Abstract:
Herein disclosed is a parallel beam shaping optical system which is an afocal anamorphic optical system. The optical system comprises two prisms for shaping a bundle of beams in a desired direction. The optical system is constructed so that an incident light is in parallel to the emergent light. Two shaping optical sub-systems each composed of the above-described optical system may be combined with each other to obtain a desired shaping of a ray of light.

Description:
This is a continuation of application Ser. No. 702737 filed Feb. 19, 1985, now abandoned. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates to an optical system for shaping the sectional configuration of a light parallel beam. 
     Emergent rays from a semiconductor laser are different in divergent angle. Therefore, in the case where a bundle of parallel rays is obtained by using a rotationally symmetric collimator lens, emergent rays from the collimator lens are elliptical in intensity distribution. 
     Therefore, in order to use the laser beam efficiently and to focus it into a spot which is rotationally symmetric in intensity distribution, it is a required to use the afocal anamorphic optical system in which the wavefront aberration has been sufficiently corrected. 
     Also, in the case of a laser beam circular in section, sometimes it is required to use for a laser beam printer optical system an afocal anamorphic optical system in which for instance the height-width ratio of the laser beam applied to the image forming lens is changed to thereby change resolving powers in horizontal and vertical direction into desired values. 
     In a conventional afocal anamorphic optical system used for the above-described purposes, two cylindrical lenses are employed, or one or two prisms are used. However, the conventional afocal anamorphic optical system is disadvantageous as follows: 
     In the afocal anamorphic optical system using two cylindrical lenses, the plane wave is applied to the cylinder surface, and therefore the occurrence of aberration cannot be avoided. Accordingly, in designing an optical system using cylindrical lenses, aberration correcting means are employed to totally negate aberration due to more than one surface as much as possible. However, the afocal anamorphic optical system using a single prism suffers from the difficulty that a large wavefront aberration remains uncorrected if the cylindrical axes of the surfaces to be corrected are even slightly not in alignment with each other. Accordingly the machining and mounting accuracy of the cylindrical lenses requires severe tolerances. 
     On the other hand, the afocal anamorphic optical system is advantageous in that no aberration takes place because the plane wave is incident on a planar surface. However, in the above optical system, the angle of the bundle of incident rays is deviated from that of the bundle of emergent rays. This will become a disadvantage in designing optical systems. 
     This disadvantage can be eliminated by a beam shaping optical system which uses two prisms as shown in FIG. 1. In the optical system, of FIG. 1 the bundle of incident rays is parallel to with the bundle of emergent rays. However, the optical system is still disadvantageous in that the system on the incident side which is disposed before the optical system and the system on the emergent side which is disposed after the optical system must be arranged with the optical axes of the two systems from one another in the same plane. 
     SUMMARY OF THE INVENTION 
     An object of this invention is to eliminate the above-described difficulties accompanying a conventional beam shaping optical system. More specifically, an object of the invention is to provide a beam shaping optical system in which the optical axis of the system on the incident side is in alignment with that of the system on the emergent side, and the machining and the mounting accuracy requirements with respect to the wavefront aberration are not severe. 
     Provided according to the invention is a parallel beam shaping optical system which is an afocal anamorphic optical system comprising two prisms which, when applied with a parallel beam, acts to increase or decrease an emergent beam which in a direction, and in which an incident light is in parallel with the emergent light thereof when the incident light is applied to one surface of said optical system at a predetermined angle, and when an incident light is applied at the predetermined angle, the effective aperture of the optical system has an incident point with which one incident ray and the emergent ray thereof form one straight line. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a sectional view of a conventional beam shaping optical system with two prisms; 
     FIGS. 2A and 2B show a first example of a beam shaping optical system according to this invention, FIG. 2A being a sectional view of the optical system taken along the X-Z plane and FIG. 2B being a sectional view of the system taken along the X-Y plane; 
     FIGS. 3A and 3B show a second example of the beam shaping optical system according to the invention, FIG. 3A being a sectional view of the optical system taken along the X-Z plane and FIG. 3B being a sectional view of the same taken along the X-Y plane; 
     FIG. 4 shows an example of the beam pattern conversion achieved by the optical system according to the invention, the beam pattern conversion achieved by the first example of the optical system according to the invention; 
     FIGS. 5A and 5B show a third example of another beam shaping optical system according to the invention, FIG. 5A being a sectional view of the optical system taken along the X-Z plane, and FIG. 5B being a sectional view of the system taken along the X-Y plane; 
     FIGS. 6A and 6B show a fourth example of the beam shaping optical system according to the invention, FIG. 6A being a sectional view of the optical system taken along the X-Z plane and FIG. 6B being a sectional view of the system taken along the X-Y plane; 
     FIGS. 7A and 7B show a fifth example of the beam shaping optical system according to the invention, FIG. 7A being a sectional view of the optical system taken along the X-Z plane and FIG. 7B being a sectional diagram of the system taken along the X-Y plane; 
     FIGS. 8A to 8C show examples of the beam pattern conversion which is achieved by the optical system according to the invention, FIG. 8A being a diagram showing an example of the beam pattern conversion which is accomplished by the third example of the optical system according to the invention, FIG. 8B being a diagram showing an example of the beam pattern conversion which is carried out by the fourth example or the optical system according to the invention, and FIG. 8C being a diagram showing an example of the beam pattern conversion which is achieved by the fifth example of the optical system according to the invention; 
     FIG. 9A is a diagram showing an example of the beam pattern conversion which is accomplished by the combination of the first and second examples of the optical system with a rotational angle of 45° in the Y-Z plane; and 
     FIG. 9B is a diagram showing an example of the beam pattern conversion which is achieved by combining two second examples of the optical system in such a manner that they are set to enlarge the beam, with a rotational angle 90°. 
     FIGS. 10A and 10B show isometric views of two combinations of optical systems, each being comprised of two subsystems of the three subsystems shown. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The beam shaping optical system according to the invention, when used to decrease a beam width, has arrangements as shown in FIGS. 2A and 2B (a first example) and FIGS. 3A and 3B (a second example). In these figures, FIGS. 2A and 3A are sectional views in an X-Z plane, and FIGS. 2B and 3B are sectional views in an X-Y plane. 
     In each of FIGS. 2A, 2B, 3A and 3B, the Z-direction is the coordinate in which the beam width changes when the optical system is used having an incident angle chose such that incident light is in parallel with its emergent light. In the Y-direction, a beam width is kept unchanged. The X-direction is the direction of the incident beam. The midpoint, in the Y-direction, of the effective aperture is the origin in the Y-direction. In the X-Z plane, the incident point with which one incident ray and its emergent ray are in one line is employed as the origin of the X- and Z-axes. 
     These optical systems are designed so as to meet the following conditions: 
     (1) θ z1  =90° 
     (2) (90°-θ z2 )/(90°-θ z1 )&gt;1 
     (3) (90°-θ z4 )/(90°-θ z1 )&lt;0 
     where θ z1  through θ z4  are the angles which are formed between the X-axis and surfaces of the prisms. 
     The conditions (1) through (3) are the fundamental ones for forming the optical system with two prisms. Because of the conditions (1) and (2), an incident light advances along an L-shaped or inverted-L-shaped optical path, the nonparallelism between the main ray of an incident light and the main ray of an emergent light can be minimized, and the incident point with which one incident ray and its emergent ray in one line can be provided in the aperture of the prism. The condition (3) is to set a beam width changing magnification to a practical value. 
     If the following conditions (4) and (5) are added to the above-described conditions (1) through (3), then the main ray of the incident light can be aligned with the incident point described above, and it is possible to form the system which car zero the deviation between the optical axis of the system on the incident side and that of the system on the emergent side which is due to the addition of the beam shaping optical system. 
     (4) d x12  / h z  &gt;0.8 
     (5) d x12  / (d x23  +d x34 )&gt;1 
     where h z  is the incident light height, in the Z-direction, on the incident surface, and d x12  through d x34  are the distances along the X-axis between the adjacent surfaces of the respective prisms. 
     The data of the first and second examples of the beam shaping optical system are as follows: 
     
         ______________________________________First Example (FIGS. 2A and 2B)______________________________________   θ.sub.z1        70.000°   θ.sub.z2        56.200°   θ.sub.z3        105.090°   θ.sub.z4        122.435°   d.sub.x12        13.30   d.sub.x23        3.20   d.sub.x34        2.60   h.sub.z        9.00   h.sub.x        9.00______________________________________ 
    
     Wavelength employed . . . 632.8 mm 
     Medium refractive index . . . 1.00000 
     First Prism refractive index . . . 1.79884 
     Second Prism refractive index . . . 1.79884 
     Beam width changing rate . . . 1 : 1.5 
     
         ______________________________________Second Example (FIGS. 3A and 3B)______________________________________   θ.sub.z1        60.0°   θ.sub.z2        45.7°   θ.sub.z3        121.3°   θ.sub.z4        149.4°   d.sub.x12        15.60   d.sub.x23        2.16   d.sub.x34        2.40   h.sub.z        9.00   h.sub.x        9.00______________________________________ 
    
     Wavelength employed . . . 632.8 mm 
     Medium refractive index . . . 1.00000 
     First Prism refractive index . . . 1.79884 
     Second Prism refractive index . . . 1.51462 
     Beam width changing rate . . . 1 : 3.0 
     In the first and second examples the X-axis is at the center of the Z-direction effective aperture; however, it is not always necessary that the effective aperture of the beam shaping optical system be symmetrical with respect to the X-axis. When the system is not symmetrical, it can be used as a beam shaping optical system in which, when the bundle of incident rays is small in width, the optical axis of the system on the incident side is aligned with the optical axis of the system on the emergent side, and when the bundle of incident rays is large in width, the optical axes are scarcely shifted from each other. When, even in the case where the bundle of incident rays is large in width, the emergent light is used without any loss of light caused by blocking the light path, because the effective diameter of the lens system on the incident side is large, the system can be used without affecting its effect on the increasing or decreasing of the resolving power. 
     FIG. 4 shows an example of the beam pattern conversion by the first example of the optical system. 
     In a beam shaping optical system above two prisms are used to shape a light beam. It is, however, noted that the optical system suffers from the difficulty that the beam width changing magnification cannot be increased without increasing the size of the optical system to some extent. That is, in order to increase the beam width changing magnification, the size of the optical system must be increased not only in the beam advancing direction but also in the beam width changing direction. 
     Therefore, sometimes it is unsuitable to add the beam shaping optical system to an existing optical system. 
     On the other hand, in another beam shaping optical according to the invention, at least one reflection surface is formed on the lower backface of a prism on the side where the beam width is decreased, namely, a prism arranged on the right-handed side of each of FIGS. 5A to 6B, so as to eliminate the difficulty that the size of a beam shaping optical system is increased by the provision of a reflection surface. Thus, although the beam shaping optical system is small both in the number of components and in size than other beam shaping optical systems, it can provide the above-described effects similarly. The effect of miniaturization according to the invention should be highly appreciated especially in manufacturing a beam shaping optical system with a high beam-width-changing magnification. 
     The other examples of a beam shaping optical system according to the invention will be described. 
     In these examples, similarly to the foregoing examples: 
     θ zn  is the angle between the X-axis and the line of intersection of the n-th surface and the X-Z plane, 
     d xnm  is the distance, along the X-axis, between the n-th surface and the m-th surface, 
     d znm  is the distance, along the Z-axis, between the n-th surface and the m-th surface, and 
     d zom  is the distance, along the Z-axis, between the original point o and the m-th surface. 
     
         ______________________________________Third Example (FIGS. 5A and 5B)______________________________________θ.sub.z1  90.000°θ.sub.z2  121.166°θ.sub.z3  53.632°θ.sub.z4  0°   The fourth surface is in parallel              with the X-axis.θ.sub.z5  157.534°d.sub.x23  0.80d.sub.z04  0.60d.sub.x35  0.83h.sub.z  1.00h.sub.y  1.00______________________________________ 
    
     The first through fifth surfaces are perpendicular to the X-Z plane. 
     The fourth surface is a reflection surface. 
     Wavelength used--632.8 nm 
     Medium refractive index--1.00000 
     Prism refractive index--1.79884 
     Beam width changing rate--1 : 5.0 
     
         ______________________________________Fourth Example (FIGS. 6A and 6B)______________________________________   θ.sub.z1        90.000°   θ.sub.z2        125.680°   θ.sub.z3        63.623°   θ.sub.z4        27.943°   θ.sub.z5        27.943°   d.sub.x23        0.68   d.sub.x34        1.27   d.sub.z45        0.84   h.sub.z        1.00   h.sub.y        1.00______________________________________ 
    
     The first through fifth surfaces are perpendicular to the X-Z plane. The fourth surface includes a reflection surface as indicated in FIGS. 6A and 6B and the remaining area of the fourth surface is a transmission surface; that is, the fourth surface is used for reflection and transmission. 
     The fifth surface is a reflection surface. 
     Wavelength used--632.8 nm 
     Medium refractive index--1.00000 
     Prism refractive index--1.51462 
     Beam width changing rate--1 : 3.0 
     
         ______________________________________Fifth Example (FIGS. 7A and 7B)______________________________________θ.sub.z1  70.000°θ.sub.z2  110.440°θ.sub.z3  69.215°θ.sub.z4  0°   The fourth surface is in parallel              with the X-axis.θ.sub.z5  151.225°d.sub.x12  0.60d.sub.x23  0.60d.sub.x35  1.70d.sub.z04  0.80h.sub.z  1.00h.sub.y  0.33______________________________________ 
    
     The first through fifth surfaces are perpendicular to the X-Z plane. 
     The fourth surface is a reflection surface. 
     Wavelength employed--780 nm 
     Medium refractive index--1.00000 
     Prism refractive index--1.798565 
     Beam width changing rate--1 : 3.0 
     The third example has one reflection surface, the fourth example has two reflection surfaces, and the fifth example has one reflection surface but does not have any surface to which rays are applied perpendicularly. 
     FIG. 8A shows an example of a beam pattern conversion by the third example of the beam shaping optical system, FIG. 8B shows an example of a beam pattern conversion by the fourth example of the beam shaping optical system, and FIG. 8C shows an example of a beam pattern conversion by the fifth example of the beam shaping optical system. 
     As in the first and second examples, also in the third to fourth examples, it is obvious that, if the beam shaping optical system is used in the opposite direction, it is possible to increase the beam width. 
     In the third and fourth examples, a light beam is applied perpendicularly to the first and third surfaces, while in the fifth example, there is no such perpendicular incident surface. This is due to the difference between laser beams used. That is, the third and fourth examples are used for He-Ne laser beams, and have the perpendicular incident surfaces to utilize light which is returned through reflection, thereby to simplify the alignment of the optical axes in the assembling work. On the other hand, a semiconductor laser has a property that, when a return light beam is returned to the semiconductor laser, the latter becomes unstable in operation, thus increasing noise. Therefore, it is essential for the semiconductor laser to prevent the phenomenon that a light beam reflected by the perpendicular incident surface is returned to the light emitting point advancing along the former optical path in the opposite direction. Accordingly, for a semiconductor laser beam shaping optical system it is important not only to use reflection preventing coatings but also to prevent the perpendicular incidence of a light beam to the surface. Hence, the fifth example of the beam shaping optical system which is used for semiconductor laser beams is so designed as to have no perpendicular incident surface. 
     While the beam shaping optical system has been described with reference to the case where it is used to decrease the width of the incident light, it is obvious that, if the beam shaping optical system is used in the opposite direction, it is possible to increase the beam width. 
     If two beam shaping optical systems according to the invention are used in such a manner that the directions in which the beam width changing actions are effected are in alignment with each other, then the resultant changing magnification is the product of the changing magnifications of the optical systems. This method is effective in eliminating the difficulty that, in the case of one high magnification beam shaping optical system, the incident angle of rays to the prism is excessively large, thus increasing the loss of rays due to reflection. If, even when the changing magnification is not large, it is required to change the magnification as in an experimental apparatus, several beam shaping optical systems different in magnification according to the invention are provided, then the magnification can be finely controlled by combining them suitably. 
     If two beam shaping optical systems according to the invention are combined in such a manner that they are turned in the Y-Z plane around the X-axis, then the ratio of the width, in the direction of the major axis, of the beam configuration to the width, in the direction of the minor axis, of the same can be continuously changed. 
     FIG. 9A shows the case where the first example, i.e., the optical system having a magnification of 1/1.5 and the second example, i.e., the optical system having a magnification of 1/3 are combined together with a rotational angle of 45°. The systems thus combined can change the ratio of major axis to minor axis continuous from 4.5 : 1 with a rotational angle 0° to 2 : 1 with a rotational angle 90°. Especially when the optical systems having the same magnification are combined together with a rotational angle 90°, an aberrationless isotropic beam enlarging (or reducing) system can be provided. FIG. 9B shows an example of the beam pattern conversion which is obtained by combining the optical systems having a magnification of 1/3 of the second example in such a manner that they are set to increase the beam width, with a rotational angle of 90°. 
     The invention further comprises a parallel beam shaping optical system wherein an incident light to the optical system is in straight relation with an emergent light by selecting at least two from the following subsystems: 
     (a) A first subsystem which is an afocal anamorphic optical system, comprising two prisms which, when applied with a parallel beam, act to increase or decrease an emergent beam width in a predetermined direction. An incident light is in parallel with the emergent light thereof when the incident light is applied to one surface of the first subsystem at a predetermined angle, and when an incident light is applied at the last-mentioned predetermined angle, an effective aperature of the first subsystem has an incident point with which one incident ray and the emergent ray thereof form one straight line; 
     (b) A second subsystem which is an afocal anamorphic optical system, comprising two prisms at least one of which has a backface employed as a reflection surface, which, when applied with a parallel beam, acts to increase or decrease an emergent beam width in a predetermined direction. An incident light is in parallel with the emergent light thereof when the incident light is applied to one surface of said second subsystem at a predetermined incident angle, and when incident light is applied at the predetermined incident angle, an effective aperature of the second subsystem has an incident point with which one incident ray and the emergent ray thereof form one straight line; and 
     (c) A third subsystem which is disposed along one straight line, comprising two prisms at least one of which has a backface employed as a reflection surface, which, when applied with a parallel beam, acts to increase or decrease an emergent beam width in a predetermined direction. An incident light is in parallel with the emergent surface of the third system at a predetermined incident angle, and when incident light is applied at the predetermined incident angle, an effective aperture of the third subsystem has an incident point with which one incident ray and the emergent ray thereof form one straight line, wherein when an incident light is applied at the predetermined incident angle so that the incident light is parallel with the emergent light thereof, the third subsystem has no surface to which incident rays are applied perpendicularly. 
     As is apparent from the above description, in the beam shaping optical system according to the invention, the optical axis of the system on the incident side is in alignment with the optical axis of the system on the emergent side, and the machining and mounting accuracy with respect to the wavefront aberration is not severe. Furthermore, by using more than one beam shaping optical system of the invention in combination, the changing magnification and the beam width ratio can be readily varied. 
     Especially, by adding the optical system of the invention to an existing optical system such as a laser beam printer optical system, its resolving power can be changed without adjusting the components of the existing optical system.