OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 6 — Mar. 14, 2011
  • pp: 5431–5441
« Show journal navigation

Integrating fault tolerance algorithm and circularly polarized ellipsometer for point-of-care applications

Chia-Ming Jan, Yu-Hsun Lee, Kuang-Chong Wu, and Chih-Kung Lee  »View Author Affiliations


Optics Express, Vol. 19, Issue 6, pp. 5431-5441 (2011)
http://dx.doi.org/10.1364/OE.19.005431


View Full Text Article

Acrobat PDF (1140 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A circularly polarized ellipsometer was developed to enable real-time measurements of the optical properties of materials. Using a four photo-detector quadrature configuration, a phase modulated ellipsometer was substantially miniaturized which has the ability to achieve a high precision detection limit. With a proven angular resolution of 0.0001 deg achieved by controlling the relative positions of a triangular prism, a paraboloidal and a spherical mirror pair, this new ellipsometer possesses a higher resolution than traditional complex mechanically controlled configurations. Moreover, the addition of an algorithm, FTA (fault tolerance algorithm) was adopted to compensate for the imperfections of the opto-mechanical system which can decrease system measurement reliability. This newly developed system requires only one millisecond or less to complete the measurement task without having to adopt any other modulation approach. The resolution achieved can be as high as 4x10−7 RIU (refractive index unit) which is highly competitive when compared with other commercially available instruments. Our experimental results agreed well with the simulation data which confirms that our quadrature-based circularly polarized ellipsometer with FTA is an effective tool for precise detection of the optical properties of thin films. It also has the potential to be used to monitor the refractive index change of molecules in liquids.

© 2011 OSA

1. Introduction

2. Design and principle

2.1. Optical arrangement configuration

Our circularly polarized ellipsometer used a 0.3mW laser diode at 635nm wavelength as the light source. A varying incidence angle system and a quadrature configuration were adopted (Fig. 1
Fig. 1 Circularly polarized ellipsometer.
). A polarizer 1 oriented at 45 deg was used to make sure the p- and s- polarizations had equal intensity levels and equal initial phases. The polarization directions were defined as shown in Fig. 1. A 50:50 ratio non-polarized beamsplitter was used to make the p- and s- polarized light beams impinge onto the sample simultaneously. The varying incidence angle configuration was composed of a triangular prism, a paraboloidal mirror and a spherical mirror. The paraboloidal mirror changed the incident angle with a positioning of the triangular prism when the paraboloidal mirror focal point was set to the center of the sensing region (Fig. 1). To precisely position the triangular prism, a linearly motorized stage with encoder possessing a 0.12406μm per count was controlled using a LabVIEW program. Our set-up easily approached a 0.0001 deg accuracy while maintaining a wide incidence ranging between 18 deg to 78 deg. The returning light from the spherical mirror passed through a quadrature configuration which includs a quarter-wavelength plate oriented on a fast axis at 45 deg and along four polarizers at 0 deg, 45 deg, 90 deg, and 135 deg orientations. The arranged incident polarization at 45 deg can be treated as the summation of a p- polarization and a s- polarization light beam with no phase difference between them. Considering that a common path configuration carries both p- and s- polarization responses, a set of orthogonal signals was obtained in the circularly polarized ellipsometer. The mathematical details are discussed further in Eq. (4).

2.2. Circularly polarized ellipsometer with fault tolerance algorithm

In the past, homodyne interferometry adopted a three-step phase-shifting method to measure phase difference [18

18. Y. Y. Cheng and J. C. Wyant, “Phase shifter calibration in phase-shifting interferometry,” Appl. Opt. 24(18), 3049–3052 (1985). [CrossRef] [PubMed]

]. In 1987, a five-step digital phase-shifting algorithm was developed by P. Hariharan that used the five known phase shifting terms to determine unknown phase data [19

19. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26(13), 2504–2506 (1987). [CrossRef] [PubMed]

]. More specifically, the relationship of a phase difference Δϕ and modulation term β solved from the intensity of the light beam detected as I1~I5 leads to

tan(Δϕ)=1-cos()sinβ(I2-I4)(2I3-I1-I5).
(1)

A rotating analyzer method developed by R. Naraoka in 2005 focused on the phase detection of surface plasmon resonance utilizing modulation of the four different polarized states. Its high repeatability and high precision characteristics made it easy to achieve a 10−7 RIU (refractive index unit) accuracy [20

20. R. Naraoka and K. Kajikawa, “Phase detection of surface plasmon resonance using rotating analyzer method,” Sens. Actuators B Chem. 107(2), 952–956 (2005). [CrossRef]

]. Our circularly polarized ellipsometer is more suitable than a rotating analyzer configuration since there is no need to rotate the analyzers. Quadrature configurations have been applied before as a phase shifting tool in SPR (surface plasmon resonance) devices for many years [12

12. J. Y. Lee, H. C. Shih, C. T. Hong, and T. K. Chou, “Measurement of refractive index change by surface plasmon resonance and phase quadrature interferometry,” Opt. Commun. 276(2), 283–287 (2007). [CrossRef]

,13

13. S. Patskovsky, M. Maisonneuve, M. Meunier, and A. V. Kabashin, “Mechanical modulation method for ultrasensitive phase measurements in photonics biosensing,” Opt. Express 16(26), 21305–21314 (2008). [CrossRef] [PubMed]

]. The Jones transformation matrix for a quarter-wavelength plate of our system (in Fig. 2
Fig. 2 Schematic diagram of quadrature configuration with PD1~4.
) when M=45o and δ=π/4can be expressed as
[ecos2M+esin2M2isinMcosMsinδ2isinMcosMsinδesin2M+ecos2M]=22[1ii1].
(2)
Herein, M denotes the azimuthal angle of the wavelength plate and δ denotes the phase retardation of the wavelength plate. Considering the initial electric field of the polarization at 45 deg, the two in phase p- and s- polarizations have the same amplitude as represented by Exexp(iϕ0p) and Eyexp(iϕ0s), where ϕ0p and ϕ0s denote the initial phase difference of the p- and s- polarizations. The ϕp and ϕs denote the phase difference caused by the samples. We denote the parameter Δ=(ϕ0p+ϕp)-(ϕ0s+ϕs), to represent the relative phase difference between the p- and s- polarizations. In our double-pass ellipsometer, Δ is one of the two ellipsometry parameters. Furthermore, rp and rs denote the reflection coefficient of the p- and s- polarizations respectively. For the configuration shown in Fig. 2, we can obtain the calculated electric field of each detector by substituting the azimuthal angle θ at 0 deg, 45 deg, 90 deg, and 135 deg into Eq. (3)
E=[ExEy]=[cos2θcosθsinθcosθsinθsin2θ]22[1ii1][rp2exp[i(ϕ0p+ϕp)]rs2exp[i(ϕ0s+ϕs)]]=[cos2θcosθsinθcosθsinθsin2θ]22[1ii1][rp2exp(i2Δ)rs2].
(3)
More specifically, the intensity of the light beams detected at I1~I4 are:

I1=12(rp4+rs4+2rp2rs2sin2Δ)                 I2=12(rp4+rs4+2rp2rs2cos2Δ)I3=12(rp4+rs42rp2rs2sin2Δ)                 I4=12(rp4+rs42rp2rs2cos2Δ)
(4)

Compared with a single-pass configuration ellipsometer, the experimental data undertook the following changes: (1) tanΨ became (tanΨ)2; and (2) Δ became 2Δ in our double-pass configuration. Considering the signs of the two terms of the intensity difference, a sine term (I1-I3), and a cosine term (I2-I4), we can extend the full dynamic range of Δ from -π to π as shown by

Δ=12tan-1(I1-I3I2-I4),          πΔπ .
(5)

For either(I1-I3)(I2-I4)>0,and(I1-I3)<0, or (I1-I3)(I2-I4)<0,and(I1-I3)>0, Δ calculated from Eq. (5) must add a π term to make sure the range of Δ is correct. Assuming that |rp|/|rs|=tanΨ, Eq. (6) contains another ellipsometry parameter Ψ where the sign of the tan Ψ is defined to be positive.

I1+I3I1-I3=(tan2Ψ)2+12(tan2Ψ)sin2Δ,    0Ψπ4.
(6)

A circularly polarized ellipsometer which has the important advantage of having no modulation during measurement will always be superior to a traditional ellipsometer. We actually obtained the ellipsometry parameters by the four intensity levels according to Eqs. (5) and (6) for static measurements. According to Eq. (4), a sine term (I1-I3), and a cosine term (I2-I4)removing the unnecessary DC signals, take the form of Lissajous PQ signals. The way to produce the Lissajous signals needed before the measurement was to rotate the HWP (half-wavelength plate) from the initial 0 deg polarization to π. This HWP rotation changes the phase difference of the sine and the cosine terms from 0 to 2π such that complete Lissajous signals are obtained. We demonstrated that some imperfections may affect the circularly polarized ellipsometer and result in the appearance of elliptical PQ signals which can only be caused by mis-adjustment or mis-alignment. More specifically, according to Eq. (4), less than perfect circular type Lissajous signals can only be caused by optical components located behind the second NPBS (Fig. 1). In other words, less than perfect circular Lissajous signals are the result of effects not appearing in the common path. That is, different reflection coefficients of the p- and s- polarizations while passing the optical components in the system will not cause the Lissajous signals deviating from the circle [17

17. C. M. Jan, Y. H. Lee, and C. K. Lee, “The circular polarization interferometer based surface plasmon biosensor,” Proc. SPIE 7577, 75770B, 75770B-12 (2010). [CrossRef]

]. The FTA (fault tolerance algorithm) can be viewed as a way to make sure various experimental tests are compared using an equal baseline. More specifically, the sensitivity over different parts of the Lissajous PQ signals will not be identical if the Lissajous figure is not a circle. The higher the ratio between the long and the short axes of a Lissajous figure, the higher the sensitivity difference. In other words, there is lower sensitivity for the data obtained along the sharp curve of an ellipse and higher sensitivity along the smooth side of an ellipse. For calibrating the eccentric ellipse cases, the following derivation shows the results of the FTA method. Equation (7) defined each position of a general ellipse with a 2×2 rotational matrix including a major radiusRA, a minor radiusRB, eccentric center(Bp,Bq), and starting phase ϕ0. Considering the p^ and q^ coordinates, Ap and Aq were individual amplitudes of the PQ signals with each phase retardation, ϕp and ϕq (Fig. 3
Fig. 3 Re-mapping schematic diagram of FTA (fault tolerance algorithm).
). Comparing Eqs. (7) and (8), the relationship between (Ap,Aq) and (RA,RB,ϕ*) are independent of ϕ0 and can be denoted by Eq. (9).
[qp]=[cos(ϕ*)-sin(ϕ*)sin(ϕ*)cos(ϕ*)][RAcos(ϕ+ϕ0)RBsin(ϕ+ϕ0)]+[BqBp]
(7)
[qp]=[Aqsin(ϕq+ϕ)Apsin(ϕp+ϕ)]+[BqBp]
(8)
[Aq2Ap2]=[cos2(ϕ*)sin2(ϕ*)sin2(ϕ*)cos2(ϕ*)]+[RA2RB2],ApAqcos(ϕp-ϕq)=ApAqcos(θ)=(RA2-RB2)sin(ϕ*)cos(ϕ*),
(9)
where θ denotes the relative phase difference between the PQ components.

Given that ϕq=0, Eq. (10) shows a linearization form with the five parameters during an inverse matrix operation, and assuming Cp=Apsin(ϕp) and Dp=Apcos(ϕp), we obtained
[cosϕsinϕ]=[0AqCpDp]-1[qi-Bqpi-Bp]=[Cq¯Dq¯Cp¯0][qi-Bqpi-Bp]=[Cq¯Dq¯Bq¯Cp¯0Bp¯][qipi1]
(10)
The Lissjous signals (pi,qi) are denoted by (I1-I3) and (I2-I4) respectively. The five significant parameters Ap, Aq, Bp, Bq, and ϕp-ϕq=θ, characterize general elliptical PQ signals through a remapping relationship instead of Bp¯, Bq¯, Cp¯, Cq¯, and Dq¯. Setting each partial derivation value of the five parameters to zero, Eq. (11) represents a simplification of the fault tolerance algorithm program.

[Cp¯Dq¯Bq¯Cq¯Bp¯]=(i=1N[qisinϕipicosϕicosϕiqicosϕisinϕi][cosϕisinϕi]T[0pi1qi0qi0001])-1(i=1N[qisinϕipicosϕicosϕiqicosϕisinϕi])
(11)

The steps of the fault tolerance algorithm can be summarized as follows:

  • 1. The resulting intensity values were obtained using a LabVIEW program. We had the measured PQ signals (pi,qi). The initial phaseϕi can be retrieved as shown by
    ϕi=tan-1(pi-Bpqi-Bq),
    (12)
    • where Bp=12(max(pi)+min(pi)),and Bq=12(max(qi)+min(qi)).
  • 2. We can use (pi,qi,ϕi)directly solve the five parameters (B¯p,B¯q,C¯p,C¯q,D¯q) using Eq. (11). During the iterative calculation, the final characterized matrix can be obtained. Herein, the calculated square sum of cosϕ and sinϕ is necessary to be one as a result of the normalization,
    [cosϕsinϕ]=[C¯qD¯qB¯qC¯p0B¯p][qp1]|[C¯qD¯qB¯qC¯p0B¯p][qp1]|.
    (13)
  • 3. The resulting five parameters can correct the measured intensity values by an optimal re-mapping conversed into a circle in Lissajous space. Figure 4
    Fig. 4 Experimental results of a Lissajous curve utilizing FTA. (Note: dark circle denotes data before FTA; light circle denotes data after FTA.)
    shows the successful adjustment of our experimental data into a modified unit circle calibrated by FTA. The following results, seen after FTA modification, allowed our imperfect system to retrieve the exact ellipsometry parameters without an over precise optical alignment.
    Fig. 4Experimental results of a Lissajous curve utilizing FTA. (Note: dark circle denotes data before FTA; light circle denotes data after FTA.)

3. Results and discussions

To verify the proposed circularly polarized ellipsometer, the experimental results included a solid phase and a liquid phase measurements. It is known that conventional ellipsometers are easily subjected to great fluctuations caused by incidences from air passing through layers of a liquid sample. A prism-coupled scheme can be used to approach liquid phase measurements precisely. We obtained ellipsometry parameters in liquids by utilizing a half-spherical prism made by a high index material, SF2 (n = 1.64) instead of an original flat sensing platform as seen in Fig. 1. More specifically, adding a half-spherical prism converted the original ellipsometer for dry samples (Fig. 1) into an ellipsometer for liquid samples. Real-time measurements of our ellipsometer enable us to monitor fast reactions in the range of a few milliseconds and to detect the temporal optical properties of film layers. More specifically, the influences of the inaccurate positions of the optical devices (e.g. rotated waveplates, polarizers, and compensators) can easily result in measurement errors [1

1. R. M. A. Azzam, and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland Pub. Co., 1977).

,21

21. I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, and R. W. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206(1-2), 300–305 (1991). [CrossRef]

23

23. N. V. Nguyen, B. S. Pudliner, I. An, and R. W. Collins, “Error correction for calibration and data reduction in rotating-polarizer ellipsometry - applications to a novel multichannel ellipsometer,” J. Opt. Soc. Am. A 8(6), 919–931 (1991). [CrossRef]

]. Compared with traditional ellipsometers, our circularly polarized ellipsometer can minimize the detection time, limited only by the capability of the data acquisition facility.

Similarly, we prepared two types of samples which were deposited on a 50 nm Au/1 nm Cr and 46 nm Au/4 nm Ti/40 nm ITO (Indium tin oxide) upon the base of the SF2 (n=1 .64) individually. Figure 7
Fig. 7 Measurement of ellipsometry parameters in (a) Sample #1 (50 nm Au/1 nm Cr) (b) Sample #2 (46 nm Au/4 nm Ti/40 nm ITO) (Note: dark circle denotes the Δ measured by CPE, and dark diamond denotes the Ψ measured by CPE; light circle denotes the Δ measured by EP3, and light diamond denotes the Ψ measured by EP3.) (The simulation curve was based on the real model with adopted incidences from 20 to 70 deg.)
shows the ellipsometric measurements Ψ and Δ, with its incidence from 40 deg to 65 deg at each step of a 5 deg increase in a non-liquid phase environments. Figure 7(a) indicates the results of the Sample #1 (50 nm Au/1 nm Cr), where the dark circle and diamond represent the Δ and Ψ obtained. The measurement results of the Sample #2 (46 nm Au/4 nm Ti/40 nm ITO) is shown in Fig. 7(b). For comparison of the experimental results, a commercially available nulling-type ellipsometer EP3 (Nanofilm Co.) was used to provide the reference data, whereas a four-zone method was adopted to measure the ellipsometry parameters. The circle and diamond represent the experimental data measured by EP3 as shown in Figs. 7(a) and 7(b). According to the variations of the ellipsometry parameters, Δ typically possesses more sensitivity than Ψ. Figure 7 shows the results measured by our system which matched very well with the simulated results. In summary, our newly developed circularly polarized ellipsometer offers a reliable measurement method for practical applications.

4. Conclusions

We designed a new circularly polarized ellipsometer based on quadrature configuration which combines a useful FTA algorithm which together can enhance system reliability. Our system possesses a precise incident angle controlled scheme and a double-pass configuration which offers more sensitivity. To overcome imperfections of an opto-mechanical configuration, the FTA was successfully incorporated which can correct misalignment induced measurement errors. Therefore, our circularly polarized ellipsometer offers more advantages than other conventional ellipsometer configurations. The minimum measurement time of our system is only limited by the data acquisition facility which allows for more real-time ellipsometric measurements. Our new design has high potential to be used as a portable instrument. In addition, our experimental results show that the obtained sensitivity can be as high as 4x10−7 RIU. We showed that our ellipsometric configuration can be used to measure Ψ and Δ in liquids or non-liquids.

Acknowledgments

This work was supported by the Taiwan National Science Council (NSC) through Project NSC 98-2627-E-002-003.

References and links

1.

R. M. A. Azzam, and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland Pub. Co., 1977).

2.

H. G. Tompkins, and E. A. Irene, Handbook of Ellipsometry (William Andrew Pub., Springer, 2005).

3.

P. A. Cuypers, W. T. Hermens, and H. C. Hemker, “Ellipsometry as a tool to study protein films at liquid-solid interfaces,” Anal. Biochem. 84(1), 56–67 (1978). [CrossRef] [PubMed]

4.

H. Nygren and M. Stenberg, “Calibration by ellipsometry of the enzyme-linked immunosorbent assay,” J. Immunol. Methods 80(1), 15–24 (1985). [CrossRef] [PubMed]

5.

G. Jin, R. Jansson, and H. Arwin, “Imaging ellipsometry revisited: developments for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67(8), 2930–2936 (1996). [CrossRef]

6.

D. Tanooka, E. Adachi, and K. Nagayama, “Color-imaging ellipsometer: high-speed characterization of in-plane distribution of film thickness at nano-scale,” Jpn. J. Appl. Phys., Part 1 40(2A), 877–880 (2001). [CrossRef]

7.

Q. W. Zhan and J. R. Leger, “High-resolution imaging ellipsometer,” Appl. Opt. 41(22), 4443–4450 (2002). [CrossRef] [PubMed]

8.

W. M. Duncan and S. A. Henck, “In situ spectral ellipsometry for real-time measurement and control,” Appl. Surf. Sci. 63(1-4), 9–16 (1993). [CrossRef]

9.

S. A. Henck, W. M. Duncan, L. M. Lowenstein, and S. W. Butler, “In situ spectral ellipsometry for real-time thickness measurement: etching multilayer stacks,” J. Vac. Sci. Technol. A 11(4), 1179–1185 (1993). [CrossRef]

10.

H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (John Wiley & Sons, 2007).

11.

C. K. Lee, W. J. Wu, G. Y. Wu, C. L. Li, Z. D. Chen, and J. Y. Chen, “Design and performance verification of a microscope-based interferometer for miniature-specimen metrology,” Opt. Eng. 44(8), 085602 (2005). [CrossRef]

12.

J. Y. Lee, H. C. Shih, C. T. Hong, and T. K. Chou, “Measurement of refractive index change by surface plasmon resonance and phase quadrature interferometry,” Opt. Commun. 276(2), 283–287 (2007). [CrossRef]

13.

S. Patskovsky, M. Maisonneuve, M. Meunier, and A. V. Kabashin, “Mechanical modulation method for ultrasensitive phase measurements in photonics biosensing,” Opt. Express 16(26), 21305–21314 (2008). [CrossRef] [PubMed]

14.

W. L. Hsu, S. S. Lee, and C. K. Lee, “Ellipsometric surface plasmon resonance,” J. Biomed. Opt. 14(2), 024036 (2009). [CrossRef] [PubMed]

15.

C. K. Lee, T. D. Cheng, S. S. Lee, and C. K. Chang, “Opto-mechatronic configurations to maximize dynamic range and optimize resolution of optical instruments,” Opt. Rev. 16(2), 133–140 (2009). [CrossRef]

16.

W. J. Wu, C. K. Lee, and C. T. Hsieh, “Signal processing algorithms for Doppler effect based nanometer positioning systems,” Jpn. J. Appl. Phys., Part 1 38(3B), 1725–1729 (1999). [CrossRef]

17.

C. M. Jan, Y. H. Lee, and C. K. Lee, “The circular polarization interferometer based surface plasmon biosensor,” Proc. SPIE 7577, 75770B, 75770B-12 (2010). [CrossRef]

18.

Y. Y. Cheng and J. C. Wyant, “Phase shifter calibration in phase-shifting interferometry,” Appl. Opt. 24(18), 3049–3052 (1985). [CrossRef] [PubMed]

19.

P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26(13), 2504–2506 (1987). [CrossRef] [PubMed]

20.

R. Naraoka and K. Kajikawa, “Phase detection of surface plasmon resonance using rotating analyzer method,” Sens. Actuators B Chem. 107(2), 952–956 (2005). [CrossRef]

21.

I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, and R. W. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206(1-2), 300–305 (1991). [CrossRef]

22.

R. M. A. Azzam and N. M. Bashara, “Analysis of systematic-errors in rotating-analyzer ellipsometers,” J. Opt. Soc. Am. 64(11), 1459–1469 (1974). [CrossRef]

23.

N. V. Nguyen, B. S. Pudliner, I. An, and R. W. Collins, “Error correction for calibration and data reduction in rotating-polarizer ellipsometry - applications to a novel multichannel ellipsometer,” J. Opt. Soc. Am. A 8(6), 919–931 (1991). [CrossRef]

24.

P. Westphal and A. Bornmann, “Biomolecular detection by surface plasmon enhanced ellipsometry,” Sens. Actuators B Chem. 84(2-3), 278–282 (2002). [CrossRef]

25.

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108(2), 462–493 (2008). [CrossRef] [PubMed]

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.4570) Instrumentation, measurement, and metrology : Optical design of instruments
(260.2130) Physical optics : Ellipsometry and polarimetry

ToC Category:
Optical Devices

History
Original Manuscript: January 4, 2011
Revised Manuscript: February 6, 2011
Manuscript Accepted: February 17, 2011
Published: March 8, 2011

Citation
Chia-Ming Jan, Yu-Hsun Lee, Kuang-Chong Wu, and Chih-Kung Lee, "Integrating fault tolerance algorithm and circularly polarized ellipsometer for point-of-care applications," Opt. Express 19, 5431-5441 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-6-5431


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. M. A. Azzam, and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland Pub. Co., 1977).
  2. H. G. Tompkins, and E. A. Irene, Handbook of Ellipsometry (William Andrew Pub., Springer, 2005).
  3. P. A. Cuypers, W. T. Hermens, and H. C. Hemker, “Ellipsometry as a tool to study protein films at liquid-solid interfaces,” Anal. Biochem. 84(1), 56–67 (1978). [CrossRef] [PubMed]
  4. H. Nygren and M. Stenberg, “Calibration by ellipsometry of the enzyme-linked immunosorbent assay,” J. Immunol. Methods 80(1), 15–24 (1985). [CrossRef] [PubMed]
  5. G. Jin, R. Jansson, and H. Arwin, “Imaging ellipsometry revisited: developments for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67(8), 2930–2936 (1996). [CrossRef]
  6. D. Tanooka, E. Adachi, and K. Nagayama, “Color-imaging ellipsometer: high-speed characterization of in-plane distribution of film thickness at nano-scale,” Jpn. J. Appl. Phys., Part 1 40(2A), 877–880 (2001). [CrossRef]
  7. Q. W. Zhan and J. R. Leger, “High-resolution imaging ellipsometer,” Appl. Opt. 41(22), 4443–4450 (2002). [CrossRef] [PubMed]
  8. W. M. Duncan and S. A. Henck, “In situ spectral ellipsometry for real-time measurement and control,” Appl. Surf. Sci. 63(1-4), 9–16 (1993). [CrossRef]
  9. S. A. Henck, W. M. Duncan, L. M. Lowenstein, and S. W. Butler, “In situ spectral ellipsometry for real-time thickness measurement: etching multilayer stacks,” J. Vac. Sci. Technol. A 11(4), 1179–1185 (1993). [CrossRef]
  10. H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (John Wiley & Sons, 2007).
  11. C. K. Lee, W. J. Wu, G. Y. Wu, C. L. Li, Z. D. Chen, and J. Y. Chen, “Design and performance verification of a microscope-based interferometer for miniature-specimen metrology,” Opt. Eng. 44(8), 085602 (2005). [CrossRef]
  12. J. Y. Lee, H. C. Shih, C. T. Hong, and T. K. Chou, “Measurement of refractive index change by surface plasmon resonance and phase quadrature interferometry,” Opt. Commun. 276(2), 283–287 (2007). [CrossRef]
  13. S. Patskovsky, M. Maisonneuve, M. Meunier, and A. V. Kabashin, “Mechanical modulation method for ultrasensitive phase measurements in photonics biosensing,” Opt. Express 16(26), 21305–21314 (2008). [CrossRef] [PubMed]
  14. W. L. Hsu, S. S. Lee, and C. K. Lee, “Ellipsometric surface plasmon resonance,” J. Biomed. Opt. 14(2), 024036 (2009). [CrossRef] [PubMed]
  15. C. K. Lee, T. D. Cheng, S. S. Lee, and C. K. Chang, “Opto-mechatronic configurations to maximize dynamic range and optimize resolution of optical instruments,” Opt. Rev. 16(2), 133–140 (2009). [CrossRef]
  16. W. J. Wu, C. K. Lee, and C. T. Hsieh, “Signal processing algorithms for Doppler effect based nanometer positioning systems,” Jpn. J. Appl. Phys., Part 1 38(3B), 1725–1729 (1999). [CrossRef]
  17. C. M. Jan, Y. H. Lee, and C. K. Lee, “The circular polarization interferometer based surface plasmon biosensor,” Proc. SPIE 7577, 75770B, 75770B-12 (2010). [CrossRef]
  18. Y. Y. Cheng and J. C. Wyant, “Phase shifter calibration in phase-shifting interferometry,” Appl. Opt. 24(18), 3049–3052 (1985). [CrossRef] [PubMed]
  19. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26(13), 2504–2506 (1987). [CrossRef] [PubMed]
  20. R. Naraoka and K. Kajikawa, “Phase detection of surface plasmon resonance using rotating analyzer method,” Sens. Actuators B Chem. 107(2), 952–956 (2005). [CrossRef]
  21. I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, and R. W. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206(1-2), 300–305 (1991). [CrossRef]
  22. R. M. A. Azzam and N. M. Bashara, “Analysis of systematic-errors in rotating-analyzer ellipsometers,” J. Opt. Soc. Am. 64(11), 1459–1469 (1974). [CrossRef]
  23. N. V. Nguyen, B. S. Pudliner, I. An, and R. W. Collins, “Error correction for calibration and data reduction in rotating-polarizer ellipsometry - applications to a novel multichannel ellipsometer,” J. Opt. Soc. Am. A 8(6), 919–931 (1991). [CrossRef]
  24. P. Westphal and A. Bornmann, “Biomolecular detection by surface plasmon enhanced ellipsometry,” Sens. Actuators B Chem. 84(2-3), 278–282 (2002). [CrossRef]
  25. J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108(2), 462–493 (2008). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited