Abstract:
Apparatus and method for measuring wavefront slope and irradiance of direct and/or reflected light beams at a plurality of points to enable calculation of optical wave front distortions. A plurality of sub-beams or groups of sub-beams is created and controlled using at least one electronically-controlled Active Light Modulation Device (“ALMD”).

Description:
FIELD OF THE INVENTION  
       [0001]     The present invention relates to wavefront distortion analysis and constitutes an improvement of known Schack-Hartmann analyzer/sensors that are used to analyze wavefront distortion/variation.  
       BACKGROUND OF THE INVENTION  
       [0002]     The Shack-Hartmann sensor (or “SHS”) was first developed by Ben Platt and Roland Shack in 1970 as part of a classified U.S. Air Force laser project and has since seen widespread use in the measurement of wavefront aberrations in a variety of optical systems in fields ranging from astronomy to opthalmics. The SHS analyzes a wavefront transmitted by, or scattered from, an object of interest by dissecting the wavefront into a large number of subfronts using an array of microscopic lenses. The object of interest is frequently a component or components of an optical system having selected and pre-defined optical properties.  
         [0003]     In the conventional SHS the array comprises micro-lenses or lenslets disposed in the same plane, such that their center points define a square lattice, with each micro-lens acting as a small aperture. A perfect plane wave incident along the optic axis of such an array will generate a square array of points of equal intensity in the back-focal-plane, each point originating from one of the micro-lenses. Any variance in the wavefront will cause a deflection of one or more points of the square lattice, giving rise to a streak of intensity in the back focal plane originating at the discrete point produced by a plane wave. It is well known in the art that, from measurements the displacement of the points of the square lattice, the wavefront slope across each sub-aperture can be determined and thus the optical properties of the object or system of interest derived. A wavefront sensor using a lenslet array is described in U.S. Pat. No. 6,396,588 to Sei. Various types of apparatus for the measurement and mapping of optical components using lenslet arrays are described in U.S. Pat. Nos. 4,725,138 to Wirth et al., U.S. Pat. No. 5,083,015 to Witthoft et al., and U.S. Pat. No. 5,825,476 to Abitol et al.  
         [0004]     An SHS utilizing an array of equal-sized microscopic lenses pre-fabricated from a transparent material as a single component will have fixed optical properties—e.g., back focal plane, numerical aperture—which places limits on existing technology.  
         [0005]     First, if the variance in wavefront slope across a lenslet in a fixed array increases above a certain value, individual wavefronts from different micro-lenses will overlap in the back focal plane, leading to a loss of all useful information. For a fixed lenslet array this problem cannot be overcome by expanding the wavefront, since the sampling density will be correspondingly decreased. Simply put, sensitivity (the smallest wavefront variation that can be detected) and dynamic range (the range of wavefront variation that can be detected) cannot be decoupled for a fixed lenslet array. The potential for overlap is one of the most commonly known shortfalls of SHS technology.  
         [0006]     Second, in a conventional SHS, the size of the micro-lenses—around 144 μm in diameter, on average—places an upper limit on the spatial sampling frequency of the SHS. Even the best commercially available SHS systems manufactured by Zeiss and WaveFront Sciences have a spatial resolution of only 210 μm. With a resolution of 210 μm, direct data acquisition from a 10 mm diameter area will produce a total of only 3680 data points, allowing for about 60% area coverage due to effects of the lens size and spacing. (The limited fill factor and optical losses of a conventional fixed lenslet array imposing a further limit on the accuracy of the wavefront sensing.)  
         [0007]     Third, the micro lenses that are used in conventional SHSs have fixed focal distances and spacings that allow for a only a limited dynamic range. As discussed above, any attempt to increase the dynamic range of a fixed lenslet array will inevitably be offset by a loss in its sensitivity.  
       SUMMARY OF THE INVENTION  
       [0008]     The present invention replaces the fixed lenslet array of a conventional SHS with one or more computer-controlled reflective or refractive active light modulation devices (“ALMDs”) that dissect the wavefront formed by passage through or scattering from an object of interest. By so doing, dynamic range and sensitivity may be dramatically increased over conventional devices and methods, thereby allowing faster and more precise wavefront profiling/analysis. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0009]      FIG. 1  shows a conventional SHS using a fixed lenslet array.  
         [0010]      FIG. 2  shows a modified wavefront sensor using an ALMD instead of a lenslet array.  
         [0011]      FIG. 3  shows an ALMD used to expand a wavefront.  
         [0012]      FIG. 4  shows an ALMD used to contract a wavefront.  
         [0013]      FIG. 5  shows multiple ALMDs being used to analyze a large area wavefront.  
         [0014]      FIG. 6  shows two ALMDs used to further dissect and direct subfronts from a large wavefront.  
         [0015]      FIG. 7  shows further processing of the elementary wavefront using smaller mirrors.  
         [0016]      FIG. 8  shows a pattern for a progressive power contact lens with three zones.  
         [0017]      FIG. 9  shows active wavefront corrections using two or more ALMDs.  
         [0018]      FIG. 10  shows the implementation of closed feedback control of an ALMD wavefront sensor.  
         [0019]      FIG. 11  shows a schematic from which the theoretical sensitivity and dynamic range of an ALMD wavefront sensor may be calculated.  
         [0020]      FIG. 12  show a method for performing three-dimensional surface reconstruction. 
     
    
     DETAILED DESCRIPTION  
       [0021]      FIG. 1  is a schematic of a conventional SHS. A wavefront  100  created by light source  10  and a condenser lens or lens system  11  is distorted by an optical or other element  12  and dissected by a lenslet array  13  into plurality of sub fronts  17  that are focused onto a photo sensor  14 . The signal from photo sensor  14  is processed by the processor  15  and sent to personal computer  16  for final data analysis and wavefront reconstruction.  
         [0022]     An embodiment of the invention is shown in the schematic of  FIG. 2 . A single ALMD  23  having reflective elements  28  is used in place of the conventional lenslet array of  FIG. 1 . (Such reflective ALMDs are commercially available from Texas Instruments (DMD), Silicon Light Machines, Corning, Agere Systems, Hitachi, Mitsubishi, Daewoo.) A wavefront or wavefront portion  100  created by light source  10  and a condenser lens or lens system  11  is distorted by an optical or other element  12  and then reflected by individual reflective elements  28  of an ALMD  23  creating a plurality of individual wave fronts  29 . The operation of ALMDs is described in U.S. Pat. No. 4,680,579 to Ott et al., and U.S. Pat. No. 4,954,789 to Sampsell. Subfronts  29  then pass through an optional imaging lens  24  and are projected onto a photosensitive device  25 , which generates a signal that is transmitted to personal computer  27  via a signal processor  26 . Photo sensor  25  may be a charge coupled device (“CCD”), a complimentary metal oxide silicon (“CMOS”) device, a position sensitive diode array (“PSD”), a p-type-doping, insulator, n-type doping (“PIN”), or other suitable detector. (Light sensitive devices such of the CCD, CMOS, PSD, PIN, etc., types are available from a variety of manufacturers, including Sony, Kodak, Panasonic, Pulnix, Dalsa, and others.). Processor  26  may be a commercially available image processing board. The central processing unit of personal computer  27  may be programmed to determine the intensity/optical flux of each subfront  29  from the processed detector ouput and to apply wavefront reconstruction methods that are well known in the art to reconstruct the wavefront.  
         [0023]     The reflective elements  28  of ALMD  23  may be steerable planar mirrors. By way of example, a typical ALMD device currently offered by Texas Instruments (see, e.g., Product Preview Data Sheet TI DN 2505686 REV C, DMD 0.7 XGA 12° DDR DMD Discovery, August 2004) has aluminium mirrors offset by 45° from the ALMD surface plane and tiltable between extrema at ±15° at a frequency of 40 kHz. In such a computer-controllable ALMD, the planar reflective elements  28  may be switched between a series of predetermined or programmed positions to define wavefront dissection patterns, which may dissect, expand and/or contract the wavefront portion that is incident on the ALMD. The switching movement of reflective elements  28  may be angular or linear. On the other hand, rather than being planar, reflective elements  28  may be parabolic or other shaped. Furthermore, reflective ALMD  23  be substituted by an ALMD having switchable refractive elements, such as prisms, or switchable transmissive elements, such as translucent windows or apertures having micro-mechanical shutters or translucent windows whose optical transmissivity may be switched electronically. Various light modulating devices are described in U.S. Pat. No. 5,311,360 to Bloom et al., U.S. Pat. No. 4,954,789 to Sampsell and U.S. Pat. No. 4,680,579 to Ott.  
         [0024]     The central processing unit of personal computer  27  may be programmed to derive the wavefront distortion from the output of photodetector/photosensor  25  using standard wavefront reconstruction techniques (see, e.g., U.S. Pat. No. 5,479,257 to Hashimoto) and control the dissection of wavefront  100  using a commercial graphics package to generate wavefront dissection patterns and a standard driver to control ALMD  23  (available from the manufacturer).  
         [0025]     In view of the rapid response time of ALMDs and the capacity to independently and controllably switch their reflective or other optical elements (currently available ALMDs manufactured by Texas Instruments may be switched at a rate of 40 kHz), such closed loop feedback allows real-time changes to be made in the size and placement of subfronts  29  on photodetector  25  by changing which reflective elements  28  contribute to each subfront  29 . Accordingly, overlap of subfronts  29  on photodetector  25  may be eliminated and an optimum number and distribution of subfronts, and thus data points, generated for any given wavefront or wavefront portion. Datapoints corresponding to a all or some of subfronts  29  may be acquired sequentially. Such sequential data acquisition may be used to minimize statistical sampling errors in wavefront portions having greater wavefront variance. Furthermore, different dissection patterns may be used to reconstruct the same wavefront or wavefront portion and the accuracy of the reconstruction checked by comparing the reconstructions obtained using the different dissection patterns.  
         [0026]     Furthermore, since the wavefront analysis and dissection may be performed in real time, a closed feedback loop may be implemented, as shown in  FIG. 10 . With reference to the components shown schematically in  FIG. 2 , the method of  FIG. 10  may comprise steps  121 - 129 . Step  121  involves generating an image dissection pattern (the initial pattern may be generated using any commercial graphics package running on personal computer  27 ). Step  122  involves transmitting a signal to ALMD  23  (this may be done using an analog or digital ALMD driver running on personal computer  27 ). Step  123  involves aligning reflective elements  28  to dissect wavefront  100  into subfronts  29 . Step  124  involves collecting data from subfronts  29  using photodetector  25 . Step  125  involves processing the output of photodetector  25  using processor  26  (this may be done using an image processor board to produce an image frame). Step  126  involves reconstructing the wavefront or wavefront portion  100  (this may be done by analyzing the image frame using the programmed central processing unit of personal computer  27 ). Step  127  involves determining whether more information about the reconstructed wavefront or wavefront portion is required (this may involve using the programmed central processing unit of personal computer  27  to compare wavefront reconstructions obtained using different dissection patterns, e.g., with square of circular symmetry, to determine whether the reconstructed wavefront is properly independent of the pattern, as discussed above, or consist of comparing the spatial data point density/sensitivity/dynamic range or other metric to some pre-determined threshold value or values). If more data is required, according to step  128 , the image dissection pattern is modified accordingly (e.g., portions of the reconstructed wavefront may require an increase or decrease in detector sensitivity of dynamic range). Step  122 , transmitting a signal to the ALMD, through step  127 , determining whether further wavefront reconstruction is required, are then repeated in a closed loop until a satisfactory wavefront reconstruction is obtained at which point the reconstructed wavefront is output at step  129 .  
         [0027]     Accordingly, because the number and position of the subfronts may be optimized in real time enabling different dissection patterns to be applied in parallel or in series, and because the fraction of the wavefront  100  sampled by ALMD  23  is greater than the fraction sampled by a conventional fixed lenslet array, and because reflective ALMDs are optically more efficient than conventional lenslets, a tremendous increase in speed, resolution and dynamic range is realized over conventional SHS devices that use fixed arrays.  
         [0028]     In different embodiments, wavefront or wavefront portion  100  may be generated by passing a reference wavefront through an optical component of interest or by scattering a reference wavefront from a surface of interest. The reference wavefront may be plane wave or may be constructed in accordance with the anticipated optical properties or shape of the object or surface of interest.  
         [0029]     In another embodiment, one or more ALMDs may be used to expand the wavefront to increase system dynamic range and avoid the overlap of individual sub fronts. Such expansion is particularly useful when dealing with very small area wavefronts, which must be magnified in order to acquire a sufficient number of data points. Wavefront expansion is also helpful for analyzing highly convergent wavefronts, where data acquisition is only available near the focal plane.  
         [0030]     The schematic of  FIG. 3  shows the use of an ALMD to expand a wavefront. Such wavefront expansion being desirable in applications such as opthamology where the diameter of the wavefront of interest may typically be only about 6 mm. As shown in  FIG. 3 , incident wavefront  300  is reflected off ALMD  32  using a plurality of two dimensional tilting mirrors  38 , where each mirror may be individually computer-controlled to tilt to a predetermined angle, enabling sub fronts  39  to be expanded and placed in a controlled manner on projection lens  34  and focused on sensor  35 . One or more partial or full reflectors/transmitters  33  may also be used to amplify or filter the expansion affected by ALMD  32 . Alternatively, the quantity, location and size of elementary sub fronts  39  arriving at photosensor  35  may be optimized using a second computer-controlled ALMD in place of the reflector/transmitter  33 . As in  FIG. 2 , computer-controlled closed loop feedback between ALMD  32  (and any ALMDs used in place of transmitter/reflector  33 ) and photosensor  35  may be used for real-time optimization of the size and placement of subfronts  39 .  
         [0031]     In another embodiment, an ALMD may be used to contract the wavefront to increase system dynamic range and avoid overlapping of the individual sub fronts. Such contraction being particularly useful for the very large in cross-section wavefront, where de-magnification is needed in order to acquire significant amount of data points. Wavefront contraction is helpful when analyzing highly diverging wavefronts, where data acquisition is only available from small fraction of the wavefront.  
         [0032]      FIG. 4  shows the use of an ALMD to contract a wavefront. Incident wavefront  41  is reflected off ALMD  42  by a plurality of two dimensional tilting mirrors  48 , where each mirror may be controlled individually and tilted at a predetermined angle to direct sub fronts  49  towards projection lens  44  that in turn focuses subfronts  49  onto sensor  45 . As further shown in  FIG. 4 , partial or full additional reflectors/transmitters  43  may be used to amplify or filter the contraction effect. Alternatively, the quantity, location and size of elementary sub fronts  49  arriving at photosensor  45  may be optimized using a second computer-controlled ALMD in place of the of the reflector/transmitter  43 . As in  FIG. 2 , computer-controlled closed loop feedback between ALMD  42  (and any ALMDs used in place of transmitter/reflector  43 ) and photosensor  45  may be used for real-time optimization of the size and placement of subfronts  49 .  
         [0033]     In yet another embodiment, a large wavefront may be processed with multiple ALMDs operating in parallel, as shown schematically in the  FIG. 5 . Large wavefront  51  is reflected off two parallel ALMDs  52 , each having a plurality of two dimensional tilting mirrors  58 , where each mirror may be controlled individually and tilted at predetermined angle, allowing sub fronts  59  to be directed onto projection lenses  54  and in turn focused onto sensors  55 . As further shown in  FIG. 5 , partial or full additional reflectors transmitters  53  may be used to amplify or filter the expansion of the wavefront. Alternatively, the quantity, location and size of elementary sub fronts  59  arriving at photosensor  34  may be optimized using one or more ALMDs in addition to ALMDs  52 , as explained below with reference to  FIG. 6 . As in  FIG. 2 , computer-controlled closed loop feedback between ALMD  52  (and any ALMDs used in place of transmitter/reflector  53 ) and photosensor  55  may be used for real-time optimization of the size and placement of subfronts  59 .  
         [0034]     In another, embodiment, two ALMDs may be used in series for the further dissection and direction of subfronts. As shown in  FIG. 6 , wavefront  61  is first dissected using ALMD  62  into subfronts  68  and then directed onto second ALMD  63 , which spreads sub-beams  67  even further apart. Correlation of the control of ALMD  62  and ALMD  63  allows for further filtering and secondary dissection of the sub-wavefront by employing different size mirrors or elements,  68  and  66 , as shown and discussed with regard to  FIG. 7 . ALMD  63  may thus be used to further expand sub fronts  67  with respect to subfronts  69  as generated by the first element to dissect the wavefront, ALMD  62 . A system of multiple sequential and non-sequential projection lenses  64  may also be used to direct the wavefront onto sensor element  65 . Using sequential ALMDs and sequential projection lenses, desired subfront separation and sizes may be obtained.  
         [0035]     The use of sequential ALMDs having different sized reflective elements is shown schematically in  FIG. 7 . Part of elementary wavefront  71  is first reflected by mirror element  72  of a first ALMD into subfronts  78  (only one of which is shown) and each subfront  78  is further dissected by reflection from multiple smaller mirror element  73  of a second ALMD to produce multiple subfronts  79 . The subfronts  79  are then focused by a system of multiple sequential and non-sequential lenses  74  (only one of which is shown schematically) onto a photo-detector  75 . Such two or more stage dissection of a wavefront may be used to produce large numbers of data points for the precise analysis of minor wavefront distortions.  
         [0036]     In many instances, the wavefront distortion produced by an object may vary in a desired and specific manner, such as the distortions produced by cylindrical, toric or progressive focal lenses. Using a computer-controlled ALMD, dissection of the wavefront produced by such objects can be performed following a specific pattern to increase or decrease the spatial density of data points for specific regions. A predefined pattern or sequence of patterns may be used that varies data point density in a controlled manner across the regions of interest. This capability is particularly important when analyzing non-linear and complex optical elements. See, e.g., U.S. Pat. No. 5,825,476 to Abitol.  
         [0037]     An example of such a defined pattern for analyzing a progressive power contact lens having three zones of different optical powers is shown in  FIG. 8 . Wavefront  80  is formed by a lens  81  having three zones  82  with different optical powers. The dissecting element  83 —constituting a sensor with one or more computer-controlled ALMDs having refractive and/or reflective optical sub-elements for dividing wavefront  80  into subfronts—may be configured such that the spatial density of the data points sampled from the wavefront  80  varies across optical zones  82 , as shown by pattern  84 .  
         [0038]     In another embodiment, active wavefront corrections may be performed using two or more ALMDs, where one or more ALMDs are used as wavefront dissecting devices and one or more ALMDs as wavefront forming (modulating) devices. As shown in  FIG. 9 , wavefront  90  is generated by light source  91  and processed by lens  92 . After reflection off ALMD  93 , having reflective elements  913 , wavefront  90  propagates through a beam splitter  94  and a small fraction of wavefront  90  is directed onto ALMD  96  having reflective elements  916  via telescopic lens  95 . Dissected subfronts  918  are then reflected onto light sensitive device  97  (a CCD, CMOS, PSD, etc.) through projection lens  917  and the resulting signal processed by personal computer  98 . Personal computer  98 , either directly or through a network, controls wavefront forming ALMD  93 , enabling active correction to take place. In such a manner, a wavefront generator with closed loop feedback may be created.  
         [0039]     Without intending to be bound by any particular theory of operation, Appendix A, with reference to  FIGS. 11 and 12 , provides what is believed to be the theoretical performance parameters of the inventive method and system which shows significant improvement over conventional systems. A typical system implemented using commercially available components has a sensitivity of 0.53 nm and a dynamic range of 560 nm, with the possibility of sub-Angstrom sensitivity without significant sacrifice to dynamic range.  
         [0040]     In another embodiment, the ALMD sensor may be used for three dimensional surface reconstruction by dissecting a wavefront reflected off a surface and then rebuilding the surface by elementary unit reconstruction. Surface reconstruction performed in such a manner being highly accurate and deterministic. The surface is illuminated by an incoming plane wave or by an incoming wave of a predetermined shape, i.e., carrying an image. Illuminating a surface with pre-imaged light can be particularly beneficial when surface is to be compared to a known dimension or profile.  
         [0041]     An elementary wavefront is reflected from the elementary surface element S i  with deflection in X, and Y axis which will determine location of the light streak on the imaging plane. Deflection angles, α i , can be computed as shown in  FIG. 11 . Using the small angle approximation (that angles measured in radians are equal to their tangents) the elementary height difference “h i ” between datum plane and next elementary sector may be derived. The “h” elements located across i-amount of columns and k-amount of rows will fully characterize the surface with a spatial resolution, corresponding to the side length of unit equal to elementary wavefront section “S.” As set forth in Appendix A, the dimensions of a unit cube for reconstructing a surface may be as small as 15 μm.  
         [0042]     In summary, the ALMD-based wave front sensor described herein with expanded range and dissection flexibility will be particularly useful in those fields where wave front analysis is already used. For example, in ophthalmics the inventive method and device may be used for analysis of the corneal surface of the human eye where system sensitivity can be set at different levels in different areas. The invention is particularly well-suited to the diagnosis and treatment of human eyesight because of its rapidity, flexibility, low energy losses and high flexibility compared to present systems. Other areas of application include astronomy, large optics, in the semiconductor industry and any optical task where very large or very small objects needed to be analyzed with high data fidelity and a large amount of data.  
         [0043]     The foregoing discussion merely illustrates the principles of the invention. Various modifications and alterations to the described embodiments will be apparent to those skilled in the art in view of the teachings herein.  
       APPENDIX A  
       [0044]     The theoretical sensitivity and dynamic range of the device described in this invention can be evaluated with reference to  FIG. 11 . Let the minimum resolution of the imaging sensor be d c ; then, the minimum angle of a single ALMD element detectable by the sensor is  
         α   =       d   c       4   ⁢   F         ,       
 
 where F is the focal length of the relay lens. Given a resolution of the ALMD sensor of d A , the smallest resolved optical path difference between adjacent elements of the wavefront is  
       δ   =       d   A     ⁢         d   c       4   ⁢   F       .           
 
         [0045]     The dynamic range may be determined by assuming the maximum distance between the spots at the sensor is of the order of typical sensor size, i.e., d c =D sensor ˜15 μm.  
         [0046]     Thus, taking commercially available systems, we have: d A  =14 μm, d c =15 μm, F=100 mm. Thus, system sensitivity δ=0.53 nm. Further increase of the focal length of the lens and detection resolution can easily bring this number to a sub-angstrom level without sacrificing the dynamic range. For the layout above, the dynamic range of the system is ˜560 nm (˜2° wavefront slope error maximum).  
         [0047]     The theoretically maximum dynamic range of 45 degrees (d A  =λ) makes 4F=D sensor . For a typical sensor with D sensor =15 mm, and dc=15 μm, the upper limit on sensitivity becomes then ˜28 nm.  
         [0048]     The relay lens could be re-positioned to magnify the ALMD elements and provide for larger sensitivity. This increase will come, however, at the expense of reduction of the system dynamic range.  
         [0049]     The reconstruction of surface topography, with reference to  FIG. 12 , may be understood according to the following relations:  
         α   i     =       tan     -   1       ⁡     (     N     L   +   l       )           
         h   ix     =         S   ix     ⁢   tan   ⁢           ⁢     α   ix       =       S   ix     ⁢     α   ix             
         h   iy     =         S   iy     ⁢   tan   ⁢           ⁢     α   iy       =       S   iy     ⁢     α   iy             
         h   i     =       1   2     ⁢     (         S   ix     ⁢     α   ix       +       S   iy     ⁢     α   iy         )           
         h   i   k     =         ∑     i   =   0     k     ⁢     h   i       =       1   2     ⁢       ∑     i   =   1     K     ⁢     (         S   ix     ⁢     α   ix       +       S   iy     ⁢     α   iy         )