Abstract:
An optical correction system for correcting thermally-induced wavefront distortions in an optical signal emanating from a crystal or other form of optical device/system. An optical output signal from the thermally sensitive optical device/system is fed to a beamsplitter, which produces a reflected optical signal and a refracted optical signal containing thermally-induced distortion. The refracted signal is fed to a wavefront distortion sensor which produces an output signal representative of the thermally-induced distortion. The output of the wavefront distortion sensor is fed to a computational device which determines the necessary degree of error correction to compensate for the thermally-induced optical distortion. A stress application device receives the output of the computational device and generates an electrical signal in accordance therewith which is then used to control a force applicator in physical contact with the crystal. The force applicator applies a precise degree of stress (either tensile or compressive) to the crystal to remove or substantially reduce the thermally-induced optical distortion.

Description:
TECHNICAL FIELD 
     The present invention relates generally to an optical system for correcting thermally-induced wavefront distortion in a crystal, and more particularly to a variable applied stress device used with a crystal to correct for optical distortion in the crystal caused by thermal factors. 
     BACKGROUND OF THE INVENTION 
     An optical system in which a crystal is utilized to generate a laser beam for experimentation and measurement should transmit a beam that is free of optical distortions. The crystal is usually a long rod used to generate a moderate power laser beam or may comprise an electro-optical or nonlinear optical element to modify the beam. The optical effects generated in a crystal due to heating from a high power or moderate power laser beam occur even though the beam is expected to provide good beam quality and high polarization purity after passing through the crystal. However, optical distortion and birefringence result from a perfectly linearly polarized moderate power laser beam through a heated crystal rod. The correction of the optical wavefront distortion and birefringence is sought if thermally induced. Distortion and birefringence depend on the temperature variation within the crystal generated by the absorption of the laser beam. The heating of the crystal produces thermal-stress-strain effects. The thermal-stress-strain effects distort the output beam from the crystal. 
     Systems and methods to correct wavefront distortion and birefringence currently employ multiple actuator deformable mirrors, which are very expensive and cumbersome. Numerous actuator signals must be produced and transmitted to each actuator and the interactions between the various actuators and their various signals must be overcome. A system and method is therefore desired which will decrease the number of signals and complexity associated with employing multiple actuator deformable mirrors. 
     SUMMARY OF THE INVENTION 
     The above and other objects are provided by an optical correction system and method in accordance with the preferred embodiments of the present invention. In one preferred embodiment, the optical correction system includes a stress application device that applies a stress to a crystal to minimize optical distortions created in a transmitted beam. The stress application device is coupled to a computational device that determines the optical distortion of the transmitted beam. A beam sensor and wavefront reconstructor is coupled to the computational device and provides a measurement of the transmitted beam. The beam sensor and wavefront reconstructor receives a refracted beam from a beamsplitter that divides the transmitted beam into a reflected beam and the refracted beam. The reflected beam, which originally includes a degree of optical distortion, is corrected via the application of a precise degree of stress to the crystal. 
     The system and method of the present invention thus forms an effective “closed-loop” system by which the optical distortion resulting from thermal factors experienced by the crystal can be continuously monitored, in real time, and precisely corrected. 
     The optical correction system and method of the present invention also does not add significantly to the overall cost of the optical system. It further does not add to the complexity of the optical system, does not require the production and transmission of signals, and can be used with a variety of crystal geometries. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The various advantages of the present invention will become apparent to one skilled in the art by reading the following specification and subjoined claims and by referencing the drawings in which: 
     FIG. 1 is a simplified block diagram showing one preferred embodiment of the apparatus of the present invention; 
     FIG.  2 ( a ) is a front perspective view showing a rectangular shaped crystal which may be used with the optical correction system of the present invention; 
     FIG.  2 ( b ) is a front perspective view showing a cylindrical shaped crystal which may be used with the optical correction system of the present invention; and 
     FIG. 3 is a flow diagram showing a preferred method in accordance with the present invention for minimizing optical distortions of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1 shows an optical correction system generally depicted at  30 . The system  30  is used for correcting, in real time, the wavefront distortion imparted to an optical beam output from a crystal  14  as a result of thermal factors acting on the crystal  14 . However, it should be appreciated that the system  30  can correct output from an anisotropic crystal, any laser beam generating device or the laser. The system  30  generally comprises a beam splitter  38 , a wavefront sensor  44 , a computational device  50  for determining the necessary degree of correction needed to be applied to the crystal, and a stress applicator device  52 . 
     In operation, an aberrated or input beam  32  is incident upon the crystal  14 . The input beam  32  can be generated by a variety of means including, but not limited to, an optical device such as a laser and any laser beam generating device, or directly from another crystal. In the preferred embodiment, the crystal  14  produces a transmitted beam or output beam  36  that is incident upon beamsplitter  38 . The beamsplitter  38  divides the output beam  36  into a refracted beam  42  and a reflected or corrected beam  40 . Beamsplitter  38  is sufficiently thin so that it does not introduce optical distortions. The corrected beam  40  is reflected by beamsplitter  38  and used for experimentation and measurement. The refracted beam  42  is transmitted by beamsplitter  38  to the wavefront sensor  44 . One preferred form of the wavefront sensor  44  comprises a Hartmann sensor, although it will be appreciated that other forms of sensors could also be employed. 
     The wavefront sensor  44  detects the slope of the wavefront at several locations across the refracted beam  42  and produces a measured signal  46  related to the refracted beam  42  which is representative of the optical distortion in the output beam  36 . The measured signal  46  produced by the wavefront sensor  44  is transmitted to the computational device  50 . The computational device  50  essentially determines the degree of error correction needed to remove the wavefront distortion in the refracted beam  42  and generates an appropriate actuator signal  48  which is transmitted to a stress application device  52 . The actuator signal  48  is such that the optical distortion of sampled beam  42  and reflected beam  40  are minimized or eliminated. 
     The computational device  50  determines a minimized optical distortion preferably via a least squares method which is well known in the art. The least squares method is applied to the optical distortion. In the preferred embodiment, computational device  50  also determines the root means square of the optical distortion which is used in the least squares method. The optical distortion due to thermal-stress-strain effects in a rectangular rod shaped crystal with light propagating along its optical axis is given by the equation:              Φ   =     kl        {           ∂     n   o         ∂   T          T     -         n   o   3     4          [         (       q   11     +     q   12       )          (       σ   1     +     σ   2       )       +     2        q   13          σ   3       +       (       q   11     +     q   12       )          (       σ     1      a       +     σ     2      a         )         ]         }               Equation                 1.                                
     where “k” is the wave number; “l” is the thickness of the rod; “∂n o /∂T” is the variation of the ordinary refractive index with respect to temperature; “T” is the transverse temperature variation in the rod; “n o ” is the refractive index of the ordinary wave in the absence of temperature rise and stress; “q 11 ,” “q 12 ” and “q 13 ” are stress photoelastic constants; “σ 1 ,” “σ 2 ” and “σ 3 ” are the thermally induced stresses in the X, Y and Z directions, respectively, and “σ 1a ,” and “σ 2a ” are the applied stresses. 
     The thermal-stress-strain optical distortion effects in a cylindrical shaped rod trigonal crystal with light propagating along its optic axis is given by the following equation where k, I, ∂n o /∂T, T and n o  are as described above for Equation 1:              Φ   =     kl        {           ∂     n   o         ∂   T          T     -           n   o   3          [         (       q   11     +     q   12       )          (       σ   r     +     σ   θ       )       +     2        q   13          σ   3       +       (       q   11     +     q   12       )          σ   ra         ]         (   4   )                          }                     Equation                 2.                                
     Here, “σ r ,” “σ θ ” and “σ 3 ” are radial, hoop and longitudinal stresses, respectively, that are generated by the thermal distribution; “σ ra ” is an applied stress which is applied uniformly along the rod; and “q 11  ,” “q 12 ” and “q 13 ” are stress photoelastic constants of the material. The optical distortion expression for a cylindrical crystal having a round cross-section and a symmetry structure simpler than trigonal will have a similar but simpler form of Equation 2. 
     With continued reference to FIG. 1, the stress application device  52 , by way of example, may comprise a piezoelectric transducer. In the preferred embodiment, the stress application device  52  is coupled between the computation device  50  and a force applicator  54 , and provides an electric stress signal  60  to the force applicator  54 . The force applicator  54  is preferably U-shaped and has plates  56 ,  58 . However, it should be appreciated that additional force applicators can have more than two plates for applying forces to the crystal. Moreover, if the crystal is cylindrical, then the force applicator  54  is substantially cylindrically shaped and sized to fit the length of the crystal  14 . In the preferred embodiment, first plate  56  and second plate  58  are movably juxtaposed to the lateral faces  16 ,  18 , respectively, of crystal  14 . However, the plates  56 , 58  can be fixed to the crystal  14  if, for example, an application of tensile stress to the crystal is desired. The plates  56 ,  58  apply a controlled compressive or tensile stress to the lateral faces  16 ,  18 , which can be varied in magnitude depending on the stress signal  60  produced by computational device  50 . The first plate  56  and second plate  58  preferably provide a uniform application of stress across the lateral surfaces  16 ,  18  of crystal  14 , and therefore minimize the thermally-induced optical distortion related to temperature variations. 
     FIG.  2 ( a ) shows a first preferred embodiment of the crystal  14  of the present invention. In this preferred embodiment, the crystal  14  has a geometry of a long, rectangular crystal rod and has two pairs of lateral faces  16 , 18  and  20 , 22  transverse to the X-axis and Y-axis, respectively. The crystal  14  also has a first end  15  and a second end  17 . Crystal  14  has a trigonal symmetry; however, it should be appreciated that crystals with simpler symmetry can be used including, but not limited to, cubic symmetry crystals such as a yttrium aluminum garnet (YAG), ruby, and isotropic symmetry class crystals. The crystal  14  preferably has a cross-section that is a substantially rectangular shape. In this embodiment, light propagates along the optic axis which is in the long direction normal to the ends  15 ,  17  of the crystal  14 . The direction of propagation is in the −Z direction of a Cartesian coordinate system. The Cartesian coordinate system has the Z-axis parallel to the optic axis of the crystal  14 . The X and Y axes are parallel to standard crystallographic axes for physical property representation. Thermally-induced normal stresses σ 1 , σ 2  and σ 3  occur parallel to the X, Y and Z directions, respectively. In this embodiment, stresses σ 1a  and σ 2a  are compressive and applied to the lateral faces to minimize the optical distortion as the temperature changes occur. It should be appreciated that stresses applied are uniform along crystal  14 . 
     Referring further to FIG.  2 ( a ), in this embodiment, stresses σ 1a  and σ 2a  are applied to the pairs of lateral faces  20 ,  22 , and  16 ,  18 , respectively; however, it should be appreciated that stress can be applied to any or all of the lateral faces. The stresses applied can be either compressive or tensile. The stress applied is preferably compressive if crystal  14  has a greater temperature toward the crystal center  24 , whereas the stress applied is preferably tensile if the crystal  14  has a lower temperature toward the crystal center  24 , relative to the lateral faces  16 ,  18 ,  20  and  22 . Heating of the crystal  14  is generally uniform in the direction parallel to the Z-axis. The crystal  14  utilized to transmit a laser beam typically has a greater temperature toward the crystal center. 
     FIG.  2 ( b ) shows a second preferred embodiment of a crystal  114  of the present invention. The crystal  114  is a cylindrical shaped crystal rod with a circular cross-section. In the preferred embodiment, light propagates along the optic axis that is in the long direction normal to the ends  115 ,  117  of crystal  114 . In the preferred embodiment, the applied stresses σ ra  are compressive and uniformly applied in the radial direction along the length of crystal  114 , as indicated by arrows  116 . 
     FIG. 3 shows a simplified flow chart representing the steps performed in executing a preferred method of the present invention. Step  62  involves transmitting an output beam from the crystal  14 . The output beam is then split into a refracted beam and a reflected beam, as indicated by block  64 . The refracted beam  42  is then processed by the wavefront sensor  44  to produce an output signal having a component which is indicative of the degree of optical distortion in the optical signal leaving the crystal  14 , as indicated in step  66 . 
     Step  68  involves computing an error correction signal for substantially reducing or eliminating the optical distortion in the refracted beam  42 . 
     Step  70  involves using the error correction signal to control the stress application device  52 , which generates signals specifically adapted to compensate for the optical distortion. 
     Step  72  involves applying the stress to the crystal  14  as needed to reduce or eliminate the thermally-induced optical distortion. 
     The invention being thus described, it will be obvious that the same may be varied in many ways. Such variations are not to be regarded as a departure from the spirit and scope of the invention, and all such modifications as would be obvious to one skilled in the art are intended to be included within the scope of the following claims.