An adaptive laser system (10) includes an adaptable laser (12), a waveform sensor (14), an amplitude distribution sensor (16), and a processor (18) for converting data from the sensors into commands for controlling the waveform of a laser beam. Amplitude distribution data is to weight waveform data as the processor determines actuator commands for deforming the laser's main mirror (22). Amplitude weighting permits more accurate determination of the waveform sensor-to-actuator-coupling matrix and more precise optimization of the on-axis intensity of the laser beam across the laser aperture.

BACKGROUND OF THE INVENTION 
The present invention relates to adaptive lasers, and, more particularly, 
to a method and system for increasing the power deliverable by an adaptive 
laser subject to wavefront distortions. 
Adaptive optical systems have been developed to deal with the loss of power 
deliverable by a laser due to wavefront aberrations. These aberrations can 
be introduced by the laser system, for example by imperfections in the 
optical train. Alternatively, nonuniformities in the laser beam media, for 
example, atmospheric anomalies, can distort the laser wavefront. 
Generally, an adaptive laser includes a laser source with optics adaptable 
to control the outgoing waveform, a waveform sensor, and a processor for 
converting sensor data into commands directed to the adaptable optical 
element of the laser. Ideally, such a system would include a waveform 
sensor with infinite resolution, a completely deformable mirror, and a 
processor which validly converts the sensor data to mirror adjustments to 
produce the desired waveform. In practice, there are limitations to the 
adaptability of the laser source, to the accuracy, precision and validity 
of the sensor measurements, and, as a result of the foregoing, to the 
validity of the translation of sensor data into commands by the processor. 
Typically, the adaptable element of the laser source is the primary mirror. 
A number of actuators can be applied to deform the mirror. The degree to 
which mirror deformation can be controlled is limited by the number of 
actuators. Thus, generally, even with ideal waveform determination and 
translation into actuator commands, the resulting waveform only 
approximates the desired uniform wavefront. 
Of course, available sensors fall short of the infinite resolution waveform 
ideal in several respects. It turns out that the most practical sensors 
measure waveform indirectly and with quite limited resolution. Examples of 
such sensors include the Hartman sensor, the shearing interferometer and 
the integrated imaging irradiance sensor. The output of these sensors is 
typically treated as wavefront slope data, which is the derivative of the 
desired waveform or optical path difference (OPD) data. 
There are several substantially equivalent ways for a processor to convert 
such sensor data into actuator commands. In one approach, the slope data 
is integrated to obtain a reconstructed wavefront. The resulting OPD data 
can then be processed according to a predetermined relationship between 
actuator commands and effects on OPD so as to minimize the 
root-mean-square of the expected OPDs. 
Another approach bypasses the conversion to OPD data by using a direct 
relationship between actuator commands and effects on wavefront slope. 
This approach applies a least squares fit of wavefront slopes to a 
discrete wavefront map, thereby attempting to minimize the sum of squares 
of the wavefront slope measurements across the laser aperture. The applied 
algorithm has the form: 
EQU a=(H.sup.T H).sup.-1 H.sup.T s 
where a is the actuator command vector estimate, H is the actuator-sensor 
coupling matrix, and s is the slope vector. The actuator command vector 
estimates the commands predicted to result in the desired wavefront figure 
of merit at the sensor. The actuator-sensor coupling matrix, also known as 
the actuator-sensor Jacobian, describes what slope value a given 
subaperture will measure when a given actuator is pushed. 
In practice, adaptive lasers in accordance with the foregoing fall far 
short of theoretical performance. In some situations, not only is the 
ideal not approached, but the "corrected" laser delivers less power than 
would the same laser without the correction. Furthermore, successive 
corrections can fail to converge and introduce dynamic instability into 
the system. 
It is anticipated that advances will permit greater numbers of actuators 
and improved sensors. However, the performance of future systems 
incorporating such refinements and present systems incorporating today's 
technology are not optimized by the current methods of translating 
waveform data into actuator commands. A need exists for a new adaptive 
optics system and corresponding method for the enhanced power delivery by 
lasers. 
SUMMARY OF THE INVENTION 
The present invention provides for amplitude weighting of waveform data in 
determining compensating adjustments for an adaptive laser. Accordingly, a 
system in accordance with the present invention includes an adaptable 
laser, a waveform sensor, an amplitude distribution sensor, and a 
processor. The processor uses amplitude distribution data to weight 
waveform data in calculating actuator command vectors. 
A recognition upon which this invention is based is that the power 
delivered to a destination is characterized by a function of an integral 
of the amplitude-weighted square of optical path differences. Greater 
accuracy and stability can be achieved by obtaining and properly 
processing the amplitude data neglected by conventional adaptive optics. 
The present invention provides for the incorporation of amplitude sensors 
of greater resolution than the resolution of the waveform sensors so that, 
in addition to the corrections made on the scale of the laser aperture, 
adjustments can be made on the scale of the-subapertures defined by the 
limited resolution of the wavefront slope sensor. In the case of sensors 
that provide unweighted OPD or slope data, the amplitude distribution is 
used to properly emphasize the higher amplitude regions within a 
subaperture in correcting the waveform. This is analogous to the procedure 
applied across the whole laser aperture. 
Many waveform sensors, such as the Hartman sensor, provide 
amplitude-affected data. Where such a sensor is employed, the amplitude 
distribution is necessary to determine the sensor-actuator coupling matrix 
so that the optimal actuator commands can be calculated. 
The advantages of the present invention are explicated below in the 
detailed descriptions. Intuitively, it is understood that a finite number 
of actuators implies that compromises must be made. The prior art system 
biases its compromises in favor of subapertures with great distortion, 
despite very small amplitude, at the expense of subapertures with moderate 
distortion and very large amplitude. The present invention properly 
balances the amplitude and distortion factors. Thus, the present invention 
performs its adjustments where they do the most good, i.e., make the 
greatest contribution to the power delivered.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
In accordance with the present invention, an adaptive laser system 10 
includes an adaptable laser 12, a waveform sensor 14, an amplitude 
distribution sensor 16, and a processor 18 for converting data from the 
sensors into commands for controlling the waveform of a laser beam exiting 
the laser 12, as illustrated in FIG. 1. The method of the present 
invention provides for enhanced power delivery by amplitude weighting 
waveform data in controlling compensating deformations in the laser beam. 
The laser 12 transmits coherent radiation through an aperture 20 in a main 
mirror 22. The radiation is then reflected by a secondary mirror 24 and 
again by a reflective surface 26 of the main mirror. The collimated 
reflection from the main mirror 22 exits toward the destination through an 
aperture 28 about the secondary mirror 24. 
The main mirror 22 has a holographic coating 25 on its reflective surface 
26 to direct a small fraction of the radiation through an aperture 30 at 
the center of the secondary mirror 24. This sample is used as the input to 
the sensors 14 and 16. As the sample exits the secondary mirror, it is 
split by a partially transmitting and partially reflecting mirror 32 so 
that beam samples are incident to both the amplitude sensor 16 and the 
waveform sensor 14. The illustrated waveform sensor 14 is a Hartman sensor 
which provides amplitude-affected slope data for each of the subapertures 
it defines. 
So that amplitude weighting can be used on the scale of the subapertures, 
the resolution of the amplitude distribution sensor 16 should provide at 
least four times the resolution of the waveform sensor 14. Preferably, the 
amplitude sensor has a resolution at least about an order of magnitude 
greater than that of the waveform sensor. 
The outputs of the sensors 14 and 16 are directed to the processor 18 which 
computes an estimated amplitude-weighted waveform and converts the 
estimate into actuator commands. In the illustrated laser system 10, the 
actuators 34 include piezoelectric elements disposed on the side of the 
deformable main mirror 22 opposite its reflective surface 26. Electrical 
commands applied to the piezoelectric elements cause them to expand or 
contract, thus controlling the shape of the deformable mirror 22. 
The present invention provides an improvement over the conventional 
adaptive laser for substantially any combination of actuators and 
wavefront slope sensors. By way of example only, the illustrated 
embodiment includes forty-nine actuators 34 and a comparable number of 
subapertures defined by the Hartman sensor; the amplitude sensor 16 is a 
charge-coupled device capable of providing a resolution at least nine 
times finer than that of the Hartman sensor 14. 
The method of the present invention can be conducted on the scale of the 
laser aperture and additionally on the scale of the subapertures defined 
by the Hartman sensor 14. On either scale, the invention provides for 
mathematically equivalent and substantially equivalent alternatives. The 
common objective of these procedures is to minimize &lt;oWo&gt;, where o is the 
optical path difference vector and W is a diagonal matrix with each 
diagonal element representing the amplitude measured at a corresponding 
sensor element. Applying standard weighted least squares, the actuator 
command vector that minimizes &lt;oWo&gt; is 
EQU a=(F.sup.T W F).sup.-1 F.sup.T W o 
where F is the predetermined unweighted OPD-to-actuator coupling matrix 
which satisfied Fa=o, and F.sup.T is the transpose of F. 
The actuator command formula above can be applied to systems incorporating 
any type of waveform sensor which can provide, directly or indirectly, the 
unweighted optical path difference vector o. In the illustrated 
embodiment, the Hartman sensor renders an amplitude-affected slope vector 
s. (Herein, underlining demarks amplitude-affected or amplitude-weighted 
variables.) 
To obtain the vector o, the amplitude data can be used to convert s to its 
unweighted counterpart s, which can then be translated: 
ti o=(G.sup.T G).sup.-1 G.sup.T s 
where G is the slope/OPD coupling matrix which satisfies the formula Go=s. 
Alternatively, the amplitude distribution can be applied to obtain G, the 
slope/OPD coupling matrix which takes into account weighting effects. Then 
o is obtained according to the formula: 
EQU o=(G.sup.T G).sup.-1 G.sup.t s. 
It is not necessary to explicitly calculate o; substitution yields: 
EQU a=(F.sup.T W F).sup.-1 F.sup.T W (G.sup.T G).sup.-1 G.sup.T s 
This expression may be converted to a form like that used in conventional 
systems: 
EQU a=(H.sup.T W' H).sup.-1 H.sup.T W' s 
Here H is the amplitude calibrated sensor/actuator derivative matrix, e.g. 
H=FG; W' is the best weight matrix: 
EQU W'=G (G.sup.T G).sup.-1 W (G.sup.T G).sup.-1 G.sup.T 
Comparison of the conventional adaptive laser with the present invention 
yields clear results. In a simulation study using the illustrated laser's 
amplitude distribution, shown in FIG. 2, the illustrated system 10 yielded 
a Strehl ratio of 96%, while the unweighted convention system using a like 
number of actuators and a waveform sensor of like resolution yielded a 
Strehl ratio of 75%. Ideal sensing, with infinite resolution, gives a 
Strehl ratio of 97%. 
The advantage of the present invention over the prior art can be 
comprehended conceptually by considering a beam in which there are no 
optical path differences, but in which the amplitude varies with a spatial 
frequency high compared to the scale of the subapertures of a Hartman 
sensor. Due to the amplitude effects, the Hartman sensor renders a 
nonconstant distribution in response to such a wavefront. A conventional 
system, ignoring amplitude effects, incorrectly determines that 
corrections are necessary and effects actuator movements which diminish 
power delivery. The present invention takes amplitude variations into 
account and does not require actuator movements in such a case. Also, on 
the scale of the aperture, the appropriate compromises between amplitude 
and optical path differences can be made, whereas in the conventional 
system, amplitude is ignored and path differences are given undue weight. 
The method involving amplitude weighting across the aperture and across 
subapertures can be considered either as a double estimation or as 
creating a proper error metric and then performing a standard weighted 
estimation. The single and double estimations are applicable to waveform 
sensors in general. Thus, amplitude-affected slope sensors other than the 
Hartman sensor can be used; unweighted and other slope sensors, weighted 
and unweighted optical path difference sensors, are all provided for by 
the present invention. In fact, any means for directly or indirectly 
characterizing the waveform of a laser beam can be incorporated by the 
present invention. 
The present invention provides for improvements over unweighted systems for 
any number of actuators and any resolutions of the sensors. Typically, the 
actuators number in the tens or into the hundreds, and the waveform 
sensors define a comparable number of subapertures. The amplitude sensors 
can have comparable resolution if the amplitude weighting is directed to 
the laser aperture. The resolution of the amplitude sensor is preferably 
about an order of magnitude or more above that of the waveform sensor to 
provide for double amplitude-weighted estimation. 
Where the amplitude distribution is constant over time, but spatially 
nonuniform, the present invention can be used to calibrate the laser. This 
calibration can involve establishing an amplitude-weighted waveform 
sensor-to-actuator coupling matrix. This permits amplitude-affected sensor 
data to be converted directly to actuator commands without real-time 
monitoring by the amplitude sensor. Alternatively, the calibration could 
be supplemented by periodic checks for drifts in the sensor-actuator 
coupling matrix. 
The invention provides for various sensor locations. In a laser 
communications system, the sensors can be located at the receivers and the 
results fed back for adjustments. Alternatively, an inverse beam generated 
by the destination station can be detected locally and used in making 
corrections as to aberrations induced by the intervening medium. 
Reflections can also be used in this way. Finally, as in the illustrated 
embodiment, the sensors can be deployed locally to calibrate the laser on 
a near-real-time or a one-shot basis. 
Generally, the goal of adaptive optics is to maximize the power at a 
destination and this is accomplished by "flattening" the wavefront. 
However, the present invention is applicable generally to optimizing 
functions of laser beam amplitude distribution and waveform. For example, 
the present invention can be used to approximate any desired wavefront 
shape, and is not limited to minimizing optical path differences. 
Thus, the present invention provides a general improvement in power 
delivery over prior systems. The improvements are greatest where amplitude 
varies considerably and where the number of actuators is not large. As 
indicated, the present invention is subject to modifications and 
variations, included those suggested above and others, so that the 
invention is limited only by the scope of the following claims.