Open Access
Add to BibSonomyAbstract
This paper presents a confocal microscanner for direct vertical optical sectioning of biological samples. Confocal imaging is performed by transverse (X-axis) and axial (Z-axis) scanning of a focused laser beam using an optical fiber and a microlens respectively. The actuators are fabricated by laser micromachining techniques and are driven by electromagnetic forces. Optical and mechanical performance of the system is predicted by simulation software packages and characterized by experimental measurements. The scanner has lateral resolution of 3.87 µm and axial resolution of 10.68 µm with a field of view of 145 µm in X and 190 µm in Z directions. Confocal imaging of a polymer layer deposited on a silicon wafer and onion epidermal cells is demonstrated.
©2011 Optical Society of America
1. Introduction
Various optical microscopy techniques have been developed for micrometer level imaging of biological tissue samples including optical coherence tomography (OCT) [1,2], multiphoton excitation microscopy (MPM) [3,4] and confocal microscopy [5,6]. Microscopic images obtained by these techniques provide high resolution morphological information approaching that offered by histology images of fixed tissue sections. Among these techniques, OCT has the largest imaging depth (~ 2 mm) and field of view, but generally, lower spatial resolution and not as good image contrast due to the speckle effect. OCT also performs vertical sectional imaging by default. MPM often employs two-photon excitation fluorescence (TPEF) and second harmonic generation (SHG) signals for high contrast and resolution image formation. However, this technique requires expensive femtosecond (fs) lasers and demanding optics for imaging. Confocal microscopy provides superior image contrast and high resolution tissue and cellular morphology images that are close to that of histology. Its major drawback is limited imaging depth (~ 0.2 mm). However, this imaging depth is sufficient for imaging superficial diseases such as early epithelial cancers.
In confocal microscopy, a beam of light is focused on a sample by an objective lens. Imaging is usually performed by raster scanning of the focused light in the X-Y plane (X-Y plane is parallel to the surface of the sample). Scanning of the light beam can be performed using micro-mirrors developed by Microelectromechanical Systems (MEMS) technology [7–10] or by optical fibers [11–13]. This will result in horizontal optical sectioning that produces an image of a section that is parallel to the surface of the sample. In conventional histopathology preparation procedures, samples are cut in transverse slices. Images obtained from this process show a vertical cross-section of the sample. Therefore, a confocal device capable of obtaining vertical cross-sectional images has advantages in clinical applications. One method of in-direct vertical sectional imaging is collecting and stacking horizontal section images obtained from various depths within the sample [14]. The disadvantage of this method is a long scanning time if high resolution imaging is desired. A better method of optical vertical sectioning is direct raster scanning of a focused laser beam in the X-Z plane (X-Z plane is perpendicular to the surface of sample). This will provide real-time images that are analogues to histopathology images which pathologist and clinicians are more familiar with.
Direct vertical confocal imaging in the X-Z plane has been previously demonstrated by various methods. This includes focusing a beam of light on a specimen and moving the sample in the X-Z plane using a piezo translation stage [15] or scanning a laser spot in transverse (X-axis) direction using a galvanometer mirror and translating the specimen using a piezo stage for axial (Z-axis) scan [16]. In another work, transverse and axial scans were performed by a galvanometer mirror and a commercial piezo-actuated macroscopic objective lens respectively [17]. The whole assembly is large in size and is intended for laboratory desktop microscopy applications. Those implementations are not suitable for in vivo clinical patient measurements, especially for internal organ imaging through an endoscope. For in vivo clinical applications, the sample (our epithelial tissues as part of our body) cannot be moved for the purpose of imaging. The scanners have to be miniaturized to the size of millimeters or several millimeters and also be safe to the patient, thus present significant engineering challenges. Utilizing MEMS technology is the way of choice to overcome these challenges. Recently, a group has proposed direct vertical imaging by mounting a micromirror developed by MEMS technology on a stage and actuating the stage in the axial direction using piezoelectric unimorph beams [18].
Here we present another way of direct vertical sectional imaging by scanning a laser beam in transverse direction using an optical fiber and in axial direction through actuating an objective lens with the aim of real-time in vivo imaging. To make the scanner potentially suitable for hand-held and endoscopy clinical applications, we utilize MEMS fabrication techniques to construct miniature lens and fiber scanning mechanisms. Various methods of moving a lens in the axial direction using microfabricated actuators have been demonstrated including electrostatic [19,20], thermal [21] and electromagnetic [22,23] actuations. In general, electrostatic actuators have a limited actuation range due to the snap-in phenomenon. Thermal actuators can achieve large scanning range; however, continuous thermal cycling can cause thermal fatigue failure. Electromagnetic actuators typically require low driving voltage, have high repeatability and provide large scanning range.
Recently, we reported a 1-axis magnetically actuated lens for non-contact confocal thickness measurement of samples [22,23]. An electroplated nickel flexure actuated in axial direction by electromagnetic force was demonstrated. In this work, we have coupled a magnetic lens actuator with a transverse fiber optic actuator to form a 2-axis confocal scanner for direct vertical cross-sectional imaging of samples. In addition, laser micromachining technique is utilized to fabricate the magnetic actuators. In this scanner, fiber and lens actuators are mechanically decoupled, eliminating translational errors and any interference or coupling effects between the actuation systems. Both actuators are driven by electromagnetic forces, hence reducing power consumption and providing large scanning range. In this paper we report both the optical and mechanical design and characterization of a 2-axis confocal scanner for vertical optical sectioning. Preliminary two-dimensional confocal imaging of samples is also demonstrated.
2. Design and principle of operation
2.1 Instrumentation
Figure 1(a) shows the optical configuration of a 2-axis confocal scanner. A beam of light is illuminated from a single mode optical fiber (SMF) and is collimated by a collimating lens. The light is then focused on a sample by an objective lens. In order to scan a vertical cross-section of the sample, both transverse and axial scanning of the focused beam is required. The frequency ratio and desired number of pixels in the image defines the scanning rate of device. In our system fast-axis scanning is performed by actuating the objective lens in axial direction and slow-axis scanning is done by moving the optical fiber in transverse direction as shown in Fig. 1(a).
Fig. 1 (a) Optical configuration of the 2-axis confocal scanner. The optical fiber and objective lens are capable of scanning in transverse (X-axis) and axial (Z-axis) directions respectively. (b) Schematic diagram of the experimental setup.
A schematic diagram of 2-axis confocal system is provided in Fig. 1(b). A beam of light with wavelength of 785 nm is emitted from a laser source (SDL XC30). The beam is directed to a single mode fiber coupler (Newport Corp.) using a 30R/70T beam splitter. After scanning the sample, the reflected light is relayed to a photomultiplier tube (PMT) through the same optical fiber. A data acquisition (DAQ) card is used to collect the intensity signal from the PMT and to generate the driving signals for the scanner. The intensity signal is converted to a two-dimensional image using a computer.
2.2 Magnetic actuators
Both fiber and lens actuators in our system are driven by alternating electromagnetic forces generated by small coils. For a sinusoidal input current of i = imaxsinωt into the coils, where imax is the maximum current, ω is frequency and t is time, the equation of electromagnetic force can be approximated as [24]:
where µ0 is the permeability of free space, A is the cross-sectional area of the electromagnet core, N is the number of turns of the coil and g is gap between the coil and the actuator.2.2.1 Fiber actuator
To prevent the fiber from scanning in unwanted directions due to misalignment with the applied magnetic field or external vibrations, the stiffness of the fiber actuator in X-axis is designed to be much smaller than that in Y-axis. This is achieved by mounting an optical fiber on a 25 mm × 2 mm cantilever beam that was fabricated by laser micromachining of a 25.4 µm thick nickel foil. A groove was created at the center and along the length of the beam to hold the optical fiber. One side of the cantilever beam was mounted to a v-groove fiber holder and an electromagnetic coil was place at the other side of the beam. When an alternating magnetic field is generated by the coil, the nickel beam is pulled toward the coil and released resulting in forced transverse actuation of the optical fiber. The length of the optical fiber is 30 mm and the tip of the fiber can actuate 450 µm in X direction. The cantilever beam undergoes simple forced actuation and can be modeled as a beam with one end fixed and the other end free (Fig. 2(a) ). The deflection at the tip of the fiber can be approximated by [25]:
where Fmag is the electromagnetic force exerted on the beam, lf is the length of the fiber, a is the length of the beam, I is the moment of inertia and E is the Young’s modulus of the beam.Fig. 2 (a) Deflection diagram of cantilever/fiber actuator for transverse scanning. (b) Deflection diagram of one of the four folded beams for axial scanning of a lens.
2.2.2 Lens actuator
Lens actuator utilizes a similar design that we described in our previous work [22,23]; however, this time instead of electroplating nickel on a silicon substrate, we used a nickel foil and laser micromachining technique to fabricate the nickel flexure. The flexure consists of four folded beams that suspend the objective lens in an electromagnetic field. The width and total length of each folded beam are 0.125 mm and 8.7 mm respectively. The flexure thickness is 56 µm. The objective lens is mounted in the lens holder using UV-curable adhesive. When the nickel flexure is placed in an alternating magnetic field, the lens actuates in Z direction.
The nickel flexure actuates at its resonant frequency. Assuming damped vibration under Fmag, the displacement, dz, of the nickel flexure at various excitation frequencies can be derived from a vibration equation of motion [26]:
where ω is the frequency of current in the electromagnetic coil (half of frequency of vibration), ωn is the natural frequency of the structure and k is the total stiffness of nickel flexure calculated by:In Eq. (4), E is the Young’s modulus of nickel, I is the moment of inertial of the flexure and lb is the total length of each folded beam. Figure 2(b) illustrates the deformation of one folded beam of the nickel flexure. Each folded beam consists of two fixed-guided beams of length lb/2 connected in series.
3. System characterizations
3.1 Actuators fabrication and assembly
A Commercial laser machining system (New Wave Research QuikLaze system) was used to fabricate the nickel flexure and cantilever beam. The selected laser wavelength was green (532 nm) with energy of 3 mJ. The cutting speed was 15 µm/s and the laser pulsed at 50 Hz. The nickel foil used to fabricate cantilever beam for fiber actuation was 25.4 µm thick and the one used for lens actuator had thickness of 56 µm. Figure 3 shows a cantilever beam for fiber actuation and a flexure for lens actuation fabricated on nickel foils using a green laser.
Fig. 3 Photo of (a) Fiber optic actuator, and (b) Lens actuator, fabricated by laser micromachining of nickel foils.
Using laser can make the fabrication process much slower than electroplating techniques because the laser removes materials only at a small spot that it is focused at each time. However, the fabricated flexure can be more uniform in thickness which can result in more accurate theoretical prediction of actuation response of the lens. Figure 4 shows the cross-section view of the 2-axis scanner demonstrating the positions of the optical fiber, collimating and objective lenses and electromagnetic coils.
A larger objective lens can have better optical quality which enhances the resolution of image; however, the increased mass of larger lens reduces the resonant frequency of the lens actuator which lowers the imaging frame rate. In the current system, the resonant frequency of lens actuator is 378 Hz and the cantilever beam for fiber actuation is moving at 2 Hz. Fiber scanning frequency defines the imaging frame rate of 2 frames per second. Both lens and fiber actuators exhibit a sinusoidal response with peak-to-peak amplitudes of 190 µm and 450 µm respectively.
3.2 Mechanical characterization
The frequency response of the nickel flexure before and after lens installation was predicted by performing finite element analysis (FEA) using COMSOL Multiphysics. This value was also calculated based on Eq. (3) and Eq. (4), and measured using a Laser Doppler Vibrometer (LDV). The FEA-predicted and calculated first mode resonant frequencies of the flexure were 564 Hz and 558 Hz before lens installation; and 401 Hz and 393 Hz after lens installation, respectively. The measured resonant frequencies of the lens actuator before and after lens installation were 549 Hz and 378 Hz respectively.
Figure 5 shows that the FEA analysis, calculation and LDV measurement agree well especially before lens installation. The measured resonant frequency after lens installation is lower than prediction. This is mainly due to the mass of the UV adhesive that was used to mount the lens to the flexure which was ignored in our calculations. Notably, the actuator’s frequency bandwidth has increased after lens installation. This indicates lower quality factor, Q, and higher damping ratio, ζ, in the system compared to that before lens installation. Quality factor is defined by the equation, where k is the stiffness of the actuator, M is mass of the system and c is damping ratio. Larger mass of the scanner after lens installation tends to increase the quality factor; however, increase in the damping coefficient dominates due to the fact that the scanner is installed on an electromagnetic coil which restricts air movement and causes increase in viscous damping after lens installation. Lower quality factor indicates higher rate of energy loss, which can be minimized by creating opening for air flow in the lens holder portion of the nickel flexure. The measured quality factors of the scanner before and after lens installation are 97 and 23 respectively. After the lens installation, the maximum displacement of the flexure at the resonant frequency of 378 Hz was 190 µm.
3.3 Optical characterization
To evaluate the optical performance of the system, lateral and axial responses are determined by performing calculations, optical simulations using ZEMAX, and experimental measurements. On-axis lateral resolution of the system was calculated by treating the fiber as a single point object and following analytical method described in [27]. This method emphasizes the sensitivity of system’s lateral resolution to the size of detection pinhole, but neglects the size of illumination source. The estimated lateral resolution of the system based on this model is 0.92 µm. The theoretical on-axis axial response of the scanner was also determined by applying analytical method described by Gu et al [28]. Fiber is considered as a detection pinhole and variation of detected intensity is plotted as a function of axial position as a perfect reflector is translated through focus. The full width at half maximum (FWHM) of the intensity plot is the axial resolution which for our system is equal to 7.60 µm.
The optical performance of the system was also predicted by ZEMAX optical system design software. Figure 6 illustrates a layout of the optical configuration. The SMF has a numerical aperture of 0.17 and mode field diameter (MFD) of 4 µm. The collimating and objective lenses are aspheric lenses with diameters of 3 mm and 2.4 mm, focal lengths of 4.5 mm and 1.45 mm, and numerical apertures of 0.30 and 0.55, respectively. Due to under-filling of the objective lens, the effective numerical aperture is 0.35. With the current lens selection, the system has a magnification of approximately 0.31 in transverse (X-axis) direction. As a result, when SMF is actuated ±225 µm, image size in the transverse direction is about 145 µm.
Lateral resolution can be predicted from full field spot diagrams. Figure 7 represents beam spot sizes at the focal point of the objective lens corresponding to three fiber locations (0 µm and ±225 µm). Field points in each spot diagram correspond to the center of fiber core ± 2 µm. Full field spot diagrams show that on-axis spot diameter is 1.2 µm while the spot size becomes larger (5.7 µm) at the edges of the field of view (FOV). In addition the diagrams show that the propagated rays do not remain within the Airy disk (black circle shown on diagrams) when the fiber is at the edges of FOV. This means that the objective is not capable of providing diffraction-limited performance at these regions.
This can also be seen in the modulation transfer functions (MTF) curves compared with the diffraction-limited curve (Fig. 8 ). The plot indicates that the performance of the system is lower than the ideal case at the edges of scanning range which is mainly due to the geometrical arrangements and imperfections of the lenses.
The axial response of the scanner can be assessed from the through focus spot diagrams by ray trace analysis at three fiber positions. Figure 9 shows the spot diagrams at various focal plane shifts, indicating how the spot size diameter changes at various distances from the focal point. From Gaussian beam propagation analysis, the depth of focus is defined as twice the Rayleigh range of the beam and is equal to 3.26 µm in our system.
On-axis lateral and axial resolutions were also measured by experiment. The lateral resolution is defined as 0.78 times the 10–90% of the intensity signal from laterally scanning edge of a surgical blade by actuating the optical fiber while holding the objective lens stationary. Axial resolution can be approximated by measuring FWHM of the intensity signal when a flat mirror is axially scanned [29] by the lens while the fiber was fixed at 0 µm displacement position. The experimental lateral and axial resolutions were 3.87 µm and 10.68 µm respectively (Fig. 10 ).
Fig. 10 Experimental measurement of (a) Axial and (b) Lateral resolutions of 2-axis confocal scanner.
Predicted values for lateral and axial resolutions are smaller than experimental results. We believe this is mainly due to the imperfect alignment of optical components and measurement samples. Both lateral and axial resolution measurements were performed by holding a blade-edge and a flat mirror stationary while actuating the optical fiber and objective lens respectively. In lateral resolution measurement, the distance between blade-edge and optical axis can significantly affect the measurement since off-axis spot size is larger than on-axis spot diameter. In addition, axial resolution measurement is sensitive to the axial and lateral misalignment of the optical fiber [30,31] during the system assembly.
4. Imaging results
Confocal scanner was used to obtain vertical cross-sectional images of samples. The lens was actuated 190 µm at 376 Hz while sampling 200 intensity data points over one actuation cycle and fiber was moved at 2 Hz, providing a 145 µm scan in transverse direction, while collecting 189 data points in each cycle. The intensity data was used to graph vertical section view of samples. Figure 11(a) shows a confocal image obtained from a SU-8 photoresist (MicroChem) channel fabricated on a silicon substrate. The width and height of the channel are 90 µm and 65 µm respectively. Figure 11(b) is the optical profile image of this channel obtained by Wyko optical profiler (Veeco Instruments Inc.) for comparison. In the confocal image, the vertical walls of SU-8 channel are not visible. This may be due to the large incident angle of illumination beam with respect to the surface of the walls and total reflection which prevents the light from going back to the optical fiber for confocal imaging. However, this image shows that the scanner is capable of detecting surfaces and edges of the samples cross-section for defining shape and dimensions of the channel.
Fig. 11 (a) Confocal image of SU-8 channel cross-section. (b) Optical profile of the channel measured by an optical profiler.
Figure 12(a) shows a microscopic transverse cross-sectional image of a yellow onion stained with Alcian blue. Depending on the size of onion, the cross-sectional shape and dimensions of epidermal cells are different. The typical cross-sectional size of the epidermal cells of the sample onion used in our experiment was about 40 µm by 40 µm. The epidermal peel was removed from the onion for conducting confocal imaging experiments. Figures 12(b), 12(c), and 12(d) show three confocal vertical optical section images of the onion peel. The images clearly show the upper and lower surfaces of the peel layer. The images also provide information regarding the position of the walls and size of the cells.
Fig. 12 (a) Microscopic image of an onion transverse section stained with Alcian blue. (b), (c), and (d) Confocal vertical optical section images of onion epidermis.
5. Conclusion and future work
The confocal scanner developed in this work provides the advantage of direct vertical optical sectioning of samples. This possesses great potential for clinical applications for performing vertical sectioning optical biopsies that mimic conventional histopathology examinations. FOV of the scanner is 145 µm in transverse and 190 µm in axial directions. The lateral and axial resolutions are 3.87 µm and 10.68 µm respectively. The current system demonstrates the functionality of the optical configuration and scanning mechanisms; however, the system has to be optically and mechanically optimized to expand FOV and enhance the image quality and resolution.
Acknowledgments
This project was supported by the Canada Foundation for Innovations (CFI), the Natural Sciences and Engineering Research Council (NSERC) of Canada, and the Canadian Institutes of Health Research (CIHR grant #: MOP – 102672). Mu Chiao is supported by the Canada Research Chairs Program. Hadi Mansoor is supported by an NSERC PGS-D Scholarship.
References and links
1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]
2. A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12(5), 051403 (2007). [CrossRef] [PubMed]
3. W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990). [CrossRef] [PubMed]
4. K. Koenig and I. Riemann, “High-resolution multiphoton tomography of human skin with subcellular spatial resolution and picosecond time resolution,” J. Biomed. Opt. 8(3), 432–439 (2003). [CrossRef] [PubMed]
5. R. L. Price and W. G. Jerome, Basic Confocal Microscopy (Springer, 2011).
6. M. Rajadhyaksha, M. Grossman, D. Esterowitz, R. H. Webb, and R. R. Anderson, “In vivo confocal scanning laser microscopy of human skin: melanin provides strong contrast,” J. Invest. Dermatol. 104(6), 946–952 (1995). [CrossRef] [PubMed]
7. C. L. Arrasmith, D. L. Dickensheets, and A. Mahadevan-Jansen, “MEMS-based handheld confocal microscope for in-vivo skin imaging,” Opt. Express 18(4), 3805–3819 (2010). [CrossRef] [PubMed]
8. J. T. C. Liu, M. J. Mandella, H. Ra, L. K. Wong, O. Solgaard, G. S. Kino, W. Piyawattanametha, C. H. Contag, and T. D. Wang, “Miniature near-infrared dual-axes confocal microscope utilizing a two-dimensional microelectromechanical systems scanner,” Opt. Lett. 32(3), 256–258 (2007). [CrossRef] [PubMed]
9. K. C. Maitland, H. J. Shin, H. Ra, D. Lee, O. Solgaard, and R. Richards-Kortum, “Single fiber confocal microscope with a two-axis gimbaled MEMS scanner for cellular imaging,” Opt. Express 14(19), 8604–8612 (2006). [CrossRef] [PubMed]
10. K. Kumar, R. Avritscher, Y. Wang, N. Lane, D. C. Madoff, T.-K. Yu, J. W. Uhr, and X. Zhang, “Handheld histology-equivalent sectioning laser-scanning confocal optical microscope for interventional imaging,” Biomed. Microdevices 12(2), 223–233 (2010). [CrossRef] [PubMed]
11. N. Dhaubanjar, H. Hu, D. Dave, P. Phuyal, J. Sin, H. Stephanou, and J.-C. Chiao, “A compact optical fiber scanner for medical imaging,” Proc. SPIE 6414, 64141Z (2006). [CrossRef]
12. M. T. Myaing, D. J. MacDonald, and X. Li, “Fiber-optic scanning two-photon fluorescence endoscope,” Opt. Lett. 31(8), 1076–1078 (2006). [CrossRef] [PubMed]
13. E. J. Min, J. G. Shin, Y. Kim, and B. H. Lee, “Two-dimensional scanning probe driven by a solenoid-based single actuator for optical coherence tomography,” Opt. Lett. 36(11), 1963–1965 (2011). [CrossRef] [PubMed]
14. H. Ra, W. Piyawattanametha, M. J. Mandella, P.-L. Hsiung, J. Hardy, T. D. Wang, C. H. Contag, G. S. Kino, and O. Solgaard, “Three-dimensional in vivo imaging by a handheld dual-axes confocal microscope,” Opt. Express 16(10), 7224–7232 (2008). [CrossRef] [PubMed]
15. M. J. Booth, R. Juškaitis, and T. Wilson, “Spectral confocal reflection microscopy using a white light source,” J. Eur. Opt. Rapid Publ. 3, 08026 (2008). [CrossRef]
16. T. D. Wang, C. H. Contag, M. J. Mandella, N. Y. Chan, and G. S. Kino, “Dual-axes confocal microscopy with post-objective scanning and low-coherence heterodyne detection,” Opt. Lett. 28(20), 1915–1917 (2003). [CrossRef] [PubMed]
17. N. Callamaras and I. Parker, “Construction of a confocal microscope for real-time x-y and x-z imaging,” Cell Calcium 26(6), 271–279 (1999). [CrossRef] [PubMed]
18. T. D. Wang, K. Kurabayashi, K. Oldham, and Z. Qiu, “Targeted dual-Axes confocal imaging apparatus with vertical scanning capabilities” US Patent App. US 2011/0125029 A1, 2011.
19. S. Kwon, V. Milanovic, and L. P. Lee, “Vertical microlens scanner for 3D imaging” Proc. Solid-State Sens. and Actuator Workshop, Hilton Head Isl., SC, 2002.
20. C. P. B. Siu, H. Wang, H. Zeng, and M. Chiao, “Dual-axis confocal microlens for Raman spectroscopy” Proc. 21th IEEE Int. Conf. on Micro Electromec. Syst., Sorrento, Italy, 2009.
21. A. Jain and H. Xie, “An electrothermal microlens scanner with low-voltage large-vertical-displacement actuation,” IEEE Photon. Technol. Lett. 17(9), 1971–1973 (2005). [CrossRef]
22. H. Mansoor, H. Zeng, and M. Chiao, “A micro-fabricated optical scanner for rapid non-contact thickness measurement of transparent films,” Sens. Actuators A Phys. 167(1), 91–96 (2011). [CrossRef]
23. H. Mansoor, H. Zeng, and M. Chiao, “Real-time thickness measurement of biological tissues using a microfabricated magnetically-driven lens actuator,” Biomed. Microdevices 13(4), 641–649 (2011). [CrossRef] [PubMed]
24. G. Rizzoni, “Electrical engineering,” in The CRC Handbook of Mechanical Engineering, F. Kreith, ed. (CRC Press LLC, Boca Raton, 2005), Chap. 5.
25. J. E. Shigley, C. R. Mischke, and R. G. Budynas, Mechanical Engineering Design, 7th ed. (McGraw-Hill, 2004).
26. S. S. Rao, Mechanical Vibrations (Addison-Wesley Publishing Company, 2001), Chap. 3.
27. T. Wilson and A. R. Carlini, “Size of the detector in confocal imaging systems,” Opt. Lett. 12(4), 227–229 (1987). [CrossRef] [PubMed]
28. M. Gu, C. J. R. Sheppard, and X. Gan, “Image formation in a fiber-optical confocal scanning microscope,” J. Opt. Soc. Am. A 8(11), 1755–1761 (1991). [CrossRef]
29. M. Rajadhyaksha, R. R. Anderson, and R. H. Webb, “Video-rate confocal scanning laser microscope for imaging human tissues in vivo,” Appl. Opt. 38(10), 2105–2115 (1999). [CrossRef] [PubMed]
30. M. D. Sharma and C. J. R. Sheppard, “Effects of system geometry on the axial response of the fibre optical confocal microscope,” J. Mod. Opt. 46(4), 605–621 (1999).
31. K. Venkateswaran, A. Roorda, and F. Romero-Borja, “Theoretical modeling and evaluation of the axial resolution of the adaptive optics scanning laser ophthalmoscope,” J. Biomed. Opt. 9(1), 132–138 (2004). [CrossRef] [PubMed]
