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Description  |
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FIELD OF THE INVENTION
The present inventions pertain to a method of manufacturing a light beam scanning apparatus and a fixed hologram plate and to a rotatable hologram and a light distributing apparatus. More particularly, the present invention refers to a method of
manufacturing a light scanning apparatus employing a hologram disk, a method of manufacturing fixed hologram plate, and to a rotatable hologram and a light distributing apparatus.
BACKGROUND ART
A high-precision and high-resolution laser-scanning optical system is used in office automation equipment including a laser printer and a laser facsimile, and in such apparatuses as a laser drawing apparatus and a laser inspection apparatus.
Conventionally, this optical system is embodied by a rotating polygonal mirror and a combination of a plurality of f-.theta. lenses.
In the above method employing a polygonal mirror, efforts to lower cost have met with difficulty because of the high precision required to fabricate a rotating polygonal mirror and because of a large number of lens groups required, including
f-.theta. lenses that serve, at the same time, as inclination correction optical system.
On the other hand, a hologram scanning apparatus employing a hologram can be mass produced. As an example of such a hologram scanning apparatus, the present applicant has filed an application for a hologram scanning apparatus for performing a
scanning with a straight beam having a high resolution and having sufficiently corrected aberration (the Japanese Laid-Open Patent Application 63-072633 and the Japanese Laid-Open Patent Application 61-060846). This light beam scanning apparatus
achieves, as a scanning optical system for a laser printer, excellent specifications characterized by a high precision, ensuring a stable print quality. However, there is now a demand for a laser-scanning optical system having even higher resolution, on
the order of 400-600 dpi or even 1000 dpi. Also, further cost reduction is desired.
In order to embody a hologram scanner having such an extremely high resolution at a low price, the following objectives need be resolved:
1 scanning beam radius should be as thin as 60 .mu.m (equivalent to 400 dpi), for example, and as uniform as possible; and
2 a scanning should be carried out at the same velocity as that of the rotation of a rotatable hologram, which rotation is at constant angular acceleration.
Since a wavelength of a semiconductor laser used therein as a scanning light source can vary according to ambient temperature and since several longitudinal modes can be produced,
3 displacement in a scanning direction of a scanning beam should be compensated for; and
4 displacement in a cross scanning direction of a scanning beam should be compensated for.
Since a scanning beam displacement is attributable to a warping of a base used in a rotatable hologram and the warping takes place as a result of using a floating glass, which is of low cost and needs no polishing, or a plastic base (PMMA, for
example) enabling injection molding,
5 a scanning beam displacement due to the plastic base being moved from its ideal position should be compensated for.
The present applicant had proposed a method of achieving the above tasks in the Japanese Laid-Open Patent Application 58-119098. The device used in the method comprises, as shown in FIG. 14, a rotatable hologram 10 and a fixed hologram plate 20
disposed between the rotatable hologram 10 and an image formation surface 4. The hologram 10 is a rapidly rotating rotatable hologram in which a plurality of hologram plates are disposed. Further, 5 is a reconstructing beam, 6 is a diffracted wave
outgoing from the hologram plate 10, and 7 is a diffracted wave outgoing from the fixed hologram plate 20. The reconstructing beam from a semiconductor not shown in the figure is diagonally incident on the rotating rotatable hologram 10, whose rotation
enables the scanning by the diffracted wave 6. The diffracted wave 6 is incident on the fixed hologram plate 20, and the diffracted wave 7, which is a wave diffracted therefrom, scans the image formation surface 4.
In the above configuration, displacement of a scanning beam position due to a wavelength variation of the semiconductor laser is compensated for, and a velocity of the scanning beam is maintained constant by a rotation of constant angular
acceleration of the rotatable hologram 10, so that a straight-line scanning by a scanning beam is achieved. Further, displacement of a scanning beam position both in the scanning direction and the cross scanning direction, which displacement is due to a
wavelength variation of the semiconductor laser, is corrected by having the fixed hologram plate 20 bend the scanning beam in a direction counter to a scanning direction of the rotatable hologram 10.
As an improved method of compensating for displacement of the scanning beam position in the cross direction due to a wavelength variation of the semiconductor laser, the present applicant filed an application for the Japanese Laid-Open Patent
Application 60-168830, in which it is proposed that a fixed hologram plate be spatially placed before the rotatable hologram.
The present applicant also made a proposition in the Japanese Laid-Open Patent Application 2-179437 (the domestic declaration of priority on the Japanese Laid-Open Patent Application 1-240720), in which is proposed a construction capable, by
employing at least two holograms, of maintaining uniform optical path lengths from an incident wave to an image formation surface, and of preventing degradation of wavefront characteristics on the image formation surface, which degradation is caused by a
wavelength variation of the reconstructing light source. Since the Japanese Laid-Open Patent Application 2-179437 relates to an optical system where at least two holograms, as mentioned above, are fixed, and therefore only one image formation point is
provided, an application of the same device to the scanning optical system now being discussed entails some difficulty in that moment-by-moment optical path length changes, which take place as the beam scanning proceeds, inevitably cause the optical path
length to be longer at the scanning end than at the scanning center. Accordingly, the aforementioned conventional technology has not resolved all of the objectives from 1 through 5 described earlier.
SUMMARY OF THE INVENTION
It is an object of the present invention to provide, as a solution to the objectives 1 through 5 above a method of manufacturing a high-resolution light-beam scanning apparatus employing only mass-producible holograms without using any auxiliary
optical system consisting of optical lenses or mirrors having curvature. It is another object of the present invention to provide a method of manufacturing a fixed hologram plate.
Another object of the present invention is to provide a method of manufacturing a light beam scanning apparatus employing at least two holograms, wherein a quality of a scanning beam or a scanning performance does not show deterioration even when
a wavelength displacement owing to a wavelength variation or a wavelength dispersion of the light source takes place.
Yet a further object of the present invention is to provide a method of manufacturing a hologram plate.
A further object of the present invention is to provide a light-beam scanning apparatus employing at least two holograms, wherein color aberration due to a wavelength displacement caused by a wavelength variation or wavelength dispersion of the
light source is corrected.
A still further object of the present invention is to obtain a hologram construction and configuration and a configuration of the front of a reconstructing wave by which construction and configurations a light beam scanning apparatus can be
obtained wherein displacement of a scanning beam position, and a blooming on the scanning surface can be minimized even when the wavelength displacement caused by a wavelength variation or wavelength dispersion of the light source arises.
In order to achieve the above objects, a light beam scanning apparatus of the present invention is configured such that a fixed plate, on which a diffraction grating is recorded, is installed between a rotatable hologram equipped with a
diffraction grating and an image formation surface scanned by this rotatable hologram, wherein:
diffraction gratings are provided in the rotatable hologram and the fixed plate for minimizing a sum total of values obtained by weighting;
a square of the difference between a light flux optical-path length an optical measured along a principal axis of a light beam incident and diffracted by the diffraction grating provided in the above-mentioned rotatable hologram, and incident on
and diffracted by the diffraction grating provided in the above-mentioned fixed plate so as to conduct a scanning and converges at a scanning point on an image formation surface, and a light flux optical-path length measured along a marginal ray
distanced from the principal axis;
or by weighting an absolute value of this optical path length difference,
the weighting being conducted at every scanning position covering an entire range of an image formation surface.
Further, a light beam scanning apparatus of the present invention is configured such that a fixed plate, on which a diffraction grating is recorded, is installed between a rotatable hologram equipped with a diffraction grating and an image
formation surface scanned by this rotatable hologram, wherein:
diffraction gratings are included in the rotatable hologram and the fixed plate for minimizing a sum total of values obtained by weighting;
a square of a sum is obtained by adding an amount of displacement of a light beam incident on and diffracted by the grating provided in the above-mentioned rotatable hologram, incident on and diffracted by the grating provided in the fixed plate
so as to perform a scan, and convergent on a scanning point on an image formation surface, the phase displacement of the diffraction grating provided in the rotatable hologram being measured along the peripheral axis distanced from the principal axis of
an incident reconstructing light flux, to an amount of displacement of the same light. The displacement being measured with respect to the principal axis of a phase recorded on the diffraction grating when the light flux is incident on the fixed plate;
or by weighting an absolute value of the above sum,
the weighting being conducted at every scanning position covering an entire range of the image formation surface.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagram describing a first embodiment of the present invention;
FIGS. 2(a)-2(c) are diagrams describing the scanning direction of a light beam scanning apparatus;
FIG. 3 is a diagram describing the cross scanning direction of a light beam scanning apparatus;
FIG. 4 is a diagram depicting a configuration of the scanning apparatus of the present invention;
FIG. 5 is a diagram depicting a manufacture of a fixed hologram plate;
FIGS. 6(a)-6(c) show graphs describing difference between optical path lengths, a beam radius, and a scanning track of the scanning apparatus;
FIG. 7 is a diagram describing waves used for constructing a fixed hologram plate;
FIGS. 8(a)-8(b) show diagrams describing spot images of a scanning beam, which images are obtained by holographic exposure;
FIGS. 9(a)-9(b) show graphs describing a scanning track and a beam radius when a spherical converging wave is incident;
FIGS. 10(a)-10(b) show diagrams describing the scanning direction and the cross scanning direction of the scanning apparatus;
FIGS. 11(a)-11(c) show graphs describing a scanning track, a beam radius, and displacement due to wavelength variation of the scanning apparatus of FIG. 10;
FIG. 12 is a diagram describing a manufacture of the fixed hologram plate;
FIG. 13 is a diagram describing an embodiment of the fixed hologram plate;
FIG. 14 is a diagram describing the conventional technology;
FIG. 15 is a diagram describing the principle of the second embodiment;
FIG. 16 is a diagram showing the first mode of the second embodiment;
FIG. 17 is a diagram showing an example of configuration of a light beam scanning apparatus employing the first mode of the second embodiment (a case where the first hologram is placed to the right of the second hologram);
FIG. 18 is a diagram showing an example of configuration of a light beam scanning apparatus employing the first mode of the second embodiment (a case where the first hologram is placed so as to be aligned with the second hologram);
FIG. 19 is a diagram showing an example of configuration of a light beam scanning apparatus employing the first mode of the second embodiment (a case where the first hologram is placed to the left of the second hologram);
FIG. 20 is a diagram showing the second mode of the second embodiment;
FIG. 21 is a diagram showing the third mode of the second embodiment;
FIG. 22 is a table showing the relationship between an incident wave and k;
FIG. 23 is a diagram showing an example of an embodiment of a light beam scanning apparatus employing the first through third modes of the second embodiment;
FIG. 24 is a table showing the relationship among x.sub.1 /F.sub.1, .theta..sub.1, .theta..sub.2 ;
FIG. 25(A) is a table showing the relationship among W, .DELTA..lambda., .xi.;
FIG. 25(B) shows examples of specifications for designing a second hologram and a scanning distance thereof;
FIG. 25(C) is a diagram depicting an example of a configuration where approximately the same image formation distance is obtained with respect to different outgoing angles;
FIG. 26 is another embodiment of the first mode of the second embodiment;
FIG. 27 is another embodiment of the first mode of the second embodiment;
FIG. 28 is another embodiment of the first mode of the second embodiment;
FIG. 29 is another embodiment of the first mode of the second embodiment;
FIG. 30 is a diagram depicting an example of a configuration where the light beam scanning apparatus shown in FIG. 29 is improved;
FIG. 31 is another embodiment of the first mode of the second embodiment;
FIG. 32 is a diagram depicting an example of a configuration of the light beam scanning apparatus, which is an improvement on that of FIG. 31;
FIG. 33 is a diagram describing a disadvantage of the first embodiment;
FIG. 34 is a diagram describing another disadvantage of the first embodiment;
FIGS. 35(A)-35(B) are diagrams describing the principle of the present invention;
FIG. 36 is a diagram describing a configuration of the first embodiment of the present invention;
FIG. 37 is a diagram depicting a manufacture of the fixed hologram of the first embodiment of the present invention;
FIGS. 38(A)-38(C) show a beam intensity distribution of the first embodiment of the present invention (part 1);
FIGS. 39(A)-39(C) show a beam intensity distribution of the first embodiment of the present invention (part 2);
FIG. 40 is a diagram depicting a configuration of the second embodiment of the present invention;
FIGS. 41(A)-41(C) are diagrams for describing a correction function for ensuring the constant velocity of the fixed hologram plate;
FIG. 42 is a diagram depicting a configuration of the first embodiment of the present invention (cross scanning direction);
FIG. 43 is a diagram depicting a configuration of the first embodiment of the present invention (scanning direction);
FIGS. 44(A)-(D) are diagrams describing the fixed hologram plate of the first embodiment of the present invention;
FIG. 45 is a diagram describing the first embodiment of the present invention;
FIGS. 46(A)-46(B) are other diagrams describing the first embodiment of the present invention;
FIG. 47 is a table showing various beam characteristics obtained when setting a length of the fixed hologram plate to be short with respect to a light beam scanning distance;
FIG. 48 is a table showing various beam characteristics obtained when setting a length of the fixed hologram plate to be long with respect to a light beam scanning distance;
FIG. 49 is a diagram depicting a configuration of an embodiment of a sixth embodiment;
FIGS. 50(A)-50(B) show a configuration and a top view of the first embodiment of the present invention;
FIGS. 51(A)-51(E) show graphs for describing an apparatus of FIG. 50;
FIGS. 52(A)-52(B) are diagrams describing holograms of the apparatus of FIG. 50;
FIG. 53 is a diagram depicting a configuration of the second embodiment of the present invention;
FIGS. 54(A)-54(B) shows a side view and top view of the second embodiment of the present invention;
FIGS. 55(A)-55(B) are diagrams describing holograms of an apparatus of FIG. 53;
FIG. 56 is a diagram depicting a configuration of an optic element, which is an embodiment of the present invention;
FIG. 57 is a diagram describing the principle of the optic element, which is an embodiment of the present invention;
FIG. 58 is a diagram depicting a variation of the optical element shown in FIG. 56;
FIG. 59 is a diagram depicting another variation of the optic element shown in FIG. 56;
FIGS. 60(A)-60(B) are diagrams describing the principle of a ninth embodiment;
FIG. 61 is a diagram depicting a configuration of an embodiment of the present invention (cross scanning direction);
FIG. 62 is a diagram depicting a configuration of an embodiment of the present invention (scanning direction);
FIGS. 63(A)-63(D) are diagrams describing the fixed hologram plate of an embodiment of the present invention (object wave);
FIG. 64 is a diagram describing the fixed hologram plate of an embodiment of the present invention (reference wave);
FIGS. 65(A)-65(B) shows diagrams describing the fixed hologram plate of an embodiment of the present invention (reference wave);
FIG. 66 are spot diagrams of an embodiment of the present invention;
FIGS. 67(A)-67(C) show diagrams describing manufacture of the fixed hologram plate of an embodiment of the present invention (part 1);
FIGS. 68(A)-68(F) show diagrams describing manufacture of the fixed hologram plate of an embodiment of the present invention (part 2);
FIGS. 69(A)-69(B) show diagrams describing the first embodiment of a hologram constructing exposure system of the present invention;
FIG. 70 is a diagram describing the second embodiment of the hologram constructing exposure system of the present invention;
FIGS. 71(A)-71(B) show diagrams describing the third embodiment of the hologram constructing exposure system of the present invention;
FIGS. 72(A)-72(B) show diagrams depicting a facet hologram of the rotatable hologram used in the first embodiment;
FIGS. 73(A)-73(B) show diagrams depicting a configuration of an embodiment of a tenth embodiment;
FIGS. 74(A)-74(C) show diagrams describing a manufacture of a hologram disk of an embodiment of the present invention;
FIG. 75 shows spot diagrams of an embodiment of the present invention;
FIG. 76 is a diagram showing a frequency distribution of the rotatable hologram and an incident beam;
FIG. 77 is a diagram describing the principle of an eleventh embodiment;
FIG. 78 is a diagram describing the rotatable hologram of the present invention;
FIG. 79 is a diagram describing a configuration of the light beam scanning apparatus of the present invention;
FIG. 80, comprising parts (A) and (B), is a diagram describing an effect of the present invention; and
FIG. 81 is a table showing a changing coefficient determined at the first to tenth order.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
A description of the principle of the present invention will be given below, followed by a description of concrete configurations and effects of the present invention. The first embodiment explained below conceptually presents a basis for each
of the embodiments that will be described herein below.
FIG. 1 is a diagram describing how a correction is carried out for a displacement of a position of a diffracted light of a scanning optical system, which displacement is caused by a wavelength variation of a semiconductor laser not shown in the
figure. A rotatable hologram 10 is equipped with a plurality of diffraction gratings 1a for carrying out a scanning. An image formation surface 4 is in the form of a photoconductive drum 3 in such apparatus as a laser printer, for example. A direction
represented by M2, at right angles to a laser scanning direction M3, is called a cross scanning direction. An assumption here is that a spherical converging wave (hereinafter called an incident wave 5) having its focus position at MO enters, and that a
scanning beam converges, owing to a rotation of the rotatable hologram 10, on a scanning point k on the image formation surface 4. Specifically, light flux of the incident wave 5, namely a reconstructing light, is incident on the rotatable hologram 10
to become a diffracted light 6, which is further diffracted by a fixed hologram plate 20 to become a diffracted light 7, which light 7 converges on the scanning point k. An optical path length L.sub.D of an optical path originating in each incident light
flux and ending in the scanning point k, the path length being measured along a beam, within the incoming wave 5, whose principal axis is a principal axis MA of the rotatable hologram 10, is given by the equation (1). Here, the incident light flux is
represented as an optical path from the rotatable hologram 10 to the reference sphere whose center is a convergent point P.sub.0. In case of a converging wave, the sign of an optical path length becomes negative. In the equation shown below,
parentheses () indicate a distance between the points entered in the parentheses. For example, (A.sup.0.sub.k P.sub.0) represents a distance between a point A.sup.0.sub.k and the point P.sub.0. The parentheses have the same meaning throughout the
equations that appear after equation (1).
An optical path length L.sub.1 of an optical path originating in the incoming light flux of the incoming wave 5, which light flux is incident along a marginal ray MI, and ending in the scanning point k is given as per the equation (2).
A condition under which the scanning beam is not removed from the scanning point k, even when the incident wave 5 from the semiconductor laser incurs a wavelength variation at the scanning point k, is represented by the equation (3).
That is, the removal is prevented as long as the optical path lengths of the incident wave 5 within the light flux, which wave is incoming on courses other than along the principal axis MA, are uniform. The condition under which a focal distance
on the scanning beam image formation surface 4 does not show a variation in response to a wavelength variation due to mode hops of the incident wave 5 from the semiconductor laser 5, is given by the equation (4).
That is, variation is prevented as long as the optical path lengths of the incident wave 5 remain the same when the wave is incident along the principal axis MA as when it is incident along the marginal ray MI. Accordingly, a configuration
fulfilling the equations (3) and (4), at the same time, at the scanning point is required in order to prevent deterioration caused by a semiconductor laser wavelength variation in the scanning beam quality across the entire scanning range of the image
formation surface 4 on the photoconductive drum 3.
The above condition of having uniform optical path lengths is met by minimizing and thus optimizing performance functions as per equations (5) or (5-1) below, where the optical path length difference is denoted by .delta.l.sup.k, and is measured
at the scanning point k between the beam that is incident along the principal axis MA and the beam that is incident along the marginal ray MI. ##EQU1##
where W.sub.k represents a weight determined by the degree of minimization of the optical path length at each scanning point.
A description will be given below of a method utilizing a phase change by a hologram. In the following, .PHI..sub.in represents a phase of the wavefront of a wave incoming into the rotatable hologram 10; .PHI..sub.H.sup.k represents a phase
transfer function of the hologram along the principal axis MA, which hologram is created by the rotatable hologram 10 as the rotatable hologram 10 scans the scanning point k; .PHI..sub.H2.sup.k represents a phase transfer function of the hologram of the
principal axis corresponding to the scanning point k of the fixed hologram plate; .delta..PHI..sub.H represents displacement, along the phase of the principal axis wavefront, of the phase of the peripheral wavefront of the incident light flux;
.delta..PHI..sub.H.sup.k represents displacement, from the phase of the principal axis wavefront, of the phase transfer function of the hologram created by the rotatable hologram 10; .delta..PHI..sub.H2.sup.k represents displacement, from the phase of
the principal axis wavefront, of the phase transfer function of the fixed hologram plate 20.
Since the condition for having regularity in the phases of the incident beams on the image formation surface, which regularity is required to form satisfactory images created by an aberration-free scanning beam, in other words to eliminate
wavefront aberration, is that the phase of the wave outgoing from the hologram is the sum of the phase of the incoming wave on the hologram and the phase transfer function of the hologram, we obtain the equation (6). ##EQU2## where k.sub.2 represents a
wavelength (2.pi./.lambda..sub.2)
This equation (6) is transformed into the equation (7) below when the equation (3), which relates to displacement of the scanning beam due to a wavelength variation, and the equation (4), which relates to a focal distance variation on the image
formation surface 4, are both fulfilled.
This equation (7) is to be fulfilled at the scanning point k for regularity in the phases incident on the image formation surface to be obtained. The equation (7) shows that, in order to maintain a good image formation quality, the sum of
displacements of the phase transfer functions recorded on the rotatable hologram 10 and the fixed hologram plate 20 should be made zero at each scanning point k. As will be later described in a detailed description of the equation (7), .delta..PHI..sup.k
in the equation (7), which represents phase displacement at the scanning point k, is minimized in a scanning range by using a performance function E expressed by the equations (8) or (8-1) below. ##EQU3##
where W.sub.k is a weight factor introduced in order to reduce displacement of phases at each scanning point. optimization of a hologram is carried out by minimizing the equations (8) or (8-1).
A description will be given next of a case where the optical path lengths are uniform. FIGS. 2(a)-2(c) describes an optical path length along the scanning direction. FIG. 2(a) depicts a parallel wave 6a outgoing from the rotatable hologram 10.
Given that an incident wave 5a is a converging spherical wave having a focus MO, the optical path lengths of the light beams contained in the light flux, which paths end at each scanning point on the image formation surface 4, are controlled to be
uniform, as can be seen from FIG. 2, by allowing diffracted waves 7a to go out approximately perpendicularly from the fixed hologram plate 20.
FIG. 2(b) depicts a divergent wave 6b, having a focus MO, outgoing from the rotatable hologram 10, where an incident wave 5b is a converging spherical wave as in FIG. 2(a). The optical path lengths of the light beams contained in the light flux,
which paths end at each scanning point on the image formation surface 4, are controlled to be uniform by directing the incident wave 7b from the fixed hologram plate 20 to be incident closer to a scanning center than the trajectory of an outgoing wave 6b
from the fixed hologram plate 20. The best configuration is the one in which the sign of the diffraction angle is not reversed.
FIG. 2(c) depicts a converging wave 6c outgoing from the rotatable hologram 10, where an incident wave 5c is a converging spherical wave as in FIG. 2(a). The optical path lengths of the light beams contained in the light flux, which paths end at
each scanning point on the image formation surface 4, are controlled to be uniform by directing an outgoing wave 7c, outgoing from the fixed hologram plate 20, to be incident closer to the scanning center than the original trajectory of a converging wave
6c incident on the fixed hologram plate 20, and by reversing the sign of the diffraction angle.
The configurations described above are designed for the scanning direction; the configurations for the cross scanning direction are described in the following. FIG. 3 is a diagram describing a scanning carried out in the cross scanning
direction, and more particularly a side view showing a configuration by which the optical path lengths in the cross scanning direction are maintained uniform. A diffracted wave 6d is produced from the incident wave 5a incident on the rotatable hologram
10. After being diffracted, the wave outgoing from the fixed hologram plate 20 forms an image on the image formation surface 4 on the photoconductive drum 3. Parts that are the same as FIG. 3 are given the same reference notations from figure to
figure. In this case, the fixed hologram plate 20 is tilted with respect to the rotatable hologram 10 so as to correct displacement of the scanning beam on the image formation surface 4 due to a wavelength variation of the reconstructing light source,
and to obtain the equal optical path lengths. This tilt angle .beta. is configured such that displacement of the scanning beam is minimized. Consequently, when the outgoing wave 6d from the rotatable hologram 10 is a parallel wave, the fixed hologram
plate 20 allows the wave to follow, at the scanning end, a trailing trajectory indicated by a broken line 6'd, so that the optical path lengths of the light flux in each scanning range are uniform and so that a straight-line scanning on the image
formation surface 4 is possible. The wave is returned to the original image formation point by means of the fixed hologram plate 20, making a straight-line scanning possible. The trajectory of the rotatable hologram 10 at the scanning center and the
scanning end can be opposite to each other.
As shown in FIG. 2(a), better scanning beam focal-distance correction for variation due to a wavelength variation of the reconstructing light source, is achieved by making the wavefront of the incident wave 5a, incident on the rotatable hologram
10, be a converging spherical wave and making equal the optical path lengths of the light fluxes, namely the light flux incident along the principal axis MA and the light flux incident along the marginal ray MI. The best compensation effect is achieved
by making the distance the converging spherical wave 5a travels between the surface of the rotatable hologram 10 and the focal point MO equal, or nearly equal, to the distance between the face of the rotatable hologram 10 and the surface of the fixed
hologram plate 20.
While the scanning velocity of a normal rotatable hologram 10 becomes higher as the scanning beam travels to the scanning end when the rotatable hologram 10 rotates at a constant angular velocity, the present invention allows the scanning beam to
be returned to the scanning center through the use of the fixed hologram plate 20, thus making it possible to provide both a quantitative matching and a compensation sufficient to make constant the scanning velocity on the scanning surface. Embodiments
of a light-beam scanning apparatus employing a hologram having the above-mentioned attributes are described in the following.
A description of the first embodiment will be given with reference to FIGS. 4, 5, and 2(a). Referring to FIG. 2(a), in this embodiment, the diffracted wave 6 of the rotatable hologram 10 is a parallel wave 6a, and the outgoing wave outgoing from
the fixed hologram plate 20 emerges approximately perpendicularly from the fixed hologram plate 20. Referring to FIG. 5, a wavelength used in constructing the fixed hologram plate 20 is the same as a wavelength 2 used at the time of reconstructing. Of
the waves used in the construction of the fixed hologram plate 20, an object wave OW is a wave having a spherical aberration and having a principal axis A of the fixed hologram plate 20 as an axial center, which axis is hit, at the scanning center, by
the outgoing wave from the rotatable hologram 10. This object wave is a so-called "positive spherical aberration wave", where a sharper bend toward the inside is observed away from the axis A and toward the outer boundary. As shown in the equation (11)
below, it is best to control the distance between a point P on the axis, at which point the spherical aberration wave is supposed to originate, and a point Q on the fixed hologram plate 20, which point Q is hit by the wave, namely the optical distance
(PQ), to be of a predetermined distance (d) at any point.
A reference wave RW is a parallel wave incoming diagonally and having an incidence angle .alpha. (.noteq.0). The above-mentioned parameters d and .alpha. are determined as appropriate so that the aforementioned performance functions (5) or (8)
are fulfilled, aberration is reduced, and a linear scanning can be performed.
The values in FIGS. 6(a)-(c) are obtained by realizing the above settings. FIG. 6(a) represents a result of optimization using the equation (5), where the horizontal axis indicates a scanning width occurring when the scanning center of the
photosensitive drum is designated as 0.0, and the vertical axis indicates an optical path length difference. This graph tells that the optical path length difference between the outermost beams of the light flux, which difference is measured in the
scanning direction when the scanning width is 108 mm (A4 size scan), has the maximum value of 30.lambda.. This value translates into a distance of 0.03 mm. Since the total optical path in this case is 641 mm, these constitute practically regular
optical paths, that is, no optical path length difference, results. In this case, the wavelength of the reconstructing wave generated by the semiconductor laser is .lambda.2=780 nm, the rotatable hologram 10 has a regular pitch, and the spatial
frequency thereof is 1765 (pcs/mm). The angle of the beam incident on the rotatable hologram 10 is 44.2.degree., and the radius of the rotatable hologram 10 is 40 mm. As for the parameters of the fixed hologram plate 20, d=364 mm, and
.alpha.=6.5.degree.. The distance between the rotatable hologram 10 and the fixed hologram plate 20 is 218 mm, and the distance between the fixed hologram plate 20 and the image formation surface 4 is 360 mm.
The tilt angle of the fixed hologram plate 20 with respect to the rotatable hologram 10 was 45.0.degree. in order to fulfill the performance function (8). FIG. 6(b) shows the scanning beam characteristic obtained therefrom. That is, for the
scanning width of 216 mm, the beam radius is within 18 .mu.m. As shown in FIG. 6(c), a deviation from a straight line of below the .+-.78 .mu.m level and a linearity of below the .+-.0.12% level resulted. Moreover, the variation of wavelength of the
semiconductor laser was controlled to be less than 1 .mu.m in the scanning direction even in the presence of a 0.3 nm wavelength variation due to a mode hop. As shown in FIG. 3, the scanning beam from the rotatable hologram 10 and incoming into the
fixed hologram plate 20 was bent in a simple manner so as to obtain a straight-line scanning on the fixed hologram plate 20, with the result that a displacement of 1 mm was observed.
Once the interference pattern on the fixed hologram plate of this embodiment is determined, the pattern can be drawn with an electron beam or a laser plotter. This method of manufacturing a fixed hologram plate by holographic exposure will be
described in the following.
It is generally known that wavelength sensitivity of a hologram material having a high diffraction efficiency is in a range shorter than that of the wavelength of a semiconductor laser. Thus, aberration owing to this wavelength ratio must
generally be taken into consideration when manufacturing a hologram plate by holographic exposure. Here, the wavelength of the wave used in constructing the hologram plate is designated as .lambda.1 and the wavelength ratio is designated as
.lambda.2/.lambda.1. It is found that, after taking into consideration aberration owing to this wavelength ratio, the construction of a spherical aberration needed for the construction of a hologram wave can be such that d of the first embodiment is
replaced by the product of d and s. As in the first embodiment, optimization was carried out by employing a diagonally incident, parallel reference wave. Once the relevant interference fringe distribution is known, a hologram, containing aberration of
the above complexity, needs to be manufactured by holographic exposure.
FIG. 7 shows a second embodiment of the fixed hologram plate 20 of the present invention, wherein a spherical aberration wave used therein is of a wavefront of a wave outgoing from a plano-concave lens, which is a spherical lens, on which
plano-concave lens a stigmatic diverging spherical wave is incident. Parameters, including a plano-concave lens, are optimized so that the above amount of aberration is obtained. That is, .lambda.1=441.6 nm (HeCd laser), and the wavelength of the
semiconductor laser is designed to be .lambda.2=780 nm. The thickness of the BK7 plano-concave lens is 3.0 mm at the center, an index of refraction is 1.51, and a curvature thereof is 115.0 mm. The distance between the point light source S.sub.0 of the
diverging spherical wave and the plano-concave lens is d.sub.0 =439.0 mm, and the distance between the plano-concave lens and the fixed hologram plate 20 is LT1=469.0 mm.
FIG. 8(a) shows aberration images of the scanning beam created by the fixed hologram 20 manufactured by holographic exposure designed in accordance with FIG. 7. In the figure, a very small aberration of below a 20 .mu.m level is evident. FIG.
8(b) also shows spot aberration images of the scanning beam created by the hologram manufactured in accordance with FIG. 5. In FIG. 8(b), approximately the same images as in FIG. B(a) are seen. This embodiment has an advantage in that holographic
exposure can be achieved by a simple spherical aberration wave and control of the exposure system is fairly easy.
In a third embodiment described below, the incident wave which is incident on the rotatable hologram 10 is a converging spherical wave. The phase transfer function in this case needs to fulfill the following equation (10). ##EQU4## It is
evident here that a point light source of the reference wave is at the distance F.sub.1 from the rotatable hologram. The distance F.sub.1 is measured along an axis of rotation of the rotatable hologram and the wavelength of the wave used in constructing
a hologram is .lambda..sub.1'. .lambda..sub.1' here is a virtual wavelength of the wave used in constructing a hologram. The object wave is a spherical wave produced by a point light source positioned at a distance Y.sub.2 and a height F.sub.2 /S from
the rotatable hologram, which distance is measured along an axis of rotation aligned with the principal scanning axis. The wavelength of the wave used in constructing a hologram is a virtual wavelength .lambda..sub.1". Thus the virtual difference is
provided, in terms of the wavelength, between the reference wave and the object wave, which are both used in construction of a hologram. S is the ratio .lambda..sub.2 /.lambda..sub.1" obtained from .lambda..sub.2 and .lambda..sub.1" of the
reconstructing wave. Optimization in accordance with the equation (5) was conducted in a scanning apparatus equipped with the rotatable hologram 10 manufactured on the basis of the equation (10), on an assumption that a converging spherical wave is
incident on the rotatable hologram.
The result of this arrangement is that a deviation from a straight line of below the .+-.0.1 mm level was obtained, as shown in FIG. 9(a). FIG. 9(b) shows that a beam radius of less than 18 .mu.m was obtained. A linearity of below .+-.0.22%
level resulted. As for displacement in the scanning direction due to a wavelength variation of the semiconductor laser, a displacement of less than 1 .mu.m in correspondence with a 0.3 nm wavelength variation was observed, which is a satisfactory
result. In this arrangement, the radius of the beam incident on the rotatable hologram 10 is 45 mm, the distance between the rotatable hologram 10 and the fixed hologram plate 20 is 182 mm, the distance between the fixed hologram plate 20 and the image
formation surface is 277 mm, and the tilt angle of the fixed hologram plate 20 with respect to the rotatable hologram 10 is 64.2.degree.. As far as the reference wave is concerned, .lambda..sub.1' =330 nm and F1=200 mm. With the object wave,
.lambda..sub.1" =78 nm, and therefore S=10, F2=1060, and Y2=95 mm.
This embodiment is configured such that the incident wave is a converging-spherical wave and that the distance between the surface of the rotatable hologram and the convergent point is 200 mm, which is approximately the distance between the
surface of the fixed hologram plate and the image formation surface. Even when a variation of 100 nm is caused for environmental reasons in the wavelength of the semiconductor laser, the beam radius incurred only a minor change from 18 .mu.m to 18.5
.mu.m, meaning that no serious deterioration in the beam radius takes place. While the configuration of a hologram represented by the equation (10) assumes that the wavelength of the wave used in the manufacture of a hologram is a virtual wavelength,
the manufacture of a hologram by an electron beam or a laser plotter drawing is possible. When the manufacture is conducted using holographic exposure, an auxiliary optical system proposed in the Japanese Laid-Open Patent Application 63-72633 filed by
the present applicant can be utilized.
A fourth embodiment will be described below. FIGS. 10(a) and (B) illustrate a compensation for displacement of the scanning beam, which displacement occurs when a removal of the base of the rotatable hologram 10 from a parallel state occurs. In
this fourth embodiment, a beam, whose convergence takes place in the cross scanning direction at right angles to the scanning direction (a direction of rotation of the rotatable hologram 10), is employed as the beam incident on the rotatable hologram 10,
as shown in FIGS. 10(a) and (B). Since the wave incident on the fixed hologram plate 20 is a cylindrical wave, a reference wave that matches this cylindrical wave is considered to be necessary. This means that a spherical aberration wave as the one in
FIG. 5 is to be used as the object wave for the manufacture of the fixed hologram plate 20. For the reference wave, one example is a wave having direction cosines as per the equation (11) below. ##EQU5## where C.sub.0, y.sub.0, and Z.sub.0 are
constants.
While the reference wave is a coma wave as shown by the equation (11) above, the object wave is a spherical aberration wave. This aberration can be controlled to be at an appropriate level so that a desired performance can be obtained. FIGS.
11(a)-11(c) show the result thereof. FIG. 11(a) illustrates the deviation from a straight line, while FIG. 11(b) illustrates the beam radius.
The present invention realizes an extremely satisfactory deviation from a straight line of below the .+-.0.4 m level. The beam radius thereof is 8 .mu.m at a maximum, which is sufficient to allow a successful aberration correction. Linearity is
below .+-.0.13% level, which is also satisfactory. As shown in FIG. 11(c), even under a wavelength variation of the semiconductor laser of 1 nm, for example, the displacement could be controlled to be less than 3 .mu.m in the scanning direction, and
less than 3 .mu.m in the cross scanning direction. The relationships among the object wave, the reconstructing wave, the parameters of the rotatable hologram 10, and the fixed hologram plate are of the same parameters as those in the first embodiment.
Also, y.sub.0 =-5 mm, and Z.sub.0 =321 mm.
The base of the rotatable hologram in this embodiment can be moved from its ideal position and still function well in the following way. That is, even the rotatable hologram 10 exhibiting a displacement as large as one minute (P--P) from its
ideal position allows a sufficient correction in which the displacement in the cross scanning direction is controlled to be less than 5 .mu.m. This means a greater tolerance compared to the conventional rotatable hologram 10, where only several seconds
of displacement was allowed from the ideal position of the base, and goes a long way toward reducing the cost of a hologram base.
As shown in FIG. 12, when manufacturing a fixed hologram plate, a spherical aberration wave for the object wave is generated by a spherical lens, and the reference wave is generated by a similar spherical lens 8 that creates direction cosines of
a coma wave 9 as represented by the equation (11).
FIG. 13 depicts the fifth embodiment. Two holograms are formed on one fixed hologram plate. The above-described object wave for manufacturing the fixed hologram, and the wavefront C are recorded on the fixed hologram plate so that one hologram
20-1 is manufactured. The other hologram 20-2 is manufactured with the above-described reference wave for manufacturing the fixed hologram plate and with the wavefront C. By superposing, as shown in the figure, characteristics similar to those of the
above embodiments are obtained. This embodiment is most suitable for the case where the fixed hologram plate is almost of an in-line type and holographic exposure is difficult.
Since each of the holograms thus manufactured is of an off-axis type, a high diffraction efficiency results. Further, these two hologram plates achieve regular optical paths and precise compensation for degradation of characteristics of the
scanning light; which degradation is due to variation of the wavelength of the semiconductor laser. The fixed hologram plates here are mass producible by means of injection, making this embodiment favorable in terms of manufacturing and pricing. The
shape of the rotatable hologram is not limited to a disk, and the present invention is applicable to other shapes including a cylinder, a cone, and a pyramid.
As has been described, the first invention is capable of providing a simple and inexpensive optical system with two holograms. A high-reliability optical system without displacement of the scanning beam, which displacement is due to variation of
the wavelength of the semiconductor laser, is realized in the above invention.
The second invention included in the present application will be described now with reference to FIGS. 15 and 16. FIG. 15 is an oblique view illustrating a light beam scanning apparatus according to the first mode of the present invention. FIG.
16 is a top view thereof. The light beam scanning apparatus 100 comprises at least two holograms, namely a first hologram plate 110 and a second hologram plate 112. 120 represents a scanning surface.
The first hologram plate 100 is a movable hologram for converting a converging spherical wave into a parallel wave, for example. The second hologram plate 112 is a fixed hologram for converting a parallel wave into a converging spherical wave,
for example. The dista | | |
