Patent Publication Number: US-2010128282-A1

Title: Phase difference comparison to measure very small spacing between bodies

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation of pending U.S. patent application Ser. No. 11/011,295 (Atty. Docket No. MP-1), filed Dec. 13, 2004, incorporated herein by reference in its entirety. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to measurement of very small separations between bodies, in particular, to the measurement of very small separations between a rotating disk and a disk read/write head. 
     BACKGROUND 
     Hard disk drives contain recording heads that read and write magnetic data to a rotating disk. The recording heads contain aerodynamic features that create an air bearing which controls the separation between the heads and disk. The thickness of the air bearing, or spacing between the head and disk is commonly referred to as “flying height.” The flying height greatly impacts the performance of a head. As flying height is reduced, data density on the disk can be increased significantly. However, the head must not contact the disk excessively or wear may occur, possibly leading to read/write failure. In order to verify head design and monitor production processes, the flying height of hard drive magnetic heads is frequently measured on a flying height tester. 
     Flying height testers commonly use a rotating transparent replica of the magnetic disk together with an actual magnetic recording head. In general, a measurement beam (1 or more) from a light source is projected through the disk onto the air bearing surface of the recording head and the reflected beam is analyzed to derive the flying height. 
     The current industry standard, DFHT IV (Dynamic Flying Height Tester-IV) distributed by the KLA-Tencor Corporation (U.S. Pat. No. 5,280,340 to Lacey) uses 1 multi-wavelength light source at normal incidence to the disk to produce interference at the head/disk interface. Three wavelengths are filtered from the reflected light and the intensities are analyzed to derive the flying height. This technique requires calibration of the light source intensity and the reflectance of the disk and air bearing surfaces. The calibration process involves mechanically separating the head from the disk. It is desirable for the head to remain parallel to the disk during the calibration, and not translate during the separation process. Unfortunately, considerable error may be introduced by the calibration. As the flying height decreases, the calibration error causes a greater error in flying height measurement. This condition has made many users aware that the accuracy of the DFHT IV flying height tester is not sufficient for many current and future head designs. While the DFHT IV flying height tester has been a great commercial success over the past 10 years, its commercial viability is becoming questionable for the ever-decreasing flying heights that are becoming common in the industry. 
     U.S. Pat. No. 5,557,399 to De Groot discloses a flying height tester that was distributed by the Zygo Corporation under the name Pegasus. The Pegasus flying height tester used polarization interferometry to measure flying height. The technique involves directing a laser at an oblique angle through the disk onto the head. The polarization state of the beam is known before it enters the disk. The beam reflected from the head is analyzed for polarization and phase changes and flying height is derived from that data. This technique has two significant difficulties. (1) The stress in the spinning glass disk causes birefringence that affects the data and is difficult to compensate for in calculations. (2) The oblique angle of incident light makes it difficult to locate the measurement spot with the required precision. Perhaps because of these reasons, the Pegasus flying height tester had little commercial success. 
     U.S. Pat. No. 5,638,178 to Lacey, et al, discloses an FHT using an imaging polarimeter. This technique was also adversely affected by stress-induced birefringence in the disk. While this technique theoretically provided advantages over the DFHT IV flying height tester distributed by the KLA-Tencor corporation, its performance was sub-par and it was not accepted in the industry. 
     U.S. Pat. No. 5,715,060 to Sides (the 060 patent) discloses a method for measuring flying height by sensing scattered light from frustrated total internal reflection. A light beam is directed through the edge of the disk onto the head air bearing surface. The incident angle of the beam striking the head is selected to produce total internal reflection. As described in “Calibration of Fly Height Measured by Scattered Total Internal Reflection” by Strunk, Low and Sides (IEEE Transactions on Magnetic Vol 36, No 5, September, 2000), the total internal reflection produces an evanescent wave on the far side of the transparent disk, where the head flies. Any material very close to the disk may interact with the evanescent wave, frustrating the total internal reflection. In particular, a typical magnetic recording head will frustrate the total internal reflection and furthermore, scatter some of the light which would have otherwise been totally internally reflected. In the 060 patent, Sides teaches that the scattered light intensity can be measured by a photo detector. The intensity of the scattered light changes as the spacing between the disk and magnetic head changes, thus this effect can be used to measure flying height. The practical difficulty in applying this technique occurs when calibrating the scattered light. Several methods are suggested in the 060 patent but they all have significant disadvantages. One method requires contacting the head and disk which can be destructive. Another method is flying the head at a known height, which requires a separate flying height measurement the method of which is unknown, or using a calibration standard that potentially does not have sufficient resolution. Even if the calibration issue was addressed, it is not clear that this technique would provide a significant improvement compared to the commercially available DFHT IV flying height tester&#39;s performance at today&#39;s very low flying heights. 
     U.S. Pat. No. 5,932,887 to Guzik teaches a method for measuring flying height by sensing frustrated total internally reflected light. A light beam is directed through the edge of the disk onto the head air bearing surface. The incident angle of the beam striking the head is selected to produce total internal reflection. The head material frustrates the total internal reflection. The amount of reflected light is measured and flying height is calculated. This technique has several difficulties; it is not easy to capture the internally-reflected light. The requirements for the light entry into and exit from the disk place restrictions on the disk hub design and the positions where the head may fly on the disk. Furthermore, the signals produced by the system are difficult to translate into a very accurate flying height, especially at the very low flying heights of today&#39;s head designs. 
     U.S. Pat. No. 6,184,993 to Duran teaches the use of a Savart plate to split an interferometric image of the head/disk interface into polarized ordinary and extraordinary beams. These beams were then retarded with respect to each other by shifting optical components in the apparatus. After shifting, the beams are superimposed and their interference is detected. The interferometric intensity is detected at a variety of phase shifts, then the phase at a giving system configuration is calculated from the data. This phase is compared to the phase measured with no head present and the flying height is calculated from the resultant phase measurements. As disclosed, this method has limitations on the possible measurement locations on the head, as the superimposed images must meet in a specific way to make the measurement. It also may be difficult to control system drift as the phase would be significantly affected by very small optical path variations caused by thermal expansion and other factors. This system has not been commercially viable. 
     Hence, what is needed in the art is a method or apparatus for measuring the distance between two surfaces, that overcomes one or more of the aforementioned shortcomings of the prior art. 
     SUMMARY 
     Methods and apparatuses for measuring the distance between two surfaces are disclosed herein. For example, according to a preferred embodiment, an apparatus for measuring the spacing between a first body and a second body includes at least one source of light. The at least one source of flight produces two simultaneously coexisting light beams, including a measurement light beam and a reference light beam. At least one beam splitter may separate the measurement light beam into a first measurement portion and a second measurement portion, and may separate the reference light beam into a first reference portion and a second reference portion. 
     A measurement optical path directs the first measurement portion to shine upon the first and second bodies, and directs the second measurement portion to shine upon a third body. A reference optical path directs the first reference portion to shine upon the first body but not the second body, and directs the second reference portion to shine upon the third body. 
     A first light detector is disposed to receive light that is reflected from the first, second, and third bodies via the measurement optical path, and produces a first output signal. A second light detector is disposed to receive light that is reflected from the first and third bodies via the reference optical path, and produces a second output signal. A movable mount can hold the second body in the measurement optical path during a first period, and can hold the second body away from the measurement optical path during a second period. 
     A phase difference comparator is coupled to the first and second light detectors, and is capable of comparing a phase difference between the first and second output signals during the first period with a phase difference between the first and second output signals during the second period. 
     The preferred embodiment described above may provide several advantages. For example, the spacing-varying calibration that is required by contemporary methods may be avoided. Moreover, the preferred embodiment described above does not require the use of polarized light (which can be adversely affected by stress-induced birefringence in a spinning glass disk, for example). It may also enable measurements to be made at substantially normal incidence, which may allow improved precision of measurement spot location compared to devices with optical configurations requiring non-normal incidence. It also has the desirable trait that its sensitivity improves as the spacing or flying height decreases below 10 nm. By contrast, according to contemporary methods the sensitivity decreases as the spacing decreases below 10 nm. 
     Certain embodiments disclosed herein illustrate exemplary methods and apparatuses as applied in the field of hard-disk magnetic recording (e.g. for performing head/disk spacing or “flying height” measurements with improved accuracy at very low flying heights compared to contemporary methods). 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of one embodiment of the measurement system according to the present invention; 
         FIG. 2   a  shows the Measurement Spot and Reference Spot with the Head present according to the embodiment of  FIG. 1 ; 
         FIG. 2   b  shows the Measurement Spot and Reference Spot with the Head not present (out of the field of view) according to the embodiment of  FIG. 1 ; 
         FIG. 3  is a plot of simulated output from the detectors, 4 sets of data from the Measurement Spot and Reference Spot in both conditions of Head present and Head not present according to the embodiment of  FIG. 1 ; 
         FIG. 4  is a plot of the 4 sets of phase data calculated from the 4 sets of data in  FIG. 3 ; 
         FIG. 5  is a plot of 2 sets of data, the Measurement Spot phase data minus the Reference Spot phase data for both conditions, Head present and Head not present according to the embodiment of  FIG. 1 ; 
         FIG. 6  is a plot of the difference between the two sets of data in  FIG. 5 ; 
         FIG. 7  is a plot of the  FIG. 6  data, compensated for the change in direction of the vibrating reflecting component; 
         FIG. 8  is a plot of the spacing or flying height calculated from the phase data in  FIG. 7 ; and 
         FIG. 9  is a plot of theoretical phase versus spacing or flying height. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     According to certain embodiments of the present invention, spacing between a transparent (or semi-transparent) medium and a reflecting object may be measured as follows. Without limiting the scope of the transparent (or semi-transparent) medium and the reflecting object, they may be referred to as the Disk and Head, respectively, in contemplation of a group of embodiments called “Flying Height Testers” (for application in the magnetic hard disk industry). In such embodiments, we can define a Measurement Spot as a relatively small spot where the spacing between the Disk and Head is substantially constant. The phase of light reflecting from the Measurement Spot on the Disk with the Head in position at a relatively small spacing from the Disk may be compared to the phase of light reflected from Measurement Spot on the Disk alone. Using the measured phase difference and the optical properties of the Head, Disk and medium between them, the spacing can be calculated. 
     Since the spacing is very small compared to dimensional variations caused by thermal expansion and other factors, the phase may be referenced to a secondary reflection (Reference Spot) on the Disk. The secondary reflection can be distinguished from the primary reflection in a number of ways. It can be located some distance away from the Measurement Spot. It can be located on the back-surface of the Disk. There are also many other methods to distinguish two light beams which are known to one with ordinary skill in the art. The reflection at the Reference Spot does not have a significant inherent phase change that is caused by removing the Head. 
     The phase at both the Measurement Spot and the Reference Spot may be measured using an interferometric technique. Light may be split and directed at two different areas. One area contains the Measurement Spot and the Reference Spot on the Disk. The other area is a Frequency Shifter. The Frequency Shifter can be composed of an optical component or mechanism that causes a relatively small shift in the frequency of the light. Examples of such a frequency shifting device would be an acusto-optic modulator or a moving reflecting object. The light reflecting from the Measurement Spot and the Reference Spot is combined with the light from the Frequency Shifter, and if properly aligned, dynamic interference fringes will result from the combination. 
     The intensity of the interference fringes corresponding to the Measurement Spot are measured and compared to the intensity of the fringes corresponding to the Reference Spot. Since the fringes are dynamic, they are changing in time and an analysis can yield the phase difference between the Measurement Spot fringes and the Reference Spot fringes. 
     However, it is not the phase difference between the Measurement Spot fringes and the Reference Spot fringes that is of primary interest. The primary interest is the difference between the phase of the light reflected from the Measurement Spot with the Head present (loaded) and the Measurement Spot with the Head not present (unloaded). However, it is not possible to directly compare the phase of these measurements, as they are not taken at the same time. Therefore, in each case (with the Head present and with the Head not present), the phase of the Measurement Spot fringes is found with respect to the Reference Spot fringes. The difference between these two Measurement Spot fringe phases with respect to the Reference Spot fringe phases yields the parameter of primary importance, the phase change caused by the presence of the Head near the Disk. 
     The phase difference between the Measurement Spot fringes and Reference Spot fringes is affected by a large number of factors including the difference in length between the two optical paths. The phase difference between the reference and measurement spot consists of K, a substantially constant value cause by optical path length differences and other factors, and in the case where the Head is present, the phase shift caused by the additional reflection at the surface of the Head. 
     In the case where the Head is not present, the phase difference between Measurement Spot and Reference Spot is the substantial constant K. When the head is present, the phase difference between the Measurement Spot and the Reference Spot is K+D, where D is the phase shift caused by the additional reflection from the Head. Taking the difference between the two differences, that is the difference of the Measurement Spot and Reference Spot with the Head loaded, minus the difference of the Measurement Spot and Reference Spot with the head unloaded, yields (K)−(K−D), or D itself. This D is the phase change caused by the presence of the Head near the Disk. 
     With the phase change due to introduction of the Head known as well as the optical properties of the Disk, the Head, and the medium between them, the spacing or flying height can be calculated by comparing the measured phase with the theoretical phase versus spacing relationship. The phase and associated spacing or flying height can be measured many times at high speed and parameters such as average spacing, minimum spacing, maximum spacing and others can be calculated. 
     Now referring to  FIG. 1 , light from first laser  1  is directed through focus optics  2  toward beam splitter  3 . The beam splitter  3  directs a portion of the light toward the top surface of disk  5  through focus optics  4 , and another portion of the light toward the top surface of the vibrating reflecting component (frequency shifter)  8  through focus optics  7 . The beam reflects from the vibrating reflecting component  8 , as well as the top surface of the disk  5  and is recombined at the beam splitter  3 . The beams interfere and the interferometric intensity is detected at first photo-diode detector  9 . The interferometric intensity at detector  9  is referred to as the Reference. 
     In a similar fashion, light from second laser  10  is directed through focus optics  11  toward beamsplitter  3 . Beamsplitter  3  directs a portion of the light to the interface between the head  6  and the disk  5 , and a portion of the light toward the back surface of the vibrating reflecting component  8 . These beams reflect and the two reflections are recombined at the beam splitter  3  and directed toward a second photo-diode detector  12 . The interferometric intensity recorded at detector  12  is referred to as the Measurement. As shown in  FIG. 1 , the light beams that interfere to produce the Reference and the Measurement are simultaneously produced and coexistent. 
     In a preferred embodiment, the vibrating reflecting component  8  is substantially the same material and thickness as disk  5 . The optics  4  and  7  are also substantially identical, such that the beamsplitter  3  and optics  4  and  7  combine to produce a “Linnik interferometer” with a vibrating reference mirror to produce dynamic interference fringes. 
     The signals from detectors  9  and  12  are carried by signal wires  13  and  14  respectively to system controller  15  which includes an analog-to-digital converter, digital memory, and a microprocessor-based signal combiner to record and analyze the output from detectors  9  and  12 . 
     The disk  5  may be rotated by spindle motor  16  which is controlled by system controller  15  using control wires  17 . The head  6  is mechanically attached to head actuator  18 . In the preferred embodiment, head actuator  18  is a linear stage driven by a lead screw rotated by an electric motor. Head actuator  18  is controlled by system controller  15  using control wires  19 . In a preferred embodiment, the vibrating reflecting component  8  may be mechanically attached to a voice-coil actuator  20 . The voice coil actuator  20  is controlled by system controller  15  using control wires  21 . 
     The motion of the vibrating reflecting component  8  is substantially synchronized with the rotation of the disk  5 , because axial runout of the disk  5  and thickness variation of the disk  5  produces a similar type of dynamic interference fringe activity as the motion of the vibrating reflecting component  8 . By synchronizing the motion of the vibrating reflecting component  8  and the rotating disk  5  using system controller  15 , control wires  19  and  21 , head actuator  18  and voice-coil actuator  20 , the signals detected by detector  9  and detector  12  are substantially repeatable from revolution to revolution of the disk  5  allowing a simplified analysis of the data. In a preferred embodiment, the motion of the vibrating reflecting component  8  is synchronized by using a microprocessor-based controller  15  that receives an index pulse from the spindle motor  16  that spins the disk  5 . The index pulse occurs once per revolution of the disk. 
     The system controller  15  may be programmed to actuate the voice coil actuator  20  with a sinusoidal current that produces one cycle of current per revolution of the disk  5 , thereby causing the vibrating reflecting component  8  to move through one cycle of motion synchronously with one revolution of the disk  5 . The system controller  15  can be programmed for different rotational speeds of the disk  5  and it can be programmed to change the phase of the motion of the vibrating reflecting component  8  with respect to the disk  5 . 
     While a preferred embodiment uses two lasers  1 ,  10  and a vibrating optical component  8 , this method may also be applied with variations of hardware. For example, a single light source could illuminate the Measurement Spot and Reference Spot in lieu of the first laser  1  and second laser  10 . Also, an acusto-optic modulator could be used in lieu of the vibrating reflecting component  8 . Furthermore, it is possible to implement this method using a stationary reflecting component in place of the vibrating reflecting component  8 . In this case the axial runout of the disk  5  acts to shift the frequency of the light relative to the reflection from the stationary reflecting component. 
     To make a measurement, the fringe intensity at both the measurement detector  12  and the reference detector  9  may be recorded by the system controller  15  for a period of time with the head  6  in close proximity to the disk  5  in the field of view of the optical system. The fringe intensity at both detector  9  and detector  12  may also be recorded for a period of time with the head  6  displaced from the field of view of the optical system. The head  6  can be displaced by head actuator  18  under control of the system controller  15 . 
       FIG. 2   a  illustrates a configuration with the head  6  in the field of view. The measurement spot  22  is located at the interface between the head  6  and disk  5 . The reference spot  23  is on the disk  5  but is not affected by the head  6 . An alternate reference spot  24  is also shown on the bottom surface of the disk  5 .  FIG. 2   b  illustrates a configuration with the head  6  out of the field of view of the optical system. In this case, the head  6  has no effect on the measurement spot  22 . As shown in  FIGS. 2   a  and  2   b , the light beams that interfere to produce the Reference and the Measurement are simultaneously produced and coexistent. 
     Data set  50  and data set  51  illustrate simulated fringe intensity corresponding to measurement photo detector  12  and reference photo detector  9  respectively with the head  5  in the field of vision. Data set  52  and data set  53  illustrate fringe intensity corresponding to the same detectors with the head  5  displaced from the field of vision. These data sets are representative of one revolution of the disk  5 . 
     The signal recorded corresponding to the measurement spot  22  with the head in the field of vision (exemplified by data set  50 ) may be denoted as Sa. The signal recorded simultaneously corresponding to the reference spot  23  (exemplified by data set  51 ) can be denoted Sb. A subsequent measurement with the head  6  out of the field of vision yields, Sc, the data corresponding to the measurement spot  22  (exemplified by data set  52 ), and Sd the data corresponding to the reference spot  23  (exemplified by data set  53 ). While shown in the figure displaced vertically for clarity, all four sets of data are normalized to a maximum of +1.0 and a minimum of −1.0. 
     Now referring to  FIG. 3 , the phase data corresponding to Sa  50 , Sb  51 , Sc  52  and Sd  53  are denoted Pa  54 , Pb  55 , Pc  56  and Pd  57  respectively. The units of Px are degrees in the plots. These phase data are calculated point by point using the following equations: 
         Px =arcCosine( Sx ) if the slope of Sx is positive 
         Px =2 PI −arcCosine( Sx ) if the slope of Sx is negative  Eq. 1 
     In Equation 1, the subscript x is taken to be used as each of the subscripts a, b, c and d independently. The slope can be determined by examining neighboring points in each data set. 
     Now referring to  FIG. 4 , the vertical values of each data set  54 ,  55 ,  56  and  57  range from 0 to 360 degrees, but they are shown displaced vertically for clarity. The data set  58  illustrates the phase corresponding to the measurement spot  22  (data set  54 ) minus the phase corresponding to the reference spot  23  (data set  55 ) with the head  5  in the field of view. 
     Now referring to  FIG. 5 , the data set  59  illustrates the phase corresponding to the measurement spot  22  (data set  56 ) minus the phase corresponding to the reference spot  23  (data set  57 ) with the head  5  out of the field of view. The vertical axis units of phase for data sets  58  and  59  are degrees. As the phase units are periodic, any negative phase values can be made positive by adding 360 degrees for convenience in further calculations. Both data sets  58  and  59  have a vertical range from 0 to 360 degrees although data set  58  is shown displaced vertically for clarity. 
     Now referring additionally to  FIG. 6 , data set  60  is data set  58  minus data set  59 . This is the difference of differences, which yields the actual change in phase caused by introducing the head  6  into the field of view. As the phase is periodic, this data is bounded from −180 degrees to +180 degrees by adding or subtracting 360 degrees if necessary for convenience in further calculations. 
     Note that there is an ambiguity in the selection of the sign of this result depending on the sign of the shift in frequency caused by the vibrating reflecting component  8 . Specifically, for one direction of motion of the vibrating reflecting component  8 , the correct phase caused by the introduction of the head  6  is the data set  58  minus the data set  59 . When the vibrating reflecting component  8  is moving in the opposite direction, the correct phase is data set  59  minus the data set  58 . 
     The change in direction of the vibrating reflecting component  8  is clearly indicated by the discontinuities at disk rotational positions of 90 degrees and 270 degrees in these sets of data. From the theoretical phase versus spacing relationship, we know that the phase caused by introducing a low flying head (less than 50 nm) into the field of view is between 0 and 180 degrees. By analyzing data with a known low flying head (less than 50 nm) we determine that on data set  60 , the data in the range of 0 to 90 degrees and the data in the range of 270 through 360 degrees is of the incorrect sign. 
     Now referring additionally to  FIG. 7 , data set  61  illustrates the phase data set  60  compensated by changing the sign of the data corresponding to disk rotational positions of 0 through 90 degrees and 270 through 360 degrees. To convert the measured phase exemplified by data set  61  into flying height, we generate a look-up table of phase vs. flying height. In the preferred embodiment, the matrix-method calculations described in “Electric Fields Produced by the Propagation of Plane Coherent Electromagnetic Radiation in a Striated Medium”, J. of Optical Society of America, vol. 58(3), March 1968, pp. 380-390, is used. Using these calculations, the look-up table can be generated for heads with one or more coatings as well as disks with one or more coatings so long as the optical properties and thickness of the coatings on the head and disk are known. Also, the optical properties of the matter in the spacing can be arbitrary, although in the preferred embodiment, it is air. A look-up table of flying height vs. phase for typical magnetic head and transparent disks with air in the spacing is partially given in Table 1 below: 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Spacing (nm) 
                 Phase (deg) 
               
               
                   
                   
               
             
            
               
                   
                 0 
                 147.86 
               
               
                   
                 1 
                 145.51 
               
               
                   
                 2 
                 143.20 
               
               
                   
                 3 
                 140.94 
               
               
                   
                 4 
                 138.72 
               
               
                   
                   
               
            
           
         
       
     
     In the preferred embodiment, the look up table is generated for each one-tenth nm. One-tenth nm is one Angstrom. 
     Now referring additionally to  FIG. 8 , data set  62  shows the spacing or flying height calculated from the phase data set  61  using the look up table method. The data set  62  shows that an error can occur on calculations where the vibrating reflecting component  8  is changing directions at disk  5  rotational positions of 90 and 270 degrees. This error is typically caused by an incorrect calculation of slope in equation 1 where the slope is very close to zero. The spacing or flying height at disk rotational positions of 90 and 270 degrees can be more accurately measured by altering the phase of the vibrating reflecting component  8  with respect to the rotational position of the disk  5 , for example by setting the change in direction to occur at 0 and 180 degrees of disk  5  rotation using system controller  15 . Alternatively, a constant frequency shifter such as an acusto-optic modulator would not be subject to such errors, because the sign of the frequency shift would be constant. 
     It should be noted that the use of an acusto-optic modulator type of frequency shifter would be an advantage in that there would be no errors in the data as there can be when the vibrating reflecting component  8  shifts direction. In the preferred embodiment, the ease of integrating the vibrating reflecting component  8  was judged to be more important than the difficulty introduced by the variation in frequency shifting caused by its direction reversal. 
     Now referring to  FIG. 9 , a more complete set of theoretical phase versus spacing or flying height given by Table 1 is plotted as data set  63 . Data set  63  shows that the phase is a periodic function of flying height, with a period of half the wavelength of the light. If the flying height is not known to be below approximately 300 nm, additional information to determine the correct cycle of the solution must be incorporated. For this purpose, a target spacing may be specified by the user of the system for which the solution will be in the range of the specified target spacing plus or minus one-quarter of the wavelength of light being used. Or another technique such as white-light interferometry may be used to determine the approximate spacing, then that approximate spacing would be treated as the target spacing mentioned above. With reference to data set  63 , it should be noted that the slope of the phase versus spacing or flying height is greatest at very low spacing values (below 20 nm). This increased slope may continue to zero spacing. The increased slope at very low spacing or flying height values may cause an advantageous increase in measurement sensitivity as the spacing decreases to zero. 
     Modifications and substitutions made by one of ordinary skill in the art are within the scope of the present invention which is not to be limited, except by the claims that follow.