*M. T. Manley, TB. Ovryn, and *L. S. Stern
Adapted from Journal of Orthopedic Research 5:144-149, Raven Press, New York. Scanned, filtered by optical character recognition. For details see original article.
*Department of Musculoskeletal Research, Cleveland Clinic Foundation, and Department of Biomedical Engineering' Case Western Reserve University, Cleveland, Ohio U.S.A.
Address correspondence and reprint requests to Dr. M. T. Manley at the Department of Musculoskeletal Research, Cleveland Clinic Foundation, 9500 Euclid Avenue, Cleveland. OH 44106, U.S.A.
To create a hologram, a coherent light source is split into an object beam and a reference beam. The object beam illuminates the object and is reflected onto the holographic recording medium The reference beam follows a path that is nominally identical in length to the object beam, but illuminates the medium directly. Any difference in length that occurs between the two beams is due to the surface contours of the object. Therefore, light falling on the medium from the two beams is out of phase, and this phase difference creates an interference pattern that can be recorded. In case of a photographic emulsion on a glass plate the medium, reillumination of the processed plate with a replica of the reference beam causes the interference pattern to be reconstructed. An apparently complete reproduction of the object is then visible through the holographic plate.
Summary: Double-exposure holographic interferometry is a nondestructive testing technique for measuring displacement and strain in a test object. A standard hologram contains three-dimensional information about an object. However, the holographic interferogram has additional information, as a series of interference bands overlaid on the three-dimensional image of the object contains information about object deformation. Interferograms were produced for intact cadaveric femora and cadaveric femora with implanted titanium alloy and cobalt-chromium alloy femoral components. A force was applied to the femoral head to simulate single leg stance, and changes in specimen deformation were observed as additional incremental loads were applied. We have observed that the femur behaves as a bending beam and that the holographic technique allows the position of maximal deflection to be identified and the magnitude of femoral displacement from the load axis to be determined at any point within the field of view. The effects of the modulus of the implanted stem on the bending characteristics of the composite structure were clearly seen in the interferograms. This communication presents a photographic analysis of the double exposure interferograms recorded, as well as a critique of the technique for biomechanical measurements in vitro. Key Words: Holographic interferometry- In vitro testing- Full-field deformation- Femur.
Holographic interferometry, a nondestructive full-field technique that measures small static or sinusoidal deformations occurring in an object, is based upon standard holographic principles. Holography is a method for recording three-dimensional information on a two-dimensional recording medium (photographic emulsion, thermoplastics, etc.). Unlike a photograph, the hologram ("Holo" -whole, 'Gram"-message) contains all the information about the surface of the object and the effects of parallax. The hologram is an interference pattern of coherent wave fronts scattered from the object and recorded by the medium.
FIG. 1. Schematic diagram of the optical arrangement.
The basic principles of holography underlie the technique in double-exposure holographic interferometry. However, in double exposure holography, two recordings are made on the same holographic medium. Between the two exposures the object is deformed in some manner, either statically or by a time-varying force. As a result of the deformation, a slightly different image is recorded on the medium during the second exposure. This difference in initial and subsequent image produces a change of optical phase that is manifest as a series of interference fringes superimposed on the image of the object. The fundamental equations of holography and holographic interferometry are given in many standard texts (6,17).
As the interference fringes contain complete information about the deformation occurring in the object,. holographic interferometry is a powerful technique. The methods available for retrieving quantitative data from the fringes fall into two broad categories, i.e., either dynamic or static technique (3). Dynamic interpretation correlates changes in localization of the fringes with object deformation as the observer's direction of view changes. Depending upon whether the fringes appear in focus on or off of the object, different motions can be inferred. However, static techniques rely directly on the relationship between the change in optical path and the interference fringe location. This approach is particularly suited when the fringes localize on the object's surface.
The static method (3,5,14,15,17) lends itself to a photographic analysis of double-exposure holographic interferograms and was the method employed in our study. The basis of the method relies on the identification of a region of the object that has remained stationary throughout the two exposures. This usually can be identified as a bright area on the object that exhibits no parallax between it and the image. From this point, successive fringes are counted and object motion is inferred. For this reason, this method is called the "zeroth-order fringe" or "frozen fringe" technique. Although some of the other interpretation schemes are sensitive to in-plane motion of the object, the frozen fringe method is most sensitive to out-of-plane displacements.
Generally, a single interferogram or its photograph does not suffice to reconstruct the three-dimensional displacement of the object under load. Instead, only a single component of the displacement along a "sensitivity vector is determined. The sensitivity vector is the bisector of the angle between the illumination and the viewing vectors. If the sensitivity vector lies along the line of the object's displacement, a single interferogram would be sufficient to determine the total displacement, otherwise only a single component of the displacement can be established. Therefore, three interferograms are required to determine object displacement. Alternatively, a single large interferogram could be used, but this method has several disadvantages including limited accuracy and difficulty of application (3,17).
MATERIALS AND METHODS
The results from one embalmed femur are reported in this short communication. The femur was tested in the intact state and after reconstruction with a current stem design (HSI, Osteonics Inc., Allendale, NJ). The level of the calcar resection cut for the HSI implant was marked on the calcar, and the distal end of the femur was resected 300 mm below this level. A threaded stainless-steel peg with a ball end was screwed into the distal medullary cavity. This method has been used by us previously (12,13) to minimize nonphysiologic bending strains in the distal femur during loading. The specimen was mounted in a hand-operated screw press with the femoral head and the distal ball joint articulating with hemispherical loading platforms. The screw press was placed in the object position of an optical holographic arrangement and a baseline load of 1350 N was applied to the specimen. The applied force was measured by a strain-gauge load cell (Endevco Inc., San Juan Capistrano, CA).
A holographic image was recorded in a 4" x 5" photographic plate (Agfa Gevaert Inc., Teterboro, NJ: Type 8E75HD-NAH) by activating a 15 mW helium-neon laser (Spectra Physics, Mountain View, CA). The exposure time was 7 s. After the first exposure, a 45-N incremental load was applied, and a second exposure was recorded in the same holographic plate to produce an interferogram.
After recording data from the intact femur, the effects on the holographic image of implanting femoral components of different moduli were investigated. The head and neck of the femur were resected at the previously-marked level, and the medullary cavity was prepared with the manufacturer's standard instrumentation. A cobalt-chromium alloy stem was coated with latex release agent (Kwikmold, Adhesive Products Corp., Bronx, NY) and subsequently implanted using standard cement technique. The reconstructed femur was mounted. in the optical arrangement, and further interferograms were recorded. The femoral component then removed from the mantle by driving a we, between component collar and the calcar. After insertion of the specimen for signs of damage, a complementary titanium-alloy stem of identical geometry was implanted with cement in the same femur residual mantle. The imaging process was repeat Previous studies in our laboratory have shown the results from this sequential testing technique are reproducible (10,13).
We employed the "frozen fringe" or zero order fringe technique for fringe analysis. For given angle of viewing and illumination of the holographic plate, a single component of the out plane displacement of the object along the sensitivity vector was determined. The displacement in the direction of the sensitivity vector was measured with respect to a reference point that was located a zeroth-order fringe.
To determine the position of the zeroth-or( fringe, a fringe-free region or a region of marked reduced fringe density has to be identified on interferogram. In the interferograms fringes were counted from a point of inflection could be identified on the femoral diaphysis (F 2A). In order to calculate displacement data, a longitudinal datum line was drawn on the photograph of each interferogram, and the fringe distribution( from the point of inflection was plotted in the proximal direction up to the femoral head and in the distal direction to the limit of the field of view of the photograph. As the wavelength of the helium-neon laser is known (632.8 nm), and the fringe to displacement is one-half wavelength, quantitative displacement data can be established by this method.
Medial view interferograms of a cadaveric specimen in its intact state and after implantation of a titanium alloy and a cobalt-chromium alloy femoral component of the HS I Osteonics design .
Quantitative displacement curves reduced from these three figures (Fig. 2B) show the difference in bending characteristics between the intact femur and the two composite structures of different stiffnesses. The curves were generated by plotting the fringe distribution from the nodal point to the femoral head and from the nodal point to the limit of the field of view within the holographic plate. Curves were then extrapolated to the location of the center of the distal ball joint. Superimposition of these three curves shows that the out-of-plane displacement at the level of the calcar resection was 9.79 um, 5.21 um, and 4.42 um for the intact, the titanium alloy, and the cobalt-chromium alloy samples, respectively. As the geometry of both implanted stems was identical and the length of the stem was known, it is possible to calculate the spatial separation between the area of maximum deflection of the femoral cortex and both the calcar resection and the tip of the femoral component. For the intact femur, maximum out-of-plane displacement occurred at 99 mm below the calcar resection. Maximum deflection of the same femur with implant occurred at 79.2 mm and 117.2 mm below the cut, or 50.8 and 12.8 mm proximally to the stem tip for the titanium alloy and the cobalt-chromium alloy stems, respectively.
Our studies using holographic interferometry have involved nine cadaveric femora, two implant designs (HSI-Osteonics and DF-80-Zimmer), and interferograms recorded from multiple viewing angles (8,9,11). The technique is in the development stage in biomechanics applications, and the majority of our recorded data do not yet produce new insights into femoral biomechanics. Therefore, in this communication, only illustrative results are presented and discussed.
Our studies have shown that double-exposure holographic interferometry can provide quantitative as well as qualitative data about the global displacement produced in cadaveric femora loaded in vitro. In each of the images recorded, a nodal point or fringe-free region on the loaded femoral diaphysis was clearly visible. At this inflection point the curvature of the specimen changed sign, and out-of-plane displacement of the femur from the load axis was maximum. The intact femur and the femur with implanted prostheses were shown to deform primarily as bending beams. This observed behavior supports the approximations used by Huiskes (7) who characterized the femur as linearly elastic and homogenous and showed that it could be modeled as a bending beam, both before and after implantation of a femoral component. The displacement curves shown in Figure 2B represent the out-of-plane displacement of the femur along the sensitivity vector and reflect the continuous bending of the femur.
When the stiffness of the reconstructed proximal femur was increased by implanting a cobalt-chromium alloy stem, the position of maximum out-of-plane deflection of the composite structure was shown to shift distally. Unexpectedly, the interferogram of the same femur with implanted titanium alloy femoral component (Fig. 2A) showed a slight proximal shift in the nodal point associated with the implantation of the stem. The discrepancy between this result and the expected finding highlights one of the complications of the holographic technique. As the method is extremely sensitive to out-of-plane displacement, small changes in loading configuration affect the interferograms. In the comparison of an intact femur and the same femur with implanted titanium prosthesis, a change in loading geometry was caused by the resection of the femoral head and neck and by the implantation of a femoral component. However, within a consistent loading geometry, the influence of one variable (i.e. stem stiffness) can be readily observed. If changes in loading configuration are small compared to changes in material properties, the data are then valid, as in the comparison between titanium and cobalt-chromium prostheses. If an uncontrolled variable such as a loading geometry change is not recognized before data interpretation is attempted, incorrect conclusions can be drawn.
Although the interference patterns recorded are unique to a given object and a given loading condition, interpretation of the out-of-plane displacement occurring requires some a priori knowledge df the motion. For example, the analysis of the fringe pattern alone results in ambiguity of assigned motion and an associated 'rose of error" .
Due to the extreme sensitivity of the method to small increments of applied load, a rapid increase in fringe density with small increases in load is observed. Although this is very useful in some applications, and motions as small as 0.316 um can be routinely detected, physiologic loading levels would cause the fringe density to increase to such an extent that individual fringes could no longer be discerned with the unaided eye. If displacement under physiologic conditions of load needs to determined by this method, a tedious approach serial interferograms and addition of the deflection data have to be adopted. However, stability of the loading apparatus and the test specimen would have to be rigorously controlled throughout this procedure, as the discrimination between rigid body motion and object displacement cannot be achieved from analysis of the interference patterns alone. An additional complication that direct comparison with published strain data from biomechanical measurements in vitro is a formidable task, as differentiation of the displacement data obtained from holographic interferometry required to yield strain data.
Despite these complications with the holographic method there are several virtues inherent in technique. The contactless nature of the method attractive. Visual results for comparative test and demonstration purposes such as teaching a readily available. These results can be interpreted even by an untrained observer, and qualitative analysis of the data can allow areas of interest in a deforming object to be identified. The results can he to determine the proper placement of strain gauge for further strain analysis. Quantitative information can be obtained from the interferogram, as information describing the total deformation of an object is contained on the holographic plate.
Although the data reduction method employed here was a static technique requiring the localization of a zeroth-order fringe, many other techniques can be used for fringe interpretation (1-3,6,17). The choice of the appropriate method for data analysis must be based upon application experience, and available equipment. By contrast dynamic fringe analysis can be used to yield in plane deformation. The choice between the two depends upon the dominant type of specimen motion although the methods are not mutually exclusive. Additionally, other methods to produce interferograms exist so that data is available in real time (3,4,16,17). Clearly, holographic interferometry is capable of providing unique data and is worthy of further investigation. The results from holographic interferometry should augment the results for contact methods for in vitro biomechanical applications in the future.
Abramson N: The Making and Evaluation of Holograms. London, Academic Press. 1981
2. Aleksandrou EB, Bonch-Bruevich AM: Investigations of surface strains by the hologram technique. Sov Phys Tech phys 12:258-265, 1967
3. Briers JD: The interpretation of holographic interferograms. Opt Quant Elec 8:469-501, 1976
4. Brown GM, Grant RM, Stroke OW: Theory of holographic interferometry J Acoust Soc Am 45:1 166-1179, 1%9
5. Ennos AE: Measurements of in-plane surface strain by hologram interferometry J Sci Instrum (J Phys E) 1:731-746, 1968
6. Hariharan P: Optical Holography: Principles, Techniques and Applications. Cambridge. Cambridge University Press. 1984, pp 1-7
7. Huiskes R: A detailed comparison of experimental and theoretical stress analysis of a human femur. In: Mechanical Properties of Bone, AMD Vol.45. ed by S Cowin, New York, American Society of Mechanical Engineers, 1981, pp 211-234
8 Manley MT, Gurtowski J. Stern LS, Halioua M. Bowins T: A biomechanical study of the proximal femur using fullfield holographic interferometry Trans Orthop Res Soc 8:99, 1983
9. Manley MT, Ovryn B, Stern LS: Evaluation of holographic interferometry for biomechanical measurements in vitro.Trans ASME AMD 68:45, 1985
10. Manley MT, Stem LS: The load carrying and fatigue properties of the stem-cement interface with smooth and porous coated femoral components. J Biomed Mat Res 19:563-575, 1985
11. Manley MT, Stem LS, Halioua M, Bowins TS: The use of holographic interferometry in assessing the performance of biomaterials in vitro. Trans Soc Bia 6:117.1983
12. Manley MT. Stern LS, Gurtowski J: Performance characteristics of total hip femoral components as a function of prosthesis modulus. Bull Hosp Joint Dis Orthop Inst 43:130-136, 1983
13. Manley MT, Stern LS, Gurtowski J, Dee R: Comparison of proximal femoral biomechanics after implantation of titanium and cobalt chromium femoral components. TransOrtho Res Soc 8:239,1983
14. Sollid JE: Holographic interferometry applied to measurements of small static displacements of dilfusely reflecting surfaces. AppI Opt 8:1587-1595. 1%9
15. Sollid JE: Translational displacements versus deformation displacements in double-exposure holographic interferometry. Opt Comun. 2:282-288,1970
16. Stetson KA. Powell RL: Interferometric vibration analysis by wavefront reconstruction. J Opt Soc Am 55:1593-1598. 1965
17. Vest CM: Holographic Interferometry. New York, John Wiley and Sons. 1979. pp 58-145