Abstract:
A process and apparatus for the calibration of an optical instrument. An optical instrument--such as a lens meter or ophthalmometer--is provided with a light source, a light detector, and an optical train of assembled optical elements therebetween. A suspect optical element to be measured is placed within the optical train at a measuring interval to deflect light passing along the optical train. An occulting moving boundary locus having at least two boundaries of differing shape, and a dedicated computer may be used to measure beam deflection. The dedicated computer also makes use of stored computer constants to transform raw measurements into the desired optical properties of the suspect optical element. The optical train of the instrument has its assembled optical elements randomly placed to production tolerances; precision registration of the optical elements to traditional close optical tolerances is omitted. Calibration occurs by manipulating the instrument&#39;s beam deflection apparatus under the control of a calibration program, by providing the optical instrument being calibrated with an umbilical cord which bypasses the central processing unit of the dedicated computer, but otherwise manipulates the entire optical instrument&#39;s beam deflection apparatus. This umbilical cord leads from a calibration computer, which substitutes central processing and contained memory as well as providing a supplemental program for the generation of customized computer constants. Customized computer constants are generated for each instrument by insertion of a series of test elements of known quantity into the samping interval of that instrument, and burned into a memory which is then placed into the dedicated computer of the instrument being calibrated.

Description:
This invention relates to a calibration procedure for optical apparatus, such as an automated lens meter or automated ophthalmometer. 
     SUMMARY OF THE PRIOR ART 
     Heretofore, an optical instrument such as a lens meter or an ophthalmometer has had its individual optical elements aligned with precision at the time of production. Typically, great care is taken to register each of the optical elements, so that the overall instrument error is minimal. A great deal of time has been consumed in such optical element registration. 
     According to the present invention, an optical instrument having a dedicated computer has its optical train permanently assembled to relatively loose production line tolerances. Measurements by the instrument of optical elements having known properties are used to generate a set of customized optical constants that become associated with that instrument&#39;s dedicated computer before the instrument leaves the production facility. 
     The broad concept of instrument self-manipulation, that is using the instrument&#39;s output to calibrate the instrument itself, has not been used generally outside the bubble chamber and streamer chamber arts. In those particular arts, subatomic particle tracks in a chamber are photographed from at least two spatially separated views. Included in each photograph, millions of which may be taken in a typical experiment, are the images of certain bench marks or &#34;fiducials&#34; which are located at various places within or about the chamber. 
     The photographs are subsequently digitized for the purpose of reconstructing the particle tracks in space. In this step of the analysis, at least some of the fiducial images are used to register the photograph in the image plane. However, the spatial reconstruction cannot proceed without a knowledge of the optical parameters of the system, such as fiducial locations in space, camera locations, focal lengths, lens distortion parameters, and lens and film plane axis tilts. Thus a procedure known as optical fitting in which a set of &#34;optical constants&#34; is generated must be carried out. 
     For the purpose of optical fitting, an extended set of fiducials (beyond the minimum number needed to register the film) is photographed and the photographs digitized to provide image plane locations of the fiducials. A set of optical constants that gives the best agreement between the measured fiducial positions on film and the predicted fiducial positions on film (based on the optical constants) is determined by a χ 2  (chi squared) minimization technique. These constants are then used in the spatial reconstruction. It is not necessary to generate new optical constants for each photograph since the optical constants do not change unless the apparatus itself changes. Several sets of constants may be generated to check apparatus consistency over time. 
     With respect to the lens meter and ophthalmometer art, these optical fitting techniques have only limited applicability. In particular, the provision of a fixed set of fiducials would have little meaning in an instrument which measures beam excursion in the region between a fixed source and a fixed detector. In effect, it would be necessary to provide the instrument with many more light sources and optical paths for calibration than were actually necessary for measurement. Moreover, the additional light paths would represent measurements of something qualitatively different from that which the instrument was meant to measure. This is only partly true in the bubble chamber and streamer chamber situations since the fiducials give rise to light paths that are typical of those that arise for some particle track configurations. Nevertheless, it can be seen that the bubble chamber and streamer calibration techniques only involve instrument self-manipulation in an approximate sense. Since they are devices for measuring particle tracks, a truly self-manipulative calibration procedure would involve the determination of optical constants from actual particle track measurements where the particle momentum or other parameters are known. In any event, the application of an interrogating computer to in effect align individual optical elements on a permanent basis at the end of a production line is nowhere disclosed or suggested to applicant&#39;s knowledge in this prior art. 
     Finally, it is known to manipulate electronic computers at their central processing units during an assembly stage. In such devices, an outside computer is wired or connected to the central processing unit of a unit being produced and in effect substituted for that central processing unit. Once this is done, the program of the computer is tested; for example, it may be single stepped, trapped, or have its various memory conditions checked. However, such central processing unit substitutions in the prior art have not been used for the purpose of optical alignment of an entire optical instrument through self-manipulation. 
     SUMMARY OF THE INVENTION 
     The present invention provides for precision calibration of an optical instrument without the necessity of precision alignment. An optical instrument--such as a lens meter or ophthalmometer--is provided with a light source, a light detector and an optical train of assembled optical elements for passing light from the light source to the detector. A suspect optical element to be measured is placed within the optical train at a measuring interval to deflect light passing along the optical train--this deflection being reflection by a suspect lens in the case of a lens meter, and reflection by a suspect cornea in the case of an ophthalmometer. An occulting moving boundary locus having at least two boundaries of differing shape, and a dedicated computer may be used to measure beam deflection. The dedicated computer also makes use of stored computer constants to transform raw measurements into the desired optical properties of the suspect optical element. These desired values may be printed out on a dedicated printer. 
     The optical train of the instrument has its assembled optical elements randomly placed to production tolerances; precision registration of the optical elements to traditional close optical tolerances is omitted. Calibration occurs by manipulating the instrument&#39;s beam deflection measurement apparatus under the control of a calibration program. The calibration program may be stored in a separate calibration computer, and calibration carried out by providing an umbilical cord between the optical instrument being calibrated and the fixed calibration computer. This connection bypasses the central processing unit (hereinafter CPU) of the dedicated computer, but otherwise manipulates the entire optical instrument&#39;s beam deflection apparatus. The calibration computer substitutes central processing and contained memory as well as providing the supplemental program for the generation of customized computer constants. 
     Customized computer constants are generated for each instrument by insertion of a series of test elements of known quantity into the samping interval of that instrument. That is, measurements are made wherein the optical properties of the suspect elements are known, but the various scale factors, points of origin, angular corrections, and the like, of the instrument are not known, but rather are to be determined. These constants, upon generation, are burned into a memory which is then placed into the dedicated computer of the instrument being calibrated. The umbilical system is then disconnected, the instrument&#39;s computer is activated, and the instrument leaves the assembly line. 
     Alternately, the calibration program may be run under the control of the dedicated computer&#39;s CPU with the calibration program stored in an auxiliary memory. The customized constants may then be printed on the instrument&#39;s printer and manually entered into a memory for subsequent placement into the dedicated computer. 
     By this process, optical elements randomly placed in the optical train to production tolerances, are utilized without individual registration to exact calibrated position. Apparatus calibration on a rapid and automated basis results. 
     SUMMARY OF THE CALIBRATION COMPUTATIONS 
     First, occultation information is taken where no suspect element is in the sampling interval (i.e. null element information). Thus, no deflection is expected to occur. 
     Second, a prism is placed in the sampling interval and occultation information recorded. The prism is then rotated through one or more known angles, e.g., 90° or 180°, and further occultation information generated. On the basis of the prism and null element occultation information, the points of origin and scale factors that allow a transformation of raw occultation information to beam deflections are computed. Moreover, the relative angle between the coordinate system of the lens table and that defined by the sampling apertures can be computed. 
     Third, occultation information is taken with one or more test elements having known spherical and/or cylindrical power. This is used to correct the constants computed above. 
     The knowledge that circular astigmatism of the sphere test element must be zero is exploited. In particular, the parameters that have been computed in the above steps do not guarantee that circular astigmatism is zero for those measurements. However, it is possible by rotating the coordinate system to insure that the circular astigmatism vanishes. The rotation effectively corrects for any misalignment of the sampling apertures. This rotational correction is applied to the scale factors and points of origin that had been computed on the basis of the prism and null element occultation information. 
     Fourth, the spherical scale factor is computed. With the corrected constants, deflection information for the null element and sphere test element occultation information is computed. The corrected sphere deflections relative to the corrected null element deflection information give rise to a spherical equivalent which can then be divided into the known spherical power to provide the scale factor. 
     Fifth, the points of origin for sphere and cross cylinder are computed on the basis of the corrected deflections from the null element occultation information. 
     OTHER OBJECTS AND ADVANTAGES 
     An object of this invention is to provide for complete assembly of an optical instrument without requiring precision alignment of the individual optical elements of the instrument. According to this aspect of the invention the optical train of an optical instrument between a light source and light detector has its individual optical elements randomly placed to production tolerances only. Precision registration of the optical elements is omitted. Light deflection measuring apparatus, such as an occulting moving boundary locus and a dedicated computer, is used to measure beam deflection. The instrument is provided with an umbilical connection which allows communication with a calibration computer. The calibration computer when connected completely supplants the function of the instrument&#39;s own central processing unit. By insertion of a series of test elements of known quantity into the sampling interval, customized computer constants are generated for each instrument having its randomly aligned optical train. By the expedient of placing the generated constants into the dedicated computer of the individual optical apparatus, calibration on a rapid and automated basis results. 
     An advantage of this invention is that laborious assembly line procedures of individual optical element calibration are avoided. Optical elements are merely placed in the instruments firmly within production tolerances. As those assembling the machine have a relatively wide latitude for the placement of optical elements, production is greatly expedited. 
     A further advantage of this invention is that the disclosed calibration technique requires each instrument to verify its own function. Through the intercession of an outside computer which manipulates the instrument, each of the active elements of the produced optical apparatus can be manipulated and verified. The required instrument constants are generated through manipulation of the very instrument in which they are required. Consequently, the instrument constants are generated to a high degree of accuracy. 
     Yet another advantage of this invention is that it is possible to obtain an automated record of instrument production. Since, in the production of medical instruments, it is customary for the manufacturer to maintain individually tailored records for each produced instrument, the disclosed calibration procedure readily meets this requirement. A record parochial to each instrument is generated, which record not only records instrument identification data, but additionally all customized computer constants. 
     A further advantage of this invention is that the calibration computer is utilized to pass or reject instruments. Where, for example, an instrument is far out of alignment, provision can be made to automatically reject such an instrument. Moreover, a manipulating calibration computer can identify problem areas which can then be corrected. 
     A further object of this invention is to disclose an optical instrument produced with an umbilical connection which can, throughout the life of the instrument, provide for exterior manipulation and calibration of the instrument by a calibrating computer. According to this aspect of the invention, the optical apparatus includes an umbilical connection, which upon connection to a calibrating computer supplants the function of the instrument computer with an outside computer, so that instrument manipulation and monitoring can occur. 
     An advantage to this aspect of the invention is that the produced instrument with its attached umbilical connection can at any time during its useful life be manipulated. By manipulation, those components requiring repair can be identified and replaced. Thereafter, rapid and automated calibration of the instrument, as well as the generation of recorded test data, can occur. True quality control results. 
     A further object of this invention is to adapt a precision calibration technique to a production line assembly of a precision optical instrument. According to this aspect of the invention, lens meters on the production line are sequentially examined at a quality control station by a manipulating calibration computer. The instruments are examined in wide tolerances for a pass-fail standard; subsequently, the instruments are precision calibrated by customized computer constants and tested in a wide variety of measurement functions. Thereafter, the customized computer constants are placed in the machine and the instrument is ready for use. 
     An advantage of this aspect of the invention is that the calibration procedure can remotely indicate to the calibration operator those procedures to follow, as well as whether the instrument has passed or failed such procedures. Not only can the calibrating operator be relatively unskilled in the optical alignment arts, but additionally, little room is left for operator error. 
     A further object of this invention is to provide an improved calibration procedure for determining scale factors and points of origin for the geometrical and optical properties of an optical instrument. According to this aspect of the invention raw data (e.g. occultation information) is generated for: no test element; prism test element (at least two orientations having known angular separation therebetween); and one or more sphere and/or cylinder test elements. 
     An advantage of this aspect of the invention is that the null element and prism information alone can be used to generate the geometric scale factors and points of origin which allow raw occultation information to be converted to deflection information. The fact that the sphere test element does not exhibit non-toricity (in particular circular astigmatism) can then be used to compute a coordinate system rotation which corrects for misalignment of the sampling apertures. 
     Another advantage of this aspect of the invention is that the spherical element information can then be combined with the null element information to generate the optical scale factor and points of origin that allow deflection information to be converted to the desired form of optical parameters (sphere, cylinder, axis, etc.). The fact that the geometric points of origin and scale factors had been corrected for spurious non-toricity effects allows the use of zero-going test functions (e.g. functions such as circular astigmatism whose non-zero values indicate the presence of non-toric surfaces) to serve as diagnostics in the computations carried out by the calibrated instrument in actual use. 
     Other objects, features and advantages of this invention will become more apparent after referring to the following specification and attached drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 illustrates an assembly line of optical instruments, here lens meters, being interrogated by a calibration computer at a quality control station on an assembly line. 
     FIG. 2a is a perspective schematic of optics inside one type of instrument--here a lens meter--capable of being calibrated by the method and apparatus of the present invention. 
     FIG. 2b is a perspective schematic of optics inside another type of instrument--here an ophthalmometer--capable of being calibrated according to the present invention. 
     FIG. 3 is a plan view of a moving boundary locus disc suitable for measuring beam deflections in a lens meter or keratometer. 
     FIG. 4a is a perspective schematic illustrating beam deflections caused by a suspect element having spherical power. 
     FIG. 4b is a perspective schematic illustrating beam deflections caused by a suspect element having 0°-90° astigmatism. 
     FIG. 4c is a perspective schematic illustrating beam deflections caused by a suspect element having 45°-135° astigmatism. 
     FIG. 5 is a block diagram of computer logic illustrating with particularity the point of supplementation of the dedicated computer logic by the attached umbilical cord to provide for manipulation of the entire instrument and individual instrument participation in the generation of its own constants. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Overview of the Calibration Procedure 
     FIG. 1 is a somewhat stylized view of an assembly line calibration station. In this picture, lens meters are being calibrated--lens meter 10 is awaiting calibration, lens meter 15 is being calibrated, and lens meter 20 has just been calibrated at this calibration station. An important feature of this invention is that these lens meters have had their optical components assembled to relatively loose production tolerances, and that no further precision alignment is required. 
     The apparatus at the calibration station is, broadly, an interrogating and calibrating computer system, the components of which include microcomputer 30, associated disc drive 32, memory mapper 35, printer 37, and display console 40. Lens meter 10 awaiting calibration, has associated electronics, the components of which are mounted on boards 42. As will be described in detail below, the associated electronics includes a dedicated computer having a microprocessor unit (hereinafter MPU) and a read-only memory (hereinafter ROM). Lens meter 20, shown leaving the calibration station, has MPU 45 and ROM 50 in place, shown for simplicity as being mounted on the same board. In advance of calibration however, lens meter 10 has MPU socket 55 and ROM socket 60, neither of which has its associated component in place yet. In principle, it is possible for lens meter 10 to have its MPU and ROM installed, but since the calibration procedure requires that the ROM be inserted into memory mapper 35 and that the MPU be removed, it is more feasible to have a supply of MPU&#39;s 65 and a supply of ROM&#39;s 70 at the calibration station. During the calibration step, microcomputer 30, is connected to the MPU socket of lens meter 15 (undergoing calibration) through signal buffer 75 and plug 77. Signal buffer 75 and plug 77 are connected by multiconnector cable 80; microcomputer 30 and signal generator 75 are connected by multiconnector cable 82. The effect of this connection between microcomputer 30 and lens meter 15 is that the calibration computer is substituted for the dedicated computer. 
     During the calibration step, a series of test elements which may include a prism 85 and a lens 90 are sequentially inserted into the sampling interval 17 of lens meter 15. The insertion and replacement of test elements, as well as the inputting of instructions to the calibration computer, are done by calibration operator 100 shown in phantom outline seated at the console 40. 
     OPERATION OF THE CALIBRATED INSTRUMENT 
     While FIG. 1 is drawn most specifically to lens meter calibration, the method and apparatus of this invention wherein a fixed calibration computer is substituted for each instrument&#39;s dedicated computer, is suitable for calibrating any optical instrument which makes use of a dedicated computer to manipulate internal constants in order to provide intelligible measurements to the user. The mathematical analysis that will be discussed below is concerned with the transformation of raw data in the form of beam measurements in order to obtain desired optical parameters in terms of sphere, cylinder, cylinder axis, and prism. This is merely illustrative, the technique being applicable to a broader class of instruments. The discussion below will also be most specifically descriptive of an instrument wherein the beam deflection is measured by a moving boundary locus. Both a lens meter for analyzing refractive suspect optics and an ophthalmometer for analyzing reflective suspect optics will be discussed. 
     In order that the details of the mathematical analysis of the calibration procedure be understood and appreciated, a digression is made to explain the operation of particular embodiments of lens meters and ophthalmometers. Both the apparatus for the generation of raw measurements of beam deflection, and the mathematics for transforming these raw measurements into optical parameters are now considered. 
     FIG. 2a shows a lens meter in which a moving boundary locus is utilized to measure the deflection, caused by suspect optical element S, of a beam between light source 314 and detector D. This configuration makes use of a beam wherein the light rays are not parallel to one another. 
     Briefly, a single light source 314 is imaged in multi-faced prism 316 to produce four apparent light sources, one of which is designated as 314&#39;. FIG. 2a illustrates the optical path from apparent light source 314&#39;, it being understood that three additional optical paths, omitted for clarity, are also present. The light from virtual image 314&#39; is divergent. The light is reflected from diagonal mirror 320 and then focused by condensing lens 322 which renders the light convergent. From lens 322, the light is reflected from mirror 330 and passes through aperture plate 332. Aperture plate 332 preferably has a separate aperture for each apparent light source. The suspect optical element S is typically registered to aperture plate 332 and each apparent light source is imaged as a tiny intense spot of light at its corresponding aperture. Thus, each aperture serves to sample a distinct region of the suspect optical element. After passing through one of the apertures, here aperture a&#39;, the light passes through a lens 334, is reflected from mirror 336, and falls on sampling mask 338. Sampling mask 338 has a central aperture which limits the amount of light to an angularly smaller bundle. The light then passes through lens 340 and mask 342, to a sector a&#39; of detector D corresponding to virtual light source 314&#39; and sampling aperture a&#39;. 
     Depending on the optical power of suspect element S, the actual optical path of the light between light source 314 and detector D will be subject to deflection. Moving boundary locus L which is, in the embodiment shown, a rotating disc is situated between lens 322 and mirror 330, but typically closer to lens 322. As is more clearly shown in FIG. 3, moving boundary locus L has a border area 120 which defines disc rotation, and internal region 125 which occults the deflected light beams. Internal region 125 comprises opaque areas 140 and 142, and transparent areas 132 and 133. Each of the four light paths corresponding to the four facets of prism 316 falls on a different region of the rotating disc and may be treated as completely independent of the other three. The boundaries between opaque areas 140 and 142, and transparent areas 132 and 133 can be described generally by the equations 
     
         R=kθ and R=-kθ 
    
     where R and θ are the radial and angular coordinates, and k is a proportionality constant. As the disc rotates, the light impinging on the disc is alternately transmitted and occulted. A knowledge of the angular position of the disc when occultation occurs also permits knowledge of the radial position on the disc. The known relation between angle and radius defines the boundaries between the opaque and the transparent areas. Once radial and angular position are known, beam deflection is defined. 
     The details of the optical train and moving boundary locus of FIG. 2a are more fully set forth in my copending U.S. Patent Application Ser. No. 813,211, filed July 5, 1977, entitled &#34;Lens Meter with Automated Read-Out&#34;. I hereby incorporate by reference my earlier above-identified U.S. Patent Application. This application is abstracted as follows: 
     &#34;An automated readout for a lens meter is disclosed in combination with a light beam deflecting type of lens meter such as that of a Hartman test. In such a light beam deflecting type of lens meter, a light source having one or more beams is passed through a suspect optical system and deflected by the suspect optical system to a deviated path. Measurement of the deviated path within a preselected area of excursion is typically equated to various powers of the suspect optical system in sphere, cylinder, cylinder axis, and prism. The invention provides for a means of measurement of deviate paths and includes a moving boundary locus with edges of distinctly different shape placed to intercept and occult said deflected beam in a known plane within the area of excursion at a distance from the suspect optical system. The moving boundary locus is typically arranged for movement along a predetermined path at a velocity within the known plane. The boundary locus includes a first substantially transparent portion, a second, substantially opaque portion, and at least two boundaries between the opaque and transparent portions. Each of the two boundaries defines a unique non-ambiguous intersection within the area of excursion for each position of the beam and sweeps the preselected area of excursion at differing angularities with respect to the predetermined path of said moving boundary locus. The beam, after leaving the moving boundary locus, is reimaged to a photosensitive detector. By the expedient of measuring the position of the moving boundary locus when the moving boundary occults the beam for two of the boundaries, the amount of beam excursion can be measured and related to optical system measurement. The detector is provided with a circuit which averages the two detector states provided by occultation. This enables lens systems of varying light transmissivity to be measured.&#34; 
     A representative patent claim is a follows: 
     &#34;1. In the combination of a suspect optical system for measurement of deflection, a light source emanating a beam passed through said suspect optical system and deflected by said suspect optical system to a deviated beam path for measurement within a preselected area of excursion; and, means for measurement of said deviated path, the improvement in said means for measurement of said deviated path comprising: a moving boundary locus placed in a known plane at a preselected distance from said suspect optical system; said moving boundary locus arranged for sweeping movement along a predetermined path within said known plane, said boundary locus including a first portion, a second portion and at least two boundaries therebetween of distinctly different shape with each of said boundaries sweeping at differing angularities with respect to the predetermined path of said moving boundary locus; means for sweeping said moving boundary locus along said predetermined path producing occulation of said beam by said boundaries; a photosensitive detector aligned to receive said beam; and, means for measuring the position of said moving boundary locus when said detector detects produced occultation of said light beam at said boundaries of said moving boundary locus whereby at least one measurement of each of said moving boundaries of said moving boundary locus at the time of detector detection of occultation measures the excursion of said beam due to deflection by said suspect optics.&#34; 
     FIG. 2a is copied from the above-referenced application, being designated there as FIG. 8. The only changes that have been incorporated into FIG. 2a are the addition of reference numerals for the moving boundary locus portions, and the addition of dashed outline 334&#39;. 
     FIG. 2b shows the optical train of an ophthalmometer used to measure reflective power, here that of a cornea 170. A single light source 172 is imaged in a multifaced prism 175 to produce four virtual images and thus establish four separate light paths between light source 172 and cornea 170. For clarity, only one of the light paths from light source 172 to cornea 170 is shown. The light from each virtual image of light source 172 is divergent. It is reflected from a small elliptical diagonal mirror 177 which serves both as a reflector and an aperture stop. Light reflected by mirror 177 then passes to a mirror 180, and through a focusing lens 182 to the suspect cornea. 
     Each of the four virtual images of light source 172 is thus focused on a separate portion of cornea 170. The light reflected from cornea 170 is then intercepted by a moving boundary locus disc 185, the precise position of interception depending on the curvature of cornea 170 which is being measured. The operation of disc 185 is substantially the same as for the lens meter described above. Moving boundary locus disc 185 is driven by a motor 186, shown in phantom. The light is then focused by light collecting optics defined by lenses 187 and 188 before passing into a detector 190. 
     Due to the geometry of the ophthalmometer, the light from the four virtual images, once reflected off cornea 170, follows four widely separated light paths and falls on four discrete portions of locus disc 185. Four separate light collecting optical subtrains and four detectors are used. Also shown in FIG. 2b are a detector 190&#39; and light collecting lenses 187&#39; and 188&#39; for a second of the four light paths. For clarity, the other two detectors with associated light collecting optics are not shown. 
     A comparison of the ophthalmometer with the lens meter shows the two devices to operate in essentially the same manner. Differences in geometry result from the need to accommodate reflective optics generally and horizontal axis reflective optics (e.g., a patient&#39;s eye) specifically. It should be noted that the lensmeter of FIG. 2a has a single optical train between the four light sources and the four detectors. The ophthalmometer of FIG. 2b, on the other hand, has four separate light collecting optical subtrains for the four detectors which are widely separated in space. Thus the ophthalmometer geometry is characterized by more internal constants for transforming raw occulation information into beam deflections. 
     Thus, the apparatus illustrated in FIGS. 2a and 2b produces, for a given suspect optical element, a total of 16 readings. That is, for each of the four sampling apertures, there are four angles of occulation corresponding to the four boundaries on the rotating disc, each boundary of which sweeps all four light beams. These hardware-generated values are designated as φ ij , where i designates the particular aperture (i.e., the particular light path or sampling interval on the suspect optical element), and j designates the particular boundary effecting the occulation. The numbering of the subscripts i and j is best understood with reference to FIG. 3 and FIGS. 4a-c. With reference to the disc shown in FIG. 3, border 135b corresponds to j=1; border 135a to j=2; border 134a to j=3; and border 134b to j=4. Reference to FIGS. 4a-4c shows that the positive x, positive y quadrant corresponds to i=1; the negative x, positive y quadrant to i=2; the negative x, negative y quadrant to i=3; and the positive x, negative y quadrant to i=4. 
     Computation of optical parameters of a suspect optical element from the raw occulation measurements φ ij , while comprising a long series of steps, can be better understood in terms of a smaller number of broader steps. 
     First, raw occulation information must be transformed into beam deflections measured in a transverse plane. In particular, scale factors and points of origin are applied to the raw occulation measurement to compute deflections. For the rotating boundary locus, these deflections are initially computed in polar coordinates so as to give radial and azimuthal deflections. These may then be transformed to cartesian coordinates. 
     Second, the deflections of the beams are manipulated to provide a plurality of numbers having certain physical significance. In particular, with four sampling apertures and a deflection in two dimensions for each, eight pieces of deflection information are produced. These are more conveniently rearranged to provide a new set of independent pieces of information. In the preferred embodiment, two prism measurements, two cross cylinder astigmatism measurements, and a spherical equivalent measurement are computed. This leaves three more pieces of information available. It is convenient and useful to compute three optical quantities that are expected to be zero for most optical elements. Thus, circular astigmatism and two power variation parameters are computed. 
     Third, a scale factor representing spherical power is applied to six of the eight optical quantities that had been computed in terms of deflections. The prism measurements are not scaled. 
     Fourth, suspicious circumstances are flagged using the extra (but not redundant) information. For example, the values of circular astigmatism and power variation are compared with predetermined numerical values as a check that the optical element being measured does not possess these unexpected properties. In particular, if either circular astigmatism or the quadratic sum of the power variation parameters is larger than a predetermined value, a suspicious circumstance is flagged. 
     Fifth, desired forms of optical parameters are calculated. The two values representing cross cylinder astigmatism are converted into cylinder and cylinder axis. In order to accomplish this, it is necessary to remain aware of the fact that the coordinate system in which the deflections were measured is not in general oriented with respect to the coordinate system of the lens table with which the suspect optical element is aligned. Thus, an angular correction to the cylinder axis and prism measurement must be made. In addition, points of origin for sphere and cylinder measurement must be taken out and spherical equivalent must be corrected for cylinder to produce the desired value of sphere. This step may be carried out before the fourth if desired. 
     Having thus described in general the computations carried out by the calibrated instrument in actual use, a more detailed mathematical description can be set forth. This description must be made with reference to a particular instrument geometry. The lens meter computations are now set forth. The ophthalmometer computations are analogous, but would involve separate constants for transforming raw occulation information into beam deflections. 
     First, the occultation data in terms of φ ij  must be converted to beam deflections x i  and y i . 
     For a given aperture i, the quantity f i  can be written where: 
     
         f.sub.i =φ.sub.i3 +φ.sub.i4 -φ.sub.i1 -φ.sub.i2 (1) 
    
     It can be seen that the quantity f i  is a measure of the radial position at which the i th  beam crosses the plane of the rotating disc. A measure of the azimuthal position of the beam is given by the quantity g i  where: 
     
         q.sub.i =φ.sub.i1 +φ.sub.i2 +φ.sub.i3 +φ.sub.i4 (2) 
    
     Since the angular separation between boundaries 135a and 135b is a constant 90° regardless of radius, and similarly the angular separation between borders 134a and 134b is 90°, the quantity t i  where: 
     
         t.sub.1 =φ.sub.i1 +φ.sub.i4 -φ.sub.i2 -φ.sub.i3 (3) 
    
     provides a check on the system since t i  should be nearly zero. 
     The radial deflection R i  and angular deflection φ i  for the beam from the aperture i can be written in terms of f i  and g i  as follows: 
     
         R.sub.i =αf.sub.i +β                            (4a) 
    
     
         φ.sub.i =γg.sub.i +δ                       (4b) 
    
     The parameters α, β, γ, and δ are constants for a given instrument, these constants, among others, being generated in the calibration procedure that is the subject of this application. (The calibration procedure is described below.) In particular, α is related to the equations of the contour (R=kθ and R=-kθ); β takes up the radial position with no radial deflection to provide R i  =0; γ is a constant of proportionality that is known independently of the calibration of the instruments, being a function of the number of divisions in the outer portion of the rotating disc; and δ determines the zero of angle. 
     The radial deflection R i  and the angular deflection φ i  for each sampling aperture are then transformed to deflections in cartesian coordinates by the standard formulae: 
     
         x.sub.i =R.sub.i cos φ.sub.i -x.sub.0                  (5a) 
    
     
         y.sub.i =R.sub.i sin φ.sub.i -y.sub.0                  (5b) 
    
     where x 0  and y 0  are parameters corresponding to the cartesian coordinates of the undeflected light beams. 
     Having obtained the vertical and horizontal cartesian deflections for each sampling aperture, it is possible to calculate combinations of the deflections that are more closely related to optical parameters. Thus, horizontal prism P x  and vertical prism P y  are given by the formulae: ##EQU1## P x  and P y  may be computed directly in terms of prism diopters if α, β, x 0 , and y 0  have been scaled with that in mind. In any event, P x  and P y  would only have to be scaled by a multiplicative factor to get the result in prism diopters. 
     FIGS. 4a-c show the beam deflections caused by suspect elements having sphere, 0°-90° astigmatism and 45°-135° astigmatism consists of a positive cylinder 154 aligned along the 45°  axis and a negative cylinder 156 aligned along the 135° axis. It should be understood that such crossed cylinders as shown in FIGS. 4b and 4c are typically composite and do not have an optical interface between the positive and negative cylinders. 
     In terms of the cartesian deflections of the beams, it is possible to express spherical equivalent (Seq), 0°-90° astigmatism (C + ) and 45°-135° astigmatism (C x ) as follows: 
     
         Seq=-x.sub.1 +x.sub.2 +x.sub.3 -x.sub.4 -y.sub.1 -y.sub.2 +y.sub.3 +y.sub.4 (7a) 
    
     
         C.sub.+ =2 (+x.sub.1 -x.sub.2 -x.sub.3 +x.sub.4 -y.sub.1 -y.sub.2 +y.sub.3 +y.sub.4)                                                 (7b) 
    
     
         C.sub.x =2 (+x.sub.1 +x.sub.2 -x.sub.3 -x.sub.4 +y.sub.1 -y.sub.2 -y.sub.3 +y.sub.4)                                                 (7c) (7c) 
    
     Seq., C + , and C x  may then be scaled by a multiplicative scale factor S so they are expressed in diopters. 
     The measurement of P x , P y , Seq, C + , and C x  is over-determined in the sense that eight deflection quantities x i  and y i  measured and only five parameters are required. While the five parameters suffice to describe normal optical elements expected to be encountered, there are certain non-toric surfaces and surfaces having a power variation, possibly due to inhomogeneity of material, that can give rise to non-zero values of circular astigmatism (CA) and of power variation parameters (PV 1  and PV 2 ) where: 
     
         CA =+x.sub.1 +x.sub.2 -x.sub.3 -x.sub.4 -y.sub.1 +y.sub.2 +y.sub.3 -y.sub.4 (8a) 
    
     
         PV.sub.1 =-x.sub.1 +x.sub.2 -x.sub.3 +x.sub.4 -y.sub.1+y.sub.2 -y.sub.3 +y.sub.4                                                  (8b) 
    
     
         PV.sub.2 =+x.sub.1 -x.sub.2 +x.sub.3 -x.sub.4 -y.sub.1 +y.sub.2 -y.sub.3 +y.sub.4                                                  (8c) 
    
     One possible method of transforming the beam deflections into sphere, cylinder, and prism as described above would be to adjust the x and y values through a X 2  minimization with the constraints that CA, PV 1  and PV 2  be zero. However, in the preferred embodiment, sphere, cylinder and prism are computed directly from the measured deflections, and CA, PV 1  and PV 2  also computed. Then, if CA or the PV&#39;s exceed a predetermined limit, this is taken to indicate a suspicious circumstance. 
     In particular, the following circumstances are flagged: 
     
         (S)(CA)&gt;0.2 or                                             (9a) 
    
     
         (S)√(PV.sub.1).sup.2 +(PV.sub.2).sup.2 &gt;0.3         (9b) 
    
     where S is the scale factor that transforms Seq, C + , and C x  to diopters. The limits of 0.2 and 0.3 are representative. 
     In fact, it is customary to describe lenses not in terms of Seq, C +  and C x , but rather in terms of sphere S 1 , cylinder C, and azimuthal angle θ. These two alternate sets of descriptive parameters are related by the following equations: 
     
         (S) (C.sub.+)=C cos 2 (θ+A)+Z.sub.c+                 (10a) 
    
     
         (S) (C.sub.x)=C sin 2(θ+A)+Z.sub.cx                  (10b) 
    
     
         (S) (Seq)=S.sub.1 +C/2+Z.sub.s                             (10c) 
    
     Where, in addition to S, the quantities Z s , Z c+  and Z cz  are parameters that have been determined during the calibration step to be described below. The parameter A is basically the relative angle between the x-y coordinate system of the apertures and the orientation of the lens table of the lens meter nessitating correction of P x  and P y . A parameter d 1  represents a small displacement of the lens measuring position along the optical train, necessitating correction of S, and C. 
     Thus, corrected prism values P x  &#39; and P y  &#39;, sphere S 1  &#39;, and cylinder C&#39; are given by: 
     
         P.sub.x &#39;=P.sub.x cos A+P.sub.y sin A                      (11a) 
    
     
         P.sub.y &#39;=P.sub.y cos A-P.sub.x sin A                      (11b) 
    
     
         S.sub.1 &#39;=S.sub.1 /[1+(d.sub.1)(S.sub.1)]                  (11c) 
    
     
         C&#39;+S.sub.1 &#39;=(C+S.sub.1)/[1+(d.sub.1) (C+S.sub.1)]         (11d) 
    
     At this point, it can be seen that the computation of sphere, cylinder, cylinder axis, and prism can be accomplished from the raw input of the θ ij , so long as the instrument has been calibrated to provide values of α, β, γ, δ, X 0 , Y 0 , S, Z s , Z C+ , Z CX , A, and d 1 . 
     The electronic circuitry required to ultimately calculate the desired quantities of sphere, cylinder, axis, and prism performs four logical functions. First, the rotational position of the rotating boundary locus L is monitored. Second, the occulations are recorded as they occur. Third, the circuitry computes the angular interval of the occulation in terms of the θ ij , typically to an accuracy of 1 part in 50,000 of the total rotation. Fourth, these angular values are converted to the desired parameters using the formulae discussed above. 
     FIG. 5 is a schematic block diagram of the electronic circuitry to perform these various functions and also the circuitry that accomplishes the calibration. The operation of the lens meter (or other instrument) circuitry is more fully described in my copending U.S. Pat. Application Ser. No. 813,211, filed July 5, 1977, and incorporated by reference above. FIG. 5 of the present application is substantially identical to FIG. 4 of the referenced application, except that blank block 200 was formerly shown to contain a CPU and the circuit elements within dashed rectangle 230 have been added. The circuit elements within dashed rectangle 230 are only connected with the rest of the circuit during the calibration step, and when the calibration is over, those elements are disconnected and a CPU chip (preferably a type 8080 MPU manufactured by Intel Corporation of Santa Clara, California) is inserted in the socket corresponding to blank rectangle 200. When the instrument with its own CPU is doing the computations required for a measurement of the suspect optical element, the CPU that occupies rectangle 200 is making use of a program stored in ROM 202. ROM 202 also contains the calibration parameters α, β, etc. that are necessary to convert the raw occultation information into lens parameters. 
     It is apparent that the calibration constants α, β, etc. are functions of the total geometry of the instrument (lens meter, ophthalmometer, etc.) that is doing the measuring, in particular, the location and orientation of the moving boundary locus, and the location and orientation of the optical train. Also, a greater number of constants may by required to define certain configurations (e.g. ophthalmometer having four measuring apertures). However, the various elements that go into making a finished optical instrument cannot easily be assembled to precise design tolerances. As an example, with reference to FIG. 2a, lens 334 may well be displaced from its design position 334&#39; shown in dashed outline. Additionally, the four apertures in aperture plate 332 may not be in a precise square, the shaft of rotating disc L may not be in its center, and any other of the elements may be displaced from its design position. Thus, the optical calibration constants α, β, etc. that correspond to an instrument that has all its elements in their precise design locations will in general not provide the best output values of lens parameters since a given instrument is not likely to have its elements precisely registered. It is in recognition of this fact that the calibration procedure of the present invention set forth herein was developed. 
     THE CALIBRATION PROCESS 
     Before the optical instrument (e.g. lens meter) is capable of generating optical parameters from occulation information, the dedicated computer must be supplied with the calibration constants α, β, etc. FIG. 5 shows the electronic circuitry that is used during the calibration step to provide a set of optical constants for a particular instrument. It cannot be over-emphasized that the procedure described herein for generating the optical constants does not rely on a precision alignment of the optical elements within the instrument being calibrated. Rather, so long as the elements have been assembled with reasonable precision, such as that achievable by relatively unskilled but careful workers, the calibration procedure results in an instrument whose overall performance is comparable to the performance of one that has been assembled with great precision. 
     The instrument itself has the electronic components shown in FIG. 5, except that the elements within dashed rectangle 230 are not present, and the block shown as blank rectangle 200 contains a CPU in the form of an MPU chip. Rectangle 230 contains the elements of the calibration computer, and for clarity, the same reference numerals as are used for the physical components themselves in FIG. 1 are used in the schematic of FIG. 5. Thus, calibration computer 30 communicates to the instrument being calibrated, and in particular to the MPU socket 200 (analogous to MPU socket 55 in FIG. 1) by a signal buffer 75. Calibration computer 30 has its own peripherals including dual disc drive 32, printer 37, ROM mapper 35, and display terminal 40. A particular configuration will be described in a separate section entitled &#34;The Calibration Program&#34;. 
     During the calibration phase, calibration computer 30 emulates the instrument&#39;s own dedicated computer which is temporarily disconnected. One portion of the program inside the calibration computer 30 is an emulator which, in conjunction with signal buffer 75, provides signals to the instrument that have similar effect to signals generated by the instrument&#39;s own CPU when in place. Thus, the instrument is under the control of calibration computer 30. During the calibration phase, calibration computer 30 does not access the instrument&#39;s memory comprising ROM 202 and RAM 204, but rather uses its own disc drive 32 or ROM capacity to perform the memory functions. (In fact, as discussed above, ROM 202 is not inserted until after the calibration process is complete.) 
     Broadly, the calibration procedure involves the insertion of a series of test optical elements within the sampling interval 17 of instrument 15 being calibrated. The deflections caused by these elements, or more strickly speaking, the occultation times generated by the moving boundary locus, are measured and made available to calibration computer 30. The operating system for calibration computer 30 allows the calibration program to communicate with the operator through control console 40. In particular, a series of instructions to the operator are displayed on the screen of control console 40. A typical sequence of instructions, to be followed by operator 100 once an instrument is connected to calibration computer 30, includes the following: 
     &#34;Insert `no lens` and type a space.&#34; 
     &#34;Place calibration lens stand over lens head. Place calibration prism on stand with No. 1 edge flush against lens table and type a space.&#34; 
     &#34;Rotate prism so that No. 2 edge is flush against lens table and type a space.&#34; 
     &#34;Rotate prism so that No. 3 edge is flush against lens table and type a space.&#34; 
     &#34;Rotate prism so that No. 4 edge is flush against lens table and type a space.&#34; 
     &#34;Remove the calibration prism and place the ten diopter calibration sphere lens on the stand and type a space.&#34; 
     It should be understood that when the operator complies with each instruction and signifies his compliance by typing a space, calibration computer 30 receives the deflection information that is generated with the particular test element, or lack of a test element, in place. Once all these steps have been complied with, the mathematical portion of the calibration program within calibration computer 30 is able to manipulate the measurements thus received, and generate a set of optical calibration constants for the instrument being calibrated. 
     Broadly, the calibration computations are the inverse of the computations carried out by the calibrated instrument (as described at length above). Thus, measurements are made wherein the optical properties of the suspect elements are known, but the various scale factors, points of origin, angular corrections, and the like, are not known, but rather are to be determined. 
     First, occultation information is taken where no suspect element is in the sampling interval (i.e. null element information). Thus, no deflection is expected to occur. 
     Second, the prism is placed in the sampling interval and occultation information recorded. The prism is then rotated through a known angle, e.g., 90° or 180°, and further occultation information generated. On the basis of the prism and null element occultation information, it is possible to compute the points of origin and scale factors that allow a transformation of raw occultation information to beam deflections. Moreover, the relative angle between the coordinate system of the lens table and that defined by the sampling apertures can be computed. 
     Third, occultation information is taken with a test element having known spherical power. The knowledge that circular astigmatism of the test element must be zero is exploited. In particular, the parameters that have been computed in the above steps do not guarantee that circular astigmatism is zero for those measurements. However, it is possible by rotating the coordinate system to insure that the circular astigmatism vanishes. The rotation effectively corrects for any misalignment of the sampling apertures. This rotational correction is applied to the scale factors and points of origin that have been computed on the basis of the prism and null element occultation information. 
     Fourth, the spherical scale factor is computed. Corrected deflections (using the corrected constants) are computed for the sphere and null elements. The corrected sphere deflections relative to the corrected null element deflections give rise to a spherical equivalent which can then be divided into the known spherical power of the test element to provide the scale factor. 
     Fifth, the points of oritin for sphere and cross cylinder are computed in the basis of the corrected deflections computed on the basis of null element occultation information. 
     The calibration constants thus generated, along with the program required to transform raw occultation measurements into desired optical parameters (i.e. to carry out the mathematical calculations discussed above under the subheading &#34;Operation of the Calibrated Instrument&#34;) are then written into a ROM which has been placed in ROM mapper 35. A hard copy of the optical calibration constants is also written out by printer 37 to provide a permanent record, as well as to make it possible to discover any bizarre results that the program is unable to analyze. The calibration computer is then disconnected from the instrument being calibrated (i.e. plug 77 is removed), an MPU is placed in the MPU socket, and the mapped ROM is placed in the ROM socket. The instrument has then been calibrated. A variation on this procedure of substituting CPU&#39;s is to substitute ROM&#39;s so that the calibration program is run under the control of the dedicated computer&#39;s CPU. This would be done by removing the ROM containing the operating program and inserting a ROM containing the calibration program. (Alternatively, the calibration program could be permanently resident along with the operating program.) The generated constants would be written on the instrument&#39;s own printer 212 and manually inserted into a ROM which would then be inserted into the instrument. 
     Having discussed the calibration procedure generally, and further having outlined the mathematical significance of the optical calibration constants α, β, etc., it is now possible to discuss the mathematical computations that must be carried out to derive the optical calibration constants from the raw occultation measurements taken with the test elements in place. For simplicity, the discussion of the mathematics that follows is based on a simplified but nevertheless viable calibration procedure in which the prism deflections are measured for only two test prism orientations, rather than the four orientations alluded to in the discussion of the instructions to the operator. 
     First, occultations occurring with no test element in place are measured. Each of the four sampling apertures gives rise to an f i  and a g i  (i=1,2,3,4) as defined in equations 1 and 2. These are summed to generate an f O  and g O  defined as follows: ##EQU2## where f i  and g i  in this equation refer to the quantities measured with no test elements in place. Recalling the relationship between φ i  and g i  from equation 4b, one can define φ O  as follows: ##STR1## where φ O  is related to g O  as follows: 
     
         φ.sub.O =γ g.sub.O =δ                      (14) 
    
     One parameter that is very well known and does not have to be determined from the calibration is γ, since it is the angular scale factor determined from the properties of the outer region 120 of rotating boundary locus disc L. For the measurement with no test element in place, φ O  can be set to zero, thereby allowing δ to be solved for. It is also convenient to set Y O  =O. 
     A test element having Δ prism diopters with a base direction at an orientation θ +   relative to the x axis is then inserted. A series of f i  and g i  are generated, and new quantities f +  and g +   are defined as follows: ##EQU3## Similarly, the measurements are taken with the prism rotated by 90°, to generate quantities f -  and g -  defined as follows: ##EQU4## 
     In terms of g +   and g - , one obtains the average azimuthal deflections φ +   and φ -   as follows: 
     
         φ.sub.+ =γ g.sub.30 +δ                     (17a) 
    
     
         φ.sub.- =γ g.sub.31 +δ                     (17b) 
    
     At this point, it is possible to solve for α, β, A, and x O , expliting the fact that the measurements were generated with prism orientations that were exactly 90° apart. Thus, independent of any knowledge of the prism strength, ξ, defined as the ratio of β over α is given by: ##EQU5## where η is given by: ##EQU6## with the relative sign taken as + when f +  &gt;f -   and - when f -  &gt;f 30  . 
     The prism strength is then used to solve for α and β absolutely as follows: ##EQU7## 
     
         β=αξ                                         (20b) 
    
     A, the relative angle between the coordinate system in which the calculation has progressed up to this point and the lens table coordinate system is given by: 
     
         A=sin.sup.-1 [4(α f.sub.+  +β)(sin φ.sub.+)/Δ]-θ.sub.+                       (21) 
    
     and x O  is given by: 
     
         x.sub.O =α f.sub.O +β                           (22) 
    
     Thus, it can be seen that the parameters α, β, γ, δ, A, x O , and Y O  which give the geometrical scale factors and points of origin have been obtained solely by using null element and prism information. 
     The additional information required to complete the calibration computation is found in the deflections generated when a test element having spherical power D is inserted. With this lens in place, an x-y deflection for each of the four sampling areas is generated, the calculation of each x i  and y i  being carried out according to equations 1-5. However, the x i  and y i  values thus calculated will generally give a non-zero value for the circular astigmatism CA defined in Equation 8a. This indicates the presence of a non-toric surface while the test element is known not to possess such a characteristic. In order to remove this effect, it is necessary to rotate the coordinate system by an angle θ s  where: ##EQU8## and where the solution of θ s  near -90° is taken. 
     The already calculated values for x O , y O , δ, and A must now be rotated by the angle θ s  to give a corresponding set of primed variables as follows: 
     
         x.sub.O &#39;=cos (-θ.sub.s)                             (24a) 
    
     
         y.sub.O &#39;=x.sub.O sin (-θ.sub.s)                     (24b) 
    
     
         δ.sup.&#39; =δ-θ.sub.s                       (24c) 
    
     
         A.sup.&#39; =A-θ.sub.s                                   (24d) 
    
     Since this is a rotation about the original origin (derived with zero prism), the prism points are still intact. Note also that α and β are invariant with respect to this rotation. 
     Using x 0  &#39;, y 0  &#39;, δ, and A&#39;, the values for x i  and y i  are recomputed. Additionally, x 0i  and y 0i  are commputed from the f i  and g i  that were generated with no test element in place. The spherical scale factor S is then given by: 
     
         S=D/[(-x.sub.1 +x.sub.2 +x.sub.3 -x.sub.4 -y.sub.1 -y.sub.2 +y.sub.3 +y.sub.4)-(-x.sub.01 +x.sub.02 +x.sub.03 -x.sub.04 -y.sub.01 -y.sub.02 +y.sub.03 +y.sub.04)]                                     (25) 
    
     The values of Z s , Z c+ , and Z cx  can now be computed, being simply the values of sphere and cross-cylinder astigmatism that result when the other parameters are applied to the x 0i  and y 0i  --that is, the the computed deflections arising where no sphere or cross-cylinder astigmatism is in the system. These parameters are given as follows: 
     
         Z.sub.s =S(-x.sub.01 +x.sub.02 +x.sub.03 -x.sub.04 -y.sub.01 -y.sub.02 +y.sub.03 +y.sub.04)                                      (26a) 
    
     
         Z.sub.c+ =S(+x.sub.01 -x.sub.02 -x.sub.03 +x.sub.04 -y.sub.01 -y.sub.02 +y.sub.03 +y.sub.04)                                      (26b) 
    
     
         Z.sub.cx =S(+x.sub.01 +x.sub.02 -x.sub.03 -x.sub.04 +y.sub.01 -y.sub.02 -y.sub.03 +y.sub.04)                                      (26c) 
    
     A refinement on the last step is to make Z c+  and Z cx  mildly linear in spherical equivalent since a small amount of cross-cylinder does tend to show up when suspect optics having a heavy sphere component are put in. The main source of this effect is irregularity of the sampling apertures. 
     The vertex correction d 1  is obtained by measurement of a second sphere test element of D&#39; diopters. In the preferred embodiment D is approximately +10 diopters and D&#39; is approximately -10 diopters. Under circumstances where the powders are approximately equal in magnitude and opposite in sign, d 1  is approximately given by: 
     
         d.sub.1 =[(M+M&#39;)=(D+D&#39;)]/(2D.sup.2)                        (27) 
    
     where M and M&#39; are the measured sphere powers for the test elements of known power D and D&#39;, respectively. A corrected scale factor S&#39; is given by: ##EQU9## 
     The constants α,β, etc. thus computed are basically unique to the particular instrument being calibrated. As described above, these customized constants are written into a ROM which then becomes part of the instrument. It is the instrument&#39;s actual response, not its precise configuration, that is the basis of the computation. Thus, a precision alignment of components within the instrument is not required. 
     The Calibration Program 
     As discussed above, the calibration computer system performs two basic functions. First, it accesses the lens meter&#39;s internal registers and produces an array of numbers corresponding to raw occultation times. This is basically timing and formatting wherein the computer acts as an input/output device for reading out raw data. Second, once the raw data is read out, the calibration computer system performs the mathematical manipulations and calculations described in detail above. Once the constants are generated, they are written into a memory for placement into the calibrated instrument. 
     It will be evident to one skilled in the art that there exists broad latitude in choosing an interrogating and calibrating computer system. As a concrete example, the particular components of the presently used system are as follows: Microcomputer 30 is an Intel MDS-800 &#34;Intellec&#34; microcomputer manufactured by Intel Corporation, Santa Clara, California. Disc drive 32 is an Intel MDS-2DS dual diskette drive unit. Memory mapper 35 is an Intel UPP-101 universal PROM programmer with a UPP-878 personality card (for a 2708 ROM). Printer 37 is an Intel MSD-PRN matrix printer. Display console 40 is a Lear-Siegler ADM-3A interactive display terminal manufactured by Lear-Siegler, Anaheim, California. Signal buffer 75 is an Intel MDS-80-ICE signal buffer. 
     While such a computer system would be suitable for performing both the interrogating and calibrating operations, an interim hybrid system more suitable for development and testing, has been used to date. In the hydrid system, the above-described computer system is used solely to interrogate the lens meter undergoing calibration and to extract binary numbers from the instrument hardware. Sixteen binary numbers are placed in an ordered array, converted to decimal, and written on the screen of display console 40. These numbers are then manually keyboarded into a programmed HP-97 programmable calculator manufactured by Hewlett-Packard Corporation, Palo Alto, California. The reason for using such a hybrid system is that the calibration operation is essentially mathematical in nature, and is more quickly and easily programmed into a calculator than a microcomputor, at least for development purposes where the operation does not have to be totally automatic. 
     With this interim hybrid system, there is no prompting for placement of test elements, but rather the programmable calculator stops at various times during execution of the calibration procedure, awaiting the input of occultation times from the different test elements. The operator is responsible for ensuring that the test elements are placed in the proper sequence. 
     Once the calibration constants have been generated, they are printed out by the programmable calculator. In order to write these constants into the ROM for insertion into the calibrated lens meter, the constants are manually entered via display console 40 under the control of standard operating programs for the Intel MDS- 800 microcomputer system. These control programs are stored on discs, and are supplied by the manufacturer with disc drive 32. The floppy disc monitor program is designated ISIS-II; the program for controlling the memory mapper is designated UPM. 
     The actual microcomputer code and the programmable calculator code are set forth in appendices below. 
     Appendix A is microcommputer code for extracting binary numbers from the instrument hardware, basically timing and formatting operations. This portion of the program puts sixteen binary numbers extracted from the instrument undergoing calibration into an ordered array. 
     Appendix B is microcomputer code for converting these binary numbers to decimal and writing them on the screen of display console 40. 
     Appendix C is programmable calculator code for performing the mathematical computations of the calibration procedure. 
     It should be understood that, in a final system, these various programs would be consolidated within a single computer system, and further that the computer system would not necessarily have to be as elaborate as the one set forth above. ##SPC1## ##SPC2## ##SPC3## ##SPC4##