Patent Publication Number: US-7222962-B2

Title: Opthalmic measuring apparatus

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to an ophthalmic measuring apparatus, and particularly to an ophthalmic measuring apparatus for obtaining an optical characteristic of a subject eye by processing plural Hartmann images. 
   2. Description of the Related Art 
   In recent years, an optical equipment used for medicine becomes popular, especially in ophthalmology, as an optical characteristic measuring apparatus for examining eye functions, such as eye refraction and adjustment, and the inside of the eye. For example, there exists an apparatus called a photo-refractometer for obtaining the refraction of the subject eye and the retina shape (for example, see patent document 1: Japanese Patent Application No. 2000-351796). The patent document 1 discloses an optical characteristic measuring apparatus which acquires a Hartmann image from a light receiving part, calculates Zernike coefficients on the basis of a distance between a Hartmann plate and the light receiving part, coordinates and the like, calculates the wavefront of the subject eye on the basis of the Zernike coefficients, and displays measurement data, image data corresponding to measurement results, and numerical data. Besides, there is disclosed an apparatus for measuring spherical refractivity, a degree of astigmatism, an astigmatic axial angle and the like from image data of a target image projected on the retina of the subject eye (for example, see patent document 2: Japanese Patent No. 2580215). Incidentally, in the measurement results of these various tests, for example, it becomes important that the subject eye of a patient as a test object is placed under what measurement conditions. 
   However, in the conventional measuring apparatus for measuring aberrations of the subject eye, in the case where there is a large difference in the distribution of an eye characteristic, such as an eye refractive index, refraction or aberration, there is a case where the measurement can not be made. The large difference like this can occur by, for example, a disease, an injury, a surgical operation or the like. 
   SUMMARY OF THE INVENTION 
   In view of the above, an object of the present invention is to provide an ophthalmic measuring apparatus capable of measuring even an eye which can not be measured through a uniform adjustment since a large difference exists in the distribution of an eye characteristic such as a refractive index, refraction or aberration. Besides, an object of the invention is to provide an apparatus in which an automatic adjustment is made so as to obtain point image data necessary for analysis, Hartmann images are acquired, and an optical characteristic is obtained by combining the acquired Hartmann images. 
   According to first solving means of the invention, an ophthalmic measuring apparatus comprises: 
   a first illumination optical system including a first light source to emit a light flux of a first wavelength, and for illuminating to be condensed on a vicinity of a retina of a subject eye with a first illumination light flux from the first light source; 
   a first light receiving optical system including a first conversion member to convert a reflected light flux reflected from the retina of the subject eye into at least 17 beams and 
   a first light receiving part to receive the plural light fluxes converted by the first conversion member as first signals, and for guiding the reflected light flux to the first light receiving part; 
   first movement means for moving a light condensing position of the first illumination optical system; 
   second movement means for optically moving the first light receiving part and the first conversion member; 
   an adjustment part for adjusting positions of the first illumination optical system and the first light receiving optical system by the first and the second movement means to measure the first signals under plural measurement conditions until a measurement of an optical characteristic of the subject eye is enabled by combining the first signals from the first light receiving part; and 
   an arithmetic part for obtaining the optical characteristic of the subject eye by combining the first signals obtained from the first light receiving part under the plural measurement conditions in a process of adjustment of the adjustment part. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a view schematically showing an optical system of an ophthalmic measuring apparatus of the invention. 
       FIG. 2  is a structural view of a Placido&#39;s disc. 
       FIG. 3  is a block diagram schematically showing an electric system of the ophthalmic measuring apparatus of the invention. 
       FIG. 4  is a view showing a Hartmann image in a case where there is no positional shift at a projection side and a light receiving side. 
       FIGS. 5A and 5B  are explanatory views of an influence on a Hartmann image due to the positional shift at the projection side and the light receiving side. 
       FIGS. 6A and 6B  are views showing Hartmann images at the time of occurrence of the positional shift at the projection side. 
       FIGS. 7A and 7B  are views showing Hartmann images at the time of occurrence of the positional shift at the light receiving side. 
       FIGS. 8A and 8B  are views showing point images measured in a case where there is a large difference in the distribution of an eye characteristic. 
       FIGS. 9A and 9B  are views showing a memory format of measurement data and inference data. 
       FIG. 10  is a flowchart for obtaining an optical characteristic of a subject eye by combining Hartmann images. 
       FIG. 11  is a flowchart of an independent mode automatic adjustment processing. 
       FIG. 12  is a flowchart of a composite point image creation processing. 
       FIG. 13  is a view showing a first modified example of the independent mode automatic adjustment processing. 
       FIG. 14  is a view showing a second modified example of the independent mode automatic adjustment processing. 
       FIG. 15  is a view showing a third modified example of the independent mode automatic adjustment processing. 
       FIG. 16  is a view showing a modified example of a flowchart for obtaining the optical characteristic of the subject eye by combining Hartmann images. 
       FIG. 17  shows Zernike polynomials (1). 
       FIG. 18  shows Zernike polynomials (2). 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Hereinafter, an embodiment of the invention will be described in detail with reference to the drawings. 
   1. Structure of an Ophthalmic Measuring Apparatus 
     FIG. 1  is a view schematically showing an optical system  150  of an ophthalmic measuring apparatus of the invention. 
   The optical system  150  of the ophthalmic measuring apparatus is, for example, an apparatus for measuring an optical characteristic of a subject eye  60  as an object, and includes a first illumination optical system  10 , a first light receiving optical system  20 , a second light receiving optical system  30 , a common optical system  40 , an adjusting optical system  50 , a second illumination optical system  70 , a third illumination optical system  75 , an illumination optical system  80  for refraction measurement, a light receiving optical system  90  for refraction measurement, first movement means  110 , and second movement means  120 . Incidentally, with respect to the subject eye  60 , a retina  61  and a corneal  62  are shown in the drawing. 
   The first illuminating optical system  10  includes, for example, a first light source  11  for emitting a light flux of a first wavelength, and a condensing lens  12 , and is for illuminating a minute region on the retina (fundus)  61  of the subject eye  60  with the light flux (first illumination light flux) from the first light source  11  so that its illumination condition can be suitably set. The first illuminating optical system  10  can move a condensing position and/or change a condensing condition by the first movement means  110 . 
   The first wavelength of the first illumination light flux emitted from the first light source  11  is, as an example, a wavelength in an infrared range (for example, 780 nm). It is desirable that the first light source  11  has a large spatial coherence and a small temporal coherence. Here, the first light source  11  is, for example, a super luminescence diode (SLD), and a point light source having high luminescence can be obtained. Incidentally, the first light source  11  is not limited to the SLD, and for example, a laser having a large spatial coherence and a large temporal coherence can also be used by inserting a rotation diffused plate or the like to suitably lower the temporal coherence. Further, an LED having a small spatial coherence and a small temporal coherence can also be used, if light quantity is sufficient, by inserting, for example, a pinhole or the like at a position of a light source in an optical path. 
   The first light receiving optical system  20  includes, for example, a collimator lens  21 , a Hartmann plate  22  as a conversion member for converting part of a light flux (first light flux) reflected and returned from the retina  61  of the subject eye  60  into at least 17 beams, and a first light receiving part  23  for receiving the plural beams converted by this Hartmann plate  22 , and is for guiding the first light flux to the first light receiving part  23 . The first light receiving optical system  20  can be moved by the second movement means  120  so that the beams converted by the Hartmann plate  22  are condensed on the first light receiving part  23 . Besides, here, a CCD with little readout noise is adopted for the first light receiving part  23 , and as the CCD, a suitable type of CCD, for example, a general low noise type of CCD, or a cooling CCD of 1000×1000 elements for measurement, can be applied. Signals (first received light signals) received by the first light receiving part  23  are used for obtaining, for example, ocular higher order aberrations. 
   The first movement means  110  is for moving the first illuminating optical system, and is driven by, for example, a motor. The condensing position of the first illumination light flux from the first illuminating optical system can be adjusted by moving the first illuminating optical system by the first movement means  110 . 
   The second movement means  120  is for moving the first light receiving optical system, and is driven by, for example, a motor. By moving the first light receiving optical system by the second movement means  120 , an adjustment can be made such that the beams converted by the Hartmann plate  22  are condensed on the first light receiving part  23 . Incidentally, a suitable apparatus and method can be used as the movement means of the first movement means  110  and the second movement means  120 . Besides, in this embodiment, the first movement means  110  and the second movement means  120  can be driven together, and besides, they can be driven independently. Incidentally, in addition of the automatic measurement by these movement means, the first movement means  110  and the second movement means  120  may be enable to drive by the operation (manual operation) of an operator. 
   The second illuminating optical system  70  includes a second light source  72  for emitting a light flux of a second wavelength, and a Placido&#39;s disk  71 . Incidentally, the second light source  72  can be omitted.  FIG. 2  shows an example of a structural view of the Placido&#39;s disk  71 . The Placido&#39;s disk (PLACIDO&#39;S DISK)  71  is for projecting an index of a pattern composed of plural co-axial rings as shown in  FIG. 2 . Incidentally, the index of the pattern composed of the plural co-axial rings is an example of an index of a predetermined pattern, and a different suitable pattern can be used. Then, after an alignment adjustment described later is completed, the index of the pattern composed of the plural co-axial rings can be projected. 
   The third illuminating optical system  75  is for mainly performing, for example, the alignment adjustment described later, and includes a third light source  31  for emitting a light flux of a third wavelength, a condensing lens  32 , and a beam splitter  33 . 
   The second light receiving optical system  30  includes a condensing lens  34  and a second light receiving part  35 . The second light receiving optical system  30  guides a light flux (second light flux), in which the pattern of the Placido&#39;s disk  71  illuminated from the second illuminating optical system  70  is reflected and returned from the anterior part or the cornea  62  of the subject eye  60 , to the second light receiving part  35 . Besides, the second light receiving optical system can guide a light flux (third light flux), which is emitted from the third light source  31  and is reflected and returned from the cornea  62  of the subject eye  60 , to the second light receiving part  35 . Besides, the second light receiving optical system can obtain the anterior eye image illuminated by the fourth light source  51  from the second light receiving part  35 . Incidentally, as the second wavelength and the third wavelength of the light fluxes emitted from the second light source  72  and the third light source  31 , a wavelength different from, for example, the first wavelength (here, 780 nm) and long (for example, 940 nm) can be selected. Besides, the signal received by the second light receiving part  35  is used for, for example, the alignment adjustment or for obtaining corneal higher order aberrations. 
   The common optical system  40  is disposed on an optical axis of the light flux emitted from the first illuminating optical system  10 , can be included in the first and the second illuminating optical systems  10  and  70 , the first and the second light receiving optical systems  20  and  30 , the third illuminating optical system  75 , and the like, and includes, for example, an afocal lens  42 , beam splitters  43  and  45 , and a condensing lens  44 . The beam splitter  43  is formed of such a mirror (for example, a dichroic mirror) that the wavelength of the third light source  31  is sent (reflected) to the subject eye  60 , the second light flux and the third light flux reflected and returned from the cornea  62  of the subject eye  60  are reflected, and the wavelength of the first light source  11  is transmitted. The beam splitter  45  is formed of such a mirror (for example, a polarization beam splitter) that the wavelength of the first light source  11  is sent (reflected) to the subject eye  60 , and the first light flux reflected and returned from the retina  61  of the subject eye  60  is transmitted. By the beam splitters  43  and  45 , the first, the second and the third light fluxes do not mutually enter other optical systems to generate noise. 
   The adjusting optical system  50  is for mainly performing, for example, an operation distance adjustment, and includes, a fifth light source  55 , condensing lenses  52  and  53 , and a third light receiving part  54 . The operation distance adjustment is performed in such a way that for example, a parallel light flux in the vicinity of an optical axis emitted from the fifth light source  55  is irradiated to the subject eye  60 , and the light reflected from this subject eye  60  is received by the third light receiving part  54  through the condensing lenses  52  and  53 . Besides, in the case where the subject eye  60  is in a suitable operation distance, a spot image from the fifth light source  55  is formed on the optical axis of the third light receiving part  54 . On the other hand, in the case where the subject eye  60  is not within the suitable operation distance, a spot image from the fifth light source  55  is formed above or below the optical axis of the third light receiving part  54 . Incidentally, since the third light receiving part  54  has only to detect the change of a light flux position on the plane including the fifth light source  55 , the optical axis, and the third light receiving part  54 , for example, a one-dimensional CCD, a position selecting device (PSD) or the like disposed on this plane can be applied. 
   The illumination optical system  80  for the refraction measurement includes a light source  81  for refraction measurement, a collimate lens  82 , a ring-shaped diaphragm  83  for refraction measurement, a relay lens  84 , a ring-shaped diaphragm  85 , and a beam splitter  87 . An illumination light flux emitted from the light source  81  for the refraction measurement becomes a parallel light flux by the collimate lens  82 , and illuminates the ring-shaped pattern  83  for the refraction measurement. A light flux from the illuminated ring-shaped diaphragm  83  for the refraction measurement becomes parallel by the relay lens  84 , passes through the ring-shaped diaphragm  85  conjugate with a pupil and the relay lens  86 , overlaps with an optical axis of the first illumination optical system  10  through the beam splitter  87 , and illuminates the retina  61  of the subject eye  60  through the common optical system  40 . This ring-shaped diaphragm  83  for the refraction measurement is made to have a conjugate positional relation to the retina of the subject eye at the time of measurement of the orthoscopic subject eye. 
   The light receiving optical system  90  for refractive power measurement includes a beam splitter  91 , a relay lens  92 , and a light receiving part  93  for refractive power measurement. A reflected light flux from the retina  61  of the ring-illuminated subject eye  60  reaches the beam splitter  91  through the common optical system  40 , is reflected here, and after being condensed by the relay lens  92 , the light flux is received as a received light signal for refractive power measurement by the light receiving part  93  for refractive power measurement. The received light signal for refractive power measurement indicating the ring-shaped pattern image for refractive power measurement projected on the retina is sent to the arithmetic part  210 . 
   The light receiving part  93  for refractive power measurement is preferably formed of a two-dimensional sensor. The arithmetic part  210  obtains the refractive power of the subject eye  60  on the basis of the received light signal for refractive power measurement and from the ring-shaped pattern image for refractive power measurement projected on the retina. 
   Next, the alignment adjustment will be described. The alignment adjustment is mainly carried out by the second light receiving optical system  30  and the third illuminating optical system  75 . 
   First, the light flux from the third light source  31  illuminates the subject eye  60  as the object with the parallel light flux through the condensing lens  32 , the beam splitters  33  and  43 , and the afocal lens  42 . The reflected light flux reflected by the cornea  62  of the subject eye  60  is emitted as a divergent light flux such as is emitted from a point of the half of the radius of curvature of the cornea  62 . The divergence light flux is received as the spot image by the second light receiving part  35  through the afocal lens  42 , the beam splitters  43  and  33 , and the condensing lens  34 . 
   Here, in the case where the spot image on the second light receiving part  35  is out of the optical axis, the optical characteristic measuring apparatus body is moved and adjusted vertically and horizontally, and the spot image is made to coincide with the optical axis. As stated above, when the spot image coincides with the optical axis, the alignment adjustment is completed. Incidentally, with respect to the alignment adjustment, the cornea  62  of the subject eye  60  is illuminated with the fourth light source  51 , and the image of the subject eye  60  obtained by this illumination is formed on the second light receiving part  35 , and accordingly, the center of the pupil may be made to coincide with the optical axis by using this image. 
   Next, a positional relation between the first illuminating optical system  10  and the first light receiving optical system  20  will be roughly described. 
   The beam splitter  45  is inserted in the first light receiving optical system  20 , and by this beam splitter  45 , the light from the first illuminating optical system  10  is sent to the subject eye  60 , and the reflected light from the subject eye  60  is transmitted. The first light receiving part  23  included in the first light receiving optical system  20  receives the light transmitted through the Hartmann plate  22  as the conversion member and generates the received light signal. 
   Besides, the first light source  11  and the retina  61  of the subject eye  60  form a conjugated relation. The retina  61  of the subject eye  60  and the first light receiving part  23  are conjugate. Besides, the Hartmann plate  22  and the pupil of the subject eye  60  form a conjugated relation. Further, in the first light receiving optical system  20 , the pupil and the Hartmann plate  22  form substantially the conjugated relation. That is, the front focal point of the afocal lens  42  substantially coincides with the pupil. 
   Besides, the lens  12  converts a diffused light of the light source  11  into a parallel light. A diaphragm  14  is positioned at an optically conjugated position with respect to the pupil of the eye and the Hartmann plate  21 . The diaphragm  14  has a diameter smaller than an effective range of the Hartmann plate  21 , and the so-called single path aberration measurement (method in which the aberration of an eye influences on only the light receiving side) is established. In order to satisfy the above, the lens  13  is disposed such that the conjugated point of the retina of the real light beam coincides with the front focal position, and in order to satisfy the conjugated relation between the lens and the pupil of the eye, it is disposed such that the rear focal position coincides with the diaphragm  14 . 
   Besides, after a light beam  15  comes to have a light path common to a light beam  24  by the beam splitter  45 , it travels in the same way as the light beam  24  paraxially. However, at the single path measurement, the diameters of the light beams are different from each other, and the beam diameter of the light beam  15  is set to be rather small as compared with the light beam  24 . Specifically, the beam diameter of the light beam  15  is about 1 mm at the pupil position of the eye, and the beam diameter of the light beam  24  can be about 7 mm (incidentally, in the drawing, the light beam  15  from the beam splitter  45  to the retina  61  is omitted). 
   Next, the Hartmann plate  22  as the conversion member will be described. 
   The Hartmann plate  22  included in the first light receiving optical system  20  is a wavefront conversion member for converting a reflected light flux into plural beams. Here, plural micro-Fresnel lenses disposed on a plane orthogonal to the optical axis are applied to the Hartmann plate  22 . Besides, in general, with respect to a measurement object part (subject eye  60 ), in order to measure a spherical component of the subject eye  60 , a third order astigmatism, and other higher order aberrations, it is necessary to perform the measurement with at least 17 beams through the subject eye  60 . 
   Besides, the micro-Fresnel lens is an optical element, and includes, for example, a ring of a height pitch for each wavelength, and a blade optimized for emission parallel to a condensing point. The micro-Fresnel lens here is subjected to, for example, optical path length difference of 8 levels applied by a semiconductor fine working technique, and achieves a high condensing efficiency (for example, 98%). 
   Besides, the reflected light from the retina  61  of the subject eye  60  passes through the afocal lens  42 , the collimate lens  21 , and is condensed on the first light receiving part  23  through the Hartmann plate  22 . Accordingly, the Hartmann plate  22  includes a wavefront conversion member for converting the reflected light flux into at least 17 beams. 
     FIG. 3  is a block diagram roughly showing an electrical system  200  of the ophthalmic measuring apparatus of the invention. The electrical system  200  of the ophthalmic measuring apparatus includes, for example, an arithmetic part  210 , a control part  220 , a display part  230 , a memory  240 , a first driving part  250 , a second driving part  260 , and an input part  270 . 
   The arithmetic part  210  receives a light receiving signal {circle around ( 4 )} obtained from the first light receiving part  23 , a light receiving signal {circle around ( 7 )} obtained from the second light receiving part  35 , a light receiving signal {circle around ( 10 )} obtained from the third light receiving part  54 , and a light receiving signal {circle around ( 12 )} obtained from the light receiving part  93  for the refraction measurement, and performs arithmetic operations on an ocular aberration, Zernike coefficients, refraction and the like. Further, the arithmetic part  210  receives input signals of desired setting, instructions, data and the like from the input part  270 . Besides, the arithmetic part  210  performs arithmetic operations on corneal higher order aberrations, aberration coefficients, a white light MTF (Modulation Transfer Function) as an index expressing a transmission characteristic of a spatial frequency, a Strehl ratio obtained by dividing the center intensity of an intensity distribution PSF (Point Spread Function) of point images by the center intensity of the PSF obtained in the case of an aberration free optical system, a Landolt&#39;s ring pattern having a size corresponding to suitable visual acuity to examine the visual acuity of a patient, and the like. Besides, the arithmetic part outputs signals corresponding to such arithmetic operation results to the control part  220  for performing the control of the whole electric driving system, the display part  230  and the memory  240 , respectively. 
   Further, the arithmetic part  210  includes an adjustment part  211 . The adjustment part  211  adjusts the positions of the first illumination optical system  10  and the first light receiving optical system  20  by the first and the second movement means  110  and  120  so that measurable Hartmann images are obtained. 
   On the basis of the control signal from the arithmetic part  210 , the control part  220  performs a control to turn on and off the first light source part  11  and the optical source  81  for the refraction measurement, and controls the first driving part  250  and the second driving part  260 . For example, on the basis the signals corresponding to the operation results in the arithmetic part  210 , the control part outputs a signal {circle around ( 1 )} to the first light source part  11 , outputs a signal {circle around ( 5 )} to the Placido&#39;s disk  71 , outputs a signal {circle around ( 6 )} to the third light source part  31 , outputs a signal {circle around ( 8 )} to the fourth light source part  51 , outputs a signal {circle around ( 9 )} to the fifth light source part  55 , outputs a signal {circle around ( 11 )} to the light source  81  for the refraction measurement, and outputs signals to the first driving part  250  and the second driving part  260 . 
   The first driving part  250  moves the whole of the first illumination optical system  10  in an optical axis direction on the basis of the light receiving signal {circle around ( 4 )} inputted to the arithmetic part  210  from the first light receiving part  23  or the movement signal inputted from input part  270  so that the light condensing position is moved and/or the light condensing state is changed, and outputs a signal {circle around ( 2 )} to the first movement means  110  and drives this movement means. By this, the first driving part  250  can move and adjust the first illumination optical system  10 . 
   The second driving part  260  moves the whole of the first light receiving optical system  20  in the optical axis direction on the basis of the light receiving signal {circle around ( 4 )} inputted to the arithmetic part  210  from the first light receiving part  23  or the input signal inputted from the input part  270 , and outputs a signal {circle around ( 3 )} to the second movement means  120  and drives this movement means. By this, the second driving part  260  can move and adjust the first light receiving optical system  20 . 
   The input part  270  includes a switch, a button, a keyboard, a pointing device and the like for inputting various input signals of desired setting, instructions, data and the like. For example, the input part  270  includes a mode changeover switch  271 . The mode changeover switch  271  is a switch for switching between an interlock mode in which the first illumination optical system  10  and the first light receiving optical system  20  are interlocked and moved and an independent mode in which they are independently moved. Besides, the input part may include an operation changeover switch for switching between measurement by an automatic adjustment and measurement by a manual adjustment, a measurement start button, and a movement switch for moving the first illumination optical system  10  or the first light receiving optical system  20  in a+ direction and a− direction. 
   Next, a Zernike analysis will be described. A method of calculating Zernike coefficients C i   2j-i  from a generally known Zernike polynomial expression will be described. The Zernike coefficients C i   2j-i  are an important parameter for grasping the optical characteristic of the subject eye  60  on the basis of tilt angles of light fluxes obtained by the first light receiving part  23  through the Hartmann plate  22 . 
   A wavefront aberrations W(X, Y) of the subject eye  60  is expressed by the following expression using the Zernike coefficients C i   2j-i  and the Zernike polynomial expression Z i   2j-i . 
   
     
       
         
           
             
               
                 
                   W 
                   ⁡ 
                   
                     ( 
                     
                       X 
                       , 
                       Y 
                     
                     ) 
                   
                 
                 = 
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       0 
                     
                     n 
                   
                   ⁢ 
                   
                     
                       ∑ 
                       
                         j 
                         = 
                         0 
                       
                       i 
                     
                     ⁢ 
                     
                       
                         c 
                         i 
                         
                           
                             2 
                             ⁢ 
                             j 
                           
                           - 
                           i 
                         
                       
                       ⁢ 
                       
                         
                           Z 
                           i 
                           
                             
                               2 
                               ⁢ 
                               j 
                             
                             - 
                             i 
                           
                         
                         ⁡ 
                         
                           ( 
                           
                             X 
                             , 
                             Y 
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 [Numerical  Expression  1] 
               
             
           
         
       
     
   
   Where, (X, Y) denotes vertical and horizontal coordinates of the Hartmann plate  22 . Besides, in the above expression, n denotes an analysis order. 
   Besides, with respect to the wavefront aberrations W(X, Y), when the vertical and horizontal coordinates of the first light receiving part  23  is (x, y), the distance between the Hartmann plate  22  and the first light receiving part  23  is f, and the movement distance of a point image received by the first light receiving part  23  is (Δx, Δy), the relation of the following expression is established. 
   
     
       
         
           
             
               
                 
                   
                     
                       ∂ 
                       
                         W 
                         ⁡ 
                         
                           ( 
                           
                             X 
                             , 
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                 [Numerical  Expression  2] 
               
             
           
         
       
     
   
   Here, the Zernike polynomial expression Z n   m  is expressed by the following numerical expression 3, and is specifically shown in  FIGS. 17 and 18 . Where, n and m correspond to i and 2j-i in  FIGS. 17 and 18 . 
   
     
       
         
           
             
               
                 
                   
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                     ⁢ 
                     
                       r 
                       m 
                     
                   
                 
               
             
             
               
                 [Numerical  Expression  3] 
               
             
           
         
       
     
   
   Incidentally, specific values of the Zernike coefficients C i   2j-i  can be obtained by minimizing a square error expressed by following numerical expression 4. 
   
     
       
         
           
             
               
                 
                   S 
                   ⁡ 
                   
                     ( 
                     x 
                     ) 
                   
                 
                 = 
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       1 
                     
                     
                       data 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       number 
                     
                   
                   ⁢ 
                   
                     [ 
                     
                       
                         
                           { 
                           
                             
                               
                                 ∂ 
                                 
                                   W 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         X 
                                         i 
                                       
                                       , 
                                       
                                         Y 
                                         i 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               
                                 ∂ 
                                 X 
                               
                             
                             - 
                             
                               
                                 Δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   x 
                                   i 
                                 
                               
                               f 
                             
                           
                           } 
                         
                         2 
                       
                       + 
                       
                         
                           { 
                           
                             
                               
                                 ∂ 
                                 
                                   W 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         X 
                                         i 
                                       
                                       , 
                                       
                                         Y 
                                         i 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               
                                 ∂ 
                                 Y 
                               
                             
                             - 
                             
                               
                                 Δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   y 
                                   i 
                                 
                               
                               f 
                             
                           
                           } 
                         
                         2 
                       
                     
                     ] 
                   
                 
               
             
             
               
                 [Numerical  Expression  4] 
               
             
           
         
       
     
   
   Where, W(X, Y): wavefront aberrations, (X, Y): Hartmann plate coordinates, (Δx, Δy): movement distance of the point image received by the first light receiving part  23 , and f: distance between the Hartmann plate  22  and the first light receiving part  23 . 
   The arithmetic part  210  calculates the Zernike coefficients C i   2j-i , and uses these to obtain the optical characteristic of the eye, such as spherical aberrations, coma aberrations, and astigmatic aberrations. 
   2. Influence of Positional Deviation of the Illuminating Optical System and the Light Receiving Optical System 
   Next, a description will be given of an influence on a Hartmann image in a case where diopter values of the first illuminating optical system  10  (projection side) and the first light receiving optical system  20  (light receiving side) are deviated. 
     FIG. 4  is a view of a Hartmann image in the case where there is no positional deviation at the projection side and the light receiving side. The drawing shows the Hartmann image in the case where a light flux emitted from the first illuminating optical system  10  is reflected by the retina  61  of the subject eye  60  and is condensed on the first light receiving part  23 , that is, in the case where there is no positional deviation at the projection side and the light receiving side. 
     FIGS. 5A and 5B  are explanatory views each showing an influence on the Hartmann image due to positional deviation of the projection side or the light receiving side. Hereinafter, with reference to  FIGS. 5A and 5B , the Hartmann images shown in  FIGS. 6A and 6B  and  FIGS. 7A and 7B  will be described. 
     FIGS. 6A and 6B  are views each showing the Hartmann image at the time of the occurrence of positional deviation of the projection side.  FIG. 6A  shows the Hartmann image in the case where only the projection side is deviated from the state of  FIG. 4  by +5 diopters (+5D). When the projection side is deviated in the+ direction, as indicated by a broken line of  FIG. 5A , since the light flux emitted from the first illuminating optical system  10  is incident from the outside of the center axis toward the inside direction, it is condensed in front of the retina  61  of the subject eye  60 . Since the light flux not condensed is reflected by the retina  61 , when the reflected light flux is received by the first light receiving part  23 , the point image of a received light signal becomes blurred, and the received light level (light quantity) of the received light signal becomes low. 
   On the other hand,  FIG. 6B  shows the Hartmann image in the case where only the projection side is deviated from the state of  FIG. 4  by −5 diopters (−5D). When the projection side is deviated in the− direction, as indicated by a solid line of  FIG. 5A , since the light flux emitted from the first illuminating optical system  10  is incident from the inside of the center axis toward the outside direction, the light flux is condensed at the rear of the retina  61  of the subject eye  60 . Similarly to the case where the projection side is deviated in the+ direction, since the light flux not condensed is reflected by the retina  61 , when the reflected light flux is received by the first light receiving part  23 , the point image of a received light signal becomes blurred, and the received light level of the received light signal becomes low. 
   As stated above, the projection side relates to the received light level of the point image of the received light signal received by the first light receiving part  23 . That is, when the projection side is moved, the point image can be blurred or sharpened. In order to enhance the received light level, the projection side is moved in one of the+ direction and the− direction in which the received light level becomes large. In the automatic adjustment, the arithmetic part  210  moves the first illuminating optical system  10  on the basis of the received light signal of the first light receiving part  23  so that the received light level of the point image becomes large, and the diopter value of the projection side is adjusted. 
     FIGS. 7A and 7B  are views each showing a Hartmann image at the time of the occurrence of positional deviation at the light receiving side.  FIG. 7A  shows the Hartmann image in the case where only the light receiving side is deviated from the state of  FIG. 4  by +5D. When the light receiving side is deviated in the+ direction, as indicated by a broken line of  FIG. 5B , since a light flux reflected by the retina  61  is incident on the Hartmann plate  22  from the outside of the center axis toward the inside direction, not in the vertical direction, it is condensed on a place closer to the center axis, and reaches the first light receiving part. The point images received by the first light receiving part  23  are collected in a place closer to the center axis on the whole, and become, as shown in  FIG. 7A , images in which point image intervals are small. 
   On the other hand,  FIG. 7B  shows the Hartmann image in the case where only the light receiving side is deviated from the state of  FIG. 4  by −5D. When the light receiving side is deviated in the− direction, as indicated by a solid line of  FIG. 5B , the light flux reflected by the retina  61  is incident on the Hartmann plate  22  from the inside of the center axis toward the outside direction, not in the vertical direction, and it is condensed apart from the center axis. The point images received by the first light receiving part  23  go away from the center axis on the whole, and become images as shown in  FIG. 7B  in which point image intervals are large. 
   As stated above, the light receiving side relates to the point image intervals of the point images of the light receiving signals received by the first light receiving part  23 . That is, the correction to a suitable diopter value can be performed by moving the light receiving side in the− direction in the case where the point image interval is small, and by moving the light receiving side in the+ direction in the case where the point image interval is large. In the automatic adjustment, on the basis of the light receiving signal of the first light receiving part  23 , the arithmetic part  210  moves the first light receiving optical system side so that the point image interval becomes a predetermined interval, and as a result, the diopter value of the light receiving side is adjusted. Incidentally, in this embodiment, the first illumination optical system  10  and the first light receiving optical system  20  can be independently moved, and the point image level and the point image interval can be independently adjusted. 
     FIGS. 8A and 8B  are views showing an example of point images measured in the case where there is a large difference in the distribution of an eye characteristic, such as a refractive index, refraction or aberration, of an eye.  FIG. 8A  shows an example in which at the first measurement, although an area near the center is a measurable area, the peripheral portion is an unmeasurable area. In such a case, the adjustment part  211  makes an adjustment so that the unmeasurable area becomes the measurable area.  FIG. 8B  is a view in which the first light receiving optical system  20  is moved in the− direction, and shows that although the center part becomes the unmeasurable area, the peripheral part can be detected as the measurable area. As a result, the total measurement becomes possible by combining data of the center part of  FIG. 8A  and data of the peripheral part of  FIG. 8B . 
   3. Data Format 
     FIGS. 9A and 9B  show memory formats of measurement data and inference data stored in the memory  240 .  FIG. 9A  shows the memory format of the measurement data, and for example, a measurement condition and a measurement result are stored correspondingly to a data identifier to identify data measured under plural measurement conditions. The measurement condition includes diopter values (D values) corresponding to the positions of the first illumination optical system  10  (projection side) and the first light receiving optical system  20  (light receiving side) adjusted by the adjustment part  211 . Besides, for example, measurable identification information corresponding to respective area identifiers related to respective areas of the Hartmann image divided into plural parts and indicating whether the respective areas are measurable areas judged by the arithmetic part  210  or unmeasurable areas, and measurement values (for example, point image coordinates) based on the signals from the first light receiving part  23  are stored in the measurement result. 
     FIG. 9B  shows the recording format of the inference data, and for example, an inference result and the like are stored correspondingly to a data identifier. The inference result includes measurable identification information corresponding to the area identifiers, and inference values (for example, point image coordinates) which suggest results of cases where measurements are made under conditions different from the measurement conditions and are inferred on the basis of the measurement values. Incidentally, as the data identifiers and the area identifiers, suitable ones of numerals, characters, symbols and the like can be used. Besides, these data formats can take suitable forms. 
   4. Flowchart 
     FIG. 10  shows a flowchart for obtaining the optical characteristic of the subject eye  60  by combining plural Hartmann images. 
   First, in the case of the preset interlock mode, the arithmetic part  210  selects the interlock mode in which the first illumination optical system  10  and the first light receiving optical system  20  are interlocked and moved, and makes an alignment adjustment (S 101 ). 
   Next, the arithmetic part  210  illuminates the retina  62  of the subject eye  60  with the ring-shaped pattern  83  for the refraction measurement through the illumination optical system  80  for the refraction measurement, receives the reflected light flux reflected from the retina  62  by the light receiving part  93  for the refraction measurement, and obtains the refraction of the subject eye  60  on the basis of the received light receiving signal for the refraction measurement (S 103 ). Since an arithmetic operation for obtaining the refraction is disclosed in Japanese Patent No. 2580215 (patent document 2), the details will be omitted here. 
   The arithmetic part  210  judges whether the measurement result of the refraction is obtained (S 105 ). The arithmetic part  210  may judge whether the measurement result of the refraction is obtained by using a condition, for example, whether a predetermined number of data necessary for the arithmetic operation of the refraction are obtained. Incidentally, a suitable condition can be used in addition to this. In the case where the refraction measurement result is obtained (S 105 ), the arithmetic part  210  interlocks and moves the first illumination optical system  10  and the first light receiving optical system  20  to a position consistent with the refractive power component of the obtained refraction (S 107 ). On the other hand, when the refraction measurement result is not obtained (S 105 ), the arithmetic part  210  proceeds to step S 109 . Incidentally, in the case where the refraction measurement result is not obtained, the arithmetic part  210  may proceed to an independent mode automatic adjustment of step S 113 . 
   Next, the arithmetic part  210  receives the first light receiving signal from the first light receiving part  23 , and detects the density distribution of point images on the basis of the received first light receiving signal (S 109 ). For example, a range of the first light receiving part  23 , which can receive light, is previously divided into a suitable number of areas, the arithmetic part  210  judges the point images existing in the respective areas from the coordinates or the like of the first light receiving signal, and may detect the number thereof to obtain the point image density. Incidentally, with respect to the calculation of the density, a suitable method can be adopted. 
   Besides, in addition to the use of the previously divided areas, the arithmetic part  210  may perform division of areas in accordance with the first light receiving signal from the first light receiving part  23 . For example, the arithmetic part  210  detects point image coordinates of vertical and horizontal ends from the first light receiving signal, and obtains the distribution range of the point images, and this distribution range can also be divided into a suitable number of parts. As a dividing method, a suitable method and a suitable number of divided parts, for example, a method in which the vertical width is divided into four parts, the horizontal width is divided into four parts, and the whole is divided into 16 parts, or a method of dividing the range into concentric areas having the center of the distribution range as the center can be adopted. The divided areas are made to correspond to area identifiers such as area numbers. Incidentally, as the area identifiers, suitable ones such as numerals, characters, or symbols can be used. 
   The arithmetic part  210  reads out a predetermined range of a previously set density from the memory  240 , and judges that it is an unmeasurable area when the density of the point images of each area is outside a predetermined range, and judges that it is a measurable area when the density is within the predetermined range. The predetermined range is, for example, d1/10 or higher and 5×d1 or less when the density of the point images in the case where the orthoscopic subject eye  60  is measured at a position of 0 diopter (0 D) is made d1. Incidentally, as the predetermined range, a suitable range may be used in addition to this. Besides, in addition to the judgment of the measurable areas on the basis of the point image density, the arithmetic part  210  may judge the measurable areas on the basis of the maximum value of the point images. In this case, the arithmetic part  210  obtains the maximum value of the respective point image levels on the basis of the first light receiving signal, and reads out a predetermined range of previously set point image levels from the memory  240 , and in the case where the maximum value of the point image levels is within the predetermined range, it is judged to be the measurable area, and in the case where the maximum value is outside the predetermined range, it is judged to be the unmeasurable area. 
   Besides, the arithmetic part  210  can store diopter values (measurement condition) consistent with the positions of the first illumination optical system  10  and the first light receiving optical system  20  when the first light receiving signal is received, and the coordinates (measurement value) of point images on the basis of the inputted first light receiving signal, which are made to correspond to the data identifier (for example, data number), into the measurement data of the memory  240  at a suitable timing. Incidentally, the arithmetic part  210  may store the measurement value which is made to correspond to the area identifier for each area. Further, the arithmetic part  210  can store the measurable identification information indicating measurability or unmeasurability, which is made to correspond to the pertinent area identifier, into the memory  240 . 
   The arithmetic part  210  judges whether the whole light receivable range of the first light receiving part  23  is a measurable area (S 111 ). That is, on the basis of the judgment at the step S 109  as to whether each area is the measurable area or on the basis of the measurable identification information of the measurement data stored in the memory  240 , when the arithmetic part  210  judges that the whole light receivable range is covered with the measurable area, it proceeds to step S 117  and obtains the optical characteristic of the subject eye  60 . On the other hand, when judging that the whole is not covered with the measurable area, the arithmetic part  210  proceeds to step S 113 . Incidentally, as a judgment condition, instead of judging whether the whole is the measurable area, the arithmetic part  210  may judge, for example, whether the number of obtained point images is a predetermined number or larger. In that case, in the case where the number of the point images is the predetermined number or larger, the arithmetic part proceeds to the step S 117 , and in the case where the number of the point images is smaller than the predetermined number, it proceeds to the step S 113 . Further, as a judgment condition, the arithmetic part  210  may judge whether the point image density is within a predetermined range and whether the number of point images is a predetermined number or larger. 
   The arithmetic part  210  performs an independent mode automatic adjustment processing (S 113 ). In the independent mode automatic adjustment processing, the arithmetic part  210  adjusts the first illumination optical system  10  and the first light receiving optical system  20  on the basis of the point images of the unmeasurable area, and acquires Hartmann images necessary for measurement. The detailed description of the independent mode automatic adjustment processing will be described later. 
   Besides, the arithmetic part  210  performs a composite point image creation processing for obtaining a composite point image on the basis of one or plural first light receiving signals captured (S 115 ). The arithmetic part  210  performs a Zernike analysis on the basis of the first light receiving signal or the composite point image, and calculates Zernike coefficients (S 117 ). 
   Next, the arithmetic part  210  performs an arithmetic processing on the optical characteristic on the basis of the first light receiving signal (S 119 ). Here, the optical characteristic is a suitable eye characteristic, for example, aberrations or eye refraction. The arithmetic part  210  calculates the optical characteristic based on the measurement principle of a Hartmann wavefront sensor with respect to the first light receiving signal. Higher order aberrations (ocular higher order aberrations) of an ocular optical system are obtained by the first light receiving signal. Further, the arithmetic part  210  displays the measured Hartmann image and the optical characteristic such as the ocular higher order aberrations on the display part  230  (S 121 ). 
   Besides, instead of the steps S 117  to S 121  or in parallel to them, the arithmetic part  210  may capture the second light receiving signal concerning the anterior eye image by the second light receiving part  35  and may calculate the optical characteristic such as higher order aberrations (corneal higher order aberrations) occurring at the cornea, and the corneal shape. After capturing the second light receiving signal, the arithmetic part  210  analyzes the position of a ring image appearing substantially concentrically with respect to the bright point of reflection of the corneal vertex by using an image processing technique. With respect to the position of the ring, for example, about 256 points are acquired over 360 degrees on the circumference. Besides, the arithmetic part  210  calculates the tilt of the cornea from the position of the ring. Besides, the arithmetic part  210  calculates the height of the cornea from the tilt of the cornea, and treats the cornea similarly to an optical lens to calculate the optical characteristic. The higher order aberrations (corneal higher order aberrations) occurring at the cornea are obtained by the second light receiving signal. The arithmetic part  210  displays the calculated corneal higher order aberrations, the corneal shape and the like on the display part  230 . Further, the arithmetic part  210  calculates the white light MTF, Strehl ratio, Landolt&#39;s ring pattern and the like and may display them on the display part  230 . 
   The arithmetic part  210  returns to the step S 101  to continue to measure, otherwise it terminates the processing (S 123 ). 
     FIG. 11  shows a flowchart of the independent mode automatic adjustment processing. First, the arithmetic part  210  refers to the measurable identification information of the measurement data of the memory  240 , and specifies an adjustment area from the unmeasurable areas in which an adjustment is to be made by moving the first illumination optical system  10  and the first light receiving optical system  20  so that the area becomes a measurable area (S 200 ). 
   Next, the arithmetic part  210  reads out the first light receiving signal from the first light receiving part  23 , detects intervals of the respective point images in the adjustment area on the basis of the read first light receiving signal, and obtains an average of the point image intervals (S 201 ). The arithmetic part  210  reads out a previously set predetermined interval from the memory  240 , and compares it with the average point image interval of the adjustment area. In the case where the average point image interval of the adjustment area is smaller than the previously set predetermined interval (S 203 ), the arithmetic part  210  outputs a signal to the second driving part  260  to move the first light receiving optical system  20  (light receiving side) in the− direction, and returns to the processing of the step S 201  (S 205 ). 
   In the case where the average point image interval of the adjustment area is larger than the predetermined interval (S 207 ), the arithmetic part  210  outputs a signal to the second driving part  260  to move the first light receiving optical system  20  in the+ direction, and returns to the processing of the step S 201  (S 209 ). The second driving part  260  receives the signal from the arithmetic part  210 , and drives the second movement means  120  in accordance with the received signal. Besides, in the case where the average point image interval of the adjustment area is the predetermined interval, the arithmetic part  210  proceeds to the processing of step S 211 . Incidentally, with respect to the comparison of the point image interval with the predetermined interval, in addition to the average of the respective point image intervals detected at the step S 201 , a suitable value such as a minimum value, a maximum value, or a summation may be used. Besides, in addition to the adjustment of the light receiving side on the basis of the point image interval, an adjustment may be made on the basis of point image density. In this case, the arithmetic part  210  obtains the point image density of the adjustment area on the basis of the first light receiving signal, and further reads out the previously set predetermined density range from the memory  240 . In the case where the point image density is larger than the predetermined range, the arithmetic part  210  outputs a signal to move the light receiving side in the − direction, and in the case where the point image density is smaller than the predetermined range, the arithmetic part outputs a signal to move the light receiving side in the+ direction. 
   Next, the arithmetic part  210  reads out the first light receiving signal from the first light receiving part  23 , detects the point image levels on the basis of the read first light receiving signal, and obtains the average of the point image levels of the adjustment area (S 211 ). The arithmetic part  210  reads out the previously set predetermined level from the memory  240 , and judges whether the average point image level of the adjustment area is larger than the predetermined level (S 213 ). Incidentally, with respect to the comparison of the point image level with the predetermined level, in addition to the average of the respective point image levels detected at the step S 211 , a suitable value such as a minimum value, a maximum value or a summation may be used. In the case where the average point image level of the adjustment area is smaller than the predetermined level (S 213 ), the arithmetic part  210  outputs a signal to the first driving part  250  to move the first illumination optical system  10  (projection side), and returns to the processing of the step S 211  (S 215 ). With respect to the movement direction of the first illumination optical system  10 , a judgment is made as to whether the point image level becomes large when it is moved in an arbitrary direction, and it may be moved in the direction where the point image level becomes large. Besides, the arithmetic part  210  may move the first illumination optical system  10  so that the point image level becomes maximum. The first driving part  250  receives the signal from the arithmetic part  210 , and moves the first illumination optical system  10  by the first movement means  110  in accordance with the received signal. On the other hand, in the case where the average point image level of the adjustment area is larger than the predetermined level (S 213 ), the arithmetic part  210  proceeds to step S 217 . 
   The arithmetic part  210  receives the first light receiving signal from the first light receiving part  23 , and stores diopter values (measurement condition) consistent with the positions of the projection side and the light receiving side and the coordinates (measurement value) of the point image based on the received first light receiving signal, which are made to correspond to the data identifier, into the measurement data of the memory  240  (S 217 ). Incidentally, the arithmetic part  210  may store the measurement value which is made to correspond to the area identifier for each area. 
   The arithmetic part  210  obtains the density distribution of point images of the inputted first light receiving signal, and judges whether the adjustment area is measurable (S 219 ). The judgment on the measurability can be made the same as the step  109 . Further, the arithmetic part  210  judges whether another area is also a measurable area. Incidentally, the arithmetic part  210  refers to the measurable identification information of the measurement data stored in the memory  240 , and may judge whether it is measurable only with respect to an unmeasurable area. The arithmetic part  210  stores the measurable identification information indicating measurability or unmeasurability, which is made to correspond to the data identifier and the area identifier of each area, into the measurement data of the memory  240 . 
   The arithmetic part  210  further refers to the measurable identification information of the memory  240 , and judges whether there is an area in which a measurable point image coordinate has not been obtained (S 221 ). When judging that the unmeasurable area exists, the arithmetic part  210  returns to the step S 200 , and on the other hand, in the case where the unmeasurable area does not exist, the arithmetic part ends the independent mode automatic adjustment processing, and proceeds to the processing of the step S 115 . 
     FIG. 12  shows a flowchart of a composite point image creation processing. Although a method of creating a composite point image from two measurement data will be described below, a composite point image can be created similarly with respect to three or more data. First, the arithmetic part  210  sequentially reads out measured diopter values from the measurement conditions of the measurement data stored in the memory  240 , and obtains an average of the diopter values (in the case of two measurement data, it becomes a center diopter value) (S 301 ). For example, the arithmetic part  210  infers point image coordinates in a case where a measurement is made while the average of the diopter values is made the measurement condition, and combines the inferred point image coordinates to create the composite point image. Besides, with respect to the calculation of the average of the diopter values, both the projection side and the light receiving side may be used, or either one may be used. Incidentally, in addition to the average diopter value, a suitable diopter value is used and point image coordinates can also be inferred. 
   The arithmetic part  210  reads out the measurement conditions and the measurement values from the measurement data stored in the memory  240  (S 303 ). Further, the arithmetic part  210  receives a pupil radius and a distance between the Hartmann plate  22  and the first light receiving part  23  from the memory  240  or the input part  270 , and obtains an average diopter value, that is, an inference value of point image coordinates under a measurement condition other than the measured diopter value (S 305 ). Hereinafter, the inference of the point image coordinates will be described. 
   For example, after the Hartmann images of plural screens are acquired, from the barycentric position of the point images which can be detected from those, it is possible to infer the barycentric position of point images under a measurement condition other than the measured diopter values (for example, position of the center value of the acquired diopter values). A movement amount of the point image is obtained from the image of the first light receiving part  23 , and the movement amount of an i-th point image is made Δx i , Δy i . The movement amount and the higher order aberrations are correlated with each other by the following partial differentiation equation. 
                       ∂     W   ⁡     (     X   ,   Y     )           ∂   X       =       Δ   ⁢           ⁢     x   i       f       ⁢     
     ⁢         ∂     W   ⁡     (     X   ,   Y     )           ∂   Y       =       Δ   ⁢           ⁢     y   i       f               [Numerical  Expression  5]               
(f: distance between the Hartmann plate  22  and the first light receiving part  23 )
 
   Here, when the wavefront W is expressed by expansion using Zernike polynomials Z i   2j-1 , the following expression is obtained. 
   
     
       
         
           
             
               
                 
                   W 
                   ⁡ 
                   
                     ( 
                     
                       X 
                       , 
                       Y 
                     
                     ) 
                   
                 
                 = 
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       0 
                     
                     n 
                   
                   ⁢ 
                   
                     
                       ∑ 
                       
                         j 
                         = 
                         0 
                       
                       i 
                     
                     ⁢ 
                     
                       
                         c 
                         i 
                         
                           
                             2 
                             ⁢ 
                             j 
                           
                           - 
                           i 
                         
                       
                       ⁢ 
                       
                         
                           Z 
                           i 
                           
                             
                               2 
                               ⁢ 
                               j 
                             
                             - 
                             i 
                           
                         
                         ⁡ 
                         
                           ( 
                           
                             X 
                             , 
                             Y 
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 [Numerical  Expression  6] 
               
             
           
         
       
     
   
   Besides, by the change of the diopter position, with respect to the wavefront W, only the Zernike coefficient C 2   0  corresponding to the diopter is changed. It is conceivable that the barycentric position of the point images is moved only by this change. 
   When a barycentric position of point images at the measured diopter positions is (X i1 , Y i1 ), a barycentric position of point images at inference (analysis) diopter positions is (X i , Y i ), a movement amount is ΔX i1 , ΔY i1 , a Zernike coefficient change amount is (C 2   0 )′, and a distance between the Hartmann plate  22  and the first light receiving part  23  is F, the relation of the following expression is established. 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           X 
                           i 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               X 
                               i1 
                             
                           
                           + 
                           
                             X 
                             i1 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               ∂ 
                               
                                 ∂ 
                                 X 
                               
                             
                             ⁢ 
                             
                               
                                 { 
                                 
                                   Δ 
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                                   ⁢ 
                                   
                                     
                                       ( 
                                       
                                         c 
                                         2 
                                         0 
                                       
                                       ) 
                                     
                                     ′ 
                                   
                                   ⁢ 
                                   
                                     
                                       Z 
                                       2 
                                       0 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         
                                           X 
                                           i1 
                                         
                                         , 
                                         
                                           Y 
                                           i1 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 } 
                               
                               · 
                               F 
                             
                           
                           + 
                           
                             X 
                             i1 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 ( 
                                 
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                                   0 
                                 
                                 ) 
                               
                               ′ 
                             
                             ⁢ 
                             
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                                 X 
                               
                             
                             ⁢ 
                             
                               
                                 
                                   Z 
                                   2 
                                   0 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       X 
                                       i1 
                                     
                                     , 
                                     
                                       Y 
                                       i1 
                                     
                                   
                                   ) 
                                 
                               
                               · 
                               F 
                             
                           
                           + 
                           
                             X 
                             i1 
                           
                         
                       
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     
                       
                         
                           Y 
                           i 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               Y 
                               i1 
                             
                           
                           + 
                           
                             Y 
                             i1 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               ∂ 
                               
                                 ∂ 
                                 Y 
                               
                             
                             ⁢ 
                             
                               
                                 { 
                                 
                                   
                                     
                                       Δ 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           c 
                                           2 
                                           0 
                                         
                                         ) 
                                       
                                     
                                     ′ 
                                   
                                   ⁢ 
                                   
                                     
                                       Z 
                                       2 
                                       0 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         
                                           X 
                                           i1 
                                         
                                         , 
                                         
                                           Y 
                                           i1 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 } 
                               
                               · 
                               F 
                             
                           
                           + 
                           
                             Y 
                             i1 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 ( 
                                 
                                   c 
                                   2 
                                   0 
                                 
                                 ) 
                               
                               ′ 
                             
                             ⁢ 
                             
                               ∂ 
                               
                                 ∂ 
                                 Y 
                               
                             
                             ⁢ 
                             
                               
                                 
                                   Z 
                                   2 
                                   0 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       X 
                                       
                                         i1 
                                         , 
                                       
                                     
                                     ⁢ 
                                     
                                       Y 
                                       i1 
                                     
                                   
                                   ) 
                                 
                               
                               · 
                               F 
                             
                           
                           + 
                           
                             Y 
                             i1 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 [Numerical  Expression  7] 
               
             
           
         
       
     
   
   Besides, an expression for calculating the Zernike coefficient Δ(C 2   0 )′ from the diopter change amount ΔS 1  is expressed by the following expression. 
                     Δ   ⁡     (     c   2   0     )       ′     =       -     1   4       ⁢   Δ   ⁢           ⁢       S   1     ·     r   2                 [Numerical  Expression  8]               
Where, r is a pupil radius (mm). Besides, the Zernike polynomial Z 2   0  is expressed by the following expression from  FIG. 18 .
   Z   2   0 =2 X   2 +2 Y   2 −1  [Numerical Expression 9] 
Thus, the barycentric position (X ia , Y ia ) of the point images at the inference diopter position can be expressed by the following expression when the barycentric position of the point images at the measured diopter value “a” used for the inference is made (X i1a , Y i1a ).
 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           X 
                           ia 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               - 
                               
                                 1 
                                 4 
                               
                             
                             ⁢ 
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 S 
                                 1 
                               
                               · 
                               
                                 r 
                                 2 
                               
                               · 
                               4 
                             
                             ⁢ 
                             
                               
                                 X 
                                 i1a 
                               
                               · 
                               F 
                             
                           
                           + 
                           
                             X 
                             i1a 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               - 
                               Δ 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 S 
                                 1 
                               
                               · 
                               
                                 r 
                                 2 
                               
                               · 
                               
                                 X 
                                 i1a 
                               
                               · 
                               F 
                             
                           
                           + 
                           
                             X 
                             i1a 
                           
                         
                       
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     
                       
                         
                           Y 
                           ia 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               - 
                               
                                 1 
                                 4 
                               
                             
                             ⁢ 
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 S 
                                 1 
                               
                               · 
                               
                                 r 
                                 2 
                               
                               · 
                               4 
                             
                             ⁢ 
                             
                               
                                 Y 
                                 i1a 
                               
                               · 
                               F 
                             
                           
                           + 
                           
                             Y 
                             i1a 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               - 
                               Δ 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 S 
                                 1 
                               
                               · 
                               
                                 r 
                                 2 
                               
                               · 
                               
                                 Y 
                                 i1a 
                               
                               · 
                               F 
                             
                           
                           + 
                           
                             Y 
                             i1a 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 [Numerical  Expression  10] 
               
             
           
         
       
     
   
   In the same way, it is also possible to infer the barycentric position of point images from other measurement data. For example, a barycentric position (X ib , Y ib ) of point images at an inference (analysis) diopter position is expressed by the following expression when a barycentric position of point images at a measured diopter position “b” used for inference is (X i2b , Y i2b ), and a diopter change amount is ΔS 2 . 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           X 
                           ib 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               - 
                               
                                 1 
                                 4 
                               
                             
                             ⁢ 
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 S 
                                 2 
                               
                               · 
                               
                                 r 
                                 2 
                               
                               · 
                               4 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 X 
                                 
                                   i 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   b 
                                 
                               
                               · 
                               F 
                             
                           
                           + 
                           
                             X 
                             i2b 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               - 
                               Δ 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 S 
                                 2 
                               
                               · 
                               
                                 r 
                                 2 
                               
                               · 
                               
                                 X 
                                 
                                   i2 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   b 
                                 
                               
                               · 
                               F 
                             
                           
                           + 
                           
                             X 
                             i2b 
                           
                         
                       
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     
                       
                         
                           Y 
                           ib 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               - 
                               
                                 1 
                                 4 
                               
                             
                             ⁢ 
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 S 
                                 2 
                               
                               · 
                               
                                 r 
                                 2 
                               
                               · 
                               4 
                             
                             ⁢ 
                             
                               
                                 Y 
                                 i2b 
                               
                               · 
                               F 
                             
                           
                           + 
                           
                             Y 
                             i2b 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               - 
                               Δ 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 S 
                                 2 
                               
                               · 
                               
                                 r 
                                 2 
                               
                               · 
                               
                                 Y 
                                 i2b 
                               
                               · 
                               F 
                             
                           
                           + 
                           
                             Y 
                             i2b 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 [Numerical  Expression  11] 
               
             
           
         
       
     
   
   When the wavefront W is calculated on the basis of the barycentric positions obtained by combining these, a result incorporating the barycentric positions obtained by the plural screens can be obtained. For example, in the Hartmann images i=1 to 100 of two screens, in the case where measurable point images at position “a” are i=1 to 50, and measurable point images at position “b” are i=51 to 100, the barycentric position of composite point images is obtained by
 
 X   i =( X   1a   , X   2a   , . . . , X   50a   , X   51b   , X   52b   , . . . X   99b   , X   100b )
 
 Y   i =( Y   1a   , Y   2a   , . . . , Y   50a   , Y   51b   , Y   52b   , . . . , Y   99b   , Y   100b )  [Numerical Expression 12]
 
   The arithmetic part  210  uses the numerical expression 10 to calculate the inference value (S 305 ), and stores the obtained inference value, which is made to correspond to the data identifier and the area identifier, into the inference data of the memory  240  (S 307 ). 
   Besides, the arithmetic part  210  refers to the measurable identification information corresponding to the data identifier of the measurement data stored in the memory  240 , and judges the measurable area. Incidentally, the arithmetic part  210  may store the measurable identification information which is made to correspond to the data identifier of the inference data and each area identifier. Further, the arithmetic part  210  extracts inference values of point images belonging to the measurable area from the inference data, and stores the extracted inference values into the composite point image data of the memory  240  (S 309 ). Incidentally, with respect to the area in which an inference value is already stored, they may not be stored or may overwrite it to store. 
   Next, the arithmetic part  210  judges whether the composite point image data is analyzable data (S 311 ). For example, the arithmetic part  210  can judge by whether data of all areas are stored in the composite point image data, or whether the number of the composite point image data is a predetermined number of point images or larger. Incidentally, as a judgment standard, a suitable one may be used. In the case where the composite point image data is analyzable, the arithmetic part  210  ends the composite point image creation processing, and proceeds to step S 117 , and on the other hand, in the case where it is not analyzable, the arithmetic part returns to the step S 303 , and obtains an inference value from another measurement value. 
   Incidentally, as the storage format of data and the creation procedure of the composite point image, a suitable method other than the above can be adopted. For example, all inference data may be first obtained from the measurement data, or measurement data may be selected so that measurement data used for the creation of composite point images becomes as small as possible. 
     FIG. 13  shows a first modified example of the independent mode automatic adjustment processing. In the modified example of  FIG. 13 , the order of the movement (S 211  to S 215 ) of the projection side on the basis of the point image level in  FIG. 11  and the movement (S 201  to S 209 ) of the light receiving side on the basis of the point image interval is reversed in the flowchart. Since processings of the respective steps are the same as  FIG. 11 , the same symbols as  FIG. 11  are given and the explanation will be omitted. 
     FIG. 14  shows a second modified example of the independent mode automatic adjustment processing. In the modified example shown in  FIG. 14 , before an adjustment is made in the independent mode, the projection side and the light receiving side are interlocked and adjusted in the interlock mode. Especially, it is effective in the case where the eye characteristics of a measurable area and an unmeasurable area are largely different from each other. 
   First, the arithmetic part carries out a processing of step S 200 . Since the details of the processing are the same as the above, the explanation will be omitted. Next, the arithmetic part  210  captures a first light receiving signal concerning a Hartmann image by using the first light receiving part  23  of low noise CCDs or the like (S 251 ). The arithmetic part  210  obtains an average of light receiving signal levels concerning the inputted first light receiving signal. 
   The arithmetic part  210  reads a predetermined signal level from the memory  240 , and judges whether the average of the light receiving signal levels is larger than the predetermined signal level (S 253 ). Incidentally, the predetermined signal level is previously set and is stored in the memory  240 . Incidentally, in addition to the use of the average of the light receiving signal levels, a suitable value such as a minimum value, a maximum value or a summation may be used. 
   In the case where the average light receiving signal level is lower than the predetermined signal level (S 253 ), the arithmetic part  210  outputs movement signals to the first driving part  250  and the second driving part  260  automatically or by the instructions from the input part  270  to interlock and move the first illumination optical system  10  and the first light receiving optical system  20 , and returns to the step S 251  (S 255 ). The first driving part  250  and the second driving part  260  receive the movement signals from the arithmetic part  210 , and interlock and move the first illumination optical system  10  and the first light receiving optical system  20  by the first movement means  110  and the second movement means  120  in accordance with the received signals. Besides, the arithmetic part  210  may move the first illumination optical system  10  and the first light receiving optical system  20  so that the signal level from the first light receiving part  23  becomes maximum. 
   On the other hand, in the case where the average light receiving signal level is larger than the predetermined signal level (S 253 ), the arithmetic part  210  carries out the processings of step S 201  to step S 221 . Since the details of the respective processings are the same as  FIG. 11 , the same symbols as  FIG. 11  are given and the explanation will be omitted. 
     FIG. 15  shows a third modified example of the independent mode automatic adjustment processing. In the modified example shown in  FIG. 15 , the order of the adjustment (S 211  to S 215 ) of the projection side on the basis of the point image level in  FIG. 14  and the adjustment (S 201  to S 209 ) of the light receiving side on the basis of the point image interval is reversed. Since the processings of the respective steps are the same as  FIG. 14 , the same symbols as  FIG. 14  are given and the explanation will be omitted. 
     FIG. 16  shows a modified example of a flowchart for obtaining the optical characteristic of the subject eye  60  by combining plural Hartmann images. In the modified example shown in  FIG. 16 , the arithmetic part  210  adjusts the first illumination optical system  10  and the first light receiving optical system  20  on the basis of the signal level of the first light receiving signal from the first light receiving part  23 , and detects the density of the point images from the Hartmann images at that time. 
   Since the processings of the respective steps are the same as the steps with the same symbols of  FIG. 10  and  FIG. 14 , the explanation will be omitted. However, at step S 253 , in the case where the average light receiving signal level is larger than the predetermined signal level, the arithmetic part  210  proceeds to the processing of step S 109 . 
   According to the present invention, there is provided an ophthalmic measuring apparatus capable of measuring even an eye which can not be measured through a conventional uniform adjustment because of a large difference in the distribution of a refractive index, refraction or aberration, or the like. Besides, according to the invention, there is provided an apparatus in which an automatic adjustment is made to obtain necessary point image data so that Hartmann images are automatically obtained, and an optical characteristic is obtained by combining the acquired Hartmann images. 
   This application claims priority from Japanese Patent Application 2002-302435, filed Oct. 17, 2002, which is incorporated herein by reference in its entirety.