Abstract:
A method for programming an active mirror to transform between a distorted wavefront and a plane wavefront requires independently moving each facet of the active mirror along a respective path. The method includes positioning the facets to respectively reflect a light beam in the wavefront, and establishing a base datum for the facets that corresponds to a plane wavefront. The individual phase shift deviation from a plane wavefront is measured for each light beam, and each respective facet is then moved to minimize the individual deviation. The method also requires that groups of facets act together in regions, such that each facet in a particular region will have a total phase shift that includes the individual deviation, the so-called modulo 2π phase shift, plus a same modular phase shift. The modular phase shift for each facet in a region is measured from a plane wavefront and is equal to n2π. Accordingly, moving facets to compensate for individual deviations is accomplished by effectively subtracting the modular from the total phase shift.

Description:
FIELD OF THE INVENTION 
     The present invention pertains generally to diagnostic equipment which is useful for analyzing refractive properties of the eye. More particularly, the present invention pertains to equipment and methods for using this equipment which are capable of modeling a distorted wavefront of light that is characteristic of the refractive properties of an eye. The present invention is particularly, but not exclusively, useful as a method incorporating wavefront analysis for programming an active mirror so that the active mirror will mimic a particular wavefront of light. 
     BACKGROUND OF THE INVENTION 
     Wavefront analysis is based on the proposition that light has a characteristic wavelength, and that phase differences in wavelength between contiguous individual light beams are descriptive of the wavefront. In order to better understand this proposition, it is helpful to also understand the meanings of “wavefront” and “phase” in the context of light. By definition, wavelength is the distance between two similar and successive points on a harmonic (sinusoidal) wave, e.g. the distance between successive maxima or minima. Accordingly, in one wavelength, the waveform will go through one complete cycle from maxima to maxima, or minima to minima. Further, by definition, phase is the fraction of a cycle of a periodic waveform which has been completed at a specific reference time. Typically, the phase of a waveform is determined relative to the start of a cycle of another waveform of the same frequency. Further, phase can be expressed either as an angle, with one cycle corresponding to 2π radians (or 360°), or as a fraction of a wavelength (λ). For example, the same phase shift can be expressed either as a 90° phase shift, or as a λ/4 phase shift. 
     A wavefront of light can be thought of as a plurality of individual light beams which are all contiguous with each other. In accordance with the definitions given above, a plane wavefront of monochromatic light occurs when all of the light is in phase as it is incident on, or passes through, a plane that is oriented perpendicular to the path of the light. Thus, for a plane wavefront, the light in the wavefront can be thought of as including a plurality of contiguous individual light beams in which the light in any one light beam is in phase with the light in all of the other light beams. On the other hand, when light in one or more of these contiguous individual light beams is out of phase with the light in other light beams, i.e. there are phase deviations in the light, the result is a distorted wavefront. These phase deviations, however, can be measured and, thus, can be used to describe or define the wavefront. For example, methods for measuring phase deviations have been disclosed in conjunction with devices like the well known Hartmann-Shack sensor and in publications such as U.S. Pat. No. 5,062,702 which issued to Bille for an invention entitled “Device for Mapping Corneal Topography.” 
     Insofar as an eye is concerned, it is known that a wavefront analysis can be used to determine the refractive properties of the eye. Also, by comparing the refractive properties of a particular eye to those of a “normal” eye, a wavefront analysis can be used to determine what corrective actions, if any, are appropriate. For these purposes, the “normal” eye is known to have a pupil that has an approximately six millimeter diameter, when dilated. Also, the “normal” eye is known to accommodate a maximum phase shift gradient of approximately one wavelength per millimeter (1λ/mm). Stated differently, a “normal” eye can effectively accommodate a phase change equal to one wavelength over a distance of one millimeter. For wavefront analysis, this one millimeter distance is taken in a direction that is perpendicular to the path of the contiguous individual light beams in the wavefront of light that is incident on the eye. 
     A widely used criteria for rating the quality of an optical system, either mechanical or anatomical, is the so-called Strehl ratio. Mathematically, the Strehl ratio, “S”, can be expressed as S=I/I o , where “I” is the maximum intensity of the real system being evaluated and, “I o ” is the maximum intensity of an ideal optical system (with the same aperture diameter and F/number). The Strehl ratio may be expressed either as a ratio or as a percentage. For an ideal optical system, the Strehl ratio is 1 or 100%. For a very good optical system the Strehl ratio is more than 0.9 or 90%, and for a diffraction limited system, the Strehl ratio should be greater than 0.8 or 80%. The Strehl ratio for a “normal” eye is 0.9 (S=90%) over a pupil with a diameter of approximately three millimeters (3 mm), under daylight illumination conditions. 
     With the above in mind, the optical capabilities of an eye can be described in terms of phase shift, phase shift gradient and the Strehl ratio. Specifically, it is known that the “normal” eye is able to accommodate an r.m.s. error in phase deviations of about λ/14 with a 3 mm pupil without any appreciable diminution in visual acuity. Insofar as phase shift gradient is concerned, as implied above, a gradient of 1λ/mm is considered “normal” beyond the 3 mm pupil and corresponds to a Strehl ratio of approximately S=0.1 over a pupil of approximately 6 mm in diameter under twilight illumination conditions. Further, it is known that the steepest gradient which can be effectively accommodated by an eye is approximately 5λ/mm. 
     Accordingly, in light of the above it is an object of the present invention to provide a method and device for programming an active mirror which will transform a distorted wavefront into a plane wavefront, and vice versa, while effectively compensating for as much as a 5λ/mm phase shift gradient. Another object of the present invention is to provide a method and device for programming an active mirror which will transform a distorted wavefront into a plane wavefront, and vice versa, while accounting for modular n2π (or nλ) phase shifts. Still another object of the present invention is to provide a method and device for programming an active mirror which is simple to use, relatively easy to manufacture and comparatively cost effective. 
     SUMMARY OF THE PREFERRED EMBODIMENTS 
     A method and device in accordance with the present invention includes an active mirror that includes an array of approximately forty thousand individual facets. Each facet in the active mirror is independently moveable along a respective substantially parallel path through a distance of approximately four tenths of a micron. Due to the fact that one wavelength of visible light (1λ) is approximately eight tenths of a micron, the individual and separate movement of each facet is able to compensate for phase shifts of about one full wavelength. 
     For the present invention, each facet in the active mirror is substantially square and is approximately forty microns by forty microns. Thus, as measured in a direction along side-by-side facets, there will be twenty-five such facets within each millimeter of length on the surface of the active mirror. This means that, from facet to facet there will be only a λ/25 phase shift error, at most. Importantly, this λ/25 phase shift error compares very favorably with the λ/14 r.m.s. error in wavefront phase shift which is accommodated by the normal eye and which corresponds to an acceptable diffraction limited performance for an eye. Further, it should be noted that the forty thousand facets in the array of the active mirror can be arranged in rows and columns that will each include two hundred facets. The result, using forty-micron square facets, is an eight millimeter by eight millimeter active mirror which can effectively accommodate all of the light that will pass through the six to seven millimeter diameter pupils of the human eye. 
     In operation, the individual facets of the active mirror are positioned so that each facet will respectively reflect a single light beam. Collectively, a plurality of these contiguous light beams make up a wavefront; which may or may not be distorted. Initially a base datum is established for all of the facets in the active mirror such that the base datum corresponds to a plane (undistorted) wavefront. Stated differently, with all facets at the base datum, the active mirror is configured substantially as a plane ordinary mirror. 
     For the present invention, a total deviation in phase shift is measured for each of the contiguous light beams in the wavefront. These phase shifts are measured relative to the phase of corresponding individual light beams in a plane wavefront, and are preferably made using a sensor of a type well known in the art, such as a Hartmann-Shack sensor. As so measured, the total phase shift deviation of a particular light beam will include two components. One is a modular “n2π” phase shift, and the other is an individual phase shift, i.e. the modulo 2π phase shift. Specifically, the modular phase shift is equivalent to a shift of whole wavelengths (nλ or n2π), where “n” is an integer. On the other hand, the individual phase shift, the so-called modulo 2π phase shift, is measured beyond the modular “n2π” phase shift, is in addition to the modular phase shift, and will, itself, always be less than 2π. Mathematically, this relationship is expressed as n2π+φ; where n2π is the modular component and φ is the modulo component. Accordingly, when n2π+φ is divided by 2π, the result is “n” plus φ as a remainder. 
     Once the total phase shift has been determined for each of the individual contiguous light beams that make up the distorted wavefront, the active mirror is divided into regions. Specifically, one region is identified with an integer “n” wherein all of the individual light beams incident on facets in the “n” region have a same modular phase shift. As indicated above, this modular phase shift is equal to n2π. Next, boundary facets in the region are detected such that all of the boundary facets have an (n+1)2π modular phase shift, with a zero individual phase shift deviation. An “n+1” region is then identified that is adjacent the boundary facets, but outside of the “n” region. All of the light beams incident on facets in this “n+1” region will have a respective modular phase shift that is equal to (n+1)2π. Similarly, other boundary facets may be detected which have an (n−1)2π modular phase shift, with a zero individual phase shift deviation. If so, an “n−1” region is identified which is adjacent these boundary facets and which is outside the “n” region. Accordingly, all of the light beams incident on facets in the “n−1” region have a respective modular phase shift that is equal to (n−1)2π. In a like manner “n+2” and “n+3” regions etc., as well as “n−1” and “n−2 regions etc. can be identified. 
     The particular modular phase shift for each region is compensated for by subtracting n2π, (n+1)2π, or (n−1)2π, etc. as appropriate, from the total phase shift of individual light beams within the region. In this manner, the individual phase shift deviations for each individual light beam in the distorted wavefront is determined. Recall, these individual phase shifts will be less than 2π or, stated differently, less than one wavelength of visible light (1λ). Also, recall that one wavelength of visible light (1λ) is approximately eight tenths of a micron and that each facet in the active mirror is moveable through a distance of approximately four tenths of a micron. Thus, each facet in the active mirror can be moved from the base datum, and through a distance on its respective path, to minimize the individual phase shift deviation of the light beam that is incident on the particular facet. Collectively, when this compensation is made for all facets, the active mirror is able to effectively transform the plurality of contiguous light beams between a distorted wavefront and a plane wavefront. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The novel features of this invention, as well as the invention itself, both as to its structure and its operation, will be best understood from the accompanying drawings, taken in conjunction with the accompanying description, in which similar reference characters refer to similar parts, and in which: 
     FIG. 1 is a schematic representation of a system for practicing the methods of the present invention; 
     FIG. 2A is a sinusoidal illustration of a phase shift of less than 2π between a light beam in a distorted wavefront and an idealized light beam of a plane wavefront; 
     FIG. 2B is a sinusoidal illustration of a phase shift of more than 2π between a light beam in a distorted wavefront and an idealized light beam of a plane wavefront; 
     FIG. 3 is a plan view of a portion of a sensor array, including a plurality of sensor reference points; 
     FIG. 4A is a single sensor reference point in the sensor array shown in FIG. 3 detecting a phase shift of less than 2π; 
     FIG. 4B is a single sensor reference point in the sensor array shown in FIG. 3 detecting a phase shift of more than 2π; 
     FIG. 5 is a plan view of the active mirror of the present invention as seen along the line  5 — 5  in FIG. 1; 
     FIG. 6A is a plan view of an individual facet in the active mirror; and 
     FIG. 6B is a cross sectional view of an individual fact in the active mirror as seen along a line  6 B— 6 B in FIG.  6 A. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Referring initially to FIG. 1, a system for practicing the methods of the present invention is shown and is generally designated  10 . As shown, the system  10  basically includes an active mirror  12 , a wavefront sensor  14 , a beam splitter  16  and a computer  18 . For purposes of the present invention, the wavefront sensor  14  can be of a type well known in the pertinent art, such as a Hartmann-Shack sensor. Likewise, the beam splitter  16  and the computer  18  can also be of types well known in the pertinent art. The active mirror  12 , however, must be selected to have certain characteristics that will become more apparent in light of the disclosure presented herein. 
     In overview, the function of system  10  is to program the active mirror  12 . Specifically, this is done to transform a distorted wavefront  20 , which can be described by the phase differences between contiguous individual light beams  22 , into a plane wavefront  24  wherein all of the contiguous individual light beams  22  are in phase with each other. For the discussion here, the individual contiguous light beams  22   a,    22   b,    22   c  and  22   d  are considered exemplary. At this point it is also helpful to appreciate that system  10  is also useful for transforming a plane wavefront  24  into a predetermined distorted wavefront  20 . For either transformation, the notions of phase differences and phase shifts for the individual light beams  22  are important and will perhaps be best appreciated with reference to FIG.  2 A and FIG.  2 B. 
     In FIG. 2A, the sinusoidal characteristic of the light beam  22   a  is shown as a function of time. Also shown FIG. 2A is the sinusoidal characteristic of the light beam  22   b.  If the light beams  22   a  and  22   b  were in phase with each other, which they are not in FIG. 2A, the light beam  22   b  would be shown superposed on top of the light beam  2   a.  As shown, however, the light beams  2   a  and  2   b  are out-of-phase relative to each other, and this difference in phase is shown as a phase shift  26 . Conceptually, the phase shift  26  can be thought of as either a difference in time or a difference in distance traveled. For instance, at the specific point in time  28 , the light beam  22   a  will be at a certain position in free space. Due to the phase shift  26 , however, the light beam  22   b  will not be at this same position until the subsequent point in time  30 . For the situation shown in FIG. 2A, and when considering that the light beam  22   a  will go through a complete period, or cycle, of 360° (2π radians) as it travels from the point in time  28  to a point in time  32 , it will be appreciated that the magnitude of the phase shift  26  between light beam  22   a  and light beam  22   b  is less than 2π. 
     Now consider the relationship between the light beams  22   a  and  22   c  as depicted in FIG.  2 B. For the particular condition shown in FIG. 2B, it is seen that the point in time  28  for light beam  22   a  corresponds to the point in time  34  for the light beam  22   c.  Thus, the total phase shift  36  which exists between the light beam  22   a  and the light beam  22   c  is more than 2π. As contemplated for the present invention, the total phase shift  36  actually includes a modular phase shift  38  which is equal to 2π, and an individual phase shift  40  which is less than 2π. Using this notation, the total phase shift  36  between any two light beams  22  can be expressed as the sum of a modular phase shift  38  which is equal to n2π, where “n” is an integer, and an individual phase shift  40 , the so-called modulo 2π phase shift, which is less than 2π. Thus, the integer “n” may take on different values (e.g. 0, 1, 2, 3, . . . ) and, specifically, for the light beam  22   b  (FIG. 2A) n=0, while for the light beam  22   c  (FIG. 2B) n=1. In all cases, the total phase shift  36  for each light beam  22  is determined by comparing it with the corresponding light beam  22  in a plane wavefront. The total modular phase shift  38  can then be subtracted from the total phase shift  36  to obtain the individual phase shift  40  for the particular light beam  22 . First, however, the total phase shift  36  should be determined. 
     A sensor array  42  is shown in FIG. 3 which can be incorporated into the wavefront sensor  14  to determine the total phase shifts  36  of each individual light beams  22  in a distorted wavefront  20 . Specifically, as typically used for a Hartmann-Shack type sensor, the sensor array  42  includes a plurality of reference points  44 , of which the reference points  44   a  and  44   b  are exemplary. As shown, these reference points  44  are arranged in columns and rows which have a length  46  and a width  48 . In a manner known in the pertinent art, when a plane wavefront  24  is detected, each of the individual light beams  22  in the plane wavefront  24  will be directly incident on a respective reference point  44 . For a distorted wavefront  20 , however, the respective light beams  22  will be diverted from the respective reference point  44 . It happens that for each light beam  22  the magnitude of this diversion from the reference point  44  is proportional to the phase shift between the light beam  22  and its corresponding light beam in a plane wavefront  24 . Thus, the total phase deviation  36  of a light beam  22  can be measured relative to a reference point  44  in the wavefront sensor  14 . 
     In FIG. 4A, the sensor reference point  44   a  is considered by way of example. By cross referencing FIG. 2A with FIG. 4A, it is to be appreciated that the light beam  22   a,  which is exemplary of a light beam  22  in a plane wavefront  24 , will be directly incident on the reference point  44   a.  On the other hand, a light beam  22  having a modular phase shift  38  of 2π (i.e. n=1), with a zero individual phase shift  40 , will be incident on the ring  50   a.  Similarly, a light beam  22  having a modular phase shift  38  of 4π (i.e. n=2), with a zero individual phase shift  40 , would be incident on the ring  52   a,  and so on. Now, while still cross referencing FIG.  2 A and FIG. 4A, specifically consider the light beam  22   b  which is incident on the sensor array  42  at the point  22   b ′. Because the light beam  22   b  has no modular phase shift  38  (i.e. n=0), but because it does have an individual phase shift  26 , the light beam  22   b  is incident on the sensor array  42  within the ring  50  and near, but not on, the reference point  44   a  (see FIG.  4 A). Next, while cross referencing FIG. 2B, FIG.  3  and FIG. 4B, consider the light beam  22   c  relative to the reference point  44   b.  Because the light beam  22   c  has a modular phase shift  38  which is equal to 2π, as well as an individual phase shift  40 , the light beam  22   c  will be incident on the sensor array  42  at the point  22   c ′ which is near reference point  44   b  but between the ring  50  and the ring  52 . In both of these examples, the computer  18  is able to account for the respective modular phase shifts  38  and consequently determine an individual phase shift  40  for each of the light beam  22   b  and  22   c.  A similar analysis, of course, can be done for each light beam  22  in a distorted wavefront  20 . 
     Once a total phase shift  36  has been determined for each light beam  22 , the modular (n2π) phase shift  38  can be easily accounted for. What is then left is the individual phase shift  40  (&lt;2π) for each light beam  22 . The individual phase shifts  40  are then converted by the computer  18  into signals that can be used to program the active mirror  12 . Specifically, by cross referencing FIG. 3 with FIG. 5, it can be appreciated that for each reference point  44  in the sensor array  42 , there is a corresponding subarray  53  of approximately two hundred facets  54  in the active mirror  12 . For example, reference point  44   a  corresponds to the subarray  53   a  of facets  54 , while reference point  44   b  corresponds to the subarray  53   b  of facets  54 . Due to this correspondence, the individual phase shift  40  of each light beam  22  can be associated with a particular subarray  53  of facets  54  of the active mirror  12 . As will be appreciated by the skilled artisan, each light beam  22  includes a plurality of light beams and, therefore, the tilt of each light beam  22  must be mimicked by a plurality of facets  54 . Specifically, for the present invention, this is accomplished by separate subarrays  53  of facets  54 . 
     In FIG. 6A, a single facet  54  within each subarray  53  of the active mirror  12  is shown to have a reflective surface  56  which is supported by four extensions  58   a-d.  As indicated above, each facet  54  is dimensioned to be approximately a forty micron by forty micron square. Accordingly, when the active mirror  12  has a length  46  and a width  48 , each equal to approximately eight millimeters, there will be two hundred facets  54  in each row along the length  46 , and two hundred facets  54  in each column along the width  48 . There are then a total of approximately forty thousand facets  54  in the active mirror  12 . 
     As contemplated for the present invention, the extensions  58  for each facet  54  are responsive to signals from the computer  18  to move the reflective surface  56  back and forth along a path as indicated by the arrows  60  in FIG.  6 B. More specifically, the distance of travel for the reflective surface  56  of each facet  54  in one direction is set to be approximately four tenths of a micron. Thus, a complete wavelength (2π), which is approximately eight tenths of a micron, can be accommodated by an individual facet  54 . Consequently, each individual phase shift  40  (&lt;2π) can be accommodated by an individual facet  54 . 
     In one mode of operation for the system  10 , a distorted wavefront  20  is directed by beam splitter  16  toward the wavefront sensor  14 . Individual light beams  22  in the distorted wavefront  20  are then detected by the wavefront sensor  14 , and the total phase shift  36  of each individual light beam  22 , from a corresponding light beam  22  in a plane wavefront  24 , is measured. Next, the computer  18  accounts for the modular phase shift  38  and, thus, determines an individual phase shift  40  for each individual light beam  22 . These individual phase shifts  40  are then converted into signals that can be used to program the active mirror  12 . Specifically, a signal that is proportional to the individual phase shift  40  of a particular individual light beam  22  activates a corresponding subarray  53  of facets  54  of the active mirror  12 . The result of this activation are movements of the reflective surfaces  56  of respective facets  54  along a path in the direction of arrows  60  that is sufficient to compensate for the individual phase shift  40  of the light beam  22 . This is done for each facet  54  in each subarray  53  of the active mirror  12 . Consequently, when the distorted wavefront  20  is incident on the active mirror  12 , the total phase shift  36  of each individual light beam  22  is compensated for, and the light in distorted wavefront  20  is reflected from the active mirror as a plane wavefront  24 . 
     In another mode of operation for the system  10 , it will be appreciated that a plane wavefront  24  can be converted into a predetermined distorted wavefront  20 . This conversion can be accomplished simply by preprogramming the active mirror  12 . Further, by using the wavefront sensor  14  and the computer  18  in a manner as described above, feedback control can be achieved to maintain the distorted wavefront  20 . 
     While the particular Method for Programming an Active Mirror to Mimic a Wavefront as herein shown and disclosed in detail is fully capable of obtaining the objects and providing the advantages herein before stated, it is to be understood that it is merely illustrative of the presently preferred embodiments of the invention and that no limitations are intended to the details of construction or design herein shown other than as described in the appended claims.