Recently, mechanobiology has received increased attention. For investigation of biofilm and cellular tissue, measurements of the surface topography and deformation in real-time are a pre-requisite for understanding the growth mechanisms. In this paper, a novel three-dimensional (3D) fluorescent microscopic method for surface profilometry and deformation measurements is developed. In this technique a pair of cameras are connected to a binocular fluorescent microscope to acquire micrographs from two different viewing angles of a sample surface doped or sprayed with fluorescent microparticles. Digital image correlation technique is used to search for matching points in the pairing fluorescence micrographs. After calibration of the system, the 3D surface topography is reconstructed from the pair of planar images. When the deformed surface topography is compared with undeformed topography using fluorescent microparticles for movement tracking of individual material points, the full field deformation of the surface is determined. The technique is demonstrated on topography measurement of a biofilm, and also on surface deformation measurement of the biofilm during growth. The use of 3D imaging of the fluorescent microparticles eliminates the formation of bright parts in an image caused by specular reflections. The technique is appropriate for non-contact, full-field and real-time 3D surface profilometry and deformation measurements of materials and structures at the microscale.
© 2013 OSA
Three-dimensional (3D) measurements of topography and displacement at the microscale can shed light in the investigations in many disciplines such as biology, medicine, biomedical engineering, materials science and engineering, and mechanical engineering. For example, the investigation in mechanobiology will benefit from a technique to measure the 3D topography and deformation of biofilms and tissues [1–3]. Traditional 3D profilometry techniques can hardly be employed for the surface profile measurement for biological cells or soft materials at the microscale. The typical characteristic in-plane dimensions of biological tissues are on the order of 1~20 mm, and the out-of-plane feature dimensions are on the order of submicron to tens of µm; these relatively small dimensions make it difficult for real-time, non-contact, full field profilometry and deformation measurements for purpose of tracking 3D deformations in-vivo or in-vitro. High-resolution imaging techniques, such as scanning tunneling microscopy (STM), atomic force microscopy (AFM), near-field scanning optical microscopy (NSOM) and scanning electron microscopy (SEM), have their limitations for probing 3D surface profiles on soft biomaterials in-vivo or in-vitro. AFM relies on a tip to scan a surface; it cannot be applied for mm size regions. NSOM utilizes the properties of evanescent waves to detect the surface by placing a detector above a sample surface at a distance smaller than the wavelength of the light. The resolution of the image is dictated by the size of the detector aperture, which is far below mm size [4, 5], such that NSOM is not appropriate for mm area scanning in real-time. SEM/STM utilize high-energy scanning electron beam at tens of kV to scan a conductive sample surface, far removed from the physiological condition of a biomaterial sample. For observations of biological samples in-vivo or in-vitro, such as the wrinkle formation in a biofilm, a new technique is needed. This paper will provide a technique, based on 3D fluorescence microscopy, to address such a need.
A number of experimental techniques have been developed to utilize fluorescent dyes or particles to track movements of material points to determine displacements, such as for flow visualization [6, 7]. Fluorescent dyes or particles are used as markers to observe biological processes, such as cell migration , growth of bacteria , interactions between colloidal particles , and mixing behavior of fluids in a microfluidic device . For 3D observation, a fluorescent particle tracking method at micron-scale using a single camera was proposed . In that method a microscope acquires a set of slightly out-of-focus images showing the increase of the ring radius of a fluorescent particle as it moves away from its reference plane and approaches the objective lens. These images are subsequently used to reconstruct a 3D image of the distributed particles inside a transparent sample. The technique is not operational in real-time, as a series of images has to be acquired to construct a single 3D image. Berfield et al.  proposed a full-field, fluorescence-based digital image correlation (FDIC) technique. They used fluorescent nanoparticles to create random texture patterns for nanosclae deformation measurement. FDIC provides a promising and practical technique for non-contact, full-field, and real-time in-plane deformation measurement with nanoscale displacement resolution appropriate for a wide range of hard and soft materials. Recently FDIC was applied to study the local strain concentrations in a micro vascular network . The application of fluorescence microscopy allows measurement of nanoscale deformation and damage in polymeric materials . However, FDIC is limited to in-plane deformation measurement. Franck et al.  dispersed fluorescent particles to a soft material sample and observed the dispersed particles on a confocal microscope before and after deformation, and further determined the 3D deformations using the digital volume correlation [17, 18] technique. The conventional laser confocal microscopy for 3D profilometry  takes relatively long time to acquire a set of images on a transparent sample, making it difficult for real-time measurement, especially when fast evolution is involved in a process. Spinning disk confocal microscopy  acquires a stack of images within 1/15 second; it is fast enough for 3D observation of some cell growth. However, it is still a challenge to apply it for real-time measurement, such as for investigation of the viscoelastic behavior of biomaterials under high strain rate loading [21, 22]; the same issue occurs for reflected light confocal microscopy . White light interferometry  is an excellent non-contact optical profilometry technique, but it does not allow for tracking material points to measure surface deformations such as displacements and strains.
In this paper we utilize stereo-imaging of fluorescent particles on a biomaterial sample to determine the surface topography and also to measure simultaneously the 3D surface deformations for situations where these particles follow the movements of material points on the material surface . Both fluorescent nanoparticles and microparticles can be used for observations at different scales. A binocular stereo vision system acquires a pair of images of the same field of a sample from two different observation directions simultaneously. The images are subsequently analyzed with the triangulation method from the corresponding image points on both images to reconstruct a 3D image of the sample surface. In this method, the fluorescent particles are used to provide distinct surface features. Instead of using random texture patterns formed by other means such as paint, colored silicone, or carbon blacks, the use of fluorescent particles allows observation at scales commensurate with the fluorescent particle sizes, on the order of nanometer to a few μm.
The use of fluorescent particles for stereo-imaging provides the following advantages: (1) the selection of fluorescent particle size is abundant, ranging from 1 nm  to several microns, suitable for formation of random texture patterns (often through conglomerate of particles) over a wide range of sizes. A sample can also be stained with multi-fluorescent probes for multi-purpose observations; and the fluorescent particles serve as random texture or markers for surface profilometry and also for tracking surface deformations at different scales; (2) Fluorescence imaging avoids unwanted specular reflections, to allow pairing the corresponding points observed on the pair of micrographs through digital image correlation; this characteristic is especially helpful for observation of biosamples under in-vivo or in-vitro conditions where moist surface usually induces reflection when white light is used; (3) The fluorescent light will not induce as much heating as white light on a sample surface to alter the environmental condition for a biomaterial under investigation; and (4) Fluorescent particles have excellent biocompatibility with biomaterials, and thus enabling investigations of living biological samples such as biofilms and tissues.
In this paper, 3D surface profilometry and deformation measurements using fluorescent stereo microscopy (FSM) system are described. The technique for 3D surface profilometry is validated using a specimen with known geometry and the technique for surface deformation measurements is demonstrated by measurements of deformations imposed by a 3-axis nano-position stage. We also demonstrate the FSM technique for 3D surface topography measurement and deformation measurement of a Bacillus subtilis biofilm.
2. Stereo-based microscopic measurement
We describe in this section the principle for the stereo microscopic technique for measurements of the 3D surface topography and deformations. The technique is based on stereo vision and digital image correlation. In digital image correlation, two images with locally distinct grayscale patterns representing the reference and the deformed states are compared to determine the surface deformations. Digital image correlation allows two images analyzed for correlating a material point with distinct grayscale features surrounding it [27–30]. In the case of stereo vision, digital image correlation allows correlation of the image of a material point acquired on one micrograph with the corresponding image of the same material point on another micrograph; in addition it also allows tracking the same material point after deformation. Stereo-imaging based measurement (also known as 3D-digital image correlation) was proposed previously  for 3D surface topography and deformation measurements. 3D digital image correlation technique measures the surface topography and surface deformations [32–34], whereas DVC [17, 18] measures internal deformations of a solid undergoing deformations through analysis of volume images acquired by techniques such as X-ray microtomography, laser tomography, nanotomography, and confocal microscopy. In this work, we use stereo-based measurement for surface topography and deformations. Stereo-based measurement has already found applications in materials science and engineering, biomechanics, polymer forming, fatigue and fracture, and high-speed impact testing . With a growing interest in measurements at the microscale or nanoscale, Sutton et al.  introduced the microscale stereo-based measurement techniques using optical stereo microscopy for 3D surface topography and deformation measurements.
For measurement of the surface profile at the microscale in this paper, a stereo microscope based on a binocular vision system is used. In this system an object is observed in two viewing directions by two cameras. In a Cartesian frame, a point (e.g., ) on the surface of an object is projected onto two points on the imaging planes by the left () and right () cameras, as shown in Fig. 1 . The binocular stereo vision technique reconstructs the 3D world coordinates from the points projected on both images, similar to the function of human eyes in observation of a 3D object. Digital image correlation is used to determine the corresponding points between the two images acquired by the two cameras. After the positions and orientations of the two cameras and the camera intrinsic parameters (the focal lengths, principle points, and distortion coefficients of the lenses) are determined through a stereo vision calibration procedure, the shape of the object is reconstructed using triangulation . For measurement of displacement of a point, digital image correlation can be used to map the images of the point in both left and right images in both the undeformed and deformed states. After 3D reconstructions, the coordinates of the same material point in both the undeformed and deformed states can be determined, thus the displacement components can be obtained by subtracting the coordinates of the point in the undeformed state from the corresponding coordinates in the deformed state. Calculation of the gradients of the displacements gives the surface strains . In classical camera calibration, an ideal pinhole camera model is used. Parameterization of the distortion functions is introduced to take into account of the distortion of each optical element. However, the combination of different optical elements in a stereo microscope leads to prohibitively complex and highly non-linear distortion function. To circumvent this problem, Schreier et al.  developed a technique, in which a virtual plane without distortion is assumed to exist, and introduced generic warping functions that are not based on specific distortion models. This method was further applied to measure 3D strain field of mouse artery under pressure loading .
In microscopic stereo vision, two cameras are used for observation from two different viewing angles. In general, there are two types of binocular stereo microscopic systems. In the first type two adjacent objective lenses with independent optical paths are used; in the second type, a common main objective lens is used. A conventional optical microscope has a small working distance, on the order of a 1~5 mm when relatively low magnifications, 5 × to 10 × are used, or a distance of 0.1~0.5 mm at higher magnifications, such as 50 × to 100 × , and at the limit, 0.01~0.3 mm in focus depth for 0.1~2 mm diameter viewing field. In this study, a stereo surgical microscope (Zeiss OPMI-1) is employed with common objective lens with 50 mm diameter. It has a large working distance, up to 150 mm (the focal length of the objective lens is 150 mm), and ~5 mm depth of field. The viewing field is 5~18 mm in diameter, to allow measurements of relatively large surface profile and deformations. Two digital cameras (Nikon D7000) with a spatial resolution of 4928 × 3264 pixels are connected to the microscope to acquire images. The shutter time of the cameras has a range from millisecond to tens of seconds. An external trigger is used to synchronize the image acquisition by the two cameras. A 0.2 mm square chessboard (Texas Industrial Optics Inc.) is used for calibration. The camera calibration method  (Camera calibration toolbox for Matlab ) is used to calibrate the system. All the intrinsic and extrinsic parameters are optimized using bundle adjustment algorithms . The Newton-Raphson  and reliability-guided digital image correlation  are employed to identify the corresponding points in those images.
3. Fluorescent stereo microscopy system and validation
A fluorescence microscope contains a set of interference filters and a dichromatic beam splitter, for excitation and emission of a fluorescent probe (or particle) attached to the surface of a specimen. Selected excitation of specimen fluorochrome and the subsequent isolation of weaker fluorescence emission are needed for generating fluorescence image. However, to the best of our knowledge, a fluorescent stereo microscope based on fluorescent imaging from two individual viewing angles is not commercially available. We developed a fluorescence stereo-imaging system by matching the excitation, emission filter properties with a particular fluorochrome on the Zeiss OPMI microscope. Leica L5 is used for illumination, it has integrated 5-position filter wheel. For tracking, blue-green fluorescent particles (430/465, Life Technology Corp., #F13080) with 1 μm nominal diameter are used. The fluorescent spherical particles in a colloid are made from an amorphous polymer such as polystyrene. Figure 2 shows the optical properties of the fluorescent particles. The primary function of the emission/barrier filter in any fluorescent system is to block the excitation wavelengths used. Therefore, based on the properties of the fluorochrome, ET420/40x and ET 480/40m (Chroma Technology Corp.) were used as the excitation and emission filters, respectively. The excitation filter has a band pass from 400 to 440 nm; the center wavelength is 420 nm. The emission filter has a band pass range of 460~500 nm; and the center wavelength is 500 nm. The properties of the filters and the fluorochrome bands are also shown in Fig. 2. The excitation filter ET 420/40 × is installed on the filter wheel of Leica L5. The two emission filters (ET 480/40m) are placed inside the beam splitter tubes of Zeiss OPMI microscope. The schematic diagram of the optical paths in the Zeiss OPMI in the FSM is shown in Fig. 3(a) . The stereo microscope setup (Fig. 3(b)), as implemented in this work, provides an overall field of view of 6.14 × 4.07 mm2, and has a spatial resolution of 1.2 μm/pixel.
The procedure for measurement of surface topography is given as follows. The system was assembled based on the schematic diagram of the FSM system shown in Fig. 3(a). Figure 3(b) shows the experimental setup of the complete system. A sample was mounted on a 3-axis nano-position stage (Thorlabs Inc., #MAX301). The stereo microscope was calibrated with a white light source using calibration pattern mounted on the specimen stage. The calibration pattern was translated and rotated, and its images were captured. A random fluorescence texture pattern on an object surface was generated by applying a droplet of fluorescent liquid on a surface using an airbrush (Iwata Inc.). A random texture pattern was created with this fine point airbrush on the sample.
3.1 Validation of the 3D surface topography measurement
A spherical steel ball with diameter 7.938 ± 0.013 mm (http://www.mcmaster.com/) was used for validation of surface topography measurement. Two fluorescent images were acquired from cameras on the left and right as shown in Figs. 4(a) and 4(b), respectively. The matching horizontal and vertical displacement fields are shown in Figs. 4(c) and 4(d), respectively. The 3D geometry of the ball is subsequently constructed as shown in Fig. 4(e) using a noise removal algorithm developed by You et al. . From the reconstructed 3D coordinates, the diameter of the ball was determined using the Levenberg-Marquardt algorithm . Five measurements were made; the average diameter was measured as 8.039 ± 0.120 mm. The relative error was 1.3%.
In order to demonstrate the flexibility of our system, we also applied this method to measure the 3D topography of a biofilm. A biofilm is an aggregation of micro-organisms in which cells adhere to each other to form a dense organism community [45, 46]. The structural and developmental complexity of biofilms, and its significance in both natural and man-made environments, has received increased attentions . In this work, a Bacillus subtilis biofilm sample was prepared . After 4 days of growth, the surface was sprayed with random fluorescent particles. Both the left and right images of the biofilm are shown in Figs. 5(a) and 5(b), respectively. The reconstructed surface of the biofilm is shown in Fig. 5(c). From the reconstructed 3D shape, the wrinkles of the biofilm are clearly seen. The system is suitable for measurements of the surface evolution of a biofilm in real-time. The 3D surface topography obtained at different growth times can be analyzed further for understanding the growth mechanism of a biofilm; as an example the surface deformations of a biofilm undergoing 4 hours of growth are described in Section 3.2.
3.2 3D deformation measurements
Figure 6 shows a glass slide sprayed with fluorescent particles. The nominally 1 µm spherical particles aggregated to form fluorescent random pattern of different shapes and sizes. After processing into a binary image , each spot was represented as a best-fit circular dot. The radial distribution of the fluorescent dot is shown in Fig. 6. Approximately 95% of all fluorescent random spots were within a range of the radii between 0.68 and 16.57 μm. Based on the subset fluctuation proposed , the mean value of various subset (or subdomain) of 201 × 201 pixels over the image is 19. In order to determine the sensitivity of this FSM system, these images were captured at different time intervals without moving the slide or the fluorescent stereo system. Since the edge regions have more pronounced image distortion, the central area of images in focus was used to evaluate the sensitivity. The sensitivity of the system used in this work was 0.13 μm for in-plane deformation measurement, and 1.26 μm for out-of-plane deformation measurement. The out-of-plane sensitivity is lower due to the small angle 8.3° formed by the axes of the two cameras [30, 49]. The sensitivity of the setup was affected by various factors, including the digital image correlation algorithm for stereo-matching, and the environmental noise such as the vibration of Nikon camera shutter, which was not considered in this study with a primary focus on demonstrating the technique.
For translation tests, the glass slide with random fluorescence patterns was attached to a precision 3-axis nano-position stage, with 1 nm resolution in each direction. Translations in 0.1, 0.2, 0.4, 0.8, 1, 2, 4, 8, 16 μm were generated using the piezo-stage in the X, Y and Z directions, respectively. The translations over 20 μm (32, 64, 128 and 256 μm) were driven by motors. Pairs of images of the random patterns on the glass slide were acquired before and after translations. The rigid body displacement field was calculated using the stereo-based measurement technique. Each translation movement was repeated for 8 times. As shown in Table 1 , the interval of applied displacements along X-, Y- and Z-axis are in equally spaced in base 2 logarithmic scales. The mean values of the measured displacements and the applied displacements greater than 1 μm in the 3-axis are nearly identical as shown in Table 1, indicating that the FSM system used in this work is appropriate for measurements of displacements of 1 μm or larger. The measured in-plane displacements (X and Y directions) are nearly identical to the prescribed displacements, and the out-of-plane displacements (Z-direction) are close, but the difference is larger. The standard deviation of the displacement in the Z-direction increases with the applied displacement. As the applied displacement in the Z-direction increases, images started to become increasingly out-of-focus, which introduces errors in displacement measurements in the Z-direction using digital image correlation for point tracking. For displacement measurements lower than 1 µm, errors are larger. These results indicate that a fluorescent stereo system with higher magnification is needed for measurements of 3D topography and deformation measurements at sub-micron scale.
For measurement of 3D deformation on a surface, the displacement is calculated by subtracting the Cartesian coordinates of a point in the reference state from the corresponding coordinates of the point in the deformed state. To demonstrate such capability a 3D deformation measurement was conducted on a Bacillus subtilis biofilm during its growth. After 24 hours of development, fluorescent particles were sprayed on the surface. A pair of images representing the reference state were acquired. After another 4 hours of development, another pair of images representing the deformed state were acquired. Figure 7 shows the 3D deformation measurement of the biofilm during its growth. In the interest of space, only the left images in the reference (Fig. 7(a)) and deformed (Fig. 7(c)) states are shown. The 3D surface profiles in the reference and deformed states of the rectangle area in Fig. 7(a) are shown in Figs. 7(b) and 7(d), respectively. The 3D deformation field as projected onto the plane of the glass slide on which the biofilm grew is shown in vector form in Fig. 7(e) (some of the points are blocked by the surface) and the contour of the out-of-plane deformation is also shown in the same figure. The technique developed in this work allows for measurement of the surface deformations of the biofilm.
4. Conclusion and outlook
In summary, we have developed a novel fluorescent stereo microscopic technique for 3D surface profilometry and deformation measurements. A 3D fluorescent microscope was set up from a Zeiss stereo microscope by selecting matching excitation and emission filters with particular fluorochrome. The technique provides a robust methodology for non-contact, full-field, real-time 3D profile and deformation measurements at the microscale. It can be used for surface profilometry and deformation measurements for a wide range of materials, such as for observation of the 3D shape and displacements during the growth of biofilms or biotissues, for measurements of the mechanical properties of biomaterials. Validation was conducted on rigid translation. The FSM setup has higher in-plane sensitivities than out-of-plane sensitivity. The standard deviation of the out-of-plane measurement increases as the translation becomes larger due to out-of-focus of an image and system configuration. Higher magnifications can be achieved with high magnification objective lenses for surface deformation measurements at the sub-micron scale.
We acknowledge the support of DOE NEUP 09-818. We also thank the additional support from NSF DMR-0907291, CMMI-1031829, CMMI-1132174, and ECCS-1307997, and NIH R01 EB013212 and R01 DC011585. We appreciate Dr. Munehiro Asally and Dr. Gürol M. Süel at the University of California, San Diego for providing the biofilm samples.
References and links
1. M. Asally, M. Kittisopikul, P. Rué, Y. Du, Z. Hu, T. Çağatay, A. B. Robinson, H. Lu, J. Garcia-Ojalvo, and G. M. Süel, “Localized cell death focuses mechanical forces during 3D patterning in a biofilm,” Proc. Natl. Acad. Sci. U.S.A. 109(46), 18891–18896 (2012). [CrossRef] [PubMed]
2. M. T. Raimondi, E. Bonacina, G. Candiani, M. Laganà, E. Rolando, G. Talò, D. Pezzoli, R. D’Anchise, R. Pietrabissa, and M. Moretti, “Comparative chondrogenesis of human cells in a 3D integrated experimental-computational mechanobiology model,” Biomech. Model. Mechanobiol. 10(2), 259–268 (2011). [CrossRef] [PubMed]
3. S. A. Maskarinec, C. Franck, D. A. Tirrell, and G. Ravichandran, “Quantifying cellular traction forces in three dimensions,” Proc. Natl. Acad. Sci. U.S.A. 106(52), 22108–22113 (2009). [CrossRef] [PubMed]
4. U. Dürig, D. W. Pohl, and F. Rohner, “Near-field optical scanning microscopy,” J. Appl. Phys. 59(10), 3318–3327 (1986). [CrossRef]
5. Y. Oshikane, T. Kataoka, M. Okuda, S. Hara, H. Inoue, and M. Nakano, “Observation of nanostructure by scanning near-field optical microscope with small sphere probe,” Sci. Technol. Adv. Mater. 8(3), 181–185 (2007). [CrossRef]
6. J. P. Kerrigan, K. Yamazaki, R. K. Meyer, T. Mori, Y. Otake, E. Outa, M. Umezu, H. S. Borovetz, R. L. Kormos, B. P. Griffith, H. Koyanagi, and J. F. Antaki, “High-resolution fluorescent particle-tracking flow visualization within an intraventricular axial flow left ventricular assist device,” Artif. Organs 20(5), 534–540 (1996). [CrossRef] [PubMed]
7. J. Sakakibara, K. Hishida, and M. Maeda, “Vortex structure and heat transfer in the stagnation region of an impinging plane jet (simultaneous measurements of velocity and temperature fields by digital particle image velocimetry and laser-induced fluorescence),” Int. J. Heat Mass Tran. 40(13), 3163–3176 (1997). [CrossRef]
8. C. M. Wells and M. Parsons, Cell Migration: Developmental Methods and Protocols (Humana, 2011).
11. O. Loh, R. Lam, M. Chen, N. Moldovan, H. Huang, D. Ho, and H. D. Espinosa, “Nanofountain-probe-based high-resolution patterning and single-cell injection of functionalized nanodiamonds,” Small 5(14), 1667–1674 (2009). [CrossRef] [PubMed]
12. M. Wu, J. W. Roberts, and M. Buckley, “Three-dimensional fluorescent particle tracking at micron-scale using a single camera,” Exp. Fluids 38(4), 461–465 (2005). [CrossRef]
13. T. A. Berfield, J. K. Patel, R. G. Shimmin, P. V. Braun, J. Lambros, and N. R. Sottos, “Fluorescent image correlation for nanoscale deformation measurements,” Small 2(5), 631–635 (2006). [CrossRef] [PubMed]
14. A. Hamilton, N. Sottos, and S. White, “Local strain concentrations in a microvascular network,” Exp. Mech. 50(2), 255–263 (2010). [CrossRef]
15. B. A. Samuel, M. C. Demirel, and A. Haque, “High resolution deformation and damage detection using fluorescent dyes,” J. Micromech. Microeng. 17(11), 2324–2327 (2007). [CrossRef]
16. C. Franck, S. Hong, S. A. Maskarinec, D. A. Tirrell, and G. Ravichandran, “Three-dimensional full-field measurements of large deformations in soft materials using confocal microscopy and digital volume correlation,” Exp. Mech. 47(3), 427–438 (2007). [CrossRef]
17. B. K. Bay, T. S. Smith, D. P. Fyhrie, and M. Saad, “Digital volume correlation: three-dimensional strain mapping using X-ray tomography,” Exp. Mech. 39(3), 217–226 (1999). [CrossRef]
18. Z. Hu, H. Luo, W. Young, and H. Lu, “Three-dimensional internal large deformation measurement of PMI foam using incremental digital volume correlation,” presented in International Mechanical Engineering Congress and Exposition, Houston, USA, 9–15 Nov. 2012.
19. S. Li, Z. Xu, I. Reading, S. F. Yoon, Z. P. Fang, and J. Zhao, “Three dimensional sidewall measurements by laser fluorescent confocal microscopy,” Opt. Express 16(6), 4001–4014 (2008). [CrossRef] [PubMed]
20. R. Gräf, J. Rietdorf, and T. Zimmermann, “Live Cell Spinning Disk Microscopy,” in Microscopy Techniques, J. Rietdorf, ed. (Springer Berlin Heidelberg, 2005), pp. 57–75.
22. H. Luo, H. Lu, C. Dai, and R. Z. Gan, “A comparison of Young’s modulus for normal and diseased human eardrums at high strain rates,” Int. J. Exp. Comp. Biomech. 1(1), 1–22 (2009). [CrossRef]
23. A. Boyde, “Combining confocal and conventional modes in tandem scanning reflected light-microscopy,” Scanning 11(3), 147–152 (1989). [CrossRef]
25. J.-J. Orteu, “3-D computer vision in experimental mechanics,” Opt. Lasers Eng. 47(3-4), 282–291 (2009). [CrossRef]
27. W. H. Peters and W. F. Ranson, “Digital imaging techniques in experimental stress-analysis,” Opt. Eng. 21(3), 427–432 (1982). [CrossRef]
28. M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vis. Comput. 1(3), 133–139 (1983). [CrossRef]
29. H. Lu, G. Vendroux, and W. Knauss, “Surface deformation measurements of a cylindrical specimen by digital image correlation,” Exp. Mech. 37(4), 433–439 (1997). [CrossRef]
30. H. Lu and P. Cary, “Deformation measurements by digital image correlation: Implementation of a second-order displacement gradient,” Exp. Mech. 40(4), 393–400 (2000). [CrossRef]
31. P. Luo, Y. Chao, M. Sutton, and W. Peters III, “Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision,” Exp. Mech. 33(2), 123–132 (1993). [CrossRef]
32. Y. Wang, Error Assessment in 3D Computer Vision Ph.D Dissertations, (University of South Carolina, 2010).
33. X. D. Ke, H. Schreier, M. Sutton, and Y. Wang, “Error Assessment in Stereo-based Deformation Measurements,” Exp. Mech. 51(4), 423–441 (2011). [CrossRef]
34. Y. Q. Wang, M. Sutton, X. D. Ke, H. Schreier, P. Reu, and T. Miller, “On error assessment in stereo-based deformation measurements,” Exp. Mech. 51(4), 405–422 (2011). [CrossRef]
35. M. A. Sutton, T. L. Chae, J. L. Turner, and H. A. Bruck, “Development of a computer vision methodology for the analysis of surface deformations in magnified images,” MiCon 90: Adv. in Video Tech. for Microstruc. Con. l, 109–131 (1990).
36. M. Sutton, J. Orteu, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications (Springer-Verlag, 2009).
37. H. Schreier, D. Garcia, and M. Sutton, “Advances in light microscope stereo vision,” Exp. Mech. 44(3), 278–288 (2004). [CrossRef]
38. M. A. Sutton, X. Ke, S. M. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. W. Schreier, “Strain field measurements on mouse carotid arteries using microscopic three-dimensional digital image correlation,” J. Biomed. Mater. Res. A 84A(1), 178–190 (2008). [CrossRef] [PubMed]
39. Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE T. Pattern Anal. 22(11), 1330–1334 (2000). [CrossRef]
40. J.-Y. Bougue, “Camera calibration toolbox for Matlab” (2010). http://www.vision.caltech.edu/bouguetj/calib_doc.
41. H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters III, “Digital image correlation using Newton-Raphson method of partial-differential correlation,” Exp. Mech. 29(3), 261–267 (1989). [CrossRef]
44. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes 3rd Edition: The Art Of Scientific Computing (Cambridge University, 2007).
46. G. Lear and G. D. Lewis, Microbial Biofilms: Current Research and Applications (Caister Academic, 2012).
47. V. Clausnitzer and J. W. Hopmans, “Determination of phase-volume fractions from tomographic measurements in two-phase systems,” Adv. Water Resour. 22(6), 577–584 (1999). [CrossRef]
48. T. Hua, H. Xie, S. Wang, Z. Hu, P. Chen, and Q. Zhang, “Evaluation of the quality of a speckle pattern in the digital image correlation method by mean subset fluctuation,” Opt. Laser Technol. 43(1), 9–13 (2011). [CrossRef]