Abstract:
A system, for determining characteristics of a beam wavefront and reshaping such wavefront, including: apparatus for sampling the wavefront curvature and generating outputs; apparatus for reshaping the wavefront; and apparatus for receiving the outputs, proportioning the outputs to match the inputs need to drive controls for the reshaping apparatus, and sending the proportioned outputs to the reshaping apparatus. The reshaping apparatus is, preferably, a deformable mirror. The sampling apparatus includes a distorted grating. The method includes: positioning the sampling apparatus in the bean path; positioning a reshaping apparatus in the beam path; sampling the curvature of the wavefront and generating outputs representative of the curvature thereof; sending the generated outputs to the proportioning apparatus; proportioning the outputs to match the inputs needed to drive the controls of the reshaping apparatus; and sending the proportioned outputs to the reshaping apparatus to change the shape thereof.

Description:
RELATED U.S. APPLICATION DATA 
     This application is a continuation-in-part of and claims the priority of provisional application Ser. No. 60/958,480, filed Jul. 3, 2007. 
    
    
     FIELD OF THE INVENTION 
     This invention relates, in general, to wavefront characterization and correction. More particularly, the present invention relates to a method (and the associated apparatus) including the steps: of sampling the curvature of a wavefront with a curvature sampling device; generating outputs representative of the curvature of the wavefront; sending the generated outputs to a proportioning device; and proportioning the outputs from the curvature sampling device to match the inputs needed to drive the controls of a wavefront reshaping device. The invention also relates to apparatus and methods for determining at least some of the characteristics of the wavefront of a beam without the use of an artificially generated reference. 
     BACKGROUND OF THE INVENTION 
     U.S. Pat. No. 6,286,959 B1 (the “&#39;959 Patent”), assigned to the assignee of this application, discloses wavefront sensing using a distorted grating to determine the characteristics of a wavefront that has passed through a cornea (either in vitro or in vivo). More specifically, this patent relates to the use of wavefront sensing using a distorted grating to identify corneas that have been surgically modified. The apparatus includes a distorted grating and an imaging lens which have a pupil plane, first and second virtual planes and an image plane. 
     With reference to FIG. 1 of the &#39;959 Patent, apparatus  11  for determining the characteristics of a wavefront includes a source of light  13 , a distorted grating (sometimes referred to as a “distorted diffraction grating”)  17 , a high quality imaging lens (or lens set)  19 , and a detector  21  (either film or electronic) having a detector plane  23 . Grating  17 , lens  19  and detector  21  are sometimes referred to as wavefront sensor  24 . Apparatus  11  also includes a beam path  25 , a pupil plane  27 , first virtual plane  29 , second virtual plane  31 , and a data processor  33 . Data processor  33 , connected to detector  21  via a data acquisition device such as a frame grabber (not shown), stores the images from detector  21  and determines the wavefront from the stored images. The representation of the virtual planes between source  13  and sensor  24  is for convenience only. 
     With grating  17  in close proximity to lens  19  (typically these two elements would, in fact, be in contact with each other along beam path  25 ), the 0, +1 and −1 diffraction orders of grating  17 , image pupil plane  27 , virtual object plane  29  and virtual object plane  31  are projected onto detector plane  23 . The higher order diffraction orders are cut off by an appropriately placed field stop (not shown) so as not to contaminate the image of the 0 and +1 and −1 orders. Further, with the zero order being an image of the pupil plane  27 , the images in the +1 and −1 diffraction orders correspond to virtual image planes equidistant from and an opposite sides of pupil plane  27 . The grating is distorted according to, 
                 Δ   x     ⁡     (     x   ,   y     )       ≂           W   20     ⁢   d       λ   ⁢           ⁢     R   2         ⁢     (       x   2     +     y   2       )             
where λ is the optical wavelength, x and y are Cartesian co-ordinates with an origin on the optical axis and R is the radius of the grating aperture which is centered on the optical axis. The parameter W 20 , defines the defocusing power of the grating, and is the standard coefficient of the defocus equivalent on the extra pathlength introduced at the edge of the aperture, in this case for the wavefront diffracted into the +1 order. The phase change (Ø m ) imposed on the wavefront diffracted into each order m is given by,
 
     
       
         
           
             
               
                 φ 
                 m 
               
               ⁡ 
               
                 ( 
                 
                   x 
                   , 
                   y 
                 
                 ) 
               
             
             = 
             
               m 
               ⁢ 
               
                 
                   2 
                   ⁢ 
                   π 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     W 
                     20 
                   
                 
                 
                   λ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     R 
                     2 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     x 
                     2 
                   
                   + 
                   
                     y 
                     2 
                   
                 
                 ) 
               
             
           
         
       
     
     With nothing in pupil plane  27  of apparatus  11  (e.g., cornea container  15  removed) and source  13  present, the images recorded on detector plane  23  are as illustrated in FIG. 1B of the &#39;959 Patent. 
     While the &#39;959 Patent discloses a sensor, it does not disclose any method or apparatus for correcting the wavefront of a beam. 
     U.S. Pat. No. 7,232,999 B1 (the “999 Patent”) and pending U.S. patent application Ser. No. 11/820,651 filed Jun. 19, 2007 (which claims the priority of the &#39;999 Patent), both assigned to the assignee of this application and incorporated by reference, disclose the use of distorted grating based wavefront sensors to measure wavefronts of radiation. More particularly, in the preferred embodiment the invention disclosed therein involves positioning a beam of light containing the wavefront to be characterized onto a distorted grating, using the grating to produce a plurality of images, determining the infrared wavefront from the plurality of images and analyzing the wavefront for features that characterize the infrared wavefront. 
     With reference to FIG. 7 of the &#39;999 Patent wavefront  101  to be measured is directed onto pupil plane  103 , the wavefront at pupil plane  103  is then redirected onto grating  105 , modifying wavefront  101 , which modified wavefront is subsequently focused onto detector  107  through lens  109 . Grating  105 , lens  109  and detector  107  constitute the wavefront sensor. Optional pupil relay and magnification optics  115  can be used to orient and resize wavefront  101  as required by the application being used. 
     With reference to FIG. 8 of the &#39;999 Patent, laser  121  generates light beam  123  which is passed through attenuator  125  and is re-directed using optics  127  and  129 . Mirrors  131  and  133  are used to disperse and re-collimate beam  123  which is then directed through aperture  135  (collimation is not required). It is the wavefront as it exists at aperture  135  that will ultimately be imaged onto detector  145 . Beam  123  is subsequently directed through lenses  137  and  139  which are used to position and magnify beam  123 . Beam  123  is then passed through diffraction grating  141  before being focused by lens  143  onto the focal plane of detector (infrared camera)  145 . Lens  143  serves to focus the beam  123  as modified by grating  141  onto a detector  145 . Grating  141 , lens  143  and detector  145  constitute the wavefront sensor. 
     The &#39;999 Patent does not, however, disclose either a method or apparatus for: (1) correcting the output beam of a laser; or (2) correcting the image of an object prior to detecting such image. 
     Some of the most widely known work in the field of adaptive optics has been done for astronomical purposes; attempting to correct atmospheric turbulence to allow telescopes at low altitudes to perform as well as high-altitude telescopes (e.g. Mauna Kea at 14,000 feet elevation) or, better yet, like space based telescopes. Most adaptive optics systems use a Shack-Hartmann wavefront sensor, which requires a point source as its reference as, basically, a Shack-Hartmann sensor calculates the centroid of an image of the reference, which requires that reference is small and well defined. Alternatively, some astronomical adaptive optics systems use a wavefront sensing technique called phase diversity, which takes two defocused images of the reference and so, again, relies on the reference being small and well defined. 
     Ideally, in order to correct the image, wavefront measurements are made on a perfect source that has propagated along the same path as the image. This way correcting the wavefront of the ideal source simultaneously corrects imaging through optics looking along the same path. The problem is finding a perfect wavefront source to measure. For astronomy, a star can be used as the reference (as it is small and well defined). However, it also has to be bright which severely limits the regions of the sky that can be observed (astronomical telescopes typically have a very small field of view and so the chances of a bright star being within the field of view of the object which an astronomer wants to observe is very small). A solution to this problem is to use a laser to create a bright virtual star (an ideal reference) by exciting sodium atoms in the upper atmosphere. This artificially generated reference is typically called a “guide star”. 
     This same basic technique (projecting a laser beam through the optical system, measuring and correcting the return beam and, hence, correcting the imaging performance of the system) has been adapted to other, non-astronomical applications (e.g. enhanced retinal imaging). U.S. Pat. No. 6,331,059 B1 (the “&#39;059 Patent”), discloses an improved fundus retinal imaging system in which a conventional fundus retinal imager is combined with a multispectral source, a dithered reference, a wavefront sensor, a deformable mirror and a high resolution camera. More specifically, the &#39;059 Patent discloses an ophthalmic instrument having a wide field of view (up to 20 degrees) including a retinal imager, (which includes optics for illuminating and imaging the retina of the eye); apparatus for generating a reference beam coupled to the imager optics for measuring the wavefront produced by optical aberrations within the eye and the imager optics; wavefront compensation optics coupled to the imager optics for correcting large, low order aberrations in the wavefront; a high resolution detector optically coupled to the imager optics and the wavefront compensation optics; and a computer (which is connected to the wavefront sensor, the wavefront compensation optics, and the high resolution camera), including an algorithm for correcting small, high order aberrations on the wavefront and residual low order aberrations. The wavefront sensor includes a Shack-Hartmann wavefront sensor having a lenslet array and a detector positioned in the front surface of the lenslet array for producing a Hartmannogram. See, generally,  FIG. 1  of this reference. 
     U.S. Pat. No. 6,736,507 B2 (the “&#39;507 Patent), which is a continuation-in-part of the &#39;059 Patent, discloses the use of a distorted grating wavefront sensor as an alternative to the Shack-Hartmann wavefront sensor. See, col. 3, ll. 18-21 and col. 5, ll. 15-27. However, regardless of which sensor is used, all the other optics and electronics remain the same. Also, overall the methodology remains unchanged. Thus, for instance, the apparatus for generating a reference beam coupled to the image optics to form a reference area on the retina is used with both the Shack-Hartmann wavefront sensor and the distorted grating sensor. 
     All of the foregoing adaptive optics systems, including the systems described in the &#39;059 and &#39;507 Patents, include wavefront characterization and correction. Further, all include the following steps (and the associated apparatus for accomplishing such steps): (a) acquiring data from the wavefront to be characterized and corrected; (b) using the acquired data to mathematically reconstruct the wavefront; (c) from the reconstructed wavefront computing either the slope or the curvature of such wavefront (depending on what type of data is needed to drive the mirror used to correct the wavefront); (d) using the slope (or curvature) data to generate signals to drive the mirror; and (e) driving the mirror to correct the wavefront. In the case of adaptive optics imaging systems, an artificially generated reference (e.g., guide star) is also necessary, in which case step (a) becomes: acquiring data from the wavefront of the artificially generated reference. 
     The foregoing, without the artificially generated reference, is schematically illustrated in  FIG. 1 , in which adaptive optics system  11  includes wavefront modulator  13 , wavefront sensor  15 , data acquisition device  17 , prior art processor  19  and amplifier  21 . Wavefront modulator  13  would, typically, be a deformable mirror (which includes actuators); sensor  15 , a Shack-Hartman sensor. As illustrated, data acquisition device  17  includes a detector  23  (e.g., CCD (Charged Coupled Device) or CMOS (Complementary Metal Oxide Semi-conductor)) and a mechanism (e.g., routine or hardware)  25  for digitizing the images captured by detector  23 . Processor  19  includes computer routine  27  for processing the raw digital data from converter  25  into information utilized by the analysis technique associated with the data acquisition device  17  (e.g., a Shack-Hartman sensor or a distorted grating wavefront sensor). Processor  19  also includes a routine  29  for mathematically recreating the detected wavefront, and a routine  31  for calculating the slope or the curvature of the created wavefront (sometimes referred to as wavefront modulator commands), depending on what type of data is needed to drive wavefront modulator  13 . Finally, processor  19  includes a routine  33  for converting the digital information from routine  31  to analog. Amplifier  21  provides the power to drive the actuators of deformable mirror  13 . Variations of the foregoing include incorporating detector  23  into wavefront sensor  15 . Converter  25  can be part of data acquisition device  17 , incorporated into processor  19  or a stand alone device. Amplifier  21  can be a separate device as illustrated, or combined with wavefront modulator  13 . 
     In addition to a deformable mirror, adaptive optics systems may include a mechanism of correcting the tip/tilt of the beam (sometimes also referred to as removing jitter). With reference to  FIG. 2 , tip/tilt correction system  41  includes tip/tilt mirror  43 , beam splitter  45  and tip/tilt sensor  47  (e.g., a quad cell or a position sensitive detector (or PSD)). The adaptive optics system also includes wavefront modulator  49 , beam splitter  51  and wavefront sensor  53 . Beam splitter  45  divides beam  55  into portion  57  which is directed to sensor  47  and portion  59  which is directed onto wavefront modulator  49 . Similarly, beam splitter  51  divides beam portion  59  into two portions,  61  and  63 , the latter of which is directed to wavefront sensor  53 . Wavefront sensor  53 , via processor  19  (shown only in  FIG. 1 ), controls wavefront modulator  49  in the manner described above with regard to  FIG. 1 . However, as is evident from  FIG. 2 , the control loop for tip/tilt mirror  43  is, and has to be, separate from the control loop for wavefront modulator  49 . 
     The foregoing adaptive optics systems have the following disadvantages: (a) they require a routine for mathematically reconstructing the measured wavefront, which routine is computationally intensive; (b) they require a routine for determining the slope (or the curvature) of the reconstructed wavefront, which routine is also computationally intensive; (c) when used for imaging they require the use of an artificially generated reference (e.g., a guide star); and (d) they require a separate data collection/control loop for a tip/tilt correction device. 
     OBJECTS OF THE INVENTION 
     It is an object of the present invention to provide an adaptive optics system that, in comparison to existing adaptive optics systems, is simpler to construct, more rugged, computationally less intensive and hence faster, and cheaper. 
     It is a further object of the present invention to provide an adaptive optics system that makes a measurement of the curvature of the beam (e.g., the image beam) and then uses that measurement to drive, through the use of a “proportioning” mechanism, a beam correction device (e.g., a deformable mirror) that provides a curvature correction to the wavefront of the beam. As used in this application, the term “proportioning” means a device, mechanism or routine (and the associated use of such device, mechanism or routine) which matches the signals from the device that measures the curvature of the beam to the signals needed to drive the curvature correction device: (a) without the need to create a wavefront from the signals acquired from the device that measures the curvature of the beam; and (b) without the need to compute either the slope or the curvature of the wavefront. 
     It is a further object of the present invention to, with the use of a distorted grating wavefront sensor, use a feature in the beam to be corrected to determine at least some of the characteristics of the associated wavefront. This removes the requirement for an artificially generated reference (sometimes referred to as a guide star) and allows a fundamental paradigm shift in the design of the wavefront sensing system. There is no known adaptive optics imaging systems constructed or proposed around any method other than the artificially generated reference method. 
     Other objects and advantages will be apparent from the description of the preferred embodiments. 
     SUMMARY OF THE INVENTION 
     The present invention relates to a system for determining at least some of the characteristics of the wavefront of a beam and, using such determined characteristics, to at least partially reshape such wavefront. The system includes apparatus, positioned in the beam path, for sampling the curvature of the wavefront and for generating outputs. The system also includes apparatus (including controls responsive to inputs), positioned in the beam path, for at least partially reshaping the wavefront. The system further includes apparatus, connected to the curvature sampling apparatus and to the wavefront reshaping apparatus, for (a) receiving the outputs from the curvature sampling apparatus, (b) proportioning the outputs from the curvature sampling apparatus to match the inputs need to drive the controls of the wavefront reshaping apparatus, and (c) sending the proportioned outputs to the wavefront reshaping apparatus to change the shape of the wavefront reshaping apparatus. 
     The wavefront reshaping apparatus is, preferably, a deformable mirror which includes a surface obeying the surface equation ∇ 2 S=aV, wherein “S” is the surface shape of the deformable mirror, “a” is a constant, “V” are the signals (voltage or current) applied to the controls of the deformable mirror, and ∇ 2 S is the rate of change in slope of the surface of the deformable mirror. 
     The curvature sampling apparatus is a wavefront sensor including a distorted grating and an associated detector. The distorted grating produces at least first and second images of the wavefront; the detector captures such images and produces the outputs (which outputs are analog outputs). In one version the detector is selected from the group including CCDs and CMOSs. Alternately, the detector is an array of photo-detectors, wherein the number of photo-detectors is proportional to the number of controls on the wavefront reshaping apparatus. As the curvature sampling apparatus determines at least some of the characteristics of the wavefront from features present in the wavefront itself there is no need for the artificially generated reference necessary in prior art adaptive optics imaging systems. 
     The proportioning portion of the receiving/proportioning/sending apparatus determines the difference between the intensities of the images of the +1 and −1 diffraction orders of the distorted grating. 
     The system further includes apparatus to adjust the tip/tilt of the beam. 
     The operation of the above described system includes the steps of: (a) positioning the curvature sampling apparatus that generates outputs in the path of the beam; (b) positioning a wavefront reshaping apparatus in the path of the beam; (c) sampling the curvature of the wavefront with the curvature sampling apparatus and generating outputs representative of the curvature of the wavefront; (d) sending the generated outputs to the proportioning device; (e) proportioning the outputs from the curvature sampling apparatus to match the inputs needed to drive the controls of the wavefront reshaping apparatus; and (f) sending the proportioned outputs to the wavefront reshaping apparatus to change the shape of the wavefront reshaping apparatus and, hence, the wavefront. Because the characteristics of the wavefront are determined from features present in the wavefront itself, the prior art step of artificially generating a reference is avoided. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic representation (part optical, part electronic) of a prior art adaptive optics system; 
         FIG. 2  is a schematic representation (again part optical and part electronic) of the separate tip/tilt and wavefront sensor loops required in prior art adaptive optics systems; 
         FIG. 3  is a partially optical/partially electronic schematic representation on an embodiment of the present invention; 
         FIG. 4  is a partially optical/partially electronic schematic representation of an alternative embodiment of the present invention which is analog only; 
         FIG. 5  is a partial schematic illustrating the addition of tip/tilt correction to the embodiment of  FIG. 3 ; 
         FIG. 6  shows, schematically, the use of the adaptive imaging system of the present invention for the correction of a laser beam; 
         FIG. 7  shows the adaptive optic system of the present invention as applied to laser communications systems and directed energy applications; 
         FIG. 8  shows an adaptive optic imaging system based on the principles of the present invention; 
         FIG. 9  shows an optical schematic of a system used to demonstrate the principles schematically illustrated in  FIGS. 6 and 8 ; 
         FIG. 10  is a series of images obtained from the apparatus of  FIG. 9  showing the image before aberration, the aberrated image and the aberrated image after correction; and 
         FIG. 11  is a graph of intensity vs. defocus demonstrating that large amounts of aberration were compensated by the deformable mirror of the apparatus of  FIG. 9 . 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     With reference to  FIG. 3 , adaptive optical system  71  includes a wavefront modulator  73  for reshaping the wavefront of beam  75 . System  71  also includes wavefront sensor  77 , data acquisition device  79 , processor  81  and amplifier  83 . Wavefront modulator  73  is, in the preferred embodiment, a deformable mirror (which includes actuators); sensor  77 , a distorted grating wavefront sensor. As illustrated, data acquisition device  79  includes a detector  85  (e.g., a CCD or a CMOS) and a mechanism (e.g., a routine or hardware)  87  for digitizing the images captured by detector  85 . Processor  81 , in sharp contrast with the prior art, includes a routine  89  for processing the raw digital data from converter  87  and a digital to analog conversion routine  91 . Variations of the foregoing include incorporating detector  85  into wavefront sensor  77 . Further, converter  87  can be part of data acquisition device  79 , incorporated into processor  81  or be a stand alone device. Amplifier  83  can be a separate device, as illustrated, or combined with wavefront modulator  73 . 
     In a distorted grating wavefront sensor, with the distorted grating in close proximity to a lens (typically these two would be in contact with each other along the beam path), the images of the 0, +1 and −1 diffraction orders of the grating will be projected onto the plane of detector  85 . An example is illustrated in FIG. 2 of the &#39;999 Patent. Other orders (e.g., +2, −2) can be cut off by an appropriately placed field stop (not shown). Routine  89  takes the images of the +1 and −1 diffraction orders and determines the differences in the intensities between these two images. In contrast to the prior art, processor  81  does not include either a routine for mathematically recreating the wavefront or a routine for calculating either the slope (or curvature) of any wavefront. Thus, in operation, the wavefront of beam  75  is measured by sensor  77  and analog signals  93  sent to detector  85 . The analog signals  95  from this detector are then digitized by converter  87  and the resulting digital signals  97  sent to routine  89  which, in turn, sends digital signals  99  to analog conversion routine  91 . Analog signals  101  are then sent to amplifier  83  which provides the power to dive the actuators of the deformable mirror. 
     While the embodiment of  FIG. 3  has considerable advantages over prior art adaptive optics systems in that it eliminates the need for both routines  29  and  31 , as identified above with regard to the discussion of  FIG. 1 , it can be further simplified. A more efficient technique is possible if the deformable mirror is constructed in a certain manner, an obeys the surface equation ∇ 2 S=aV. 
     Recalling that the intensity transport equation is: 
                 ∇   2     ⁢   ϕ     =       -   k     ⁢       ∂   I       ∂   z               
A mirror control equation for a deformable mirror is:
 
∇ 2 S=aV
 
If we require that:
 
φ=S
 
then the uniqueness theorem states that:
 
∇ 2 φ∇ 2 S
 
Substituting and rearranging for V
 
     
       
         
           
             aV 
             = 
             
               
                 
                   ∇ 
                   2 
                 
                 ⁢ 
                 S 
               
               = 
               
                 
                   
                     ∇ 
                     2 
                   
                   ⁢ 
                   ϕ 
                 
                 = 
                 
                   
                     - 
                     k 
                   
                   ⁢ 
                   
                     
                       ∂ 
                       I 
                     
                     
                       ∂ 
                       z 
                     
                   
                 
               
             
           
         
       
       
         
           
             V 
             = 
             
               
                 - 
                 
                     
                 
                 ⁢ 
                 
                   k 
                   a 
                 
               
               ⁢ 
               
                 
                   ∂ 
                   I 
                 
                 
                   ∂ 
                   z 
                 
               
             
           
         
       
     
     Where:
         S is the surface shape of the deformable mirror;   a is a constant;   V are the signals (typically voltages; alternately currents) applied to the electrodes of the deformable mirror;   φ is the shape of the wavefront;   k is a constant; and       

               ∂   I       ∂   z           
is the intensity gradient of the light along the direction of propagation.
 
     As is evident from the foregoing, V is a linear function of the difference in intensity of the two wavefront sensor images. This offers a unique optimal signal that can serve as the error signal in a closed loop system along with being able to be directly mapped onto the deformable mirror. This processing scheme has been verified experimentally. 
     Rather than performing these calculations in a digital computer, it is possible to construct an analog system, using an array of photo-detectors, and an analog computer scheme to calculate the signals (e.g., voltages) to output to the deformable mirror. The advantage of such a system will be the bandwidth can be in the MHz correction frequency using inexpensive components, as opposed to the kHz correction frequency achieved by expensive digital systems. 
     With reference to  FIG. 4 , analog only system  111  is illustrated which includes a wavefront modulator  113 , for reshaping the wavefront of beam  115 , and wavefront sensor  117 . Modulator  113  and sensor  117  are the same as described in reference to the system illustrated in  FIG. 3 . However, in place of data acquisition device  79 , detector  119  is an array of photodiodes. Further, processor  121  is now an array of differential op-amps  123 , which eliminates the need for a separate amplifier  83  as illustrated in  FIG. 3 . 
     As is also evident from inspection from  FIG. 4 , the signals  125  from sensor  117  to photodiode array  119  is analog, as are signals  127  and  129 . In operation op-amps  123  put out a signal proportional to the difference in the inputs from the photodiodes of detector  119 . 
     A tip/tilt correction system may be incorporated into the system illustrated in  FIG. 3 . With reference to  FIG. 5 , tip/tilt correction system  141  includes wavefront modulator  73 , routine  87  and amplifier  83 , all as previously described. Thus, the beam (not shown) is sensed by wavefront sensor  77  which sends analog signals to data acquisition device (not shown) which, in the manner previously described, sends digital signals  97  to processor  143 . Processor  143  (like processor  81 ) includes a routine  145 , which functions in the same manner as routine  89  to determine the differences between the images of the +1 and −1 diffraction orders and sends digital signals  147  to digital to analog conversion routine  149  (which functions in the same manner as digital to analog conversion routine  91 ). Further, as with the embodiment of  FIG. 3 , routine  149  sends analog signals  151  to amplifier  83 , which via analog connection  103  provides the power to drive the actuators of the deformable mirror. In addition, processor  143  includes a routine  153  to extract from digital signals  155  tip/tilt data from the images of the +1 and −1 diffraction orders by, for instance, tracking the motion of the images. Tip/tilt routine  153  sends digital signals  157  to digital to analog conversion routine  159  which, in turn, sends analog signals  161  to amplifier  163 . Amplifier  163  sends analog signals  165  to tip/tilt modulator  167  to power the associated actuators (not shown) to move tip/tilt modulator  167  to remove jitter from the beam. 
     With reference to instrument  181  in  FIG. 6 , laser beam  183  from source  185  is reflected off a tip/tilt correction mirror  187  for removing the tip/tilt (jitter) from the beam. The beam  183  then reflects off deformable mirror  189  for reshaping the wavefront of the beam to remove unwanted aberrations, or add wanted wavefront shapes. Beam  183  is then split by beam splitter  191  into two beams: beam  193  which is the output of system  181 ; and beam  195  which is sampled by wavefront sensor  197 . Wavefront sensor  197  consists of grating  197 A, lens  197 B and detector  197 C. The incorporation of detector  197 C in wavefront sensor, as opposed to data acquisition device  79  of system  71  ( FIG. 3 ), is a matter of design choice. Processor  199  is, in one preferred embodiment, the same as processor  81 , except that it includes a routine or hardware that functions in the same manner as mechanism  87 . Again, the location of mechanism  87  is a matter of design choice, so long as the functionality remains unchanged. The analog output  201 , which is the same as analog output  101 , is sent to an amplifier (not shown) which, in turn, drives the actuators (also not shown) of deformable mirror  189 . As instrument  181  includes tip/tilt mirror  187 , it also includes a tip/tilt correction system such as illustrated in  FIG. 5 , to send analog signals  203  to an amplifier (not shown) which, in turn, drives the actuators (also not shown) associated with tip/tilt mirror  187 . Alternately, the analog system described in reference to  FIG. 4  can be utilized. For convenience in describing  FIGS. 7 and 8 , tip/tilt correction mirror  187 , deformable mirror  189 , wavefront sensor  197 , processor  199  and their associated components are collectively referenced as beam correction system  205 . 
     The instrument described above with reference to  FIG. 6  is suitable for correction of a high power laser in industrial cutting and welding applications, and a beam correction scheme for directed-energy systems. 
     The instrument  211  illustrated in  FIG. 7  is identical to that of  FIG. 6  in that it includes beam correction system  205 , as described above. Beam  213  is still a laser beam, typically low power. However, for the applications listed below, instrument  211  includes a laser beam  215  from source  217  which is back-propagated through the system via beam splitter  219 . With this arrangement, beam  215  is pre-distorted by deformable mirror  189  and tip/tilt mirror  187  and is then propagated through the aberrating medium (e.g., the atmosphere). Thus, when beam  215  reaches the intended object (not shown) it will be aberration-free, due to the pre-distortion of the beam. Further, the correction of beam  213  by the beam correction system  205  insures that data receiver  221  (e.g., a fast photocell) will obtain corrected images of the object (i.e., the source of beam  213 ). Such an instrument forms the basis of a laser communications system, and directed-energy applications. 
     With reference to imaging instrument  331  in  FIG. 8  light  333  from an object (not shown) is collected by telescope  335  to form beam  337  which is directed along the optical path of beam correction system  205 . Hence, the beam reflects off tip/tilt mirror  187  and then deformable mirror  189  to correct for jitter and aberrations in the beam. Beam  337  is then divided by beam splitter  191  into beams  339  and  341 . Wavefront sensor  197  (including grating  197 A, lens  197 B and detector  197 C) samples beam  341 . Wavefront sensor  197 , processor  199  and their associated components function as described above to generate analog outputs  201  and  203  to drive the actuators associated with, respectively, deformable mirror  189  and tip/tilt correction mirror  187  to obtain the desired wavefront of output beam  339 . This corrected beam is then directed onto an imaging detector  343 , to obtain a corrected image of the object. Applications include long-range surveillance and target identification. 
     The experimental setup  361  shown in  FIG. 9  consists of laser  363  acting as a light source or object, then pinhole  364  followed by an aperture  365  to define a pupil of the system. The light  367  is then re-imaged by lens system  369  and beam splitter  371  onto deformable mirror  373 . The mirror is a 20 element bimorph mirror, consisting of two piezo-electric disks with different actuator patterns, enabling large deformations (&gt;20 μm for defocus) to be induced on the mirror surface. The light  375  from deformable mirror  373  passes through reimaging lens system  374  and is split into two parts by beam splitter  376 . One beam part  377  is directed to wavefront sensor  379  which consists of a distorted phase grating  379 A, lens  379 B and a Dalsa CCD camera  379 C. Wavefront sensor  379  is coupled to a data processor (not shown) which, in turn, uses the information from the wavefront sensor to calculate the necessary electrical signals to apply to deformable mirror  373 . The other part  381  is directed, via optics  382 , to an imaging sensor  383  (also referred to as a “scoring” camera) to allow for visual and quantitative analysis of the corrected light. A standard ⅔ inch CCD is used. Setup  361  also includes mirror/stop  385 . 
     In operation, immediately after aperture  365  aberrations are introduced to test the correction ability of system  361 . These aberrations consisted of lenses of known refractive power (not shown) and sheets of plastic with unknown aberrations (also not shown).  FIG. 10.A . shows the image of light  367  ( 381 ) before any aberrations are introduced into the system.  FIG. 10.B . shows the image of light  367  ( 381 ) after aberrations are introduced, but before any correction. Finally,  FIG. 10.C . shows the image after correction.  FIG. 11 , which is a graph of intensity vs. defocus showing how, in the absence of correction, the intensity decreases as defocus increases.  FIG. 11  also shows that with wavefront sensing and a deformable mirror to correct for the aberrations, the intensity remains essentially the same, despite increasing defocus. 
     Whereas the drawings and accompanying description have shown and described the preferred embodiment of the present invention, it should be apparent to those skilled in the art that various changes may be made in the form of the invention without affecting the scope thereof.