Abstract:
A method of combining holograms or phase images of an object is disclosed, where attributes of the data used to record two phase images of overlapping portions of the surface of an object are compared and used to match pixels of the two recordings. A relative tilt angle and direction correction is added, and a third phase image is generated. Phase images of objects which are too large to be imaged in an interferometric imaging system can thus be produced.

Description:
FIELD OF THE INVENTION  
       [0001]     The field of the invention is the field of interferometric measurement of the surface topography of objects.  
       OBJECTS OF THE INVENTION  
       [0002]     It is an object of the invention to produce a method of combining a plurality of interferograms of an object into a single interferogram to measure, for example, the surface topography of objects too large to be measured without moving the objects in the optical system.  
       RELATED PATENTS AND APPLICATIONS  
       [0003]     U.S. Pat. No. 5,907,404 by Marron, et al. entitled “Multiple wavelength image plane interferometry” issued May 25, 1999;  
         [0004]     U.S. Pat. No. 5,926,277 by Marron, et al. entitled “Method and apparatus for three-dimensional imaging using laser illumination interferometry” issued Jul. 20, 1999  
         [0005]     U.S. patent application Ser. No. 10/893052 filed Jul. 16, 2004 entitled “Object imaging system using changing frequency interferometry method” by Michael Mater  
         [0006]     U.S. patent application Ser. No. 10/349651 filed Jan. 23, 2003 entitled “Interferometry method based on changing frequency” by Michael Mater,  
         [0007]     The above identified patents and patent applications are assigned to the assignee of the present invention.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0008]      FIG. 1  shows a sketch of a prior art Michelson interferometer.  
         [0009]      FIG. 2  shows a sketch of a prior art imaging Michelson interferometer.  
         [0010]      FIG. 3  shows the intensity recorded for a single pixel.  
         [0011]      FIG. 4  shows a block diagram of an embodiment of the invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0012]      FIG. 1  shows a sketch of a prior art interferometer. The particular interferometer shown in  FIG. 1  is conventionally called a Michelson interferometer, and has been used since the nineteenth century in optical experiments and measurements. A light source  10  produces light which is collimated by passing through a lens system  11  to produce a parallel beam of light  12  which passes to a beamsplitter  13 . The beam of light  12  is partially reflected to a reference mirror  14  and partially transmitted to an object  15 . Light reflected from the reference mirror  14  partially passes through the beamsplitter to an image receiver  16 . Light reflected from the object is partially reflected from the beamsplitter  15  and is passed to the image receiver  16 . The image receiver  16  may be film, or may be an electronic photodetector or CCD or CMOS array.  
         [0013]     If both the reference mirror  14  and the object  15  are flat mirrors aligned perpendicular to the incoming light from beam  12 , and the light path traversed by the light from the light source to the image receiver is identical, the light from both the reference mirror and the object mirror will be in phase, and the image receiver will show a uniformly bright image. Such devices were the bane of undergraduate optics students before the advent of lasers, since the distances had to be equal to within a small part of the wavelength of light and the mirrors had to be aligned within microradians. Even with the advent of lasers, such devices are subject to vibration, thermal drift of dimensions, shocks, etc.  
         [0014]     However, the Michelson interferometer design of  FIG. 1  is useful to explain the many different types of interferometers known in the art. In particular, suppose the reference mirror  14  is moved back and forth in the direction of the arrow in  FIG. 1 . As the reference mirror is moved, the phase of the light beam reflected from the reference mirror and measured at the image receiver  16  will change by 180 degrees with respect to the phase of the light reflected from the object  15  for every displacement of one quarter wavelength. The light from the two beams reflected from the object  15  and the reference mirror  14  will interfere constructively and destructively as the mirror moves through one quarter wavelength intervals. If the intensity on both the reference and object beam is equal, the intensity at the image receiver will be zero when the mirrors are positioned for maximum destructive interference. Very tiny displacements of one of the mirrors  14  or  15  can thus be measured.  
         [0015]      FIG. 2  shows a sketch of an interferometer much like the interferometer of  FIG. 1 , except that diffusely reflecting objects  25  can be imaged on the image receiver  16  by using an additional lens  20 .  FIG. 2  shows also the problem solved by the method of the present invention, where the object  25  which is to be measured has a surface which is bigger than the field of view of the imaging optics.  
         [0016]     Another inspection technique which is very useful is when the Michalson interferometer of  FIG. 1  or  FIG. 2  is used to compare the flatness of the surface of object  15  with the flatness of the reference mirror. As noted, if there is a difference in distance between the object mirror and the corresponding part of the reference mirror, the light from the two beams will interfere constructively or destructively and produce a pattern in the image receiver. Such patterns are generally called fringe patterns or interferograms, and can be likened to the lines on a topographic map. Such lines, as on a topographic map, can be interpreted as slopes, hills and depressions, The lines are separated in “height” by a half wavelength of the light from the light source  10 .  
         [0017]     One problem with the above description is that there are no numbers telling the difference between a depression and a hill, or in which direction the slope runs. However, if the reference mirror is moved, the lines will move, and, for example, the circles on a hill will shrink and a depression will expand for a particular direction of travel.  
         [0018]     Interferometric techniques work very well for optical surface inspection to check whether the surface is flat, or curved to within a certain specification. However, for many surfaces which are rough on the scale of the wavelength of visible light, or have height variations or steep slopes, the “lines” of equal phase (or height) of the interferogram will be very close together. Any disturbances, noise, or other variation will make it difficult or impossible to “count” the fringes and thus measure the “height” of the various features. As an analogy, the result would be like trying to hike using a topographic map with lines every inch in height difference! 
         [0019]     U.S. Pat. Nos. 5,907,404 and 5,926,277, assigned to the assignee of the present invention, show that a number of such interferograms taken with various phase delays in the reference beam and various wavelengths of the light source  10  may be recorded and computer analyzed to construct a “synthetic interferogram”, which is an interferogram which one would measure if one had a light source of much different wavelength from the wavelengths from the light source  10 . Thus, the “lines” on the interferogram could show height differences of, say, 100 microns instead of 0.4 micron height differences, so the lines would be much further apart and much easier to keep track of. The advantage, of course, is that lasers of 200 micron wavelength are hard to find, and electronic imaging equipment for such wavelengths is even harder to find, and spatial resolution of such a detector, if available, could not possibly match the resolution of detectors for visible and near infra-red light.  
         [0020]      FIG. 3  shows the intensity recorded for a single pixel of the imaging device  16  as the reference mirror  14  is moved in steps perpendicular to the incident beam. The step distances can be converted to a phase shift of the reference beam measured at the image receiver  16 . In a perfect world, the measurements would lie on a sinusoidal curve. If the intensity of the beams received from the object and the reference mirror were equal, the intensity would be zero when the two beams interfered destructively. For the usual case that the intensities in the two beams are not equal, the intensity of the interfering beams never reaches zero, and varies with an amplitude A about an average intensity I 0  which is related to the reflectivity of the object. The phase of the object beam at one pixel can be measured with respect to the phase at another pixel by inspecting the data shown by  FIG. 3  for each pixel.  
         [0021]     Manual inspection of results from a megapixel imaging device of course is difficult for humans, but easy for a computer programmed with a fast Fourier transform (FFT) program or other statistical analysis program. The FFT of a perfect sine wave gives a delta function telling the frequency of the wave, and in the case of a sine wave displaced from the origin also gives a “phase”, as well as the amplitude A and average intensity I 0 . Since the “frequency” of the results from all the pixels is the same, the relative “phase” for each pixel can be recorded from sufficient measurements of pixel intensity as the reference mirror is moved to change the phase of the reference beam. The multiple measurements remove much of the “noise” which would complicate the interpretation of an interferogram taken with an object fixed with respect to the reference mirror, as the maximum height peak of the FFT is easily identified and lower height peaks introduced by noise are ignored. The recorded measurements of phase and amplitude are sometimes called a digital hologram. The phase, amplitude, or other measurements so recorded as images are called, for the purposes of this specification, as synthetic “phase images”, and can be printed out as a two dimensional image where brightness or color is directly related to phase, intensity, etc. I 0  can be printed out, and looks similar to the image which would be recorded in absence of the reference beam or a normal photographic or digital image of the object.  
         [0022]     When the field of view of the optical system is too small to “see” the entire surface of the object  25 , one could translate the object a known distance in a known direction perpendicular to the object beam, and record a new interferogram, and combine the interferograms. Unfortunately, systems to hold and transport objects macroscopic distances, and place them within a small part of a wavelength in position without introducing errors and microradian tilts are extremely expensive and delicate.  
         [0023]     The method of the invention records at least two digital phase images of different parts of the surface of an object, each interferogram recording at least one overlapping image of the same portion of the surface of the object. The at least one of thetranslation vector of the relative motion of the two images, the relative phase, the tilt angle, and the direction difference between the two digital phase images are then calculated using attributes of the measurements, such as phases, amplitudes, intensities, or other statistical information generated from the data recorded to produce the recorded phase images, and the corresponding pixels of the two images are identified. Then, at least one of the phase images is corrected to account for the relative translation vector, phase, tilt angle, and tilt angle direction differences in the two images. The two phase images are then combined into one digital phase image.  
         [0024]      FIG. 4  gives a flow chart of the most preferred embodiment of the invention, for the general case of where a synthetic phase image of an object too large to be imaged by the optical system is required. In general, images are recorded from the image receiver for a number n max  different wavelengths. For each wavelength, a number m max  different phases of the reference beam are recorded. In the algorithm shown on the block diagram of  FIG. 4 , integers n and m are set to 1 in step  40 , then a portion of the surface of the object is illuminated in step  41  with light of wavelength λ n  for n=1. Decision step  42  checks if m=m max , and, if not, sets m=m+1 in step  43 A and then returns to step  41 . If m=m max  in decision step  42 , another decision step  43 B checks whether n has reached n max , and, if not, moves to step  44  to reset n=n+1 and m=1, and return to step  41 . If all phases for all wavelengths have been recorded, step  43  B moves to decision step  45 . If not all portions of the surface required have not been recorded, step  46  A moves the object and optical system relative to one another in step  46  A , and the system is returned to the beginning in step  40  to begin the recording process anew for the new portion of the surface. If all the portions of the surface have been completely recorded, decision step  45  moves the process to step  46 B, where synthetic phase images for each wavelength are computed, A final synthetic phase image for the desired “synthetic wavelength” is computed for each portion of the surface measured, and the corresponding pixels of the overlapping sections of each portion of the object surface are identified as discussed below. Once the corresponding pixels have been identified, the relative tilt angle and direction introduced in the object by the motion are determined from the synthetic phase images, and the synthetic phase images are corrected by the appropriate addition of phase to the various pixels, as discussed below.  
         [0025]     The number of phases and the number of frequencies used for the measurements are interrelated. For a single frequency, the number of phases required to make measurements such as shown in  FIG. 3  is preferably 3 or more. More preferably, 4 phases, and even more preferably 5 phases are set by moving the reference mirror. Most preferably, 6 or more phases are used.  
         [0026]     The number of wavelengths of the interfering light may be as small as one, for surfaces which have no discontinuities or slopes which would give more than a change of phase of about 90 degrees per pixel of the image on the image receiver. However, if there are such discontinuities and slopes, preferably at least three different wavelengths of light are used to record the synthetic phase image. More preferably, at least 5 wavelengths are used, and most preferably more than 7 wavelengths are used. 16 wavelengths ensures multiple redundancies in the data, and can be used for especially “noisy” results.  
         [0027]     For interferometers with unequal object and reference arm path lengths, changing the frequency also changes the relative phase of the interfering light beams at the detector. Thus, measurements such as shown by  FIG. 3  may be generated without changing the position of the reference mirror, and synthetic phase images can be constructed from such data.  
         [0028]     The corresponding pixels of the overlapping sections of each portion of the object surface are identified most easily if there are features on the surface of the object which give good contrast in the reflected intensity of light in absence of the reference beam. I 0 , as shown in  FIG. 3 , is extracted as the DC component of the Fourier transform of measurements, and the spatial Fourier transform of the I 0  measurements M 1  is recorded for the first portion of the surface measured. Similarly, M 2  is recorded for the second portion of the surface. Then, M 1 *M 2 * gives a peak which is the translation and rotation angle that the object has moved. If there is little contrast in light reflected from the object, such as would be apparent in pieces of machined metal, an attribute of the digital hologram other than the features given by images of I 0  should be used. One attribute, for example, is the features on a phase image when there are scratches, digs, hollows, or hills on the surface of the object. Tooling marks on pieces of metal show up as discontinuities in the phase “lines”, and can be used as features to “line up” the pixels of the two images. Changes of slope give attributes where the “density” of the equal phase lines change. Another attribute is the surface texture, which can change in a way that normal incidence reflectivity and phase is unchanged, but the speckle pattern from the part changes and shows up in the statistical ratios of the heights of peaks in the FFT. Any convenient attribute of the phase images may be used to calculate the translation distance and direction and identify corresponding pixels in the two images. In fact, subpixel resolution is easy to achieve, and new synthetic phase images are calculated by averaging neighboring pixel counts with appropriate weighting factors.  
         [0029]     The images are most preferably segmented so that only the overlapping portions of the images are used in the calculations.  
         [0030]     Once the phase images have been remapped to make the correspondence between each pixel in the overlapping images, the phase images may be corrected. A relative phase difference, tilt angle and tilt direction is chosen as a starting point, and one of the phase images has phase added to each pixel to account for the change of height and tilt introduced when the object is moved. Then, the phase differences between the images is minimized for each pixel, for example by minimizing the square of the differences as the chosen relative phase and tilt angle and direction are varied.  
         [0031]     Once the best measure of the relative phase, relative tilt angle and direction has been found, appropriate phase can be added to the phases recorded for each of the synthetic phase images for each portion of the surface, and the phase images are combined to give one phase image of the entire measured portion of the surface of the object.  
         [0032]     All patents, patent publications, and publications referred to herein are included by reference in their entirety, including included references.  
         [0033]     Obviously, many modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that, within the scope of the appended claims, the invention may be practiced otherwise than as specifically described.