Patent Publication Number: US-2022214537-A1

Title: Optical path adjusting mechanism

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation application of and claims the priority benefit of U.S. patent application Ser. No. 16/986,279, filed on Aug. 6, 2020, now allowed. The prior U.S. patent application Ser. No. 16/986,279 is a continuation application of and claims the priority benefit of U.S. patent application Ser. No. 16/403,619, filed on May 6, 2019, now patented. The prior U.S. patent application Ser. No. 16/403,619 is a continuation application of and claims the priority benefit of U.S. application Ser. No. 15/088,144, filed on Apr. 1, 2016, now patented, which claims the priority benefits of Taiwan application serial no. 104119521, filed on Jun. 16, 2015 and Taiwan application serial no. 104140907, filed on Dec. 4, 2015. The entirety of each of the above-mentioned patent applications is hereby incorporated by reference herein and made a part of this specification. 
    
    
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The invention relates to a projector and a three-dimensional printing apparatus respectively with an image displacement module. 
     Description of Related Art 
     Most rear projection display products generate and project an image onto a screen via an optical engine. In order to increase the image resolution of the image projected on the screen by the optical engine, the optical engine needs a display element having higher resolution. Moreover, existing ultra-high-definition resolution liquid crystal displays can already provide image resolutions in the two specifications of 3840×2160 and 4096×2160. In contrast, the resolution provided by existing full HD rear projection display products no longer meets the market demand, and therefore rear projection display products need higher resolution to meet market demand. However, since the costs of higher resolution display elements are greater, under cost considerations, how to achieve high-resolution image screen effect via a light valve having low resolution pixels to increase production yield and reduce costs of the display apparatus is an issue to be solved. 
     SUMMARY OF THE INVENTION 
     One aspect of the invention is to provide an optical path adjusting mechanism, capable of providing relatively high resolution. 
     An embodiment of the invention provides an optical path adjusting mechanism including a rotating base, an optical element, a coil, a first spring and a second spring. The rotating base includes a first corner and a second corner opposite to the first corner. A first area and a second area are disposed along a line passing through the first corner and the second corner on the rotating base. The optical element is disposed on the rotating base. The coil is disposed around a periphery of the rotating base. One terminal of the first spring is connected to the first area of the rotating base. One terminal of the second spring is connected to the second area of the rotating base. 
     Another embodiment of the invention provides an optical path adjusting mechanism including a base, a frame, an optical element, a first spring and a second spring. The frame includes a first side, a second side, a third side, a fourth side, a first area at which the first and second sides are closest and a second area at which the third and fourth sides are closest. The optical element is disposed in on the frame. The first spring includes a first terminal and a second terminal, wherein the first terminal is connected to the first area of the frame, the second terminal is connected to one terminal of the base. The first plane is disposed between the first terminal and the second terminal. In addition, the second spring includes a third terminal and a fourth terminal. The third terminal is connected to the second area of the frame. The fourth terminal is connected to another terminal of the base. The second plane is disposed between the third terminal and the fourth terminal. 
     In order to make the aforementioned features and advantages of the disclosure more comprehensible, embodiments accompanied with figures are described in detail below. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention. 
         FIG. 1  is a structural schematic of an optical apparatus. 
         FIG. 2  illustrates a stereoscopic schematic of an image displacement module of an embodiment of the invention. 
         FIGS. 3, 4, 5, 6, and 7  respectively illustrate structural schematics of image displacement modules of different embodiments of the invention. 
         FIGS. 8A and 8B  respectively illustrate schematic views of the movement directions and the imaging positions of the plane image of an embodiment of the invention. 
         FIG. 9A  illustrates a schematic view of the movement directions and the imaging positions of a plane image of another embodiment of the invention. 
         FIG. 9B  illustrates a comparison schematic of the imaging positions of the plane image of the carrier of the embodiment of  FIG. 9A  rotating relative to different directions in a frame time. 
         FIGS. 10A, 10B and 10C  respectively illustrate stereoscopic structural schematics of image displacement modules of different embodiments of the invention. 
         FIGS. 11A and 11B  respectively illustrate schematic views of the movement directions and the imaging positions of the plane image of another embodiment of the invention. 
         FIG. 12A  illustrates a stereoscopic structural schematic of an image displacement module of an embodiment of the invention. 
         FIG. 12B  illustrates a stereoscopic structural schematic of a elastic member of the embodiment of  FIG. 12A . 
         FIG. 12C  illustrates the relationship between amplitude and time of the elastic member of the embodiment of  FIG. 12A . 
         FIG. 12D  illustrates the relationship between amplitude and time of the signal configured to drive the elastic member of the embodiment of  FIG. 12A . 
         FIGS. 13A and 13B  respectively illustrate schematics of different three-dimensional printing equipment adopting any one of the image displacement module of the above embodiments of the invention. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     The foregoing and other technical contents, features, and efficacies of the invention are intended to be described more comprehensively in the plurality of embodiments below accompanied with figures. In the following embodiments, wordings used to indicate direction, such as “up,” “down,” “front,” “back,” “left,” and “right”, merely refer to directions in the accompanying drawings. Therefore, the directional wordings are used to illustrate rather than limit the invention. 
       FIG. 1  illustrates a structural schematic of an optical apparatus. Referring to  FIG. 1 , an optical apparatus  200  includes an illumination system  210 , a light valve  220 , a projection lens  230 , an image displacement module  240 , and a screen  400 . The illumination system  210  has a light source  212  adapted to provide a beam  214 , and the light valve  220  is disposed on the transmission path of the beam  214  to convert the beam  214  into a plane image  214   a.  The projection lens  230  and the image displacement module  240  are disposed on the transmission path of the plane image  214   a,  and the light valve  220  is located between the illumination system  210  and the projection lens  230 . The illumination system  210  is, for instance, a telecentric illumination system or a non-telecentric illumination system. The light valve  220  is, for instance, a digital micromirror device (DMD), LCD or LCoS (Liquid Crystal on Silicon), and the present embodiment is exemplified by a digital micromirror device (“DMD”). The light valve  220  is not limited to a reflective light valve, and may be a transmissive light valve in another embodiment. The light valve  220  outputs the plane image of multiple pixelized light or area image light, which is different with the image light provided by the laser-scanning device (https://en.wikipedia.org/wiki/Laser_scanning). The area image light contains multiple pixels in two directions. 
     When the plane image  214   a  (area image light) goes through the image displacement module  240 , which changes the transmission path of the plane image  214   a.  In other words, the plane image  214   a  is projected on a first position on the screen  400 , and the plane image  214   a  is projected on a second position on the screen  400  within another time, wherein the first position and the second position are separated by a fixed distance on the horizontal direction (x-axis) and/or the vertical direction (z-axis). Therefore the horizontal and the vertical resolutions of the plane image can be increased. 
     The beam  214 ) provided by the light source  212  is an illumination light. The beam  214  passes through a color wheel  216 , a light integration rod  217 , a lens group  218 , and a total internal reflection (TIR) prism  219  in order, and the prism  219  reflects the beam  214  to the light valve  220 . Then the light valve  220  converts the beam  214  into the plane image  214   a  of multiple pixelized light (light with multiple pixels) or area image light, which goes through the image displacement module  240  and the prism  219  in order or goes through the prism  219  and the image displacement module  240  in order, then the plane image  214   a  is projected on the screen  400  via the projection lens  230 . The plane image  214   a  includes at least N pixels along the horizontal direction (x-axis) and at least N pixels along the vertical direction (z-axis) respectively, wherein N&gt;100 is preferable. It should be mentioned that, if LEDs having different colors are used as the light source  212 , then the color wheel  216  is not needed. Moreover, a lens array can also replace the light integration rod  217  to perform light homogenization. 
       FIG. 2  illustrates a stereoscopic schematic of an image displacement module  1000   c  of an embodiment of the invention applied on the inside of a projection lens  230 , but the image displacement module  1000   c  can also be placed outside of the projection lens  230 , such that the projected image resolution is larger than the image resolution of the light valve. 
     Referring to  FIG. 3 , the image displacement module  240  includes a base  410  and a carrier  420 . The carrier  420  is connected to the base  410 . Preferably, the carrier  420  is pivoted on the base  410 , which controls the carrier  420  to spin (or vibrate) back and forth within a finite angle θ (not shown), which is not larger than 10 degrees. In another embodiment, the finite angle θ is smaller than 5 degrees. The carrier  420  has an optical element  422 , which receives the plane image  214   a  (as shown in  FIG. 1 ). When the carrier  420  vibrates back and forth, the optical element  422  can move respectively the positions of the plane image  214   a  on the horizontal direction (x-axis) and/or the vertical direction (z-axis) by a distance at the same time. 
     The base  410  includes, for instance, a magnetic material base  412 , two magnets  414   a  and  414   b,  and a sensor module (not shown). The carrier  420  includes, for instance, an optical element  422 , an optical element base  424 , a coil module  426 , and a rotational axis  428 . The upper and lower ends of the rotational axis  428  are fixed via holes  432 . In an embodiment of the invention, the sensor module includes, for instance, a circuit board (not shown) and a sensor (not shown). The sensor is configured to sense the oscillation amplitude of the rotational axis  428  of the carrier  420 , and when the rotational axis  428  oscillates a certain amplitude toward the magnet  414   a,  the circuit board changes the magnetic properties of the coil module  426 , such that a repulsion force is generated between the coil module  426  and the magnet  414   a  (attraction force is generated between the coil module  426  and the magnet  414   b ), such that the coil module  426  is far away from the magnet  414   a.  When the rotational axis  428  oscillates a certain amplitude toward the magnet  414   b,  the circuit board changes the magnetic properties of the coil module  426 , such that a repulsion force is generated between the coil module  426  and the magnet  414   b  (attraction force is generated between the coil module  426  and the magnet  414   a ), such that the coil module  426  is far away from the magnet  414   b.  By keeping the coil module  426  close to/far from or far from/close to the magnets  414   a/   414   b,  the carrier  420  can vibrate back and forth, such that the imaging positions of the plane image  214   a  are changed. It should be noted that the carrier  420  rotating relative to the rotational axis  428  is driven by the coil module  426  and the magnets  414   a/   414   b  that locate on the same plane in the present embodiment. 
     The coil module  426  includes, for instance, a coil base  426   a  and a coil  426   b,  and the coil  426   b  surrounds the coil base  426   a.  In this embodiment, the rotational axis  428  and the optical element  422  can be integrally molded via an injection mold process. In another embodiment, the rotational axis  428  and the optical element  422  can also be separately manufactured, and then the optical element  422  and the rotational axis  428  are assembled together. Moreover, the optical element  420  includes a reflecting mirror and/or a lens. The optical element is not limited to include a single lens, and may also include a plurality of transmissive lenses to form a lens group. 
       FIG. 4  illustrates a stereoscopic structural schematic of an image displacement module of another embodiment of the invention. The main difference between the present embodiment and the embodiments of  FIG. 3  is, the upper and lower ends of the rotational axis  428  in  FIG. 3  are respectively horizontally and vertically disposed, and in the present embodiment, the upper and lower ends of the rotational axis  428  are horizontally disposed. Moreover, in the present embodiment, the coil module is divided into two portions  427   a  and  427   b.  By keeping the coil modules  427   a  and  427   b  close to/far from or far from/close to the magnetic materials  414   a/   414   b,  the carrier  420  can vibrate back and forth, such that the imaging positions of the plane image  214   a  are changed. 
     Referring to  FIG. 5 , an image displacement module  1000   a  includes a frame  1110 , a base  1120  and a carrier  1200 . The carrier  1200  rotates relative to two axes of a reference plane S. In this embodiment, the two axes of the reference plane S are, for instance, a first axis  1610  on a first direction X and a second axis  1620  on a second direction Y. The angle between the first axis  1610  and the second axis  1620  is 90 degrees, and the first axis  1610  and the second axis  1620  define the reference plane S. The frame  1110 , the base  1120  and the carrier  1200  are symmetric relative to the first axis  1610 . The carrier  1200  rotating relative to the first axis  1610  is driven by the coil C 1  and the magnets M 1  and M 2  that locate on the same plane, and the carrier  1200  rotating relative to the second axis  1620  is driven by the coils C 2  and C 3  and the magnets M 3  and M 4  that locate on the same plane in this embodiment. 
     Moreover, the image displacement module  1000   a  further includes an optical element  1500 , which is disposed on the carrier  1200 . The optical element receives a plane image  214   a  from the light valve  220  (as shown in the  FIG. 1 ). The plane image  214   a  includes at least N pixels along the horizontal direction and at least N pixels along the vertical direction respectively, N&gt;100. The optical element includes a reflecting mirror and/or a lens. The optical element is not limited to include a single lens, and may also include a plurality of transmissive lenses to form a lens group. 
     In this embodiment, the at least one elastic member  1300  includes a first elastic pair  1310  (a first connection part) and a second elastic pair  1320  (a second connection part). The frame  1110  is connected to the base  1120 , which surrounds the frame  1110 . The frame  1110  is connected to the carrier  1200  via the first elastic pair  1310  and the base  1120  is connected to the frame  1110  via the second elastic pair  1320 . Moreover, in the present embodiment, the rotation of the carrier  1200  or the frame  1110  is not necessary to exceed 180 degrees. The rotation in an angle within 10 degrees will be acceptable. The first elastic pair  1310  is disposed at two opposite sides of the frame  1110  along the second axis  1620 , and the second elastic pair  1320  is disposed at two opposite sides of the base  1120  along the first axis  1610 . In this embodiment, the at least one elastic member  1300  is a spring, but the at least one elastic member  1300  can also be other elastic deformable objects such as a metal part, sheet metal, a torsion spring, a plate or plastic, and the invention is not limited thereto. 
     The image displacement module  1000   a  further includes a plurality of actuators  1400 , which are disposed on at least one of the frame  1110 , the base  1120  and the carrier  1200 . A first actuator  1410  arranged along the second direction Y and a second actuator  1420  arranged along the second direction X. The carrier  1200  rotates around the first axis  1610  via the first actuator  1410  and rotates around the second axis  1620  via the second actuator  1420 . 
     In this embodiment, the first actuator  1410  includes two magnets M 1  and M 2  and one coil C 1 . M 1  and M 2  are disposed on the base  1120  in a manner in which M 1  and M 2  are symmetric to the first axis  1610 . C 1  is disposed on the first axis  1610  and is disposed between M 1  and M 2 . The second actuator  1420  includes two magnets M 3  and M 4  and two coils C 2  and C 3 . M 3  and M 4  are disposed on the base  1120  in a manner in which M 3  and M 4  are symmetric to the second axis  1620 . C 2  and C 3  are disposed on the carrier  1200  in a manner in which C 2  and C 3  are symmetric to the second axis  1620  and are located between the M 3  and M 4 . M 3 , M 4 , C 2  and C 3  are arranged along the first direction X. It should be mentioned that, the total length of coils used by the image displacement module  1000   a  of this embodiment is smallest, and the rotational inertia thereof is smallest. 
     A sensor module (not shown) controls the carrier  1200  to rotate relative to the two axes of the reference plane S by changing the magnetic properties of C 1 , C 2 , and C 3 . The sensor module (not shown) includes a circuit board and a sensor. The sensor is configured to sense the oscillation amplitude of the first axis  1610  and the second axis  1620 . When the first axis  1610  or the second axis  1620  oscillates to a certain amplitude, the circuit board changes the magnetic properties of C 1 , C 2 , and C 3  by changing the current direction on C 1 , C 2 , and C 3 . Therefore, a repulsion force or an attraction force is generated between C 1 , C 2 , and C 3  and M 1 , M 2 , M 3 , and M 4 , such that C 1 , C 2 , and C 3  are far away from or close to M 1 , M 2 , M 3 , and M 4 , and the carrier  1200  is thereby controlled to rotate relative to the two axes of the reference plane S. It should be noted that the carrier  1200  rotating relative to the first axis  1610  is driven by C 1 , M 1  and M 2 , and the carrier  1200  rotating relative to the second axis  1620  is driven by C 2 , C 3 , M 3  and M 4  in the present embodiment. C 1 , C 2  and C 3  are separate, individually controlled, and operated independently. In other embodiments, the same actuation effect in this embodiment can also be achieved via piezoelectric materials or stepper motors, and the invention is not limited thereto. 
     The following embodiments use the reference numerals of the embodiments above and a portion of the contents thereof, wherein the same numerals are used to represent the same or similar elements and descriptions of the same technical contents are omitted. The omitted portions are as described in the embodiments above, and are not repeated in the embodiments below. 
       FIG. 6  illustrates a stereoscopic structural schematic of an image displacement module of another embodiment of the invention. The main difference between an image displacement module  1000   b  and the image displacement module  1000   a  is: a coil C 4  surrounds the carrier  1200 . It should be mentioned that, the two coils are used, therefore the manufacture is relatively simpler. 
       FIG. 7  illustrates a stereoscopic structural schematic of an image displacement module of another embodiment of the invention. In addition to being symmetric relative to the first axis  1610 , the base  1120 , the frame  1110  and the carrier  1200  are also symmetric relative to the second axis  1620 . The first pair of elastic members  1310  are disposed at two opposite sides of the frame  1110  along the first axis  1610 , and the second pair of elastic members  1320  are disposed at two opposite sides of the base  1120  along the second axis  1620 . The first actuator  1410  includes two magnets M 5  and M 6  and two coils C 5  and C 6 . M 5  and M 6  are both symmetric to the first axis  1610  and C 5  and C 6  are both symmetric to the first axis  1610 . M 5 , M 6 , C 5  and C 6  are arranged along the second direction. Since the first actuator  1410  and the second actuator  1420  of the image displacement module  1000   c  have high symmetry, and the motors can be set to provide the same output, and therefore the control is easier. The first actuator  1410  provides a first signal (not shown) to control the spin of the first connection part and the second actuator  1420  provides a second signal (not shown) to control the spin of the second connection part. The first signal and the second signal go through different paths. 
     Moreover, the first actuator  1410  and the second actuator  1420  have longer arms of force in comparison to the previous embodiments, and therefore the power needed to start the image displacement module  1000   c  is relatively smaller. Since the distance between the four magnets or the four coils is greater, in comparison to previous embodiments, interference between them occurs less readily. 
       FIG. 8A  illustrates a schematic view of the movement directions of the plane image of an embodiment of the invention.  FIG. 8B  illustrates a schematic view of imaging positions of the plane image of the embodiment of  FIG. 8A . Referring to  FIGS. 8A and 8B , the image displacement module switches the imaging positions of the plane image, such that the plane image  500  is moved by a distance along one of a plurality of movement directions. The positions of the plane image  500  are decided according to the rotation method of the carrier  1200 . When the carrier  1200  rotates relative to one of the first axis  1610  and the second axis  1620 , the positions of the plane image  500  are, for instance, on the screen  400  of  FIG. 1  and moved by a distance along one of a plurality of movement directions, wherein the plurality of movement directions are, for instance, the first direction X or the second direction Y. In the present embodiment, the distance is about 0.7 pixel widths. Therefore, the plane image  500  can be oscillated to four different positions (dotted grids) from the original positions (solid grids). In other words, the image resolution can be increased to four times the original image resolution. In another embodiment, the plane image  500  can be moved along one of a plurality of movement directions such as the first direction X, the second direction Y, a third direction XY 1 , and a fourth direction XY 2 . More specifically, when the carrier  1200  rotates relative to the first axis  1610  and the second axis  1620  at the same time, the plane image  500  are, for instance, moved by a distance on the third direction XY 1  or the fourth direction XY 2 , wherein the third direction XY 1  and the fourth direction XY 2  are between the first direction X and the second direction Y. 
       FIG. 9A  illustrates a schematic view of the movement directions and the imaging positions of plane image of another embodiment of the invention.  FIG. 9B  illustrates a comparison schematic of the imaging positions of the plane image of the embodiment of  FIG. 9A  rotating relative to different directions in a frame time. Referring to  FIG. 9A , when the carrier rotates relative to at least one of the first axis and the second axis, the positions of the plane image  500  are displaced along the directions X′, Y′, X′Y′ 1 , and X′Y′ 2 . In the present embodiment, the distance moved by the plane image  500  on the direction X′ and the direction Y′ are both 1 pixel width, and the distance moved by the plane image  500  on the direction X′Y′ 1  or the direction X′Y′ 2  is about 1.4 pixel widths. 
     More specifically, in  FIGS. 9A and 9B , the numeric labels  1  to  9  respectively represent the same plane image located at different positions at different times. The plane image is moved on a basis of nine fixed positions in the present embodiment, but the invention is not limited thereto. The numeric label  1  represents the position of the plane image without moving. The numeric labels  3  and  7  represent the positions of the plane image  500  moving to the right or to the left on the direction X′. The numeric labels  5  and  9  represent the positions of the plane image  500  moving up or moving down on the direction Y′. The numeric labels  2  and  6  represent the positions of the plane image  500  moving on the direction X′Y′ 1 . The numeric labels  4  and  8  represent the positions of the plane image  500  moving on the direction X′Y′ 2 . 
     The numeric labels  1  to  9  in  FIG. 9B  represents that, within the time interval, the plane image  500  are on the positions corresponding to the numeric labels  1  to  9  of  FIG. 9A . The vertical axis of  FIG. 9B  represents that the plane image  500  can be moved along different directions (direction X′ and/or direction Y′) within different time intervals. For instance, when the numeric label is 1, the vertical axis values thereof corresponding to the direction X′ and the direction Y′ are both 0, meaning the plane image  500  are not actuated in the direction X′ and the direction Y′. When the numeric label is 2, the vertical axis values thereof corresponding to the direction X′ and the direction Y′ are both positive, meaning the plane image  500  are moved from position  1  toward the direction between the direction X′ and the direction Y′ to position  2 , which is the direction X′Y′ 1 . When the numeric label is  4 , the vertical axis value thereof corresponding to the direction X′ is positive, the vertical axis value thereof corresponding to the direction Y′ is negative, meaning the plane image  500  are actuated from position  1  toward the direction composed of the vectors of the direction X′ and the negative direction Y′ to position  4 , which is the opposite direction of the direction X′Y′. The other numeric labels are defined in the same manner and are not repeated herein. Moreover, the plane image  500  (solid grids) can be moved to nine different positions (dotted grids) in  FIG. 9A . In other words, the image resolution can be increased to nine times the original image resolution. 
       FIG. 10A  illustrates a stereoscopic structural schematic of an image displacement module of another embodiment of the invention. The main difference between an image displacement module  1000   d  and the image displacement module  1000   b  is: the angle between the first axis  1610  and the second axis  1620  is 45 degrees, in other words, the first axis  1610  and the second axis  1620  are not limited to be perpendicular to each other. 
       FIG. 10B  illustrates a structural schematic of an image displacement module of another embodiment of the invention. The main difference between an image displacement module  1000   f  and the image displacement module  1000   d  is: the architectures of the elastic member  1300  and the actuators  1400  of the present embodiment. For instance, the first elastic pair  1310  are disposed at two opposite sides of the base  1120  along the first axis  1610 , and the second elastic pair  1320 , integratedly manufactured in one-piece, are disposed on the frame  1110  and connects the carrier  1200  along the second axis  1620 . The angle is between the first axis  1610  and the second axis  1620  is 45 degrees. The first actuator  1410  includes two magnets M 1  and M 2  and two coils C 1  and C 2 . M 1  and M 2  are located inside C 1  and C 2  respectively. The second actuator  1420  includes two magnets M 3  and M 4  and one coil C 4 , which surrounds the carrier  1200 , like that illustrated in  FIG. 6 . 
       FIG. 10C  illustrates a structural schematic of an image displacement module of another embodiment of the invention. The main difference between an image displacement module  1000   g  and the image displacement module  1000   d  is: the architectures of the elastic member  1300  and the actuators  1400  and the forms of the carrier  1200  and the optical element  1500 . The forms of the carrier  1200  and the optical element  1500  are combined to be formed in one piece (Only  1500  is shown). In other words, the carrier  1200  could be removed and the optical element  1500  is directly connected to the frame  1710  by a connection part  1320 . The first elastic pair  1310  is disposed at two opposite sides of the base  1120  along the first axis  1610 , and connects the base  1120  and the frame  1110 . The second elastic pair  1320  is disposed at two opposite sides of the carrier  1200  along the second axis  1620 , and connects the frame  1110  and the carrier  1200 . The first elastic pair  1310  and the second elastic pair  1320  are separately manufactured. The first actuator  1410  includes two magnets M 1  and M 2  and one coil C 2 . The second actuator  1420  includes two magnets M 4  and one coil C 3 . C 2  located on a surface of the bobbins  1820 ,  1810  facing to the carrier  1200 . M 1 , M 2  and C 2  cooperate with the bobbins  1810 ,  1820  and drive the carrier  1200  to rotate relative to the first axis  1610 . M 4  located under the yoke  1710  and the yoke  1720  and C 3  surrounds the carrier  1200 . M 4  and C 3  drive the carrier  1200  to rotate relative to the second axis  1620 . 
       FIG. 11A  illustrates a schematic view of the movement directions of plane image of another embodiment of the invention.  FIG. 11B  illustrates a schematic view of the imaging positions of the plane image of the embodiment of  FIG. 11A . Referring to  FIG. 11A , the distance is double the pixel width along the direction X″, and is about 1.1 pixel widths along the direction Y″. Therefore, the original positions (solid grids) of the plane image can be oscillated to four different positions (dotted grids). In other words, the image resolution can be increased to four times the original image resolution. The plane image are moved on a basis of four fixed positions in the present embodiment, but the invention is not limited thereto. The number of the fixed positions for movement reference is smaller than  10  in the embodiments of the present invention. 
       FIG. 12A  illustrates a stereoscopic structural schematic of an image displacement module of an embodiment of the invention.  FIG. 12B  illustrates a stereoscopic structural schematic of an elastic member of  FIG. 12A .  FIG. 12C  illustrates the relationship between amplitude and time of the elastic member of  FIG. 12A .  FIG. 12D  illustrates the relationship between amplitude and time of the signal configured to drive the elastic member. 
     Referring to  FIG. 12A , the elastic member pair  1310  includes a first elastic member  1311  and a second elastic member  1312 . The first elastic member  1311  and the second elastic member  1312  are disposed perpendicular to each other along the first axis  1610  of an image displacement module  1000   e,  and such a disposition method allows the first axis  1610  to pass through the axis of the optical element  1500 . In general, when the amplitude of the first elastic member  1311  is converted from one direction to another direction, the time needed for the amplitude conversion process is referred to as a transition time T. The length of the conversion time T decides the display quality of the plane image. Since the conversion time T and the natural frequency of the first elastic member  1311  are inversely proportional, the natural frequency and the structural parameters of the first elastic member  1311  are related. Therefore, the factors recited in the above affecting natural frequency can all be factors affecting the conversion time T. 
     Please refer to  FIG. 12B . Based on the above, the conversion time T and the structural parameters of the first elastic member  1311  are related. In the present embodiment, the structural parameters of a neck width NW of the first elastic member  1311  are, for instance, 0.2 to 0.6 times those of a width w of the first elastic member  1311 . Moreover, a thickness t of the first elastic member  1311  is also one factor affecting the conversion time T. In an embodiment, the thickness t of the first elastic member  1311  is at least 0.2 mm. The thickness design allows the natural frequency of the first elastic member  1311  to be at least greater than 90 Hz. Since the natural frequency and the conversion time T are inversely proportional, the thickness design can also effectively reduce the conversion time T. 
     In addition to the structural parameters of the first elastic member  1311  affecting the conversion time T, factors affecting the conversion time T further include the vibration method of the first elastic member  1311 . Referring to  FIGS. 12C and 12D  at the same time, the conversion time T is reduced by changing the vibration method of the first elastic member  1311 . Specifically, when the oscillation of the first elastic member  1311  is changed from one direction to another direction, the driving signal waveform thereof is as shown in  FIG. 12D . Moreover, the driving signal waveform is not limited to the square wave driving signal shown in  FIG. 12D , and can also be a sine wave driving signal waveform. The conversion time T is less than 1 millisecond, and is preferably between 1 millisecond and 0.05 milliseconds, such that the optical apparatus can provide good display quality. 
       FIGS. 13A and 13B  respectively illustrate schematics of different three-dimensional printing equipment adopting any one of the image displacement module of the above embodiments. Referring first to  FIG. 13A , the three-dimensional printing technique adopted by a three-dimensional printing equipment  1900   a,  for instance, stereo lithography (SLA), and the three-dimensional printing equipment  1900   a  includes a tank  1910 , a projection apparatus  1920 , an lifting platform  1930 , and an image displacement module  1940  mentioned in any one of the above embodiments, wherein the three-dimensional printing equipment  1900   a  is configured to form a three-dimensional printed object OB, wherein the three-dimensional printing equipment of  FIG. 13A  is, for instance, a sunken three-dimensional printing equipment  1900   a.    
     The tank  1910  is configured to house a photosensitive material  1912 , wherein when the photosensitive material  1912  is irradiated by a beam having a specific wavelength, a photopolymerization reaction occurs and the photosensitive material  1912  is cured. The projection apparatus  1920  has a light-emitting device, and the adopted light-emitting device can be a light-emitting diode (LED), a laser, or other suitable light-emitting devices, and the light-emitting device is adapted to emit a beam B, wherein the image beam B can provide light (such as UV) of a wave band capable of curing the photosensitive material  1912 . However, the wave band of the image beam B is not limited thereto, and any wave band capable of curing the photosensitive material  1912  can be adopted. The lifting platform  1930  has a platform  1932 . The platform  1932  receives the photosensitive material  1912  and works as a printing region, and might be adapted to move inside the molding tank  1910 . The image displacement module  1940  is disposed on the outside of the projection apparatus  1920 , and the image displacement module  1940  is disposed in the path of the image beam B. In other embodiments, the image displacement module  1940  can be disposed inside the projection apparatus  1920 , as long as the image displacement module  1940  is disposed in the path of the image beam B, and the location at which the image displacement module  1940  is disposed is not limited thereto. 
     It can be seen from  FIG. 13A  that the print region  1932  is immersed in the photosensitive material  1912 , the image beam B is irradiated on a portion of the photosensitive material  1912  via the scanning path of the first sliced layer, and a photopolymerization reaction occurs to this portion of the photosensitive material  1912  such that this portion of the photosensitive material  1912  is cured. As a result, one of the cross-sections of the three-dimensional printed object OB is generated, and therefore a first cured layer adhered on the print region  1932  is obtained. Then, the lifting platform  1930  is moved downward a short distance, and the originally formed first cured layer is correspondingly moved downward a short distance, and the upper surface of the originally formed first cured layer can be used as a carrying surface, such that another layer of the photosensitive material  1912  covers the first cured layer. Moreover, the image beam B is precisely controlled according to the scanning path of the second sliced layer, such that the image beam B is irradiated on the surface of the other layer of the photosensitive material  1912  via the scanning path of the second sliced layer, and a second cured layer is obtained as a result. After a plurality of layers is continuously manufactured in this manner, the three-dimensional printed object OB can be formed. 
     Referring to  FIG. 13B ,  FIG. 13B  illustrates a schematic of another three-dimensional printing equipment adopting the image displacement module in the above embodiments of the invention. Referring first to  FIG. 13B , a three-dimensional printing equipment  1900   b  shown in  FIG. 13B  is similar to the three-dimensional printing equipment  1900   a  shown in  FIG. 13A , and the main difference thereof is: the material of the molding tank  1910  includes a transparent material or a light-transmitting material, and the lifting platform  1930  and the projection apparatus  1920  are respectively disposed at two opposite sides of the molding tank  1910 , wherein the three-dimensional printing equipment  1900   b  of  FIG. 13B  is, for instance, a pull-up type of three-dimensional printing equipment  1900   b.  Since the material of the molding tank  1910  includes a transparent material or a light-transmitting material, the image beam B can be irradiated on the photosensitive material  1912  through the molding tank  1910 . 
     Referring to both  FIG. 13A  and  FIG. 13B , since the image displacement module  1940  is disposed in the path of the image beam B, after the image beam B passes through the image displacement module  1940 , the image beam B is projected to different locations at different times. Specifically, the solid lines illustrated in  FIG. 13A  and  FIG. 13B  are the locations of projection of the image beam B at a certain time; and the dashed lines illustrated in  FIG. 13A  and  FIG. 13B  are the locations of projection of the image beam B at another certain time. Therefore, since the three-dimensional printing equipment  1900   a  and  1900   b  of the present embodiments have the image displacement module  1940  mentioned in any of the above embodiments, such that higher resolution can be obtained when the three-dimensional printing equipment  1900   a  and  1900   b  cure the photosensitive material  1912 . As a result, the three-dimensional printed object OB has better surface precision. 
     Based on the above, since in the optical apparatus of the embodiment, an image displacement module is disposed on the transmission path of a plane image, wherein the image displacement module controls a rotating base to rotate relative to two axes of a reference plane via a carrying base so as to decide any movement direction of the plane image on a two-dimensional plane, the resolution of the plane image in any direction can be increased via the image displacement module. The optical apparatus of the embodiment can adopt a reflective light valve having lower resolution to project an image having higher resolution. 
     Although the invention has been described with reference to the above embodiments, it will be apparent to one of ordinary skill in the art that modifications to the described embodiments may be made without departing from the spirit of the invention. Accordingly, the scope of the invention is defined by the attached claims not by the above detailed descriptions.