## Miniature fiber-optic force sensor based on low-coherence Fabry-Pérot interferometry for vitreoretinal microsurgery |

Biomedical Optics Express, Vol. 3, Issue 5, pp. 1062-1076 (2012)

http://dx.doi.org/10.1364/BOE.3.001062

Acrobat PDF (2713 KB)

### Abstract

During vitreoretinal surgery, the surgeon manipulates retinal tissue with tool-to-tissue interaction forces below the human sensory threshold. A force sensor (FS) integrated with conventional surgical tools may significantly improve the surgery outcome by providing tactile feedback to the surgeon. We designed and built a surgical tool integrated with a miniature FS with an outer diameter smaller than 1 mm for vitreoretinal surgery based on low-coherence Fabry–Pérot (FP) interferometry. The force sensing elements are located at the tool tip which is in direct contact with tissue during surgery and the FP cavity length is interrogated by a fiber-optic common-path phase-sensitive optical coherence tomography (OCT) system. We have calibrated the FS's response to axial and lateral forces and conducted experiments to verify that our FS can simultaneously measure both axial and lateral force components.

© 2012 OSA

## 1. Introduction

6. A. Uneri and M. Balicki, J. Handa, P. Gehlbach, R. Taylor, and I. Iordachita, “New Steady-hand eye robot with microforce sensing for vitreoretinal surgery research,” in *2010 3rd IEEE RAS and EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob)*, (IEEE, 2010), pp. 814–819.

8. I. Iordachita, Z. Sun, M. Balicki, J. U. Kang, S. J. Phee, J. Handa, P. Gehlbach, and R. H. Taylor, “A sub-millimetric, 0.25 mN resolution fully integrated fiber-optic force-sensing tool for retinal microsurgery,” Int. J. CARS **4**(4), 383–390 (2009). [CrossRef] [PubMed]

9. K. Kim, Y. Sun, R. Voyles, and B. Nelson, “Calibration of multi-axis MEMS force sensors using the shape-from-motion method,” IEEE Sens. J. **7**(3), 344–351 (2007). [CrossRef]

11. P. J. Berkelman, L. L. Whitcomb, R. H. Taylor, and P. Jensen, “A miniature microsurgical instrument tip force sensor for enhanced force feedback during robot-assisted manipulation,” IEEE Trans. Robot. Autom. **19**(5), 917–922 (2003). [CrossRef]

12. P. J. Berkelman, L. L. Whitcomb, R. H. Taylor, and P. Jensen, “A miniature instrument tip force sensor for robot/human cooperative microsurgical manipulation with enhanced force feedback,” in *Medical Image Computing and Computer-Assisted Intervention—MICCAI 2000*, Vol. 1935/2000 of Lecture Notes in Computer Science (Springer, 2000), pp. 897–906.

8. I. Iordachita, Z. Sun, M. Balicki, J. U. Kang, S. J. Phee, J. Handa, P. Gehlbach, and R. H. Taylor, “A sub-millimetric, 0.25 mN resolution fully integrated fiber-optic force-sensing tool for retinal microsurgery,” Int. J. CARS **4**(4), 383–390 (2009). [CrossRef] [PubMed]

17. H. Su, M. Zervas, C. Furlong, and G. S. Fischer, “A miniature MRI-compatible fiber-optic force sensor utilizing Fabry-Perot interferometer,” in *Conference Proceedings of the Society for Experimental Mechanics Series**2011, Volume 999999*, Vol. 4 of MEMS and Nanotechnology (Springer, 2011), pp. 131–136.

18. Y. Zhang, H. Shibru, K. L. Cooper, and A. Wang, “Miniature fiber-optic multicavity Fabry-Perot interferometric biosensor,” Opt. Lett. **30**(9), 1021–1023 (2005). [CrossRef] [PubMed]

20. J. U. Kang, J.-H. Han, X. Liu, K. Zhang, C. G. Song, and P. Gehlbach, “Endoscopic functional Fourier domain common path optical coherence tomography for microsurgery,” IEEE J. Sel. Top. Quantum Electron. **16**(4), 781–792 (2010). [CrossRef]

21. J. Zhang, B. Rao, L. Yu, and Z. Chen, “High-dynamic-range quantitative phase imaging with spectral domain phase microscopy,” Opt. Lett. **34**(21), 3442–3444 (2009). [CrossRef] [PubMed]

22. C. Joo, T. Akkin, B. Cense, B. H. Park, and J. F. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett. **30**(16), 2131–2133 (2005). [CrossRef] [PubMed]

## 2. Principle and tool design

### 2.1. System overview and tool fabrication

23. X. Liu, M. Balicki, R. H. Taylor, and J. U. Kang, “Towards automatic calibration of Fourier-Domain OCT for robot-assisted vitreoretinal surgery,” Opt. Express **18**(23), 24331–24343 (2010). [CrossRef] [PubMed]

^{3}MPa to 75 × 10

^{3}MPa; therefore, the fabricated tool has extremely high force sensitivity. As shown in Fig. 1(d), the flexure—with 0.80mm outer diameter (OD) and 0.60mm inner diameter (ID)—has five layers; each layer consists of three 40-micrometer struts; and between adjacent layers there is a 100 micrometer slot. The multi-layered configuration can further increase the elasticity of the flexure in the axial direction and therefore achieve a high sensitivity for force measurement. The total length of the flexure is 3 mm, with 1 mm between the distal end and the first slot. The pick was made using a stainless steel SS304 hypodermic tube, 21 gauge (OD = 0.80mm, ID = 0.55mm). The tip was bevel cut (at 75 degrees) and bent at around 45 degrees relative to the axis. The pick total length is 2.5mm, with a 1.5mm length bevel section. Loctite medical instant adhesive (Henkel, Dusseldorf, Germany) was used to bond all the parts together: first the mirror with the pick, next the flexure, and finally the tool shaft. The optical fibers were embedded into slots machined to the tool shaft. The distance between the fiber tips and the polished metal surface was manually adjusted before finally bonding the fibers with the tool shaft. It is worth mentioning that we made the FP cavities to have different lengths. This allows us to detect the length change of each cavity respectively. The CAD model for the FPI-FS probe integrated with the pick is shown in Fig. 1(e). For calibration and future manual or robotic use, the force sensing probe is attached to a custom-made handle, as shown in Fig. 1 (f). Figure 1(g) is a photo of the tool pictured below a U.S. quarter.

### 2.2. OCT signal and phase-sensitive detection

*r,*is about 4% according to Fresnel equation [24], we calculated the finesse of the FPI to be about 1.25. The round trip loss of optical power in the FP cavity is larger than 4% due to beam divergence; therefore, the actual finesse of FPIs are even lower than 1.25. Moreover, we have measured the fringe visibility of interferograms obtained from the FPIs and the values are very small (0.39, 0.047 and 0.049, for three FPIs, respectively). Therefore, in our multiplexed FPIs, signals due to higher order reflections are small and therefore can be neglected in the following analysis.

*L*is the length of

_{i,0}*i*

^{th}FP cavity at neutral when there is no force exerted. δ

*l*indicates change of cavity length due to force exerted to the tool.

_{i}*i*

^{th}fiber,

*l*varies significantly from other fibers (much more than several millimeters), E

_{i},_{1}

*or E*

_{i}_{2}

*does not interfere if*

_{j}*i*≠

*j*. Based on this fact, the spectral interferogram

*S*(

*k*) can be expressed as in Eq. (2):

*η*indicates the responsive coefficient of the system; * denotes complex conjugate; Re() refers to the real part of a complex signal. The third term of the right-hand side of Eq. (2) is the interference term. OCT signal,

*I*

_{OCT}(

*z*), can thus be obtained by performing inverse Fourier transform on

*S*(

*k*):

*h*(

*z*), which equals

*F*^{−1}(|

*E*

_{0}(

*k*)|

^{2}), we can rewrite Eq. (3) as Eq. (4) with approximation when the bandwidth is relatively small:

*l*can be extracted from

_{i}*ϕ*, the phase of OCT signal at delay

_{i}*L*

_{i}_{,0}, which equals tan

^{−1}{

**Im**[

*I*(

_{OCT}*L*

_{i}_{,0})]/

**Re**[

*I*(

_{OCT}*L*

_{i}_{,0})]}. However, the function tan

^{−1}gives value in the range of [-π/2, π/2]; therefore

*N*is the integer that makes (δ

_{i}*l*+

_{i}*N*λ

_{i}_{0}/4) to fall within the range of [-λ

_{0}/8, λ

_{0}/8]. With small force variation,

*N*stays constant. Denoting the first term in the RHS of Eq. (6) as

_{i}*d*and the second term as

_{i}*d*which is assumed to be a constant, we have

_{i,0}*ϕ*jumps from -π/2 directly to π/2 or from π/2 directly to -π/2—a phase unwrapping technique can be used to obtain continuous phase or displacement [21

_{i}21. J. Zhang, B. Rao, L. Yu, and Z. Chen, “High-dynamic-range quantitative phase imaging with spectral domain phase microscopy,” Opt. Lett. **34**(21), 3442–3444 (2009). [CrossRef] [PubMed]

*L*

_{1,0}= 100μm,

*L*

_{2,0}= 150μm, and

*L*

_{3,0}= 200μm; the light source has central wavelength of 800nm and FWHM bandwidth of 60nm. Superposed spectral interference signals from three FP cavities are simulated and shown in Fig. 2(a) according to Eq. (2). Performing inverse Fourier transform on this interference signal leads to complex-valued spatial domain OCT signal

*I*

_{OCT}(

*z*), which contains three coherence peaks at

*z*=

*L*

_{1},

*L*

_{2}, and

*L*

_{3}corresponding to the length of the three FP cavities. The amplitude of OCT signal is shown in Fig. 2(b). With force exerted, the cavity length changed proportionally to the force. In this simulation, we assumed

*δl*

_{1}= 20nm,

*δl*

_{2}= 40nm and

*δl*

_{3}= 60nm. However, such small change in cavity length cannot be seen directly from the amplitude of OCT signal described in Fig. 2(b). On the other hand, as shown in Fig. 2(c) which is the central part of the interference spectrum, change in cavity length in the order of nanometer shifts the original spectrum (black) to the red one. To demonstrate that the small displacement can induce measurable phase change to the complex-valued OCT signal at the coherence peak, we show complex OCT signals at the 1st, 2nd, and 3rd coherence peaks in the complex plane using a polar coordinate system in Fig. 2(d). Black symbols and red symbols represent OCT signals with and without additional displacement

*δl*

_{i}. Clearly, the vector that represents the complex OCT signal rotates due to phase shift induced by

*δl*

_{i}.

### 2.3. 3D force measurement

*F*) along an arbitrary direction can be decomposed into axial and lateral components. In the force coordinate attached to the tool tip,

*z*axis or axial direction is along the tool shaft. We denote force along the tool shaft direction as axial force

*F*.

_{z}*x-y*plane is perpendicular to

*z*axis and force in

*x*-

*y*plane is denoted as lateral force

*F*. The choice of

_{l}*x*and

*y*axes is arbitrary as long as

*x*,

*y*and

*z*axes form a right-hand coordinate system.

*δl*

_{i,z}which equals (

*F*)/(

_{z}D*A*

_{0}

*E*) [25]. Here

*D*is the length of cantilever beam;

*E*is the effective Young's modulus of the cantilever beam;

*A*is the cross-sectional area on which the force is exerted. When lateral force is applied, the beam deflects with an angle

_{0}*α*that equals (

*F*

_{l}D^{2})/(2

*EI*) where

*I*is the area moment of inertia of the wire cross section [25]. We show the beam deflection with exaggeration in Fig. 3(c). In fact,

*α*is extremely small due to the small force exerted during vitreoretinal microsurgery. Therefore, the slight change in light beam propagation direction does not reduce the coupling efficiency when light gets reflected back to the single-mode fiber and does not reduce the OCT signal amplitude either.

*δl*

_{i,}

*due to lateral force can be expressed as [-2*

_{l}*L*

_{i,}_{0}sin

^{2}(

*α*/2)/cos(

*α*) +

*b*tan(

_{i}*α*)]. As

*α*is extremely small, the following approximation is valid: sin(

*α*/2)≈

*α*/2; tan(

*α*)≈

*α*; cos(

*α*)≈1. Moreover, sin

^{2}(

*α*/2) is a higher order term of the already extremely small value

*α*and therefore can be negligible compared to tan(

*α*). As a result,

*δl*

_{i,}

*=*

_{l}*b*. Here,

_{i}α*b*is the distance between the center of the

_{i}*i*

^{th}fiber and the neutral surface which is perpendicular to the applied force and passes through the center of the tool shaft cross-section. Denoting the angle between vector

*F*and

_{l}*x*axis as θ as in Fig. 3(e), we find that

*b*equals (

_{i}*x*cosθ-

_{i}*y*sinθ) where (

_{i}*x*,

_{i}*y*) is the transversal coordinate of the

_{i}*i*

^{th}fiber. Therefore

*b*can also be expressed as:

_{i}*ε*= tan

_{i}^{−1}(

*y*/

_{i}*x*). Assume that the cavity change induced by force

_{i}*F*is the linear superposition of the effect of

*F*and

_{z}*F*. In other words, the cavity length change of the

_{l}*i*

^{th}FP cavity

*δl*

_{i}equals

*δl*

_{i,z}+

*δl*

_{i,}

*and we can express*

_{l}*δl*

_{i}as follows:

*F*sinθ and

_{l}*F*cosθ as

_{l}*F*and

_{x}*F*;

_{y}*D*

^{2}

*x*/(2

_{i}*EI*) and

*D*

^{2}

*y*/(2

_{i}*EI*) as

*A*and

_{ix}*A*;

_{iy}*D*/(

*A*

_{0}

*E*) as

*A*, we can re-write Eq. (9) as

_{iz}*F*and

_{x}*F*,

_{y}*δl*is linearly dependent on

_{i}*F*and

_{x}*F*with constant coefficients

_{y}*A*and

_{ix}*A*which are independent of the direction of applied lateral force, as shown in Eq. (9). Therefore,

_{iy}*A*,

_{ix}*A*and

_{iy}*A*can be obtained from a linear regression procedure if we know the force applied to the tool and the corresponding displacements.

_{iz}*F*,

_{l}*F*and

_{x}*F*take different values if θ varies, we can always calculate

_{y}*F*with Eq. (11), which is independent of θ:

_{l}**can be obtained from a calibration procedure shown in detail in the following section. Once**

*A***is obtained, we are able to calculate the force in three dimension using Eq. (13):**

*A**d*

_{0}

*from the displacement*

_{i}*d*to obtain correct force measurement. Above

_{i}*d*

_{0}

*is the displacement measured from the phase of OCT signal when no force is applied to the FS. If the subtraction or biasing procedure is taken with a certain force*

_{i}

*F*_{0}applied to the FS, the measurement provides force relative to

*F*_{0}rather than absolute force.

## 3. Results

### 3.1. Axial calibration

*F*and

_{x}*F*equal to 0. Therefore, pure axial force along the tool shaft was applied in this setup and coefficients

_{y}*A*could be obtained. In our calibration experiments, each testing weight was 0.897 ( ± 0.005) mN.

_{iz}*N*= 0. The measured displacements are equal to change in the length of FP cavities. With different numbers of testing weights i.e. axial forces, we obtained

_{i}*d*

_{1},

*d*

_{2,}and

*d*

_{3}, displacements corresponding to the three FP cavities, shown as black circles in Figs. 4(c), 4(d) and 4(e), respectively. Afterwards, with the known axial force

*F*and the measured displacement

_{z}*d*=

_{i}*d*+

_{0i}*A*, we were able to perform linear regression to extract

_{iz}F_{z}*A*

_{1}

*,*

_{z}*A*

_{2}

*, and*

_{z}*A*

_{3}

*. The linear fitting results are shown as red lines in Figs. 4(b), 4(c) and 4(d).*

_{z}### 3.2. Lateral calibration

*z*axis of the force coordinate) perpendicular to the gravity direction so that the force induced by the gravity of the testing weights had only a lateral component in the force coordinate that was attached to the tool tip; in other words,

*F*= 0. As indicated by Eq. (9), the displacement induced by lateral force not only depends on the magnitude of lateral force exerted to the FS, but also depends on θ, which essentially is the direction of lateral force in

_{z}*x*-

*y*plane as shown in Fig. 3 (e). Therefore, to characterize the tool's response to lateral force, we needed to apply force in the lateral plane (

*x-y*plane) with different magnitudes as well as at different azimuth angles θ. In order to do this, we attached the tool to a rotary stage in

*x*-

*y*plane to change the angle between the

*x*axis of our force coordinate and the direction of gravity. Since our force coordinate was attached to the tool tip, θ changes in the same manner as the rotation of the tool.

*i*

^{th}FP cavity takes a different transversal coordinate (

*x*,

_{i}*y*) and therefore the phase

_{i}*ε*= tan

_{i}^{−1}(

*x*/

_{i}*y*). Moreover, our results also show that the displacements increase proportionally as lateral force increases. To demonstrate this more clearly, in Figs. 5(f)–5(h), we show displacements obtained with different lateral forces when θ was 3π/2. A linear relationship between displacement and lateral force can be observed in Fig. 5(f)–5(h).

_{i}*A*and

_{ix}*A*using data shown in Fig. 5(c)–5(e), we performed a two-dimensional linear regression to solve the linear model

_{iy}**=**

*d*

*A*

_{l}

*F**. Here*

_{xy}

*A**= [*

_{l}*A*

_{1}

_{x}A_{1}

*;*

_{y}*A*

_{2}

_{x}A_{2}

*;*

_{y}*A*

_{3}

_{x}A_{3}

*].*

_{y}

*F**indicates known vectors with*

_{xy}*F*and

_{x}*F*as elements:

_{y}**= [**

*F*_{xy}*F*;

_{x}*F*];

_{y}*F*=

_{x}*F*cosθ;

_{l}*F*=

_{y}*F*sinθ;

_{l}*F*is the known gravity of testing weights.

_{l}**indicates the vectors with measured displacements from different FP cavities as elements**

*d***= [**

*d**d*

_{1};

*d*

_{2};

*d*

_{3}].

*A**obtained from linear regression of the lateral calibration data, we could calculate*

_{l}*F*inversely.

_{l}*F*and

_{x}*F*were obtained by solving the linear equation

_{y}**=**

*d***in a least-square manner:**

*A*_{l}F_{xy}**= (**

*F*_{xy}

*A*

_{l}^{T}

*A**)*

_{l}^{−1}

*A*

_{l}^{T}

**. Here ()**

*d*^{−1}indicates to take the inverse of a matrix and ()

*indicates to take the transpose of a matrix.*

^{T}*F*,

_{x}*F*, and

_{y}*F*extracted are shown in Fig. 6 . Only two curves are visible in results with θ = 0 degree, because

_{l}*F*is almost 0 and therefore

_{y}*F*is almost overlapped with

_{l}*F*. Similarly, only two curves are visible in results with θ = 90 degree, because

_{x}*F*almost is 0. Clearly, although

_{x}*F*and

_{x}*F*depend on θ for the same lateral force,

_{y}*F*calculated from Eq. (13) is independent of tool orientation, shown as black curves in Fig. 6.

**:**

*A**A*

_{1}

*= −30.3nm/mN;*

_{x}*A*

_{1}

*= 27.5nm/mN;*

_{y}*A*

_{1}

*= 4.3nm/mN;*

_{z}*A*

_{2}

*= 33.9nm/mN;*

_{x}*A*

_{2}

*= 8.9nm/mN;*

_{y}*A*

_{2}

*= 6.2 nm/mN;*

_{z}*A*

_{3}

*= −11.8nm/mN;*

_{x}*A*

_{3}

*= −30.9nm/mN;*

_{y}*A*

_{3}

*= 6.5nm/mN.*

_{z}*A*=

_{ix}*D*

^{2}

*x*/(2

_{i}*EI*) and

*A*=

_{iy}*D*

^{2}

*y*/(2

_{i}*EI*); and

*x*and

_{i}*y*can take different values, positive and negative as shown in Fig. 3(e); therefore,

_{i}*A*and

_{ix}*A*can take different value and have different signs for the same channel. Force could thus be calculated using Eq. (13) with

_{iy}**and the measured displacements.**

*A*### 3.3. 3D Force measurement

*x*-

*y*plane, another rotary stage was used to change

*φ*, the intersection angle between the tool shaft and the gravity direction, as shown in Figs. 7(a) and 7(b). With the same load attached to the FS, different values of

*φ*leads to different values of axial and lateral force. Here

*G*is the gravity of the load which equals 8.2mN for this experiment. We used a rotation stage (as indicated by Rotation 1 in Figs. 7(a) and 7(b)) to change

*φ*and therefore change

*F*,

_{x}*F*,

_{y}*F*correspondingly, because:

_{z}*φ*= π/2 and the FS was exerted with a non-zero force. As shown in Eq. (7) and discussed at the end of Section 2.3, the forces measured were values relative to the force when biasing was taken. As a result, the measured forces are

*F*=

_{x,m}*F*(

_{x}*φ*)-

*F*(

_{x}*φ*)|

_{φ =}_{π/2};

*F*=

_{y,m}*F*(

_{y}*φ*)-

*F*(

_{y}*φ*)|

_{φ =}_{π/2};

*F*=

_{z,m}*F*(

_{z}*φ*)-

*F*(

_{z}*φ*)|

_{φ =}_{π/2}. Incorporating Eq. (14), we have

*F*=

_{l,m}*G*(1-sin

*φ*) and

*F*=

_{z,m}*G*cos

*φ*, which are also shown in Figs. 7(c) and 7(d) as black curves. The consistency between force measured from our FS and the calculated black curves implies that our FS is able to measure force with both axial and lateral components. With the known load gravity (

*G*= 8.2mN), we may bias the data in post processing and obtained the results shown in Figs. 7(e) and 7(f). Results in Figs. 7(e) and 7(f) show maximum axial force and minimum lateral force with

*φ*= 0; as well as minimum axial force and maximum lateral force with

*φ*= π/2.

## 4. Discussion

*F*and

_{z}*F*. Second, the displacement introduced by lateral force

_{l}*F*is angle (θ) dependent, as shown in Eq. (9). As a result, it is more convenient to decomposition

_{l}*F*in

_{l}*x*-

*y*plane as

*F*,

_{x}*F*and afterwards use Eq. (11) to calculate

_{y}*F*, which would be independent of the choice of

_{l}*x*or

*y*axis of our force coordinate. As we need to determine three unknowns—

*F*,

_{x}*F*, and

_{y}*F*—it requires at least three independent linear equations based on measurements from three different FP cavities.

_{z}*A*

_{1}

*= 4.3nm/mN;*

_{z}*A*

_{2}

*= 6.2nm/mN;*

_{z}*A*

_{3}

*= 6.5nm/mN). However, as indicated by Eq. (9), the sensitivity of our FS to axial force should be identical for different FP cavities because*

_{z}*A*=

_{iz}*D*/(

*A*

_{0}

*E*). The difference in axial sensitivity might be due to the asymmetry in mechanical property of our FS. Similarly, lateral sensitivity (

*A*

_{ix}^{2}+

*A*

_{iy}^{2})

^{1/2}=

*D*

^{2}

*r*/(2

*EI*) should be the same for different cavities as in Eq. (9); however, our experimental values are 43.2nm/mN, 35.0nm/mN, and 33.1nm/mN for the first, second, and third FP cavities, respectively. The difference in the lateral force sensitivities might be the result of the asymmetry in mechanical property of our FS, as well as the misalignment of the fibers. Due to the extremely small scale of our tool, it is almost impossible to make sure that the fibers have the same distance to the center of the tool shaft to make (

*A*

_{ix}^{2}+

*A*

_{iy}^{2})

^{1/2}identical for the three FPIs.

**, coefficients relating cavity length change, and force. According to Eq. (13), the variance of force**

*A*

*σ*_{F}^{2}= Var(

**) can be calculated from the covariance matrix of Gaussian random vector**

*F**δ*

**cov(**

*l,**δ*

**): cov(**

*l***) =**

*F*

*A*^{−1}cov(

*δ*

**)[(**

*l*

*A*^{−1})

^{T}], and

*σ*

_{F}^{2}is the diagonal elements of the matrix cov(

**) [26]. To estimate the magnitude of**

*F*

*σ*_{F}^{2}, we further assume

*δl*

_{1},

*δl*

_{2},

*δl*

_{3}are independent random Gaussian variables with the same variance

*σ*

_{l}^{2}. This simplifies the expression of

*σ*_{F}^{2}, which becomes

*σ*_{F}^{2}=

*σ*

_{l}^{2}

*A*^{−1}[(

*A*^{−1})

^{T}]. Although the fundamental lower limit of

*σ*

**is determined by the signal-to-noise ratio (SNR) of the OCT system [17**

_{l}17. H. Su, M. Zervas, C. Furlong, and G. S. Fischer, “A miniature MRI-compatible fiber-optic force sensor utilizing Fabry-Perot interferometer,” in *Conference Proceedings of the Society for Experimental Mechanics Series**2011, Volume 999999*, Vol. 4 of MEMS and Nanotechnology (Springer, 2011), pp. 131–136.

*σ*

**was 0.5nm from a long-term (10s) measurement while**

_{l}*σ*

**was 0.1nm from a short-term (0.5s) measurement. Using**

_{l}*σ*

**= 0.5nm and the obtained calibrating matrix**

_{l}**, we were able to calculate cov(**

*A***) and further extract**

*F***:**

*σ*_{F}**≈0.01mN;**

*σ*_{Fx}**≈0.01mN;**

*σ*_{Fy}**≈0.05mN. There results indicate that our FS can achieve sub-millinewton sensitivity in force measurement.**

*σ*_{Fz}*d*is from −100nm to +100nm and therefore we can obtain displacement without ambiguity only in a range of 200nm. Since our FS has 30 ~40 nm/mN sensitivity to lateral force, a 200nm displacement range allows us to measure 5mN ~6mN lateral force at most. Therefore, a severe restriction in the dynamic range of our force measurement is placed by the limited range of displacement measurement. However, we implemented a well-established method called

_{i}*phase unwrapping*in this work to increase the dynamic range of our force measurement [16]. In our C++ software, we continuously calculate the phases corresponding to each coherence peak and check whether there is an abrupt change of ±π between two consecutive phases:

*ϕ*

_{n},

*ϕ*

_{n+1}. If such phase discontinuity occurs, we modify the phases obtained after

*ϕ*

_{n}by subtracting or adding π. This method can increase the dynamic range in the measurement of displacement and thus force, because the force is assumed to be continuous and usually cannot lead to such a big change in

*ϕ*due to the short time between two sampling points (1ms). However, if the force varies quickly (

*d*F/

*d*t>5mN/ms), the unwrapping technique cannot provide correct force measurement.

## 5. Conclusion

## Acknowledgments

## References and links

1. | P. K. Gupta, P. S. Jensen, and E. de Juan, “Surgical forces and tactile perception during retinal microsurgery,” in |

2. | M. J. Massimino and T. B. Sheridan, “Sensory substitution for force feedback in teleoperation,” IFAC Symp. Ser. |

3. | M. Kitagawa, D. Dokko, A. M. Okamura, B. T. Bethea, and D. D. Yuh., “Effect of sensory substitution on suture manipulation forces for surgical teleoperation, ” in |

4. | T. Akinbiyi, C. E. Reiley, S. Saha, D. Burschka, C. J. Hasser, D. D. Yuh, and A. M. Okamura, “Dynamic augmented reality for sensory substitution in robot-assisted surgical systems,” in |

5. | M. Balicki, A. Uneri, I. Iordachita, J. Handa, P. Gehlbach, and R. H. Taylor, “Micro-force sensing in robot assisted membrane peeling for vitreoretinal surgery,” in |

6. | A. Uneri and M. Balicki, J. Handa, P. Gehlbach, R. Taylor, and I. Iordachita, “New Steady-hand eye robot with microforce sensing for vitreoretinal surgery research,” in |

7. | Z. Sun, M. Balicki, J. Kang, J. Handa, R. Taylor, and I. Iordachita, “Development and preliminary data of novel integrated optical microforce sensing tools for retinal microsurgery,” in |

8. | I. Iordachita, Z. Sun, M. Balicki, J. U. Kang, S. J. Phee, J. Handa, P. Gehlbach, and R. H. Taylor, “A sub-millimetric, 0.25 mN resolution fully integrated fiber-optic force-sensing tool for retinal microsurgery,” Int. J. CARS |

9. | K. Kim, Y. Sun, R. Voyles, and B. Nelson, “Calibration of multi-axis MEMS force sensors using the shape-from-motion method,” IEEE Sens. J. |

10. | A. Menciassi, A. Eisinberg, G. Scalari, C. Anticoli, M. C. Carrozza, and P. Dario, “Force feedback-based microinstrument for measuring tissue properties and pulse in microsurgery,” in |

11. | P. J. Berkelman, L. L. Whitcomb, R. H. Taylor, and P. Jensen, “A miniature microsurgical instrument tip force sensor for enhanced force feedback during robot-assisted manipulation,” IEEE Trans. Robot. Autom. |

12. | P. J. Berkelman, L. L. Whitcomb, R. H. Taylor, and P. Jensen, “A miniature instrument tip force sensor for robot/human cooperative microsurgical manipulation with enhanced force feedback,” in |

13. | D. Jagtap and C. N. Riviere, “Applied force during vitreoretinal microsurgery with handheld instruments,” in |

14. | C. Yeh, |

15. | P. Puangmali, H. Liu, K. Althoefer, and L. D. Seneviratne, “Optical fiber sensor for soft tissue investigation during minimally invasive surgery,” in |

16. | S. Hirose and K. Yoneda, “Development of optical 6-axial force sensor and its signal calibration considering non-linear interference,” in |

17. | H. Su, M. Zervas, C. Furlong, and G. S. Fischer, “A miniature MRI-compatible fiber-optic force sensor utilizing Fabry-Perot interferometer,” in |

18. | Y. Zhang, H. Shibru, K. L. Cooper, and A. Wang, “Miniature fiber-optic multicavity Fabry-Perot interferometric biosensor,” Opt. Lett. |

19. | U. Sharma, N. M. Fried, and J. U. Kang, “All-fiber Fizeau optical coherence tomography: sensitivity optimization and system analysis,” IEEE J. Quantum Electron. |

20. | J. U. Kang, J.-H. Han, X. Liu, K. Zhang, C. G. Song, and P. Gehlbach, “Endoscopic functional Fourier domain common path optical coherence tomography for microsurgery,” IEEE J. Sel. Top. Quantum Electron. |

21. | J. Zhang, B. Rao, L. Yu, and Z. Chen, “High-dynamic-range quantitative phase imaging with spectral domain phase microscopy,” Opt. Lett. |

22. | C. Joo, T. Akkin, B. Cense, B. H. Park, and J. F. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett. |

23. | X. Liu, M. Balicki, R. H. Taylor, and J. U. Kang, “Towards automatic calibration of Fourier-Domain OCT for robot-assisted vitreoretinal surgery,” Opt. Express |

24. | M. Born and E. Wolf, |

25. | A. Pytel and J. Kiusalaas, |

26. | R. D. Yates and D. J. Goodman, |

**OCIS Codes**

(050.2230) Diffraction and gratings : Fabry-Perot

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(170.4500) Medical optics and biotechnology : Optical coherence tomography

(280.4788) Remote sensing and sensors : Optical sensing and sensors

**ToC Category:**

Ophthalmology Applications

**History**

Original Manuscript: March 27, 2012

Revised Manuscript: April 16, 2012

Manuscript Accepted: April 16, 2012

Published: April 19, 2012

**Citation**

Xuan Liu, Iulian I. Iordachita, Xingchi He, Russell H. Taylor, and Jin U. Kang, "Miniature fiber-optic force sensor based on low-coherence Fabry-Pérot interferometry for vitreoretinal microsurgery," Biomed. Opt. Express **3**, 1062-1076 (2012)

http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-3-5-1062

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### References

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