Abstract:
Embodiments of the present invention provide method and apparatus for measuring a wavefront of a beam of radiation. In particular, one embodiment of the present invention is an apparatus for measuring a wavefront of a beam of radiation at a first plane which includes: (a) relay optics adapted to relay the wavefront from the first plane to a second plane; (b) a moving boundary locus apparatus disposed between the first and second planes; (c) a two-dimensional photodetector array comprising—at least 4×4 photodetector elements disposed in the second plane, wherein each photodetector element produces a time varying signal in response to movement of a portion of the moving boundary locus apparatus; (d) a synchronizer adapted to synchronize each of the time varying signals with a position of the portion of the moving boundary locus apparatus; and (e) an analyzer, responsive to synchronized time varying signals output from the synchronizer, to measure the wavefront of the beam.

Description:
TECHNICAL FIELD OF THE INVENTION 
     The present invention pertains to method and apparatus for measuring a wavefront of a beam of radiation. In particular, the present invention pertains to method and apparatus for measuring a wavefront of a beam of radiation having a large slope variation for use in applications including, but not limited to, characterization of optical quality of optical elements and systems, and diagnosis of eye function. 
     BACKGROUND OF THE INVENTION 
     As is well known, a wavefront sensor provides comprehensive measurements relating to a wavefront of a beam of radiation, and can therefore be used to characterize the optical quality of optical elements and systems. Traditionally, such wavefront sensors include an interferometer and, recently, much use has been made of a “Hartmann-Shack” sensor. 
     An interferometer-based wavefront sensor requires a high quality reference beam having substantial coherence length and sub-wavelength stability. A Hartmann-Shack-based wavefront sensor is preferred over the interferometer-based wavefront sensor because: (a) the Hartmann-Shack-based wavefront sensor does not require a reference beam; and (b) it is easier to use outside of a laboratory environment. As is well known, the Hartmann-Shack-based wavefront sensor comprises a lenslet array disposed in front of a CCD camera, and it measures the tilt distribution of ray bundles associated with the wavefront to be measured. A perceived advantage of the Hartmann-Shack-based wavefront sensor is its simplicity and reliability. Among the key parameters which are involved in using a Hartmann-Shack-based wavefront sensor are: (a) sensitivity to resolve minimum wavefront tilt; (b) dynamic range to cover the maximum wavefront tilt; (c) spatial resolution; and (d) sampling time. 
     The Hartmann-Shack-based wavefront sensor has been used for adaptive optics applications in astronomy. In such applications, a short sampling time (for example, less than 30 ms) is desirable to follow fluctuations caused by air turbulence, and small dynamic ranges (for example, less than 1 mR) are sufficient. However, for other types of applications, much larger dynamic ranges are required, while relatively longer sampling times can be acceptable. One example of such other applications is a comprehensive measurement of eye aberration errors useful for eye diagnosis. In particular, wavefront measurement data can be used to guide photorefractive surgery to achieve optimal results from surgery. In such an application, a wavefront measurement apparatus is expected to measure a wavefront over a dynamic range of ±60 mR with a tilt resolution of 0.1 mR. Such a dynamic range is well beyond the results obtainable from current Hartmann-Shack-based wavefront sensors. 
     As one can readily appreciate from the above, a need exists in the art for method and apparatus for measuring a wavefront over a wide dynamic range, and with small tilt resolution. 
     SUMMARY OF THE INVENTION 
     Embodiments of the present invention advantageously satisfy the above-identified need in the art, and provide method and apparatus for measuring a wavefront over a wide dynamic range, and with small tilt resolution. 
     Specifically, one embodiment of the present invention is an apparatus for measuring a wavefront of a beam of radiation at a plane which comprises: (a) a moving boundary locus apparatus disposed before the plane; (b) a two-dimensional photodetector array comprising a plurality of photodetector elements disposed in the plane, wherein each photodetector element produces a time varying signal in response to movement of a portion of the moving boundary locus apparatus; (c) a synchronizer adapted to synchronize each of the time varying signals with a position of the portion of the moving boundary locus apparatus; and (d) an analyzer, responsive to synchronized time varying signals output from the synchronizer, to measure the wavefront of the beam. 
    
    
     BRIEF DESCRIPTION OF THE FIGURES 
     FIG. 1 shows a block diagram of a wavefront measurement apparatus that is fabricated in accordance with one embodiment of the present invention; 
     FIG. 2 shows a block diagram of a moving boundary locus apparatus in the prior art that is used to fabricate a preferred embodiment of the present invention; 
     FIG. 3 shows a block diagram of a prior art wavefront measurement apparatus using a Hartmann-Shack sensor; 
     FIGS. 4A-4D illustrate wavefront measurements made with a prior art Hartmann-Shack sensor for: (a) a flat wavefront, (b) a converging wavefront, (c) a diverging wavefront, and (d) a flat-converging wavefront, respectively; 
     FIGS. 5A-5E illustrate wavefront measurements made with an embodiment of the present invention for: (a) a flat wavefront, (b) a converging wavefront, (c) a diverging wavefront; (d) a flat-converging wavefront, and, (e) a flat-diverging wavefront, respectively; and 
     FIG. 6 shows a block diagram of an embodiment of the present invention for use in measuring eye aberration. 
    
    
     DETAILED DESCRIPTION 
     FIG. 1 shows a block diagram of wavefront measurement apparatus  100  that is fabricated in accordance with the present invention. As shown in FIG. 1, wavefront measurement apparatus  100  comprises relay optics assembly  40  and wavefront sensing assembly  150 . 
     As further shown in FIG. 1, relay optic assembly  40  comprises lens systems  40   a  and  40   b , which lens systems  40   a  and  40   b  may each comprise one or more lenses. Wavefront sensing assembly  150  comprises two-dimensional photodetector array  50 , moving boundary locus apparatus  60 , synchronizer  70 , and analyzer  80 . 
     As shown in FIG. 1, radiation beam  10  impinges upon wavefront measurement apparatus  100 , and wavefront  11  of beam of radiation  10  is to be measured at plane P. Relay optics assembly  40  relays wavefront  11  to plane P′, which plane P′ is conjugate to plane P. As is well known to those of ordinary skill in the art, wavefront  12  at plane P′ is identical to wavefront  11  at plane P up to a predetermined scale factor when lens systems  40   a  and  40   b  are arranged in a confocal configuration. 
     In accordance with the embodiment of the present invention shown in FIG. 1, two-dimensional photodetector array  50  comprises a matrix of photodetector elements which is disposed in plane P′ to receive radiation from beam  10 . In accordance with this embodiment, each photodetector element receives a beam segment from beam  10 , and thereby wavefront  12  is divided into wavefront segments. As is well known to those of ordinary skill in the art, wavefront  12  at plane P′ can be measured if each wavefront segment is measured accurately. 
     It should be clear to those of ordinary skill in the art that relay optics assembly  40  provides for convenient use of apparatus  100 , but that relay optics assembly  40  is not a necessary part of each embodiment of the present invention. For example, when apparatus  100  is used where there is a substantial amount of working space in front of plane P, measurements can be made directly at plane P, i.e., two-dimensional photodetector array  50  may be disposed at plane P. 
     As is well known to those of ordinary skill in the art, each beam segment of wavefront  12  can be associated with a ray bundle. Further, in accordance with this embodiment of the present invention, the average tilt of the ray bundle is taken to be perpendicular to the mean slope of the wavefront segment of the corresponding beam segment. The average tilt of the ray bundle can be determined using centroid positions of the two ends of the ray bundle. In accordance with this embodiment of the present invention, one end of each ray bundle is determined by the centroid position of a photodetector element in photodetector array  50 , and the other end of each ray bundle is determined by moving boundary locus apparatus  60 . This is contrasted with a Hartmann-Shack wavefront sensor where one end of each ray bundle is determined by a lenslet element in a lenslet array, and the other end of each ray bundle is determined by a CCD camera. 
     Moving boundary locus apparatus  60  is fabricated in accordance with a teaching regarding a moving boundary locus apparatus that is disclosed in U.S. Pat. No. 4,180,325 (&#39;325 patent), which &#39;325 patent is incorporated by reference herein. The &#39;325 patent teaches how such a moving boundary locus apparatus can be used, together with an edge detector and a synchronizer, to determine a centroid of a ray bundle falling onto a photodetector element of photodetector array  50 . As shown in FIG. 1, motor  61  rotates moving boundary locus apparatus  60 , and edge detector  62  (in accordance with the teaching of the &#39;325 patent) monitors an angular position of moving boundary locus apparatus  60 . FIG. 2 shows one embodiment of moving boundary locus apparatus  60  that is fabricated in accordance with the teaching of the &#39;325 patent. Many other embodiments of moving boundary locus apparatus  60  may be fabricated by those of ordinary skill in the art in accordance with the teaching of the &#39;325 patent. 
     In accordance with this embodiment of the present invention, output from each photodetector element of photodetector array  50  is applied as input to an independent amplifier. As moving boundary locus apparatus  60  moves (for example, rotates for the embodiment shown in FIG.  2 ), each photodetector element produces a time varying signal, which time varying signal is synchronized with a spatial position (for example, the angular position for the embodiment shown in FIG. 2) of moving boundary locus apparatus  60  by edge detector  62  and synchronizer  70 . The synchronized time varying signals output from synchronizer  70  are applied as input to analyzer  80  (for example, a computer such as a personal computer). Using timing signatures of the synchronized time varying signals, analyzer  80  calculates a centroid position of one end of ray bundles falling onto corresponding photodetector elements in accordance with the teaching of the &#39;325 patent. Embodiments of synchronizer  70  are fabricated in accordance with the teachings of the &#39;325 patent. 
     In accordance with this embodiment of the present invention, each photodetector element receives a beam segment, and thus defines the other end of a ray bundle falling onto the photodetector element. For example, the x, y, z position of a centroid of the photodetector element determines one end of the ray bundle. In a preferred embodiment of the present invention, each photodetector element of two-dimensional photodetector array  50  is about 1×1 mm, and such a photodetector array is, for example, commercially available from Hamamatsu of Japan. Then, analyzer  80  determines the slope of each beam segment using the coordinates of the two ends of each ray bundle. 
     Finally, in one embodiment, analyzer  80  uses any one of a number of methods that are well known to those of ordinary skill in the art to use the slopes of the beam segments to reconstruct the wavefront of beam  10  at plane P′. For example, in one such embodiment, analyzer  80  fits the slopes of the beam segments to a set of Zernike polynomials to reconstruct the wavefront in accordance with the teaching of an article entitled “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor” by J. Liang et al.,  J. Opt. Soc. Am. A , Vol. 11, No. 7, July 1994, pp. 1949-1957 (the “Liang article”), which Liang article is incorporated by reference herein. The wavefront of beam  10  is then reconstructed at plane P via a scale factor determined by the relay optics. In accordance with this embodiment of the present invention, photodetector array  50  has at least 4×4 photodetector elements in order to fit coefficients of the first 16 Zernike polynomials. However, a larger array, for example and without limitation, a 10×10 array, is preferred to achieve better spatial resolution and higher accuracy. 
     FIG. 3 shows a block diagram of a prior art wavefront measurement apparatus using a Hartmann-Shack sensor. A comprehensive review of the Hartmann-Shack wavefront sensor, and wavefront reconstruction is found in U.S. Pat. No. 5,777,719. As shown in FIG. 3, prior art wavefront sensor  200  comprises relay optics assembly  240  (includes lens systems  240   a  and  240   b ) and Hartmann-Shack sensor  250  (includes lenslet array  251  disposed in front of CCD camera  252 ). 
     As shown in FIG. 3, radiation beam  210  impinges upon wavefront sensor  200 , and wavefront  211  of beam of radiation  210  is to be measured at plane P. Relay optics assembly  240  relays wavefront  211  to plane P′, which plane P′ is conjugate to plane P. As further shown in FIG. 3, lenslet array  251  is disposed in plane P′ and CCD camera  252  is located in the focal plane of lenslet array  251 . As is well known, lenslet array  251  divides a beam of radiation onto an array of beam segments, and focuses each beam segment onto CCD camera  252  (each lenslet element is related to a beam segment and to a focal spot on CCD camera  252 ). In wavefront sensor  200 , the position of a lenslet element, and the centroid position of the corresponding focal spot determine the centroid of a ray bundle passing through the lenslet element. The centroid of the ray bundle is then used to resolve the mean slope of the beam segment. Analyzer  280 , for example, a personal computer, fits the slopes of the beam segments to a set of Zernike polynomials to reconstruct the wavefront of beam  210  in accordance with the method disclosed in the Liang article. 
     As one can readily appreciate from comparing FIGS. 1 and 3, in inventive wavefront measurement apparatus  100 , two-dimensional photodetector array  50  is disposed at plane P′, and as a consequence, moving boundary locus  60  determines an end position of a ray bundle. In contrast, in prior art Hartmann-Shack wavefront sensor  200 , lenslet array  251  is disposed at plane P′, and as a consequence, CCD camera  252  determines an end position of a ray bundle. Because of this difference, inventive wavefront measurement apparatus  100  has advantages over prior art Hartmann-Shack wavefront sensor  200  that are best understood in conjunction with FIGS. 4A-5E. 
     FIG. 4A illustrates a wavefront measurement made with prior art Hartmann-Shack sensor  200  for flat wavefront  291 . As shown in FIG. 4A, a ray bundle that passes through each lenslet element of lenslet array  251  is focused at one spot on CCD  252 , and the separation between focal spots is equal to the spacing between the lenslet elements. FIG. 4B illustrates a wavefront measurement made with prior art Hartmann-Shack sensor  200  for converging wavefront  294 . As shown in FIG. 4B, in this case, the separation between focal spots is smaller than the spacing between lenslet elements, and as a result, the dynamic range of tilt measurement of prior art sensor  200  is limited by overlapping of focal spots. FIG. 4C illustrates a wavefront measurement made with prior art Hartmann-Shack sensor  200  for diverging wavefront  296 . As shown in FIG. 4C, in this case, the separation between focal spots is larger than the spacing between lenslet elements, and as a result, the dynamic range of tilt measurement of prior art sensor  200  is limited by a size of CCD camera  252 . Lastly, FIG. 4D illustrates a wavefront measurement made with prior art Hartmann-Shack sensor  200  for flat-converging wavefront  298  (this is a typical wavefront obtained from a patient after photorefractive surgery to correct myopia in a central portion of the eye). As shown in FIG. 4D, in this case, focal spots from the central, flat portion of wavefront  298  are uniformly distributed while focal spots from an edge of wavefront  298  tilt toward the center. As a result, the dynamic range of tilt measurement is limited by overlapping of focal spots. 
     FIG. 5A illustrates a wavefront measurement made with wavefront measurement apparatus  100  for flat wavefront  192 . FIG. 5B illustrates a wavefront measurement made with wavefront measurement apparatus  100  for converging wavefront  194 . FIG. 5C illustrates a wavefront measurement made with wavefront measurement apparatus  100  for diverging wavefront  196 . FIG. 5D illustrates a wavefront measurement made with wavefront measurement apparatus  100  for flat-converging wavefront  198 . Lastly, FIG. 5E illustrates a wavefront measurement made with wavefront measurement apparatus  100  for flat-diverging wavefront  199 . 
     As seen in FIGS. 5A-5E, the intensity distribution on photodetector array  50  is approximately uniform. As was described above, for a ray bundle associated with any beam segment, a photodetector element of photodetector array  50  defines a position at one end of the ray bundle, and moving boundary locus apparatus  60  detects a centroid position at the other end of the ray bundle. Advantageously, in accordance with this embodiment of the present invention, detection relating to a ray bundle associated with one beam segment by moving boundary locus apparatus  60  is independent of detection relating to ray bundles associated with other beam segments. Therefore, even though the ray bundles associated with different beam segments may overlap with each other on the plane of moving boundary locus  60 , precise measurement is not interfered with. This advantageous feature of embodiments of the present invention enables measurement of wavefront having large tilt variation. In addition, the distance between photodetector array  50  and moving boundary locus  60  can be big in comparison with the distance between lenslet  251  and CCD camera  253  of Hartmann-Shack wavefront sensor  200 . This advantageous feature of embodiments of the present invention enables better resolution in tilt measurement than that provided by Hartmann-Shack wavefront sensor  200 . 
     FIG. 6 shows a block diagram of wavefront aberration measurement apparatus  300  which is fabricated in accordance with the present invention for use in measuring eye aberration. As shown in FIG. 6, wavefront aberration measurement apparatus  300  comprises probe beam projector  320 , dichroic beamsplitter  330 , a relay optics assembly comprised of relay optics system  340   a  and relay optics system  340   b ; and wavefront sensing assembly  301 . Relay optics systems  340   a  and  340   b  could each comprise one or more lenses. As further shown in FIG. 6, wavefront sensing assembly  301  comprises two-dimensional photodetector array  350 , moving boundary locus apparatus  360 , synchronizer  370 , and analyzer  380 . 
     In accordance with this embodiment of the present invention, probe beam projector  320  projects linearly polarized probe beam  321  which produces a small illumination spot  311  on retina  312 . Radiation beam  313  scattered from spot  311  is relayed by the relay optics assembly (comprised of relay optics system  340   a  and relay optics system  340   b ) onto photodetector array  350  which is disposed at plane P′, which plane P′ is conjugate to pupil plane P. Polarizing beamsplitter  351  is located in front of photodetector array  350  to allow only a depolarized portion of scattered beam  313  to pass therethrough (polarizing beamsplitter  351  rejects reflections from relay optics system  340   a , cornea  314 , and retina  312 ). The wavefront of scattered beam  313  is then reconstructed in the manner described in detail above by wavefront sensing assembly  301 . Finally, eye aberrations are calculated by analyzer  380  in accordance with any one of a number of methods that are well known to those of ordinary skill in the art using the reconstructed wavefront. For example, one such method is disclosed in a publication of Frey et al. on Jun. 3, 1999, WO 99/27334 entitled “Objective Measurement and Correction of Optical Systems Using Wavefront Analysis” wherein distortions of the wavefront are taken as an estimate of the aberrations, which publication is incorporated by reference herein (see also the Liang article). 
     The range and resolution of wavefront tilt measurements obtained using embodiments of the present invention can be estimated as follows. Assume that an aperture of about 30 mm is provided in moving boundary locus apparatus  60 , and a spacing of about 100 mm exists between moving boundary locus apparatus  60  and photodetector array  50 . It is known in the art that the moving boundary locus technique can resolve the centroid position of an end of a ray bundle to better than ten (10) microns. The full cone angle that ray bundles may pass through moving boundary locus apparatus  60  and fall onto photodetector array  50  is approximately 300 m-Radians (30 mm/100 mm). Thus, the maximum tilt angle that can be measured is ±150 m-Radians and the tilt resolution is approximately 0.1 m Radian (10 microns/100 mm). 
     Eye aberration can be characterized by the wavefront of scattered beam  313 . As such, a wavefront tilt measurement of about ±80 m-Radian is desirable to cover ±20 D of refractive error over an 8 mm pupil. Besides, a resolution of ±0.1 D or better is expected in a refractive error measurement. This translates to ±0.4 m-Radian or better in wavefront tilt measurement. As estimated above, wavefront measurement in accordance with embodiments of the present invention can meet these requirements for eye aberration diagnosis. 
     Those skilled in the art will recognize that the foregoing description has been presented for the sake of illustration and description only. As such, it is not intended to be exhaustive or to limit the invention to the precise form disclosed.