JPS633290B2 - - Google Patents

Description

[Detailed description of the invention]

The present invention relates to an optical scanning device used as a means for reading or recording images. 2. Description of the Related Art Optical scanning devices have been widely used in many fields, and their scanning performance has been improved in various ways to meet the demands of use. In recent years, scanning devices are often incorporated into systemized devices such as information processing terminal devices as a component thereof, and therefore there is a demand for miniaturization of scanning devices. Various methods can be considered to reduce the size of this scanning device, and one method is to reduce the size of the scanning imaging lens system. However, reducing the number of lens groups that make up the imaging lens system
The degree of freedom in design is reduced, and various problems such as aberration correction arise. One of the problems is to scan the surface to be scanned at a constant speed. Conventionally, the scanning surface is scanned at a constant speed using a scanning lens consisting of four lenses, as shown in USP3687025.
USP3946150 discloses that a scanning lens consisting of three lenses scans a surface to be scanned at a constant speed. Further, as an apparatus that uses a small number of scanning lenses, US Pat. No. 4,099,829 discloses an apparatus that scans a surface to be scanned with a single scanning lens.
However, US Pat. No. 4,099,829 does not disclose any technique for scanning a surface to be scanned at a constant speed. SUMMARY OF THE INVENTION An object of the present invention is to provide a scanning device that is downsized by configuring a scanning imaging lens with a single lens. A further object of the present invention is to provide a scanning device capable of scanning a surface to be scanned at a constant speed even when a single lens is used as a scanning lens. A further object of the present invention is to provide a scanning device that is capable of scanning a surface to be scanned, particularly a flat surface to be scanned, with good imaging characteristics even if the imaging lens for scanning is composed of a single lens. It is about providing. In the scanning device according to the present invention, the distortion is corrected by the rotational characteristics of the deflector (for example, constant angular velocity deflection or sinusoidal oscillation deflection) and the shape selection of the light source, deflector, and scanning lens. We are trying to keep the scanning speed constant at the top. In the scanning device according to the present invention, when the scanning lens is a spherical single lens, the rotation characteristic of the deflector is sinusoidal vibration rotation, and by selecting the sinusoidal vibration amplitude, modulation is performed at equal time intervals. The signal is scanned at equidistantly spaced spots on the scanned surface. In the scanning device according to the present invention, spot scanning at equidistant intervals on the surface to be scanned can be achieved by introducing an aspherical surface into the scanning lens and making it a single aspherical lens. At this time, spot scanning at equidistant intervals can be achieved for any amplitude of the deflector without imposing restrictions on the rotational characteristics of the deflector. Furthermore, in the scanning device according to the present invention, even when a single lens is used as a scanning lens, by actively utilizing the Petzvaar sum of the scanning lens, a flat scanned surface can be effectively used. It is possible to use it. The present invention will be explained in detail below. When the incident beam diameter D is small compared to the focal length of the lens, that is, when the F number is relatively dark, it is important to pay less attention to the correction of spherical aberration and coma aberration required for a scanning lens. There is no need to correct the aberrations related to the angle of view, such as astigmatism, Petzvaar's sum P, and distortion V. The scanning lens in the apparatus of the present invention has a relatively dark F number and aberrations are corrected while paying attention to the above points. According to the description in "Lens Design Method" by Yoshiya Matsui (Kyoritsu Shuppan Co., Ltd.), the astigmatism, Betsuvial sum P, and distortion V when the lens thickness is small (thin-wall system) are expressed as follows. It can be done. When the scanning lens is composed of a thin-walled system with i=1 to m groups, the astigmatism, Betsuvial sum P, and distortion V of the entire lens system are written as follows. In equation (1), a〓, b〓, c〓, _av , _bv , and _cv are called characteristic coefficients, which are constants determined by the object point position, pupil position, and power arrangement. case,
Depends on light source position, deflection mirror position, and power arrangement.
ψ is the power and is the reciprocal of the focal length of the thin system. 〓
₀ , 〓 ₀ , and P ₀ are called eigenvalues and are determined by the shape and refractive index of the thin-walled system. i is the saphix indicating the i-th thin-walled system, P, V
is the astigmatism of the entire lens consisting of m thin-walled systems,
It is the Betsuvial sum and the distortion aberration coefficient. Furthermore,
The spherical curvature aberration is written as: =+P (3) Fig. 1 is a diagram for explaining the scanning device according to the present invention, in which a light beam from a light source 1 is deflected by a deflector 2, and an image is formed on a scanned surface 4' by a scanning lens 3. It shows how to do it. As shown in FIG. 1, the position y' of the spot Pi on the scanned surface 4' formed by the scanning lens 3 having the distortion aberration coefficient V is within the range of the third-order aberration, and the deflection angle θ (=
It is expressed as follows using 2φ; φ is the rotation angle of the deflection mirror. y'=f~(θ+U ₃ θ ³ ) (4) Since the scanning position is related to the rotational characteristics of the deflector and the distortion aberration coefficient of the scanning lens, this point will be described next. Now, the rotation of the deflector is expressed as follows. φ=φ ₀ sinkt (6) Here, φ is the rotation angle, φ ₀ is the amplitude, k is a constant,
Let t be time. It is assumed that the deflected beam when t=0 coincides with the optical axis of the scanning lens. Equation (6) is considered to represent the characteristic of the deflector rotating within a certain fixed period of time. Equation (6) has the following meaning. If the amplitude φ ₀ is sufficiently large within a certain period of time, the rotation can be regarded as a constant angular velocity deflection. On the other hand, if the amplitude is not so large within a certain period of time, the rotation is a sinusoidal vibration deflection. For example, by appropriately selecting the value of k according to φ ₀ , the rotational characteristics can be changed as shown in FIG. 2. Figure 2 shows that in equation (6), for example, kK ₁ /φ ₀ (K ₁ : constant), φ ₀ =K ₂ (constant), φ ₀ =2K ₂ , φ ₀ =3K ₂ ,
This shows the fluctuation of the rotation angle φ for each case of φ ₀ = ∞. As φ ₀ increases within the range of -t ₀ to _{t 0} , the fluctuation of φ approaches a straight line proportional to time. Finally, when φ=∞, a straight line becomes φ=φ ₀ sinK ₁ /φ ₀ t K ₁ t. In the present invention, the rotational characteristics of the deflector are considered in terms of constant angular velocity deflection and sinusoidal vibration deflection,
Equation (6) will be used as a general equation expressing these rotational characteristics. As shown in FIG. 1, it is assumed that the position of the imaging point Pi on the surface to be scanned is at a position y' from the optical axis of the scanning lens. The condition is that the change in the position of y' caused by the rotation of the deflector is kept constant over time (that is, uniform speed scanning). If the time interval τ for lighting the light source is constant,
By bringing the value of the distortion aberration coefficient of the scanning lens close to the V ₀ value shown below, the scanning spot spacing can be made constant. V ₀ = 2/3 (g + t ₁ /g) ² {1-1/2 (1/2φ ₀ ) ²
}(7) Here, we show that the above equation (7) is an effective equation that indicates uniform velocity. If the amplitude φ ₀ of the sinusoidal oscillating deflection mirror is selected and the value of V ₀ given by equation (7) matches the value of the distortion aberration coefficient V of the scanning lens, then from equations (5) and (7), U ₃ = 1/6 (1/2φ ₀ ) ² (8), and substituting this into equation (4) yields y'=2φ ₀ f ~ {(θ/2φ ₀ ) + 1/6 (θ/2φ ₀ ) ³ }
(9) is obtained. Here, equation (4) is the scanning position defined in the third-order aberration region, so within this range, equation (9) can be expressed as y'=2φ ₀ f~sin ^-1 (θ/2φ ₀ ) (10) are also completely equivalent. (When formula (10) is expanded to the third degree or less of θ, formula (9) is obtained.) Here, since θ=2φ ₀ sinKt, formula (10) becomes as follows. y′=2kf˜φ ₀ ·t This is differentiated to give dy′=2kf˜φ ₀ ·dt, and in this case, since the lighting time interval of the light source is constant, dt=constant. Therefore, dy′=constant,
The spacing between the scanning spots is also constant. Next, when the deflector is a constant angular velocity deflector, U ₃ =0, and substituting this into equation (4) yields y'=f~·θ. Now, since θ is a constant angular velocity deflection, it can be expressed as θ=k′t (k′ is a constant value), so dθ=k′dt, and therefore dy′=f~dθ=k′f~dt. Become. In this case, the lighting time of the light source is constant, so dt is constant. Therefore, dy' is constant and the interval between scanning spots is also constant. In a device such as the present invention, it is common to perform spot scanning on the surface to be scanned by blinking the light source (using a modulator, for example), and the above-mentioned change in the position of y' is Making it constant is the same as making the distance between spots on the surface to be scanned constant at constant time intervals. As shown in Fig. 3, the distance between the spots on the scanned surface is l,
Let the time interval corresponding to this be τ. When the scanning lens is a single spherical lens, the lens shape that has no astigmatism (), that is, realizes stigmatic imaging, is determined by the following procedure. In equation (1), =a〓〓 ₀ +b〓〓 ₀ +c〓=0. In addition, in the case of a single lens, between 〓 ₀ and 〓 ₀ 〓 ₀ =Amn〓 ₀ ² +Bmn〓 ₀ +Cmn (11) Because there is a relationship however, As in 〓 ₀ is determined. Furthermore, the radius of curvature of the first and second surfaces of the lens
The relationship among R ₁ , R ₂ , 〓 ₀ is given by the following equation. R ₁ = {n ₂ / (〓 ₀ − n ₁ )}・f R ₂ = {R ₁ (1−N) / (R ₁ − N+1)}・f(14) Therefore, 〓 ₀ is found. Therefore, R ₁ and R ₂ can be determined. At this time, the value of the distortion aberration coefficient V is V=a _v 〓 ₀ +b _v 〓 ₀ +c _v =a _v Amn〓 ₀ ² +(a _v Bmn+b _v )〓 ₀ +a _v Cmn+c _v
(15). Here, using equation (7) and setting V=V ₀ , The amplitude of the rotational characteristic is determined as follows. As mentioned above, when using a spherical single lens, the amplitude is It is sufficient to use a deflector having rotational characteristics as follows. Next, the case of an aspherical single lens in which an aspherical surface is introduced into the above scanning single lens will be described. In general, the values of and V for an aspherical single lens are =a〓〓 ₀ +b〓〓 ₀ +c〓+a〓ψe V=a _v 〓 ₀ +b _v 〓 ₀ +c _v +a _v ψe (17). Here, ψe is the sum of the aspheric coefficients of both sides of the single lens, is given by Here, Nν and N′ν are respectively ν
The refractive index bν of the medium before and after the surface is related to the amount of deviation ΔX~ν of the aspherical surface from the spherical surface by the following formula, as shown in FIG. 4. ΔX~ν≡bν/8H ⁴ 〓 (19) The number of aspheric surfaces introduced here may be one or two, and the independent quantity is ψl given by equation (18). In equation (17), 〓 ₀ and 〓 ₀ are the characteristic coefficients when each surface of the lens is regarded as a spherical surface with a paraxial radius of curvature, and as in equation (11) above, the value of 〓 ₀ It will be determined once it is determined. Here, the desired value of V is ₀ , V ₀ , and the shape of the aspherical lens that realizes this is 〓 ₀ ≡ (a _{v 0} −a〓・V ₀ )−a _v C〓−a〓c _v ／a _v b〓−a
〓b _v (21) ψl＝ ₀ − (a〓〓 ₀ +b〓〓 ₀ +c〓)/a〓(22). In the above description, the desired ₀ and V ₀ are, respectively, It is. The independent quantities in this case are 〓 ₀ , ψl, and φ ₀ , and if one of them is determined, the remaining two are determined dependently. For example, if the rotation amplitude φ ₀ is determined, 〓 ₀ and ψe are determined. Alternatively, if 〓 ₀ is determined, ψl and φ ₀ are determined. Next, consider the case where the scanning lens used in the present invention is a single lens and scans a flat surface to be scanned. In this case, the general formula (2) reduces to the formula (1), and the spherical field curvature aberration at this time is expressed as =+P. Here, when the light source position is at an infinite distance from the deflector, in order to scan the scanned plane, which is the imaging surface of the scanning lens, without curvature of field, in equations (1) and (24), = 0, =0. However, when the scanning lens is a single lens made of a glass material with a refractive index of N, and the focal length of the lens is f=1, P=
Since it is 1/N, it is impossible to satisfy both of the above-mentioned =0 and =0. That is, in the case of a single lens, since the Petzvaar sum remains, only either astigmatism or spherical field curvature can be corrected. Therefore, the imaging position Pi deviates from the scanned plane. On the other hand, if the light source position is placed at a finite distance, both astigmatism and spherical field curvature can be corrected even if the Petzvaar sum remains, and the imaging position can be aligned on the scanned plane. It is. The present invention realizes this, and this point will be described in more detail with reference to FIG. 1 above. In FIG. 1, a light beam emitted from a light source 1 located at a finite distance is deflected by a deflection mirror 2, and is deflected by a scanning lens 3.
After passing through, the image is formed at point Pi. In this case, 1' is a virtual image of the light source 1 by the deflection mirror, which is located on a circular arc 4 centered on the rotation axis 5 of the deflection mirror. In the present invention, By adopting a lens shape that satisfies the following, it becomes possible to form an image of the imaginary light source on the circular arc 4 in FIG. 1 onto the surface to be scanned 4'. g is the distance from the deflection mirror to the light source. In this application, the distance is positive when measured in the direction in which the luminous flux travels, and negative when measured in the opposite direction to the traveling direction of the luminous flux. Therefore, the above g is g<0. Equation (24) and (2
From equation 5), we obtain P=-1/g (26). On the other hand, from equation (1), P=ψP ₀ =1/Nf (27), and g=-Nf (28) from equations (26) and (27). Here, N is the refractive index of the glass of the single lens, f
is the focal length of the lens. That is, by setting the distance g between the deflector and the light source so as to satisfy equation (28), it becomes possible to form an image of the virtual light source on the arc 4 on the surface to be scanned 4'. In the case of a single lens, the shape for correcting astigmatism and spherical field curvature is such that the radius of curvature of the surface on the deflector side is R ₁ and the scanned surface is Assuming that of the side as R ₂ , when the lens thickness is small, And it is sufficient. Here, N is the refractive index of the lens, f is the focal length, and 〓 ₀ ≡ (−B〓±√〓 ² −4〓〓)/2A〓(30) It is. At this time, 〓 ₀ is determined by the following formula. (From Matsui's "Lens Design Method") 〓 ₀ =Amn〓 ₀ ² +Bmn〓 ₀ +Cmn (33) Therefore, the value of V in equation (1) is determined using equations (29) to (34). That is, in the case of a single lens, when a lens shape is determined to correct astigmatism and field curvature as shown in equation (25) above, its distortion aberration coefficient is inevitably determined. In the case of a single lens incorporating an aspherical surface, the lens can be provided with a desired distortion aberration coefficient V after astigmatism and field curvature are corrected. In the distortion processing method for a single lens with an aspherical surface, there is no need to select the rotation amplitude of the deflection mirror, and the value of V ₀ determined corresponding to an arbitrary rotation amplitude φ ₀ from equation (7) can be calculated. Equipitch scanning can be realized by the shape determined from equations (20) to (22) as the desired distortion aberration coefficient of the lens. Furthermore, when an aspherical single lens is introduced, the deflector may have any rotational characteristic other than that shown in equation (7). Regarding the technique of scanning a light beam at a constant speed on the surface to be scanned, the position of the light source is not limited in both the case of a spherical single lens and the case of an aspheric single lens. Therefore, with respect to the deflector, there is no problem whether the light source is located at a finite position or at an infinite position. As described above, for each case where the scanning lens is a spherical single lens or an aspherical single lens, the imaginary light source on the arc 4 in Fig. 1 can be affected by setting the light source position, deflection mirror position, lens shape, etc. It has been mentioned that an image can be formed on a scanning plane and that equipitch scanning can be realized. The actual position of the light source, the position of the deflection mirror, and the shape of the lens can be determined satisfactorily based on the principles of the present invention. In this principle, the lens shape was determined within the range of third-order aberrations, but this is for the sake of simplifying the explanation; practical design that includes higher-order aberrations is easy using ordinary design techniques based on this principle. It can be carried out. Further, in this principle, the values of the astigmatism coefficient and Betsuvial sum P are strictly set to 0 and -1/g, respectively, but in an actual device, there is a permissible range for these values. For example, when the deflector uses a rotating polygon mirror whose rotation center does not lie on the reflecting surface, field curvature remains on the imaging plane even if the astigmatism coefficient Petzval sum P is corrected to the above value. The respective field curvatures △M and △S in the meridional section and the spherical section are (Matsui: "Lens Design Method") where △ and △ are the allowable values of the astigmatism coefficient and the spherical field curvature coefficient, respectively, In each case, the amount of field curvature is set within the depth of focus determined by the diffraction limit. Here, Fe is the effective F number of the lens, and λ is the wavelength of the light source. In this case, from Figure 1, tanω≡gsinθ/(g+t ₁ ) (37), and from equations (35), (36), and (37), △ and △ are If the following is satisfied, each field curvature in the meridional section and the spherical section falls within the depth of focus of the diffraction limit. The allowable value ΔV of distortion aberration is determined as follows. From the above equation (4), let △V be the slight unsatisfactory amount of the distortion aberration coefficient value, and △y′ be the shift in the scanning position caused by it, △y′=f〜θ ²・△U ₃ △U ₃ ≡−1 /2(g/g+t ₁ ) ²・△V ∴△y′=−g^′/2(g/g+t ₁ ) ³・θ ³・△V is obtained. If the allowable value of the deviation from the ideal position of the spot when the deflection angle θ is △Y′, then it is within the range that satisfies ｜△V｜≦2/｜g^′ (g+t ₁ /gθ) ³・△Y′ The desired value given by equation (7) is
It is sufficient to enter the distortion aberration coefficient value based on V ₀ . As described above, when a scanning device according to the present invention scans a scanned plane with a deflection mirror using a light source located at a finite position, the scanning device utilizes the fact that the virtual light source created by mirror rotation is on an arc. This is due to the simplified structure of the lens. and,
When the scanning lens is a spherical single lens, by selecting the sinusoidal vibration amplitude of the deflector's rotational characteristics, the scanning lens can be set at equal distance intervals on the scanned plane in response to blinking (modulation) of the light source at equal time intervals. spot scanning can be achieved. In addition, if the scanning lens is an aspherical single lens, it is possible to image an imaginary light source on an arc onto the scanned plane, and it can also be used with arbitrary amplitude Equidistantly spaced spot scanning can also be achieved with respect to φ ₀ . In the above description, spot scanning at equidistant intervals is achieved by setting the distortion V of the single lens for scanning, but it is possible to achieve equidistant interval spot scanning by changing the flashing time interval of the light source. Spot scanning can be achieved. That is, the sinusoidal vibration amplitude φ ₀ of the deflector is arbitrarily set, and the blinking time τ of the light source ^is determined as follows according to the distortion aberration coefficient _V of the scanning lens at that _{time :} ² kt) (39). Examples are shown below. In the case of a spherical single lens Based on the present invention, when the parameters g and t ₁ that determine the arrangement of the light source and the deflection mirror lens and the amplitude φ ₀ that determines the rotational characteristics of the deflection mirror are set, The shape of the spherical single lens that forms the imaging spot (the radius of curvature on both sides), and the ideal values of the astigmatism coefficient and curvature coefficient of the truncated field surface of the system, ₀ ,
Table 1 shows the spherical curvature coefficient of the system, the ideal value of the distortion aberration coefficient V ₀ to realize equal pitch scanning, the distortion aberration coefficient V of the system, and the values of − ₀ and V−V ₀ . Raise it. Table 1 shows that the light source, deflection mirror, and lens positions are arranged at fixed positions (g+t ₁ =-2, t ₁ =-
0.2), and when the amplitude of the deflection mirror that vibrates sinusoidally is changed from φ ₀ = 5 to ∞, the unsatisfactory amount of distortion aberration (V-V ₀ ) for equal pitch scanning in each case.
This is what is shown. Looking at this Table 1, the above (V
It can be seen that the amplitude φ 0 of the deflection mirror where the value of -V ₀ ) is small, that is, the amplitude φ ₀ of the deflection mirror that can realize equal pitch scanning with a constant time interval of electric signals, is around 25° to 30°. In other words, when using a scanning lens that is a single spherical lens, by selecting the amplitude of the deflection mirror that vibrates sinusoidally, it is possible to realize equipitch scanning with a constant time interval of electrical signals. .
A more precise value of the amplitude is found to be φ ₀ ≈27.5° from FIG. 5, which is an illustration of Table 1, with φ ₀ on the horizontal axis and V−V ₀ on the vertical axis. The lens shape in this case is R ₁ = −0.55718, R ₂
= -0.32843, which is a thin lens. (R ₁ is the surface on the light source side, R ₂ is the surface on the scanned surface side) In order to obtain equal pitch scanning for other amplitudes, as described in the above principle, the time interval τ of the electric signal is 39) can be set according to formula. The configuration (g, t ₁ , g^'', R ₁ , R ₂ ) data of each example in Table 1 and Tables 2 to 9 below are obtained by normalizing the focal length f of the lens to f = 1. The refractive index N of these lenses is N = 1.8. Tables 2 to 4 show examples for the case of a spherical single lens, and are equivalent pitch scans (V-V ₀ = 0), the imaging position of the light source corresponding to the deflection angle θ is ΔM (imaging position deviation in the meridional section) and ΔS (imaging position deviation in the spherical section) from the scanned surface. image position shift), and each amount satisfies equation (36).As mentioned above, the right side of equation (36) is the effective F number Fe and wavelength λ
represents the depth of focus determined by the diffraction limit. Then, the imaging position deviation falls within the above depth of focus when |θ|≦15°, Fe=60, and λ=6328 Å. (This depth of focus is ±5.6 mm) In addition, equation (36) is equivalent to equation (38), and the astigmatism unsatisfactory amount (=△) and spherical defect for each example in Tables 2 to 4 The surface curvature aberration unsatisfactory amount - ₀ (=Δ) satisfies equation (38). However, in equation (38), g^' is calculated as g^' = 300 mm, and Tables 2 to 4
In the data, the focal length of the lens is f = 1mm.
This is the case when normalized. That is, Table 2
~ Among the configurations in Table 4, for example, for Example No. 20, if the distance g^' between the lens and the scanned surface is set to g^' = 300 mm, then the distance from the lens to the light source is (g+t ₁ ) is -300 mm, the distance (g) from the deflection mirror to the light source is -277.5 mm, the distance t ₁ from the lens to the deflection mirror is -22.5 mm, and the radius of curvature on the light source side of the lens (R ₁ ) is −53.673 mm, the radius of curvature (R ₂ ) on the scanned surface side is −37.086 mm, and the focal length (f) of this lens is 150 mm. In the configuration actually used in this way, the depth of focus (±
5.6mm). Similarly, in the other examples shown in Tables 2 to 4, when the configuration data is proportionally converted with g^' = 300 mm, the image formation position shift falls within the focal depth (±5.6 mm). Table 2 shows that the amplitude φ ₀ of the deflection mirror is 25°, and Table 3
Table 4 is for the case where φ ₀ is 30°, and Table 4 is for the case where φ ₀ is 35°.
In each case, the distance g+ from the lens to the light source
t ₁ and the distance t ₁ from the lens to the deflection mirror are varied. Looking at the unsatisfactory amount of astigmatism and unsatisfactory amount of spherical curvature aberration in Tables 2 to 4, it can _be seen that for any amplitude, when the value of the distance g + t ₁ from the lens to the light source is -2. , it turns out to be good. That is, it can be seen that when the value of g+t ₁ is around -2, the deviation of the imaging position from the scanned surface is the smallest. When the thin lens described above is made thicker, if the value of d/f, which is obtained by dividing the lens thickness by the focal length f, is small, the aberration fluctuation due to the thickening is small.
Thickening can be easily achieved if the thinning data in Tables 1 to 4 are available. This was implemented using the configuration shown in Figure 6 to display the configuration data.
Table 11 shows the aberration coefficient values in Table 10, and FIG. 7 shows the deviation of the imaging position from the scanned surface 4'. FIG. 8 shows the ratio of deviation of the actual image height Y' in this configuration from the ideal image height y' expressed by equation (9) to achieve equal pitch scanning, Y'-y'/y' x 100. (%) is plotted on the horizontal axis and the deflection angle θ is plotted on the vertical axis. In the case of an aspherical single lens Examples in which an aspherical surface is introduced are listed in Tables 5 to 9. Table 5 shows examples that achieve uniform pitch scanning with a constant electric signal time interval and form an image of the light source on the scanned plane. This completely satisfies the above two conditions. In Tables 5 to 9, configuration parameters other than ψl (φ ₀ , g+t ₁ , t ₁ , g′, R ₁ ,
R ₂ ) has the same meaning as in the case of the spherical single lens described above, and ψl is the aspherical coefficient defined by equations (18) and (19) described in the principle. Also, the aberration coefficient, −
₀ , V- _V0 , ₀ , and _V0 have the same meanings as described in the embodiment of the spherical single lens. In the case of a spherical single lens, it was only possible to achieve equal pitch scanning and to form an image of the light source on the scanned plane for a specific amplitude of the vibrating mirror, but it can be seen from Table 5. By introducing an aspherical surface, there is a configuration that can satisfy the above two conditions for various amplitudes. As described in the principle, the configuration is such that the distance g from the deflection mirror to the light source has a relationship with the refractive index N of the lens and the focal length f as shown in equation (28). In the examples shown in Tables 6 to 9, as described for the spherical single lens, there is a deviation in the imaging position from the scanned plane within the depth of focus, and uniform pitch scanning with a constant time interval of electrical signals is achieved. It's something you get. Looking at these tables, we found that the above two conditions could be satisfied for various amplitudes, various distances from the lens to the light source, and various distances from the lens to the deflection mirror, so we introduced these aspheric surfaces. In this case, the difference from the case of a single spherical lens is that astigmatism can be completely corrected. In other words, in the case of a spherical single lens, the lens shape is determined only by the conditions of evenly pitched scanning with a constant time interval of electrical signals, as described in the principle, and astigmatism and spherical defects are determined according to the shape. The field curvature aberration is a dependent decision. On the other hand, when an aspheric surface is introduced, even if the above equation (28) is not completely satisfied, it is necessary to perform equal pitch scanning with a constant time interval of electrical signals and to correct astigmatism. can be satisfied at the same time. However, △=-
₀ remains. In the case of the aspherical single lens in Tables 6 to 9, the imaging position deviations △M and △S from the scanned plane are the same as in the case of the spherical single lens, g^' = 300 mm, |θ|≦15°, Fe
Depth of focus (±
5.6mm), and the configuration data is normalized to f=1. Each of the examples in Tables 5 to 9 is thin lens data as in the case of a spherical single lens, but even if the lens thickness is increased, the lens thickness d is smaller than the focal length, that is, the value of d/f. If is small, aberration fluctuations will be small.
Therefore, the aberration due to this variation can be easily corrected using ordinary techniques. This was carried out by
Display the configuration data with the configuration shown in Figure 9.
Table 12 shows the aberration coefficient values, and FIG. 10 shows the deviation of the imaging position from the scanned plane 4'. FIG. 11 shows the ratio of deviation of the actual image height (Y') in the configuration from the ideal image height (y') expressed by equation (9) to achieve equal pitch scanning, Y'-y'/ The horizontal axis is y′×100 (%), and the vertical axis is the deflection angle θ. A twelfth embodiment in which the scanning device of the present invention is applied is shown in the twelfth embodiment.
As shown in FIG. All of them use a semiconductor laser as a light source; FIG. 12 shows an example using a rotating polygon mirror that rotates at a constant angular velocity, and FIG. 13 shows an example using a galvanometer mirror that vibrates sinusoidally. 6 is a semiconductor laser, 7 is its light emitting part, 8 is a rotating polygon mirror, 9 is a rotation axis, 10 is a drive system, 8' is a mirror surface, 11 is a scanning lens, 12 is a photosensitive recording medium, 13 is a scanning line, 14 is a galvanometer mirror, 1
4' is its mirror surface, and 15 is its drive system.
In such a device, by creating the above-mentioned organic relationship among the light source position, the deflector position, the scanning lens position, the rotational characteristics of the deflector, and the configuration of the scanning lens. The recording scanning speed of the recording scanning line 13 can be kept constant by controlling the modulated electric signal given to the semiconductor laser 6 by the modulation system 16 and by moving the recording medium 12 in a direction orthogonal to the scanning line 13. ,
Spot recording as shown in FIG. 14 can be performed.

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【table】 [Brief explanation of the drawing]

FIG. 1 is a diagram for explaining the scanning device of the present invention,
Figure 2 shows the relationship between φ and t when the value of φ ₀ of a deflector with vibration characteristics of φ = φ ₀ sinkt is changed, and Figure 3 shows the relationship between FIG. 4 is a diagram showing the amount of deviation △X~ν between the aspherical surface and the spherical surface, and FIG. 5 is a diagram showing the time interval given to the light source in an embodiment of the scanning device according to the present invention. Fig. 6 shows an example of the configuration when the scanning lens is a spherical _single lens; Fig. 7 The figure shows the image formation position deviation (field curvature) from the scanned plane 4' corresponding to the embodiment of FIG. 6, and FIG. 8 shows the uniform velocity characteristic corresponding to the embodiment of FIG. Figure 9 is a diagram showing the configuration of an embodiment using an aspherical single lens as a scanning lens.
Figure 0 is a diagram showing the field curvature of the lens in Figure 9, Figure 11 is a diagram showing the uniform velocity of the lens in Figure 9, and Figures 12 and 13 are diagrams showing the field curvature of the lens in Figure 9. As an application example, Fig. 12 shows an example in which a constant angular velocity rotating polygon mirror is used as a deflection mirror, Fig. 13 shows an example in which a sine oscillation mirror is used as a deflector, and Fig. 14 shows an example in which a sine oscillation mirror is used as a deflector.
The figure shows an example of an image recorded by the scanning recording apparatus of FIG. 12 or 13. 1...Light source, 2...Deflector, 3...Scanning lens, 4'...Scanned surface.

Claims (1)

[Scope of Claims] 1. An optical system comprising a light source section, a deflector that deflects the light beam from the light source section in a predetermined direction, and a scanning lens that focuses the light beam deflected by the deflector onto a surface to be scanned. In the scanning device, the light source of the light source section is arranged at a finite distance from the deflector, and the scanning lens is composed of a single lens, and the single lens has almost no astigmatism. 0, and the single lens has a Petzvaer sum for forming a virtual image of the light source on an arc formed as the deflector rotates on the flat surface to be scanned, and the deflection When the rotation angle of the deflector is φ, the amplitude is φ ₀ , t is time, and k is a constant, the rotation of the deflector is φ = φ ₀ sinkt , and t ₁ is the distance between the single lens and the deflector. If g is the value measured from the lens toward the deflector, g is the value measured from the deflector toward the light source at the distance between the deflector and the light source, and V is the distortion of the single lens, An optical scanning device characterized by substantially satisfying the following relationship. 2. The effective F number of the scanning single lens is Fe,
If the wavelength of the light flux from the light source is λ, the amount of field curvature in the meridional image plane is △M, and the amount of field curvature in the sagittal image plane is △S, then ｜△M｜≦2.44Fe ² λ ｜ The optical scanning device according to claim 1, which satisfies the relationship ΔS|≦2.44Fe ² λ.