Patent Publication Number: US-2006007395-A1

Title: System and method for wavefront measurement

Description:
BACKGROUND  
      Improving eyesight is vitally important. Precise measurement of the eye&#39;s physical characteristics, including features of the eye, is necessary to accurately prescribe vision correction. With the advent of technologies capable of creating highly complex optical surfaces, a resurgence of interest has arisen in the tools required to measure the eye&#39;s optical characteristics to a higher degree of complexity than was previously possible. In particular, wavefront measurement systems have been developed to measure the physical characteristics of the eye.  
      In a typical wavefront measurement system, a light beam is projected into the eye, which focuses the light beam onto the retina of the eye. The light beam then reflects back out of the eye through the optical components of the eye. A relay lens system typically collects the light reflected from the eye, and projects the collected light through one or more reticles. The light that passes through the reticle(s) is projected onto a translucent screen to create an image on the screen. A charged coupled device (CCD) camera, or similar device, is focused onto the screen to “see” the shadow patterns created by the reticle(s), and the shadow pattern data is imaged onto a CCD chip. A computer or other processor converts the CCD camera images into digital data. The computer then analyzes the data to determine the refractive condition of the eye.  
      In such a system, the information contained within the shadow patterns is generally somewhat degraded because the light is passed onto a screen, and through the camera&#39;s focus optics, before being imaged onto the CCD chip. Additionally, the system requires significant optical length to allow space for the imaging screen and the focus optics of the camera. Accordingly, a need exists for an improved wavefront measuring system that exhibits reduced image degradation, requires less optical length, and/or is less costly than existing measurement systems.  
     SUMMARY OF THE INVENTION  
      The invention is directed to systems and methods for determining aberrations in, or the shape of, a wavefront (i.e., a coherent electromagnetic wavefront). The system includes one or more reticles that are positioned in the path of the wavefront, and a light detector positioned in the wavefront path downstream from the reticles. The light detector is located at a diffraction pattern self-imaging plane, commonly referred to as a Talbot plane, relative to the reticle. Shadow patterns of the wavefront that are produced by the reticle(s) are imaged onto the light detector. A computer or other processor receives an output signal from the light detector identifying the shadow patterns. The computer then analyzes the shadow patterns to calculate aberrations in the wavefront.  
      The light detector may be a CCD camera, or any other suitable electronic camera or other light-detecting device. By locating the light detector at a diffraction pattern self-imaging plane relative to the reticle, i.e., directly at the plane where shadow patterns form, the shadow patterns can be imaged directly onto the light detector.  
      Other features and advantages of the invention will appear hereinafter. The features of the invention described above can be used separately or together, or in various combinations of one or more of them. The invention resides as well in sub-combinations of the features described. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
      In the drawings, wherein similar reference characters denote similar elements throughout the several views:  
       FIG. 1  is a schematic diagram of a preferred wavefront measuring system using one reticle.  
       FIG. 2  is a schematic diagram of a preferred wavefront measuring system using two reticles. 
    
    
     DETAILED DESCRIPTION OF THE DRAWINGS  
       FIG. 1  illustrates a wavefront measuring system according to a first preferred embodiment. The wavefront measuring system includes a light source  5  for creating a source wavefront  10 . The light source  5  is preferably a laser source, a light-emitting diode, or any other suitable light-generating device. The wavelength spectrum of the wavefront produced preferably has a narrow width, for example, approximately 20 nanometers, but the system could function with a broader spectrum. The wavefront preferably has a wavelength of approximately 780 nanometers. Higher wavelengths, which are less representative of an eye&#39;s true refractive index, and lower wavelengths, which may cause a patient&#39;s pupil to constrict upon exposure to the light, may alternatively be used.  
      A beam splitter  15  for reflecting a first portion  12  of the source wavefront  10  toward an object  20  to be measured is located downstream from the light source  5 . A second portion  11  of the source wavefront  10  generally passes through the beam splitter  15  as loss. The object  20  to be measured may be any object with refractive properties, and is preferably a human eye.  
      The first portion  12  of the wavefront reflects from the object  20  and passes through the beam splitter  15 , as a third wavefront portion  25 , toward a relay optics system  30  or a similar device. The third wavefront portion  25  is projected, as a wavefront to be measured  35 , by the relay optics system  30  toward a reticle  40  having one or more grating lines. The wavefront to be measured  35  passes through the reticle  40 , and travels a specific path distance  45  to a light detector  50 . The specific path distance  45  represents the longitudinal distance from the reticle  40  to a diffraction pattern self-imaging plane, or Talbot plane, relative to the reticle  40 .  
      Determination of the specific path distance  45  is well known to those skilled in the art, and is described in detail in “Fourier Transform Method For Automatic Processing of Moiré Deflectograms,” Quiroga et al., Opt. Eng. 38(6) pp. 974-982 (June 1999), and “Refractive Power Mapping of Progressive Power Lenses Using Talbot Interferometry and Digital Image Processing,” Nakano et al., Opt. Laser Technology. 22(3), pp. 195-198 (1990), which are hereby incorporated by reference.  
      In general, the location of a Talbot plane is dependent upon the wavelength of the wavefront being measured and the spacing between grating lines in a reticle, and can be readily calculated by those skilled in the art. The location of a Talbot plane, i.e., of the diffraction pattern self-imaging plane, is generally at a longitudinal distance of approximately 
 
 d =( np 2/λ) 
 
 from a reticle, where p is the grating spacing of the reticle, λ is the spectral wavelength of the wavefront, and n is an integer representing the desired Talbot plane (for example, if n=2, then d represents the longitudinal distance from the reticle to the second Talbot plane). 
 
      A self-image of the wavefront is formed on the light detector  50 , preferably in the form of shadow patterns. The light detector is preferably a CCD camera chip or other suitable detecting device. The light detector  50  outputs the self-image of the shadow patterns to a computer  55  or other processor, which preferably digitizes the shadow patterns. The computer  55  analyzes the shadow patterns to extract refractive information pertaining to the object  20 . Mathematical processes for extracting the refractive information from the shadow patterns are well known to those skilled in the art, and are described in detail in, for example, the incorporated Nakano et al. reference.  
      One basic method for extracting the refractive information involves examining a shadow pattern of a known reference object, and comparing it to the shadow pattern of the object  20  to be measured. The displacement of the shadow patterns between the reference object and the object  20  to be measured, both in terms of direction and magnitude, indicates the refractive properties of the object  20 .  
      By locating the light detector  50  at a diffraction pattern self-imaging plane, or Talbot plane, relative to the reticle  40 , i.e., directly at the plane where the shadow patterns form, the shadow patterns can be imaged directly onto the light detector  50 . As a result, the need for a translucent imaging screen and camera focus optics, which could otherwise degrade information contained in the shadow patterns, is eliminated. Accordingly, the wavefront measurement system exhibits less image degradation, and requires less space and fewer costly optical components, than existing systems using those components.  
       FIG. 2  illustrates an alternative preferred embodiment of a wavefront measuring system. In this embodiment, the system&#39;s operation is the same as described in  FIG. 1 , up to the point where the wavefront to be measured  35  passes through the reticle  40 . Instead of self-imaging on the light detector  50 , the wavefront  35  self-images onto a second reticle  42 , which is preferably rotated slightly with respect to the initial reticle  40 , creating a moiré effect. Moiré effects are well known to those skilled in the art, and are described in detail in the incorporated Quiroga et al. reference.  
      A second self-imaging occurs at the plane where the light detector  50  is located, and the shadow patterns of the wavefront  35  are imaged directly onto the light detector  50 . An advantage of adding a second reticle  42  is that the moiré effect created by changing the rotation between the two reticles  40 ,  42  can control the density of fringe shadow patterns. As a result, the amount of movement of the shadow patterns per wave of change in the wavefront being measured is increased, thus making the system more responsive.  
      The distance  41  between the two reticles  40 ,  42  preferably corresponds to a Talbot plane location, i.e., the second reticle  42  is preferably located at the first Talbot plane, or the second Talbot plane, etc. relative to the first reticle  40 . Any deviation from this Talbot plane spacing will result in a diminishing of intensity of the shadow patterns produced. Additional reticles may be used to add further control to the resolution and response of the movement of the shadow patterns. Each reticle is preferably located at a Talbot plane relative to the previous reticle, and the light detector  50  is preferably located at a Talbot plane relative to the last reticle, so that the detector  50  receives and detects shadow patterns from the last reticle.  
      In a preferred embodiment, a computer program quantifies how much the wavefront deviates from perfectly flat, or in other words, from the phase gradient of the wavefront phase-front. The deviations are expressed mathematically, preferably as polynomials, and are generally quantified in terms of the numbers of waves of light, or fractions of waves of light, by which the wavefront deviates from flat at any given location in the wavefront.  
      The wavefront information is preferably obtained by performing a Fourier Transform on the wavefront, or in other words, a transformation of the wavefront from the spatial image domain into the spatial frequency domain. While performing this step, the orientation of the reticle(s) must be taken into account. In a preferred method, the wavefront is analyzed in at least two directions (derivatives of specific phases of the wavefront may be determined), generally across the wavefront&#39;s horizontal and vertical axes, and the results are categorized into predefined aberrations known as “Zernike polynomials.” Zernike polynomials are commonly used to express wavefront measurements, and have been proposed as the ANSI standard in this regard.  
      In one method, coefficients representative of aberrations in the wavefront are determined by fitting derivative functions of a set of known polynomials to the measured deviations in the wavefront. In some instances, only selected portions of the wavefront in the spatial frequency domain are used to determine the coefficients. Once directional derivatives associated with a light beam that has passed through a reticle are determined, the derivatives can be used to output a measure of aberrations in the light beam.  
      One method for measuring wavefront deviation from flat includes passing a wavefront through an object, or reflecting it off of an object, then passing the wavefront through one or more reticles. Derivatives are then calculated as described above, and are used to describe the wavefront shape, as it deviates from flat. The aberrations in the wavefront are created by the optical components through which the wavefront passes.  
      The computer program analyzes the images produced by the wavefront, or a frequency transformation of the wavefront, as it passed through the reticle(s). The computer program converts these images into digital signals that are preferably stored in the computer&#39;s memory. The computer then executes the program to report the aberrations in the wavefront being analyzed. The output can be expressed in many ways, one of which is to find a best fit With the Zernike polynomials.  
      One or more filtering devices, such as a computational matte screen, may be used to remove unwanted noise from signals in the system, as is known in the art. Corrective optics, such as contact lenses or eyeglasses, may be designed based on the measured aberrations, to correct a patient&#39;s vision.  
      While embodiments and applications of the present invention have been shown and described, it will be apparent to one skilled in the art that other modifications are possible without departing from the inventive concepts herein. The invention, therefore, is not to be restricted except by the following claims and their equivalents.