fold mirror 84 
processor unit 90 
means for reading 92 
means for controlling 94 
image surface 99 
photosensitive medium 100 
support 100'