OPTICAL BEAM SCANNING APPARATUS, AND METHOD FOR MANUFACTURING STATIONARY HOLOGRAM PLATE, AND HOLOGRAM ROTOR

Abstract: An optical beam scanning apparatus of a high resolution, compensates the increase and change of the diameter of a scanning beam, uneven rotation of a hologram rotating body, the positional changes in the directions of main and subscannings by the mode hopping of the wavelength of a semi-conductor laser, and the deterioration of the parallelism of the base of the hologram rotating body, etc., which mar the resolution and impede the cost reduction of a hologram scanner. The apparatus uses only the holograms that are duplicated in large quantities, without using auxiliary optical systems such as optical lenses and mirrors with curvatures. On a rotating body (1) and a fixed plate (2), provided are respectively diffraction gratings (1a, 2a) which minimize the sum of the weighted values of the squared or absolute values of the differences of two light path lengths, the weighting being conducted for each of scanning points on the entire image-forming surface (4). One of the two optical path length is of a light beam on the principal axis (MA), which is diffracted by the diffraction grating (1a) and by the diffraction grating (2a) and then, is focused at a scanning point (k) on the image-forming surface (4); the other is of a light beam on a peripheral axis (MI) different from the principal axis (MA). Alternatively, the diffraction gratings (1a, 2a) minimize the sum of the weighted values of the squared or absolute value of the sum of two phase differences, the weighting being conducted for each of scanning points on the entire image-forming surface (4). One of the two phase differences is the shift of the phase of the diffraction grating (1a) on the rotating body (1) from the principle axis (MA) when the light beam is focused at the scanning point (k); the other is the shift of the phase recorded on the diffraction grating (2a) from the principle axis (MA) when the light beam strikes the stationary plate (2).

Description: 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 inventions refer 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- 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-  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 - 600dpi or even 1000dpi. 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 ○a scanning beam radius should be as thin as 60 µm (equivalent to 400dpi), for example, and as uniform as possible; 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; 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, a scanning beam displacement due to the plastic bases 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 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. In the same figure, 10 represents a rapidly rotating rotatable hologram in which a plurality of hologram plates are disposed, 20 a fixed hologram plate, 4 an image formation surface, 5 a reconstructing beam, 6 a diffracted wave outgoing from the hologram plate 10, and 7 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 a method of compensating, in a better way, 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 devise 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. EP-A-0 214 018 discloses a light beam scanning apparatus according to the preamble of accompanying claim 1. In this apparatus, the fixed hologram is located upstream of the rotatable hologram. According to one aspect of the present invention, there is provided a light-beam scanning apparatus comprising: a rotatable hologram plate disposed in an optical path of an incident optical beam, said rotatable hologram plate carrying thereon a first diffraction grating having a regular interference fringe pitch, said first diffraction grating causing a diffraction of said incident optical beam to form a first diffraction optical beam; a fixed hologram plate carrying thereon a second diffraction grating; and an image formation surface disposed in an optical path of a diffraction optical beam generated by said rotatable hologram plate and said fixed hologram plate; characterised in that: said second diffraction grating has a pattern of interference fringes that appear when an object wave and a reference wave cause interference on said fixed hologram plate, said object wave being a spherical wave incident on said fixed hologram plate perpendicularly with a positive spherical aberration such that a spherical aberration of a ray increases with increasing offset of a ray path from an optical axis that is perpendicular to said fixed hologram plate, and wherein for each ray, a point on the axis at which the spherical wave appears to originate is separated from a point where the ray is incident on said fixed hologram plate by a distance d, and said reference wave being a parallel wave incident on said fixed hologram plate obliquely at an angle α; said fixed hologram plate is disposed in the optical path of said first diffraction optical beam, so that said second diffraction grating causes a diffraction of said first diffraction optical beam incident thereto to form a second diffraction optical beam, said first diffraction beam thereby scanning a surface of said fixed hologram plate in response to a rotation of said rotatable hologram plate; said image formation surface is disposed in an optical path of said second diffraction optical beam, said second diffraction optical beam thereby hitting said image formation surface at a scanning point, said scanning point scanning over said image formation surface in response to said rotation of said rotatable hologram plate; and the value of said parameters d and α are selected so as to minimize a weighted sum total of quantities each defined for a scanning point on said image formation surface and indicative of either an absolute value or the square of an optical phase difference between a ray travelling along said first and second diffraction beams to said image formation surface along the principal axis of said incident optical beam, and a marginal ray travelling along said first and second diffraction beams to said image formation surface offset from said principal axis, said weighted sum total being conducted at every scanning point on said image surface. The present invention also embraces a method of manufacturing the light-beam scanning apparatus. In one such method, the first diffraction grating is formed by causing interference between two diverging spherical waves on the rotatable hologram plate, and the second diffraction grating may be formed by directing a spherical aberration wave as an object wave and a coma wave as a reference wave onto the fixed hologram plate. According to a further aspect of the present invention, there is provided a light-beam scanning apparatus, comprising at least first and second holograms, and a light source provided by a semiconductor laser or a light-emitting diode, said first hologram being a movable hologram and said second hologram being a fixed hologram disposed behind said first hologram, characterised in that said first hologram produces a divergent optical beam as a first diffraction optical beam and said second hologram produces a convergent optical beam as a second diffraction optical beam, and an optical phase difference ΔΦ as measured along an optical path of an optical beam travelling from said light source to an image formation surface consecutively through said first hologram and said second hologram, is related by ΔΦ < c (λ 2 /Δλ) wherein c is a dimensionless constant smaller than 0.5, λ represents a central wavelength of the optical beam produced by said light source and Δλ represents the deviation of wavelength of said incident optical beam from said central wavelength. FIG.1 is a diagram describing an embodiment of the invention; FIG.2 is a diagram 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 inventions; FIG.5 is a diagram depicting a manufacture of a fixed hologram plate; FIG.6 shows 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; FIG.8 shows diagrams describing spot images of a scanning beam, which images are obtained by holographic exposure; FIG.9 shows graphs describing a scanning track and a beam radius when a spherical converging wave is incident; FIG.10 shows diagrams describing the scanning direction and the cross scanning direction of the scanning apparatus; FIG.11 shows 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; and FIG.14 is a diagram describing the conventional technology. 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 inventions. The first invention explained below conceptually presents a basis for each of the inventions that will be described in the following. 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 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 0 . In case of a converging wave, the sign of an optical path length becomes negative. In the equation shown below, brackets [ ] indicate a distance between the points entered in the bracket. For example, [A 0 k P 0 ] represents a distance between a point A 0 k and the P 0 . The brackets have the same meaning throughout the equations that appear after the equation (1). L 0 = - [A 0 k P 0 ] + [A 0 k B 0 k ] + [B 0 k k] An optical path length L 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). L 1 = - [A i k P 0 i ] + [A i k B i k ] + [B i k k] 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). - [A i k P 0 i ] + [A i k B i k ] + [B i k k] = - [A j k P 0 j ] + [A j k B j k ] + [B j k k] 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). - [A 0 k P 0 ] + [A 0 k B 0 k ] + [B 0 k k] = - [A i k P 0 i ] + [A 0 k B i k ] + [B i k k] 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 δℓ 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 . where W 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, Φ in represents a phase of the wavefront of a wave incoming into the rotatable hologram 10; Φ H 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; Φ H2 k represents a phase transfer function of the hologram of the principal axis corresponding to the scanning point k of the fixed hologram plate ; δΦ in represents displacement, along the phase of the principal axis wavefront, of the phase of the peripheral wavefront of the incident light flux; δΦ H 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; δΦ H2 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). Φ in + Φ H k + k 2 [A 0 k B 0 k ] + Φ H2 k + k 2 [B 0 k k] = Φ in + δΦ in + Φ H k + δΦ H k + k 2 [A i k B i k ] +  H2 k + δ H2 k + k 2 [B i k k] where k 2 represents a wavelength (2π/λ 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. δΦ k ≡ δΦ H k + δΦ H2 k = 0 This equation (7) is to be fulfilled at the scanning point k for regularity in the phases of the 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), δΦ 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. where W 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. FIG.2 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 β 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 surfface 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. [First embodiment] 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 axial center, which axis is hit, at the scanning center, by the outgoing wave from the rotatable hologram 10. This object wave is so-called a "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. d = P 0 Q 0 = P 1 Q 1 = P 2 Q 2 = ····· = P n Q n A reference wave RW is a parallel wave incoming diagonally and having an incidence angle α (≠ 0). The above-mentioned parameters d and α 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 FIG.6 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 photosensitve 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 108mm (A4 size scan), has the maximum value of 30λ. This value translates into a distance of 0.03mm. Since the total optical path in this case is 641mm, 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 λ 2 = 780nm, 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°, and the radius of the rotatable hologram 10 is 40mm. As for the parameters of the fixed hologram plate 20, d = 364mm, and α = 6.5°. The distance between the rotatable hologram 10 and the fixed hologram plate 20 is 218mm, and the distance between the fixed hologram plate 20 and the image formation surface 4 is 360mm. The tilt angle of the fixed hologram plate 20 with respect to the rotatable hologram 10 was 45.0° 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 216mm, the beam radius is within 18 µ m. As shown in FIG.6(c), a deviation from a straight line of below the ±78 µ 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 µ 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 1mm 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. [Second embodiment] 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 λ1 and the wavelength ratio is designated as λ2/λ1. 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 the 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, λ 1 = 441.6nm (HeCd laser), and the wavelength of the semiconductor laser is designed to be λ 2 = 780nm. The thickness of the BK7 plano-concave lens is 3.0mm at the center, an index of refraction is 1.51; and a curvature thereof is 115.0mm. The distance between the point light source S 0 of the diverging spherical wave and the plano-concave lens is d 0 = 439.0mm, and the distance between the plano-concave lens and the fixed hologram plate 20 is LT1 = 469.0mm. 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 µ 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.8(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. [Third embodiment] In the 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). ψ = 2 /λ 1 ' X 2 + Y 2 + F 2 1 -2 /λ 1 " X 2 + (Y - Y 2 ) 2 + (F 2 /S) 2 It is evident here that a point light source of the reference wave is at the distance F 1 from the rotatable hologram; the distance F 1 is measured along an axis of rotation of the rotatable hologram and the wavelength of the wave used in constructing a hologram is λ 1 '. λ 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 2 and a height F 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 λ 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 λ 2 /λ 1 " obtained from λ 2 and λ 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 ±0.1mm level was obtained, as shown in FIG.9(A). FIG.9(b) shows that a beam radius of less than 18 µ 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 µ m in correspondence with a 0.3nm wavelength variation was observed, which is a satisfactory result. In this arrangement, the radius of the beam incident on the rotatable hologram 10 is 45mm, the distance between the rotatable hologram 10 and the fixed hologram plate 20 is 182mm, the distance between the fixed hologram plate 20 and the image formation surface is 277mm, and the tilt angle of the fixed hologram plate 20 with respect to the rotatable hologram 10 is 64.2°. As far as the reference wave is concerned, λ1' = 330nm and F1 = 200mm. With the object wave, λ 1 " = 78nm, and therefore S = 10, F2 = 1060, and Y2 = 95mm. 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 200mm, which is approximately the distance between the surface of the fixed hologram plate and the image formation surface. Even when a variation of 100nm is caused for environmental reasons in the wavelength of the semiconductor laser, the beam radius incurred only a minor change from 18 µ m to 18.5 µ 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. [Fourth embodiment] A fourth embodiment will be described below. FIG.10(a) and (b) illustrates 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 FIG.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. ℓ = x/ z 0 2 + x 2 - x/ z 0 2 + x 2 + (y - y 0 ) 2 m = c 0 - (y - y 0 )/ z 0 2 + x 2 + (y - y 0 ) 2 where c 0 , y 0 , and z 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. FIG.11 shows 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 µ 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 1nm, for example, the displacement could be controlled to be less than 3 µm in the scanning direction, and less than 3 µm 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 0 = -5mm, and Z 0 = 321mm. The base of the rotatable hologram in this embodiment can be moved from its ideal position and still functions 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 µ 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). [Fifth embodiment] 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. As has been described, the light beam scanning apparatus according to the present invention can provide a simple and inexpensive optical system by using two holograms and can realize a highly reliable apparatus free from scanning beam displacement caused by a wavelength variation of the semiconductor laser. Therefore, the scanning apparatus of the present invention is useful as a laser scanning optical system to be incorporated in office automation equipment such as a laser printer and a laser facsimile, or in a laser drawing apparatus, and a laser inspection apparatus, for example.

Claims: A light-beam scanning apparatus comprising: a rotatable hologram plate (10) disposed in an optical path (MA) of an incident optical beam (5), said rotatable hologram plate carrying thereon a first diffraction grating (1a) having a regular interference fringe pitch, said first diffraction grating causing a diffraction of said incident optical beam to form a first diffraction optical beam (6;6a;6b;6c); a fixed hologram plate carrying thereon a second diffraction grating (2a); and an image formation surface disposed in an optical path of a diffraction optical beam generated by said rotatable hologram plate and said fixed hologram plate; characterised in that : said second diffraction grating (2a) has a pattern of interference fringes that appear when an object wave (OB) and a reference wave (RW) cause interference on said fixed hologram plate, said object wave being a spherical wave incident on said fixed hologram plate perpendicularly with a positive spherical aberration such that a spherical aberration of a ray increases with increasing offset of a ray path from an optical axis that is perpendicular to said fixed hologram plate, and wherein for each ray, a point (P) on the axis at which the spherical wave appears to originate is separated from a point (Q) where the ray is incident on said fixed hologram plate by a distance d, and said reference wave being a parallel wave incident on said fixed hologram plate obliquely at an angle α; said fixed hologram plate (20) is disposed in the optical path of said first diffraction optical beam, so that said second diffraction grating causes a diffraction of said first diffraction optical beam incident thereto to form a second diffraction optical beam (7; 7a; 7b: 7c), said first diffraction beam thereby scanning a surface of said fixed hologram plate in response to a rotation of said rotatable hologram plate; said image formation surface (3) is disposed in an optical path of said second diffraction optical beam, said second diffraction optical beam thereby hitting said image formation surface at a scanning point (k), said scanning point scanning over said image formation surface in response to said rotation of said rotatable hologram plate; and the value of said parameters d and α are selected so as to minimize a weighted sum total of quantities each defined for a scanning point on said image formation surface and indicative of either an absolute value (|δl k |) or the square ((δl k ) 2 ) of an optical phase difference between a ray travelling along said first and second diffraction beams to said image formation surface along the principal axis (MA) of said incident optical beam, and a marginal ray travelling along said first and second diffraction beams to said image formation surface offset from said principal axis (MA), said weighted sum total being conducted at every scanning point on said image surface. A light-beam scanning apparatus as claimed in claim 1, wherein said weighted sum total is indicative of the square ((δl k ) 2 ) of said optical phase difference. A light-beam scanning apparatus as claimed in claim 1, wherein said weighted sum total is indicative of said absolute value (|δl k |) of said optical phase difference. A light-beam scanning apparatus as claimed in any of claims 1 to 3, wherein said fixed hologram plate (20) is tilted with respect to said rotatable hologram plate (10). A light-beam scanning apparatus as claimed in any of claims 1 to 4, wherein said first diffraction grating (1a) produces said first diffraction optical beam (6a,6c) in a first diffraction direction, and wherein said second diffraction grating (2a) produces said second diffraction optical beam (7a,7c) in a second diffraction direction opposite to said first diffraction direction. A light-beam scanning apparatus as claimed in claim 5, further comprising a light source (1) for generating a convergent optical beam. A light-beam scanning apparatus as claimed in any of claims 1 to 4, wherein said first diffraction grating (1a) produces said first diffraction optical beam (6) in the form of a divergent optical beam, and wherein said second diffraction grating (2a) diffracts said first diffraction optical beam, incident thereto with an incident angle with respect to a normal drawn to said fixed hologram plate (2), in a direction opposite to said incident angle with respect to said normal as said second diffraction optical beam, said second diffraction grating forming said second diffraction optical beam in the form of a convergent optical beam. A light-beam scanning apparatus as claimed in claim 6 or 7, wherein a distance between said rotatable hologram plate (10) and a point of convergence (MO) of said convergent incident optical beam is set generally identical to a distance between said rotatable hologram plate and said fixed hologram plate (20). A method of manufacturing the light-beam scanning apparatus of claim 1, comprising the step of forming said second diffraction grating by causing interference between an object wave (OB) and a reference wave (RW) on said fixed hologram plate, said object wave being incident on said fixed hologram plate (20) perpendicularly and having a spherical aberration such that a ray in said objective wave is bent more toward a central point of scanning on said fixed hologram plate as said ray deviates from a central axis that passes said fixed hologram plate at said central point perpendicularly. A method as claimed in claim 9, wherein said ray in said object wave (OW) has an optical path length as measured along said ray from a point (Q 1 - Q 4 ) on said fixed hologram plate (20) to a point (P 1 - P 4 ) on said optical axis, such that said optical path length is substantially constant for all the rays included in said object wave, and wherein said reference wave (RW) is a parallel beam incident obliquely to said fixed hologram plate (20). A method as claimed in claim 10, wherein said object wave (OW) is a spherical-aberration wave incident on said fixed hologram plate (20) perpendicularly at said central point and having a wavelength shorter than a wavelength of said incident optical beam, said spherical-aberration being such that an optical path length in a ray included in said object wave is generally equal to a ratio of a wavelength (λ 2 ) of said incident optical beam to a wavelength (λ 1 ) of said object wave, multiplied with a constant. A method as claimed in claim 11, wherein said object wave (OW) is formed by causing a divergent beam free from aberration to pass through a lens. A light-beam scanning apparatus as claimed in claim 1, further comprising means (1,31,32) for generating said incident optical beam (5) with a converging wave front or a planar wave front in a first hypothetical cross-sectional plane that includes an optical axis of said incident optical beam and a scanning line defined on said image formation surface by said scanning point, and with a converging wave front in a second hypothetical cross-sectional plane perpendicular to said first hypothetical cross-sectional plane. A light-beam scanning apparatus as claimed in claim 13, wherein said second diffraction grating (2a) of said fixed hologram plate (20) has an interference fringe pattern formed by interference of a spherical-aberration object wave and a coma reference wave. A method of manufacturing the light-beam scanning apparatus of claim 14, including the step of forming said second diffraction grating (2a) on said fixed hologram plate (20) by directing a spherical-aberration wave as an object wave and a coma wave as a reference wave. A method as claimed in claim 15, wherein said spherical-aberration wave and said coma wave are formed by causing a light beam to pass through a lens. A light-beam scanning apparatus as claimed in any of claims 1 to 8, 13 or 14 wherein said second diffraction grating (2a) on said fixed hologram plate (20) includes a plurality of diffraction patterns. A light-beam scanning apparatus as claimed in any of claims 1 to 8, 13 or 14, wherein a scanning beam track formed by means of said rotatable hologram (10) is curved on a surface of said fixed hologram plate (20). A light-beam scanning apparatus, comprising at least first and second holograms (110,112), and a light source provided by a semiconductor laser or a light-emitting diode, said first hologram (110) being a movable hologram and said second hologram (120) being a fixed hologram disposed behind said first hologram (110), characterised in that said first hologram (110) produces a divergent optical beam as a first diffraction optical beam and said second hologram (120) produces a convergent optical beam as a second diffraction optical beam, and an optical phase difference ΔΦ as measured along an optical path of an optical beam travelling from said light source to an image formation surface (120) consecutively through said first hologram (110) and said second hologram (112), is related by ΔΦ < c (λ 2 /Δλ) wherein c is a dimensionless constant smaller than 0.5, λ represents a central wavelength of the optical beam produced by said light source and Δλ represents the deviation of wavelength of said incident optical beam from said central wavelength. A light-beam scanning apparatus as claimed in claim 19, wherein said optical beam incident on said first hologram (110) is a converging wave.

Inventors: ARITAKE HIROKAZU, HASEGAWA SHINYA, HOKARI MAMORU, IWATA SHIGETAKE, KAYASHIMA SHIGEO, MAEDA SATOSHI, NAKASHIMA MASATO, YAMAGISHI FUMIO, ARITAKE, HIROKAZU, HASEGAWA, SHINYA, HOKARI, MAMORU, IWATA, SHIGETAKE, KAYASHIMA, SHIGEO, MAEDA, SATOSHI, NAKASHIMA, MASATO, YAMAGISHI, FUMIO, ARITAKE, HIROKAZU, FUJITSU LIMITED, HASEGAWA, SHINYA, FUJITSU LIMITED, HOKARI, MAMORU, FUJITSU LIMITED, IWATA, SHIGETAKE, FUJITSU LIMITED, KAYASHIMA, SHIGEO, FUJITSU LIMITED, MAEDA, SATOSHI, FUJITSU LIMITED, NAKASHIMA, MASATO, FUJITSU LIMITED, YAMAGISHI, FUMIO, FUJITSU LIMITED
Applicants: FUJITSU LTD, FUJITSU LIMITED
Application year: 1992
Main classification: G02B26
IPC codes: G02B5, G02B26