Patent Publication Number: US-8975571-B2

Title: Off-axial three-mirror system

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims all benefits accruing under 35 U.S.C. §119 from China Patent Application No. 201210437743.6, filed on Nov. 6, 2012 in the China Intellectual Property Office. This application is also related to application entitled, “OFF-AXIAL THREE-MIRROR SYSTEM”, filed Dec. 12, 2012 (Ser. No. 13/712,960). Disclosures of the above-identified applications are incorporated herein by reference. 
     BACKGROUND 
     1. Technical Field 
     The present disclosure relates to all-reflective optical systems, and particularly to an off-axial three-mirror system. 
     2. Description of Related Art 
     All-reflective optical systems have long been the champions of the astronomical community, primarily because of their small size, lightweight construction and broad spectral coverage. One type of all-reflective optical systems is an off-axial three-mirror system, which includes a primary mirror, a secondary mirror, and a tertiary mirror. 
     In some related art, spherical mirrors and conicoid mirrors such as ellipsoidal mirrors, parabolic mirrors, and hyperbolic mirrors are employed in the off-axial three-mirror system. There are not many degrees of freedom in said mirrors that the off-axial three-mirror system cannot provide a superior performance in imaging. 
     Another problem in some related art is the assembling and aligning of the mirrors, for the primary mirror, the secondary mirror, and the tertiary mirror in the off-axial three-mirror system are all separate from each other. 
     What is needed, therefore, is to provide an off-axial three-mirror system, in which the mirrors have more degrees of freedom, and the mirrors are easier to be assembled and aligned. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Many aspects of the present disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, the emphasis instead being placed upon clearly illustrating the principles of the present embodiments. 
         FIG. 1  is a diagram of optical path of an off-axial three-mirror system according to one embodiment. 
         FIG. 2  is a schematic diagram of configuration of the off-axial three-mirror system in  FIG. 1 . 
         FIG. 3  is a plot of modulation transfer function of the off-axial three-mirror system in  FIG. 1 . 
         FIG. 4  is a diagram of optical path of an off-axial three-mirror system according to another embodiment. 
         FIG. 5  is a schematic diagram of configuration of the off-axial three-mirror system in  FIG. 4 . 
         FIG. 6  is a plot of modulation transfer function of the off-axial three-mirror system in  FIG. 4 . 
     
    
    
     DETAILED DESCRIPTION 
     The disclosure is illustrated by way of example and not by way of limitation in the figures of the accompanying drawings in which like references indicate similar elements. It should be noted that references to “another,” “an,” or “one” embodiment in this disclosure are not necessarily to the same embodiment, and such references mean at least one. 
     Referring to  FIG. 1  and  FIG. 2 , an off-axial three-mirror system  10  of one embodiment includes a primary mirror  102 , a secondary mirror  104 , a tertiary mirror  106 , and an image sensor  108 . The secondary mirror  104  is located on a reflective optical path of the primary mirror  102 . The tertiary mirror  106  is located on a reflective optical path of the secondary mirror  104 . The image sensor  108  is located on a reflecting optical path of the tertiary mirror  106 . The primary mirror  102  and the tertiary mirror  106  are formed as one piece. The surface type of the primary mirror  102  is freeform surface. The surface type of the tertiary mirror  106  is freeform surface also. The freeform surface of the primary mirror  102  and the tertiary mirror  106  introduces more degrees of freedom to the off-axial three-mirror system  10 , which can be used to improve the performance and image quality of the whole system. 
     An optical path of the off-axial three-mirror system  10  of one embodiment can be depicted as follows. Firstly, an incident light reaches the primary mirror  102  and is reflected by the primary mirror  102 . Secondly, the incident light reaches the secondary mirror  104  and is reflected by the secondary mirror  104 . Thirdly, the incident light reaches the tertiary mirror  106  and is reflected by the tertiary mirror  106 . Finally, the incident light is received by the image sensor  108 . 
     The primary mirror  102  is a concave mirror as a whole. The tertiary mirror  106  is a concave mirror as a whole also. 
     According to one embodiment, the surface type of the primary mirror  102  is XY polynomial surface, and the surface type of the tertiary mirror  106  is XY polynomial surface also. The XY polynomial equation can be expressed as follows: 
             z   =           x   2     +     y   2         R   ⁡     (     1   +       1   -       (     1   +     C   1       )     ⁢       (       x   2     +     y   2       )     /     R   2               )         +       C   2     ⁢   x     +       C   3     ⁢   y     +       C   4     ⁢     x   2       +       C   5     ⁢   xy     +       C   6     ⁢     y   2       +       C   7     ⁢     x   3       +       C   8     ⁢     x   2     ⁢   y     +       C   9     ⁢     xy   2       +       C   10     ⁢     y   3       +       C   11     ⁢     x   4       +       C   12     ⁢     x   3     ⁢   y     +       C   13     ⁢     x   2     ⁢     y   2       +       C   14     ⁢     xy   3       +       C   15     ⁢       y   4     .               
R in the equation represents radius of the primary mirror  102  and the tertiary mirror  106 , while C 1 ˜C 15  represent coefficients in the equation. The values of coefficients and R in the equation of the primary mirror  102  are listed in TABLE 1. The values of coefficients and R in the equation of the tertiary mirror  106  are listed in TABLE 2.
 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
             
            
               
                 R 
                 C 1   
                 C 2   
                 C 3   
                 C 4   
                 C 5   
                 C 6   
                 C 7   
               
               
                 361.890 
                 −0.481 
                 −4.476 × 10 −7   
                 −4.904 × 10 −2   
                 −2.247 × 10 −3   
                  1.690 × 10 −9   
                 −2.348 × 10 −3   
                 −1.374 × 10 −12   
               
               
                 C 8   
                 C 9   
                 C 10   
                 C 11   
                 C 12   
                 C 13   
                 C 14   
                 C 15   
               
               
                 5.312 × 10 −7   
                 −3.204 × 10 −12   
                  4.731 × 10 −7   
                 −1.724 × 10 −9   
                  1.327 × 10 −14   
                 −3.698 × 10 −9   
                  2.308 × 10 −14   
                 −2.122 × 10 −9   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
             
            
               
                 R 
                 C 1   
                 C 2   
                 C 3   
                 C 4   
                 C 5   
                 C 6   
                 C 7   
               
               
                 −188.938 
                 0.305 
                 −3.908 × 10 −7   
                 7.408 × 10 −2   
                 2.620 × 10 −5   
                 −1.176 × 10 −9   
                  1.272 × 10 −4   
                 −1.707 × 10 −12   
               
               
                 C 8   
                 C 9   
                 C 10   
                 C 11   
                 C 12   
                 C 13   
                 C 14   
                 C 15   
               
               
                 7.241 × 10 −7   
                 −6.562 × 10 −12   
                  6.047 × 10 −7   
                 1.591 × 10 −9   
                 3.267 × 10 −14   
                  2.011 × 10 −9   
                 −6.012 × 10 −14   
                  1.207 × 10 −9   
               
               
                   
               
            
           
         
       
     
     According to other embodiments, the surface types of both the primary mirror  102  and the tertiary mirror  106  can be Zernike polynomial surface, Bezier surface, or NURBS surface. 
     The surface type of the secondary mirror  104  is not restricted. In one embodiment, the surface type of the secondary mirror  104  is aspherical surface. The equation of the aspherical surface can be expressed as follows: 
             z   =           x   2     +     y   2         R   ⁡     (     1   +       1   -       (     1   +     C   1       )     ⁢       (       x   2     +     y   2       )     /     R   2               )         +       A   ⁡     (       x   4     +     2   ⁢     x   2     ⁢     y   2       +     y   4       )       .             
R in the equation represents radius of the secondary mirror  104 , while C 1  and A represent coefficients in the equation. In one embodiment, R=−166.561, C 1 =3.424, and A=1.956×10 −8 .
 
     The primary mirror  102  and the tertiary mirror  106  form a bulk structure  100 . Once the bulk structure  100  is manufactured, the primary mirror  102  and the tertiary mirror  106  are also fabricated simultaneously. The design of the bulk structure  100  reduces the difficulty of assembling and aligning of the primary mirror  102  and the tertiary mirror  106 . It also improves the precision of assembling and aligning of the primary mirror  102  and the tertiary mirror  106 . In one embodiment, the surfaces of the primary mirror  102  and the tertiary mirror  106  extend smoothly on one surface of the bulk structure  100 . 
     The materials of the primary mirror  102 , the secondary mirror  104  and the tertiary mirror  106  can be aluminum, copper or other metals. The materials of the primary mirror  102 , the secondary mirror  104  and the tertiary mirror  106  can also be silicon carbide, silicon oxide or other inorganic materials. A reflection enhancing coating can also be coated on said metals or inorganic materials to enhance the reflectivity performance of the three mirrors. In one embodiment, the primary mirror  102 , the secondary mirror  104 , and the tertiary mirror  106  are all made of aluminum. A gold film is coated on surface of the aluminum as a reflection enhancing coating. 
     The surface shape of both the primary mirror  102  and the tertiary mirror  106  is a rectangle while the surface shape of the secondary mirror  104  is a circle. In one embodiment, a size of the surface of the primary mirror  102  is 140 mm×140 mm. A size of the surface of the tertiary mirror  106  is 140 mm×120 mm. A diameter of the surface of the secondary mirror  104  is 55 mm. 
     A distance α between the primary mirror  102  and the secondary mirror  104  is in a range from 133 mm to 134 mm. A distance β between the secondary mirror  104  and the tertiary mirror  106  is also in a range from 133 mm to 134 mm. A distance γ between the tertiary mirror  106  and the image sensor  108  is also in a range from 133 mm to 134 mm. In one embodiment, the distance α, β, and γ are all 133.7 mm. 
     A space coordinates system is set in  FIG. 1 . An optical axis of the off-axial three-mirror system  10  is parallel to Z-axis of the space coordinates system. The primary mirror  102  and the secondary mirror  104  have no decentering and tilting in the space coordinates system respecting to the optical axis. The tertiary mirror  106  and the image sensor  108  have no decentering in the space coordinates system either. Define a direction θ in the space coordinates system and the direction θ represents a direction rotating from Z-axis to Y-axis. Both the tertiary mirror  106  and the image sensor  108  have a tilting angle along the direction θ in the space coordinates system respecting to the optical axis, wherein the tilting angle of the tertiary mirror  106  is 10° and the tilting angle of the image sensor  108  is −5.292°. 
     The image sensor  108  can be a charge-coupled device (CCD) type or a complementary metal-oxide semiconductor (CMOS) type. In one embodiment, a planar array CCD is employed as the image sensor  108 . The size of the planar array CCD is 7.2 mm×9.6 mm. 
     The entrance pupil diameter (EPD) of the off-axial three-mirror system  10  is more than 60 mm. In one embodiment, the EPD of the off-axial three-mirror system  10  is 100 mm. Thus, the off-axial three-mirror system  10  is a large-EPD off-axial three-mirror system. 
     The field of view (FOV) of the off-axial three-mirror system  10  is 3°×4°. 
     The effective focal length (EFL) of the off-axial three-mirror system  10  is −136.719 mm. 
     A plot of modulation transfer function (MTF) of the off-axial three-mirror system  10  of one embodiment is shown in  FIG. 3 . The MTF of the off-axial three-mirror system  10  is higher than 0.6 at 20 cycles/mm, close to the diffraction limit. 
     Referring to  FIG. 4  and  FIG. 5 , an off-axial three-mirror system  20  of another embodiment includes a primary mirror  202 , a secondary mirror  204 , a tertiary mirror  206 , and an image sensor  208 . The secondary mirror  204  is located on a reflective optical path of the primary mirror  202 . The tertiary mirror  206  is located on a reflective optical path of the secondary mirror  204 . The image sensor  208  is located on a reflecting optical path of the tertiary mirror  206 . The primary mirror  202  and the tertiary mirror  206  are formed as one piece. The surface type of the primary mirror  202  is freeform surface. The surface type of the tertiary mirror  206  is freeform surface also. The freeform surface of the primary mirror  202  and the tertiary mirror  206  introduces more degrees of freedom to the off-axial three-mirror system  20 , which can be used to improve the performance and image quality of the whole system. 
     An optical path of the off-axial three-mirror system  20  of one embodiment can be depicted as follows. Firstly, an incident light reaches the primary mirror  202  and is reflected by the primary mirror  202 . Secondly, the incident light reaches the secondary mirror  204  and is reflected by the secondary mirror  204 . Thirdly, the incident light reaches the tertiary mirror  206  and is reflected by the tertiary mirror  206 . Finally, the incident light is received by the image sensor  208 . 
     The primary mirror  202  is a convex mirror as a whole. The tertiary mirror  206  is a concave mirror as a whole. 
     According to one embodiment, the surface type of the primary mirror  202  is XY polynomial surface, and the surface type of the tertiary mirror  206  is XY polynomial surface also. The XY polynomial equation can be expressed as follows: 
             z   =           x   2     +     y   2         R   ⁡     (     1   +       1   -       (     1   +     C   1       )     ⁢       (       x   2     +     y   2       )     /     R   2               )         +       C   2     ⁢   x     +       C   3     ⁢   y     +       C   4     ⁢     x   2       +       C   5     ⁢   xy     +       C   6     ⁢     y   2       +       C   7     ⁢     x   3       +       C   8     ⁢     x   2     ⁢   y     +       C   9     ⁢     xy   2       +       C   10     ⁢     y   3       +       C   11     ⁢     x   4       +       C   12     ⁢     x   3     ⁢   y     +       C   13     ⁢     x   2     ⁢     y   2       +       C   14     ⁢     xy   3       +       C   15     ⁢       y   4     .               
R in the equation represents radius of the primary mirror  202  and the tertiary mirror  206 , while C 1 ˜C 15  represent coefficients in the equation. The values of coefficients and R in the equation of the primary mirror  202  are listed in TABLE 3. The values of coefficients and R in the equation of the tertiary mirror  206  are listed in TABLE 4.
 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
             
            
               
                 R 
                 C 1   
                 C 2   
                 C 3   
                 C 4   
                 C 5   
                 C 6   
                 C 7   
               
               
                 358.016 
                 −0.366 
                 5.790 × 10 −2   
                  6.188 × 10 −2   
                 1.088 × 10 −3   
                  8.842 × 10 −5   
                  2.318 × 10 −4   
                 −8.609 × 10 −7   
               
               
                 C 8   
                 C 9   
                 C 10   
                 C 11   
                 C 12   
                 C 13   
                 C 14   
                 C 15   
               
               
                 1.343 × 10 −7   
                 2.578 × 10 −7   
                 9.240 × 10 −7   
                 −4.185 × 10 −8   
                 1.235 × 10 −8   
                 −9.941 × 10 −9   
                 −9.248 × 10 −12   
                 −7.091 × 10 −9   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
             
            
               
                 R 
                 C 1   
                 C 2   
                 C 3   
                 C 4   
                 C 5   
                 C 6   
                 C 7   
               
               
                 −241.763 
                 0.430 
                 −1.655 × 10 −2   
                 4.061 × 10 −2   
                 4.056 × 10 −5   
                 −9.874 × 10 −6   
                 −8.263 × 10 −5   
                 −3.297 × 10 −7   
               
               
                 C 8   
                 C 9   
                 C 10   
                 C 11   
                 C 12   
                 C 13   
                 C 14   
                 C 15   
               
               
                 3.963 × 10 −7   
                 −1.295 × 10 −7   
                  3.713 × 10 −7   
                 4.014 × 10 −9   
                 2.517 × 10 −9   
                  3.940 × 10 −9   
                  2.192 × 10 −10   
                  1.971 × 10 −10   
               
               
                   
               
            
           
         
       
     
     According to other embodiments, the surface types of both the primary mirror  202  and the tertiary mirror  206  can be Zernike polynomial surface, Bezier surface, or NURBS surface. 
     The surface type of the secondary mirror  204  is not restricted. In one embodiment, the surface type of the secondary mirror  204  is aspherical surface. The equation of the aspherical surface can be expressed as follows: 
             z   =         r   2       R   ⁡     (     1   +       1   -       (     1   +   K     )     ⁢       r   2     /     R   2               )         +     Ar   4     +     Br   6     +     Cr   8     +       Dr   10     .             
In the equation, r=√{square root over (x 2 +y 2 )}, R represents radius of the secondary mirror  204 , while K and A˜D represent coefficients in the equation. In one embodiment, the values of coefficients and R in the equation of the secondary mirror  204  are listed in TABLE 5.
 
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
               
                 R 
                 K 
                 A 
                 B 
                 C 
                 D 
               
               
                   
               
             
            
               
                 −478.425 
                 143.657 
                 9.263 × 10 −8   
                 5.907 × 10 −10   
                 −7.450 × 10 −12   
                 3.036 × 10 −14   
               
               
                   
               
            
           
         
       
     
     The primary mirror  202  and the tertiary mirror  206  form a bulk structure  200 . Once the bulk structure  200  is manufactured, the primary mirror  202  and the tertiary mirror  206  are also fabricated simultaneously. The design of the bulk structure  200  reduces the difficulty of assembling and aligning of the primary mirror  202  and the tertiary mirror  206 . It also improves the precision of assembling and aligning of the primary mirror  202  and the tertiary mirror  206 . In one embodiment, the surfaces of the primary mirror  202  and the tertiary mirror  206  extend smoothly on one surface of the bulk structure  200 . 
     The materials of the primary mirror  202 , the secondary mirror  204  and the tertiary mirror  206  can be aluminum, copper or other metals. The materials of the primary mirror  202 , the secondary mirror  204  and the tertiary mirror  206  can also be silicon carbide, silicon oxide or other inorganic materials. A reflection enhancing coating can also be coated on said metals or inorganic materials to enhance the reflection performance of the three mirrors. In one embodiment, the primary mirror  202 , the secondary mirror  204 , and the tertiary mirror  206  are all made of aluminum. A gold film is coated on surface of the aluminum as a reflection enhancing coating. 
     The surface shape of both the primary mirror  202  and the tertiary mirror  206  is a rectangle while the surface shape of the secondary mirror  204  is a circle. In one embodiment, a size of the surface of the primary mirror  202  is 200 mm×14 mm. A size of the surface of the tertiary mirror  206  is 140 mm×22 mm. A diameter of the surface of the secondary mirror  204  is 12 mm. 
     A distance μ between the primary mirror  202  and the secondary mirror  204  is in a range from 185.5 mm to 186.5 mm. A distance ν between the secondary mirror  204  and the tertiary mirror  206  is also in a range from 185.5 mm to 186.5 mm. A distance σ between the tertiary mirror  206  and the image sensor  208  is in a range from 181.0 mm to 182.0 mm. In one embodiment, the distance μ and ν are both 186.078 mm and the distance σ is 181.604. 
     A space coordinates system is set in  FIG. 4 . An optical axis of the off-axial three-mirror system  20  is parallel to Z-axis of the space coordinates system. The primary mirror  202  and the secondary mirror  204  have no decentering and tilting in the space coordinates system respecting to the optical axis. The tertiary mirror  206  and the image sensor  208  have no decentering in the space coordinates system either. Define a direction φ in the space coordinates system and the direction φ represents a direction rotating from Z-axis to Y-axis. Both the tertiary mirror  206  and the image sensor  208  have a tilting angle along the direction φ in the space coordinates system respecting to the optical axis, wherein the tilting angle of the tertiary mirror  206  is 4° and the tilting angle of the image sensor  208  is 2.09°. 
     The image sensor  208  can be a CCD type or a CMOS type. In one embodiment, a linear array CCD is employed as the image sensor  208 . The size of the linear array CCD is 51 mm. 
     The FOV of the off-axial three-mirror system  20  is more than 45°. In one embodiment, the FOV of the off-axial three-mirror system  20  is 64°. Thus, the off-axial three-mirror system  20  is a wide-FOV off-axial three-mirror system. 
     The EPD of the off-axial three-mirror system  20  is between 5 mm to 10 mm. In one embodiment, the EPD of the off-axial three-mirror system  20  is 7.5 mm. 
     The EFL of the off-axial three-mirror system  20  is −44.794 mm. 
     A plot of modulation transfer function (MTF) of the off-axial three-mirror system  20  of one embodiment is shown in  FIG. 6 . The MTF of the off-axial three-mirror system  20  is higher than 0.6 at 48 cycles/mm, close to the diffraction limit. 
     It is to be understood that the above-described embodiment is intended to illustrate rather than limit the disclosure. Variations may be made to the embodiment without departing from the spirit of the disclosure as claimed. The above-described embodiments are intended to illustrate the scope of the disclosure and not restricted to the scope of the disclosure. 
     It is also to be understood that the above description and the claims drawn to a method may include some indication in reference to certain steps. However, the indication used is only to be viewed for identification purposes and not as a suggestion as to an order for the steps.