Abstract:
An adaptive optics system configured as an optical phase front measurement system which provides for relatively high resolution sampling as in holographic techniques but without the need for a reference beam. The optical phase front measurement system includes one or more lenses and a spatial light modulator positioned at the focal plane of the lenses and a camera which enables the phase front to be determined from intensity snapshots. The phase front measurement system allows for relatively long range applications with relatively relaxed criteria for the coherence length of the laser beam and the Doppler shift. As such, the system is suitable for a wide variety of applications including astronomy, long range imaging, imaging through a turbulent medium, space communications, distant target illumination and laser pointing stabilization.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an adaptive optics system and more particularly to an adaptive optics system configured as an optical phase front measurement system which relies on diffraction rather than interference and includes a spatial light modulator for decoding a beam phase front and provides relatively dense phase front sampling as in holographic systems but without the need for a reference beam. 
     2. Description of the Prior Art 
     Optical signals are known to be distorted when passed through a time varying inhomogeneous medium, such as a turbulent atmosphere, ocean or biological tissue. Various optical systems are known which compensate for the distortion in a wavefront during such conditions. Such adaptive optics systems include one or more wavefront sensors for estimating the distortion of the wavefront of an optical signal. These distortion estimates are used to generate correction signals, which, in turn, are typically fed to the actuators of a deformable mirror or a spatial light modulator in order to correct for the wavefront distortion. 
     Various wavefront sensors are known in the art. Such wavefront sensors are known to have limitations during certain conditions. For example, both unit shear lateral shearing interferometer (LSI) wavefront sensors and Hartmann wavefront sensors are extremely well known in the art. Such sensors are disclosed, in general, for example, in “Principles of Adaptive Optics,” Second Edition, Robert K. Tyson, Academic Press, 1991, hereby incorporated by reference. 
     Hartmann sensors utilize a mask with a matrix of holes or an array of lenslets, for example, for dividing the wavefront into a matrix of subapertures. Each of the beams from the subapertures is focused onto one or more position sensing detectors forming an array of the spot intensity on the detectors. The location of the spots provides a direct indication of the wavefront tilt at each subaperture. Unfortunately, the number of sample points of the phase front with such Hartmann sensors is relatively sparse. As such, the applications of such Hartmann sensors are limited to relatively mild turbulent conditions. 
     In unit shear (LSI) wavefront sensors, a copy of the wavefront is made and shifted in the x direction by a distance equal to the spacing between the actuators in the deformable mirror. The original and shifted beams are interfered in order to find the phase difference therebetween. The interference pattern is applied to an array of detectors. The intensity of the light interference pattern provides a measure of the wavefront x-tilt. Such unit shear LSI wavefront sensors may also be implemented in the y direction to obtain the y-tilt. With such unit shear LSI wave front sensors, the sampling resolution is limited by the size of the lateral shift. Unfortunately, selecting a shift that is too small causes serious degradation in the measurement accuracy. In addition, the inevitable accumulation of measurement noise also leads to reconstruction errors. 
     Holographic techniques are also known for detecting the wavefront of a light beam. Such holographic techniques utilize a reference beam with a known wavefront. The reference beam is heterodyned or mixed with the unknown wavefront to obtain an interference pattern or hologram. The phase front of the unknown beam is computed from the intensity profile of the interference pattern. There are two distinct advantages of the holographic technique over the other known techniques: (1) dense sampling and (2) heterodyning gain. Unfortunately, these advantages are also significant weaknesses. More particularly, to create a hologram, the reference beam needs to be coherent with the unknown incoming wave to satisfy the Fourier condition of Δf·Δt&lt;&lt;1, where Δf is the relative frequency drift and Δt is the exposure time. For a continuous wave (CW) laser source, Δt is typically limited to the photon flight time. Commercial CW lasers with sophisticated cavity control can achieve a Δf down to about 300 kHz. Even then the coherence length, and thus the maximum range of operation, is still limited to only a few hundred meters. For longer range applications, a pulse laser with a Δt of about 10 ns may be selected. However, overlapping the return and reference pulses to within a few nanoseconds is relatively difficult in a dynamic situation. An even greater obstacle is the uncompensated Doppler shift for a moving target. If, during the time of exposure, the optical path difference varies by more than λ/4, the hologram becomes washed out. For example, if the wavelength is 1 μm and Δt equals 10 ns, to maintain a good contrast, the optical path difference must not vary faster than 25 m/s. Such parameters are relatively restrictive even for mobile targets. As such, laser coherence and target motion often render the holographic techniques impractical. In addition, such holographic adaptive optics systems require a reference beam. Thus, an adaptive optics system is needed which can provide relatively dense sampling of the phase fronts while eliminating the need for reference beam and allowing for relatively long range applications. 
     SUMMARY OF THE INVENTION 
     Briefly, the present invention relates to an adaptive optics system configured as an optical phase front measurement system which provides for relatively high resolution sampling as in holographic techniques but without the need for a reference beam. The optical phase front measurement system includes one or more lenses and a spatial light modulator positioned at the focal plane of the lenses and a camera which enables the phase front to be determined from intensity snapshots. The phase front measurement system allows for relatively long range applications with relatively relaxed criteria for the coherence length of the laser beam and the Doppler shift. As such, the system is suitable for a wide variety of applications including astronomy, long range imaging, imaging through a turbulent medium, space communications, distant target illumination and laser pointing stabilization. 
    
    
     DESCRIPTION OF THE DRAWINGS 
     These and other advantages of the present invention can be readily understood with the reference to the following specification and attached drawing wherein: 
     FIG. 1 is a diagram of a light beam partitioned into a matrix of pixels. 
     FIG. 2 is a block diagram of a phase front measurement system incorporating a phase spatial light modulator (SLM) in accordance with the present invention. 
     FIG. 3 is a block diagram of an optical system demonstrating beam point stabilization and image reconstruction utilizing phase front correction in accordance with the present invention. 
    
    
     DETAILED DESCRIPTION 
     The present invention relates to a optical phase front measurement system for measuring phase distortions in an optical wavefront which can be used in a closed feedback control loop to compensate for phase distortion, for example, due to turbulent atmosphere. The optical phase front measurement system includes a spatial light modulator disposed at the focal plane of a pair of spaced apart lenses and a camera to determine the phase distribution of the distorted wavefront. 
     The optical phase front measurement system is configured to determine or decode the phase front of a light beam from, for example, two snapshots of the wavefront. More particularly, for an optical beam that originates from a distant monochromatic source with phase front distorted by a turbulent medium, the mathematical description of the phase front is provided by equation (1) below. 
       E ( x, y )·exp{− j·[k   x   x+k   y   y +θ( x, y )]}= A ·exp{− j[k   x   x+k   y   y]}+B ( x, y )·exp{− j·[k   x   x+k   y   y +φ( x, y )]}.  (1) 
     The expression after the equal sign is selected to distinguish the ideal (unperturbed) portion (first term) from a distorted portion (second term). The coefficients A, B(x, y) and E(x, y) are the corresponding amplitudes and can be selected to be positive and real. Since an ideal wavefront is virtually planar, the coefficient A is nearly independent of the variables x and y. The terms k x  and k y  are momentum vector components which contain angular information regarding the incoming wave. The term θ(x, y) is the distribution of the overall system phase distortion. The term φ(x, y) is an intermediate term describing the phase distortion of the distorted wavefront. 
     In order to correct the wavefront, the variables k x , k y  and θ(x, y) must be determined. These variables cannot be measured directly because a photodetector can only measure the intensity of a light source. However, as will be discussed in detail below, the configuration of optics system associated with the optical phase front measuring system in accordance with the present invention allows the variables k x , k y  and θ(x, y) to be determined. Once these variables are known, the phase profile of the entire wavefront can be determined as set forth below. 
     Referring the FIG. 1, the wavefront of a light beam, generally identified with the reference numeral  20 , may be visualized by an array of pixels, e.g. pixel  22 . Each of the pixels may be considered independent and may be encoded with intensity encoding and phase encoding. The intensity encoding is simply the square of the amplitude of the light beam for any given pixel. The phase encoding, unfortunately, cannot be measured directly since a photodetector can only measure intensity. As will be discussed in more detail below, the optical phase front measurement system is able to determine the system phase components k x , k y  and θ(x, y) utilizing the optics system illustrated in FIG.  2 . The system illustrated in FIG. 2, generally identified with the reference numeral  24 , relies on two relatively simple assumptions. First, in the Fourier representation as set forth in Equation (1) above, the pixel intensity contribution from the second term is much smaller than the peak of the first term for all of the pixels forming the beam  20 . The first assumption is a reasonable assumption because the random phase term, φ(x, y), effectively spreads out or dilutes the energy of the second term, even if the term B(x, y) is greater than A. The second assumption is that the term B(x, y) consists mainly of low spatial frequency components. Essentially, this assumes that the scintillation is induced primarily by the randomness of the term φ(x, y). This assumption is also reasonable since the phase front is much more susceptible to turbulence than the amplitude front. 
     Given the first and second assumptions, a system for measuring the phase distribution can be developed as set forth in below with a pair of lenses  30  and  34 , two cameras  32  and  33 , and a beam splitter  35 . In particular, it is known that the field of the light beam at the focal plane of a lens is the Fourier transform of the field in front of the lens, such as the lens  30  in FIG.  2 . Incorporating this fact with the first assumption indicates that the field exhibits a peak at the location &lt;k x , k y &gt;−λf/(2π), where λ is the wavelength and f is the focal length. With the beam splitter  35 , a camera  33  can sample the beam at the focal plane  28  to measure the relative peak intensity A and its location &lt;x p , y p &gt;. The variables &lt;k x , k y &gt; will be equal −2π&lt;x p , y p &gt;/(λf). As will be demonstrated below in connection with FIG. 3, with a more sophisticated set up, the cameras  32  and  33  may be replaced with just one camera. 
     The first assumption ensures that the coefficient A is very closely proportional to the peak intensity reading. Next, assuming the spatial light modulator  26  is placed at the focal plane  28  of the lenses  30  and  34 , with the Fourier transform of the beam by the first lens  30  is reversed by the second lens  34 . If all of the pixels produced by the SLM are in the same state, the output field is equivalent to the spatially flipped version of the input field. The intensity of this field as seen by camera  32  is given Equation (2). 
       I   1   =A   2   +B   2 (− x,−y )+2 A·B (− x,−y )·cos[φ(− x,−y )].   (2) 
     As is known in the art, the SLM  26  can provide a 90° phase shift to the pixel corresponding to the peak intensity or the A term. After the phase shift, the field is as described in terms of its quadrature components as shown in Equation (3) below. 
     
       
           j·A ·exp{ j·[k   x   x+k   y   y]}+B (− x,−y )·exp{ j·[k   x   x+k   y   y+φ ( x, y )]}.  (3) 
       
     
     The intensity of this field as seen by camera  32  is provided by Equation (4). 
     
       
           I   2   =A   2   +B (− x,−y ) 2 +2 A·B (− x,−y )·sin[φ(− x,−y )].   (4) 
       
     
     The first two terms can be removed by high pass filtering as set forth in the second assumption. The phase distribution θ(x, y) of the pixels  20  (FIG. 1) can then be determined from equation (5). 
     
       
         θ(− x,−y )=ATAN2 {B (− x,−y )·sin[φ( −x,−y )], A+B ( −x,−y )·cos[φ(− x,−y )]}=ATAN2{2 A·B (− x,−y )·sin[φ(− x,−y )],  
       
     
     
       
         2 A   2 +2 A·B (− x,−y )·cos[φ(− x,−y )]}=ATAN2[HP(I 2 ),2 A   2 +HP(I 1 )],  (5) 
       
     
     where HP denotes high pass filtering. 
     As mentioned above, the coefficient A is determined from the peak intensity in the focal plane while the variables k x  and k y  are determined from the location of the peak intensity. The variable θ(x, y) is determined as set forth in Equation (5). Knowing k x , k y  and θ(x, y) enables the entire phase front to be decoded in the accordance with Equation (1) from the two snapshots (I 1  and I 2 ). 
     The phase measurement system in accordance with the present invention may be implemented by the system is based upon the principles discussed above and illustrated in FIG. 2 which includes a pair of spaced apart lenses  30  and  34  and a spatial light modulator  26  disposed at the focal plane of those lenses. As mentioned above, the system also includes a beam splitter  35  as well as the camera  33  to measure the peak pixel intensity and location and the camera  32  to sample two quadrature signals that are used to compute or decode the phase front of the incoming light beam. Upon determining the variables k x , k y  and θ(x, y) from the measurements information, as detailed above, the phase front of the light beam  20  is then completely characterized. This phase front information can now be used in part of a closed loop feedback system (not part of the present invention) to provide phase compensation of the individual wavefront elements. 
     The lenses  30  and  34  may be two identical plano/convex lenses with the focal lengths chosen lenses to set the magnification to match the SLM pixel size. The spatial light modulator  26  may be a liquid crystal (LC) phase spatial light modulator, for example, a 512×512 small array analog LC SLM by Boulder Nonlinear Systems, Inc. The cameras  32  and  33  need to be of high frame rate and may be a DALSTAR CA-06 by Dalsa, which can sample at nearly 1 KHz. 
     A practical implementation of the phase measurement illustrated in FIG. 2 is shown in the box  36  illustrated in FIG.  3  and identified as a phase mapping analyzer. In particular, the phase mapping analyzer  36  includes a pair of lenses  38  and  40 , oriented such that their optical axis are generally perpendicular to one another. A reflective mirror  42  is disposed behind the lens  40  while a reflective spatial light modulator (SLM)  44  is positioned at the focal plane of lens  38 . The SLM  44  may be a phase SLM, for example, as discussed above, which includes a back plate reflector so that light transverses the phase shifting elements twice. Such a configuration reduces the amount of nonlinear phase shifting the individual element must introduce and thus reduces the response time. The configuration of the lens  38  and the reflective SLM  44  is equivalent to the pair of lenses  30  and  34  and non-reflective SLM  26 , illustrated in FIG. 2, if the output is separated from the input. Referring back to FIG. 3, the separation of the input and the output beams is accomplished by way of a λ/4-wave plate  46  and a polarizing beam splitter  48 . Traveling through the λ/4-wave plate  46  twice rotates the linearly polarized input beam by 90°, causing the return beam to be almost entirely reflected by the beam splitter  48  onto an analysis camera system  50 . A small portion of the input beam is sampled by the lens  40  and the mirror  42  and focused onto the same analysis camera system  50 . Here, the camera  50  takes the place of both cameras  32  and  33  in FIG. 2, and it may be of the DALSTAR CA-06 by Dalsa. Thus, in one snapshot, the Fourier peak location and intensity along with one intensity profile needed for calculating the phase profile can be determined. In order to increase the image quality, a laser line interference filter  52  may be utilized to attenuate background noise. 
     A practical application of the phase front measurement system  36  is illustrated in FIG.  3  and generally identified with the reference numeral  54 . The system  54  incorporates the phase measurement system  36  for both beam point stabilization and image construction to: (1) maximize the beam delivery of the laser onto a distant target and (2) compensate for phase distortion by turbulence. 
     The system  54  includes a beam delivery subsystem, generally identified with the reference numeral  56 . The beam delivery subsystem includes, a laser  58  such as a Helium-Neon, a VAG, or a semiconductor laser, as described in detail in “Laser Electronics,” Third Edition, Joseph T. Verdeyen, Prentice Hall, 1994, hereby incorporated by reference. The laser output beam  60  is directed to a totally reflective mirror  62  disposed, for example, at a 45° angle relative to the optical axis of the laser  58  to rotate the beam  60  at roughly 90° relative to the optical axis of the laser  58  and direct the beam  60  to a partial beam splitter  64 . The probe beam  66  from the partial beam splitter  64  is directed to a pair of spaced apart plano/convex lenses  68  and  70  to expand the beam to match the dimensions of a reflective SLM  70 . The expanded beam, identified with the reference numeral  72 , is directed through polarizing beam splitters  74 , a λ/4-wave plate  76  and is phase modulated by the phase SLM  70 . The SLM  70  induces the phase correction, as measured by the phase mapping analyzer  36 , onto the outgoing beam. It may be of the same type as SLM  44  by Boulder Nonlinear Systems, Inc. The phase SLM  70  is provided with a reflective plate to allow the beam to be reflected back to the λ/4-wave plate  76  with a 90° polarization rotation, The polarizing beam splitter  74  reflects the beam out to the target by way of another λ/4-wave plate  80  and a telescope beam expander  82 , formed from a pair of spaced apart lenses  84  and  86 . The output beam from the telescope beam expander  82  defines the outgoing probe beam  86 . 
     The probe beam  86  is directed to a distant target. Reflected signals from the target are received from the telescope beam expander  82  and are redirected to the λ/4-wave plate  80  resulting in another 90° polarization rotation which transmits the reflected beam through the polarized beam splitter  74  to the phase measurement device  36 . 
     Initially, all of the pixels in the SLM  70  are off. As the phase measurement device  36  maps out the phase front, the complement of the phase front is displayed in the SLM  70  to modulate the phase conjugate of the phase front onto the outgoing laser beam. This phase conjugation reverses the turbulence distortion, thus enhancing the beam delivery onto the target. This, in turn, increases the strength of the return signal, which, in turn, increases the accuracy of the phase mapping. Such positive feedback can converge very quickly and can significantly improve the system performance. 
     As mentioned above, the system illustrated in FIG. 3 also provides for image enhancement. In particular, a portion of the initial laser beam is reflected by the partial beam splitter  64  through an aperture λ/4-wave plate  90  to form an illumination beam  92 . The wave plate  90  is configured such that the polarization of the illumination beam  92  is orthogonal to that of the probe beam  86 . The reflected illumination beam is collected by the telescope  82  and travels through the wave plate  80  and is reflected by the partial beam splitter  74  to the SLM  70 . Here, the SLM  70  undoes the phase front distortion and, with the help of the wave plate  76 , reflects these signals onto an imaging camera  94  by way of a partial beam splitter  64  and a lens  96 . The camera  94  may be of the same type of camera  50 , the DALSTAR CA-06 by Dalsa. However, because speed is not critical for the camera  94 , it can be replaced with a less costly commercial camera. The aperture  88  is used to minimize the amount of light onto the camera that has not arrived through telescope  82 . The illumination beam  92  is not expanded by a telescope  82 ; thus it has a much larger divergence than the outgoing probe beam  86  and is of larger in area at a far distance. In essence, the probe beam  86  seeks out the brightest spot and uses it as a guide start to map out the aberration front while the illumination beam  92  lights the scenery for the imaging camera  94 . 
     In accordance with the present invention, a numerical reconstruction of the phase front is computationally simple and can be accomplished in real time with a relatively fast PC, for example, a Pentium II or better system. The system in accordance with the present invention is relatively light and compact and can be built using commercially available off-the-shelf parts. 
     Obviously, many modification and variations of the present invention are possible in light of the above teachings. For example, thus, it is to be understood that, within the scope of the appended claims, the invention may be practiced otherwise than as specifically described above.