Abstract

A monitoring technique using the equivalent optical admittance loci of thin films to control the deposition is presented. Real-time broadband spectrum measurements are employed to extract the real-time thin film refraction index and thickness, and the corresponding equivalent optical admittance is thereby obtained. This monitoring method can predict the termination point of the deposition process and avoid the termination ambiguities, which generally appear with other broadband monitors. Compared to other monitoring methods, the experimental results of the proposed monitoring technique show better error compensation ability.

© 2012 OSA

1. Introduction

Monitoring is the major factor influencing the performance of fabricated optical coatings. In time counting monitors and quartz monitors, the errors in the layer thickness cannot be compensated for and will accumulate with each successively deposited layer. Optical monitoring, in which the real-time optical performance of thin films can be directly observed, is generally thought a better way to help operators determine the suitable termination point for each thin film layer during the coating process. This is because what we are concerned with during optical coating fabrication is whether the optical performance of the film stack satisfies our needs. The transmittance (T) or reflectance (R) typically does not change the same way as the expectation during deposition does, since the refraction index may change during deposition, or thickness errors may be induced in the previously deposited films. Monitoring methods, such as Level Monitoring (LM) [1] and Turning Point Monitoring (TPM) [2], are popularly applied during coating production. The monitoring sensitivity of TPM is low. In LM, the monitoring wavelength can be selected to make the signals sensitive to changes in thickness near the termination point of the deposition [3], but the error compensation ability is lower. The precision of single wavelength monitoring is lower than that of the broadband monitoring, because only one wavelength signal is provided. Not only is it not as comprehensive as broadband monitoring, but the signal errors for the monitoring wavelength dominate the monitoring results. For example, TPM is generally employed to control deposition in narrow-band pass filter (NBF) fabrication, and the central wavelength is selected as the monitoring wavelength for error compensation. However, the T or R signals in the final deposition layer could be strongly distorted, because the bandwidth of the monitoring light might be larger than that of the NBF bandwidth.

Thanks to the highly developed processing technology, the real-time broadband monitor has become more and more popular in recent years. In the Broadband Monitor (BM) [4,5], the T or R values are evaluated simultaneously in different wavelengths. The proper termination time is typically thought to be when the real-time spectrum is the closest to the design spectrum of the termination point. However, the merit function that evaluates the difference between the real-time spectrum and the design spectrum at the termination point may have local minimums during the deposition process. Therefore, the quartz monitor is sometimes necessary in order to assist in avoiding the ambiguities or untimely termination with the BM. Even so, ambiguities among the local minimums and the global minimum cannot be totally avoided, especially for the deposition of a very thin layer. Moreover, only after the merit function value of the termination point is smaller than the merit function values of the successive deposition layers can we know that the termination point has been reached. Unlike the single wavelength monitoring method, the termination point in the BM cannot be predicted, and this may result in that a surfeit of the deposition. Although the broadband wavelength monitor can provide more information about the deposited films, it has some defects in determining the termination point.

The equivalent optical admittance loci are broadly used in film stack growth to find revised termination points in monochromatic monitors [3,611]. By analyzing equivalent optical admittance loci in one central wavelength, the whole shape of the design spectrum and position can be maintained as designed. An admittance real-time monitoring method with good performance was proposed by C. C. Lee et al. [7]. However, it is sometimes difficult to obtain the equivalent optical admittance precisely from one single wavelength measurement. In this article, the authors propose a novel method to obtain the refractive index and thickness from the broadband spectrum measurements instead of from a single wavelength measurement and convert this information into the equivalent optical admittance loci of a single wavelength to process the monitor. The admittance values can be acquired with higher precision and less noise. This method combines the advantages of both broadband and single wavelength monitors, to let operators terminate the deposition process at one predicted point, with good error compensation. Furthermore, a strategy to increase the monitoring sensitivity is also demonstrated.

2. Theory and working procedures

The equivalent optical admittance cannot be directly converted from a single transmittance or reflectance measurement. This is because the optical admittance includes the phase term, and the refraction index of the deposited material is not a known constant during the film deposition process. However, if the refraction index and thickness can be acquired from the broadband T or R measurements first, the equivalent optical admittance value of a growing film stack can be obtained. Consider a monitoring light beam normally incident into the growing thin film. To satisfy the electromagnetic boundary conditions at the interfaces in a multilayer thin film stack, as shown in Fig. 1 , the following equation should be satisfied [12]:

[BC]=[EaEkHaEk]=j=1m[cosδjiyjsinδjiyjsinδjcosδj][1HkEk]=j=1m[cosδjiyjsinδjiyjsinδjcosδj][1ys]=j=1m[cosδjinjyvsinδjinjyvsinδjcosδj][1nsyv]
where Ex and Hx represent the electric and magnetic fields of incident light at interface x, respectively. Here, we set Ea/Ek = B and Ha/Ek = C; yj and δj represent the optical admittance and phase thickness in the jth medium, respectively; and δj = 2πnjdjj, where dj and λj are the thickness and reference wavelength of the jth layer, respectively. Here, yv is the optical admittance in the vacuum. If the whole film stack is viewed as a new bulk, its equivalent optical admittance will be

 

Fig. 1 Multilayer thin films.

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yE=HaEa=CB

The corresponding transmittance (T) and reflectance (R) of the thin film are [12]

T=4n0yVns(n0yVB+C)(n0yVB+C)*R=(n0yVBCn0yVB+C)(n0yVBCn0yVB+C)*
where n0 is the incident medium refraction index. In later calculations of the optical admittance, yV will be viewed as the unit. Both T and R are functions of the wavelength, refraction index and thickness. In other words, the thin film refraction index and thickness of the jth layer can be extracted from T or R measurements by finding the minimum of the merit function M listed below.
M=i[Tmeasured(λi)Tcal(nj(λi),dj,λi)]2
where Tmeasured is the measured real-time transmittance values; and Tcal is the calculated transmittance from Eq. (3); λi is the wavelength for which the transmittance is measured. For all monitoring wavelengths, the values of the thickness dj are the same, and the refraction index n can be greatly simplified by using the dispersion law. Notice that the monitoring wavelength for which the optical admittance is employed for analysis during the coating process is not necessarily the same one for which transmittances are measured, since the optical admittance can be derived with the refractive index and thickness obtained from Eq. (4). Operators could select the wavelengths for which the transmittance or reflectance values show distinguishable changes near the termination point into the calculations to increase the monitoring precisions.

If the measurements are offered for a larger number of wavelengths in a broader range, more information will be provided to find the answers for the thickness and refractive index, and the calculation precision will be improved. Once the thickness and refraction index are found, the equivalent optical admittance yE can be obtained by Eqs. (1) and (2).

Figure 2 shows a simulation of the equivalent optical admittance loci for the two quarter-wave thick layer stack (one layer of a high refraction index material, called H, and one layer of a low refraction index material, called L) and its corresponding T loci with respect to thickness. The points on the real axis correspond to the T locus turning points (local peak or valley points), as shown in Fig. 2. In Fig. 2, the interval between each adjacent point pair has a 3nm phase thickness. One can see that, near the turning point, the signal of the transmittance changes very slowly as the thickness grows, and the sensitivity of the monitor will be very low. It is not easy for an operator to judge where the correct termination point is. Therefore, TPM has low sensitivity of thickness control.

 

Fig. 2 Admittance and transmittance loci of two quarter wave layers.

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The equivalent optical admittance loci monitor has the greatest sensitivity on the termination points located near the right side cross point with the real axis. On the other hand, it shows the lowest sensitivity at the termination points located near the left side cross point with the real axis. From Eqs. (1) and (2), for a thin film with a constant refraction index, we can derive the equivalent optical admittance locus as the thickness increases as a circle [12]. The radius of the circle is determined by two factors, the refraction index and the equivalent optical admittance of the deposited layers [12]. Although the refractive index is typically not a constant during deposition, the locus basically follows a circle. For a quarter-wave stack, in which high and low refraction index materials are alternatively deposited, the locus of each layer will be a half circle, and the circle radius changes from layer to layer, as shown in Fig. 3 . If we plot a circle with a radius of y = y0n and its center at the origin of the complex admittance coordinate, there are intersections with the equivalent optical admittance locus, at Point B and D, as shown in Fig. 4 . From Eqs. (1) and (2) we know that the phase thickness from Point A to B is π/4 and from A to C is π/2 [12]. One can see that the distribution of the phase thickness, or optical thickness on the locus is not uniform. When the locus becomes a larger circle in a latterly deposited layer, the non-uniformity becomes more serious. For instance, the 3rd layer of the stack is deposited with the same high refraction index material as the 1st layer, as shown in Fig. 4, and its phase thickness distribution is still confined by the circle with its center at the origin and the real axis. In other words, A’ to B’ and B’ to C’ have the same change in thickness, that is π/4, but the equivalent optical admittance change from B’ to C’ is much larger than from A’ to B’. In B’ to D’, the interference among reflections from the interfaces inside the film stack causes the ratio of the total electric field to magnitude field to change enormously with respective to the thickness change. This results in the monitoring sensitivity in the layer where the deposition termination point is near the right side of the admittance circle to be much higher than when the termination point is at the left side of the admittance locus [13]. The sensitivity can be analytically calculated by taking the derivative of the admittance with respect to the phase thickness [8]. The monitoring sensitivity can be improved by adding the proper phase to the corresponding reflection phase [8]. The equivalent optical admittance can be simply converted into the reflection coefficient by the following equation [9]:

reiδr=y0yEy0+yE
where δr and r are the reflection coefficient phase and magnitude, respectively.

 

Fig. 3 Equivalent optical admittance loci of a quarter-wave stack (ns = 1.52, nH = 2.18, nL = 1.46).

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Fig. 4 Optical thickness phase distribution on the optical admittance loci.

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After the phase is added to the phase of the reflection coefficient, we can convert the newly obtained reflection coefficient back to the corresponding equivalent optical admittance. The loci of the reflection coefficient of the film stack can then also be used in the monitor. Figure 5 shows the change in the locus of the optical admittance after the addition of the reflection phase with π.

 

Fig. 5 Phase shifting technique for the optical admittance to increase monitoring sensitivity (1 dot/ nm).

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3. Experiments and discussion

Various monitoring methods were used to monitor the fabrication process for comparison. An ion-beam sputtering deposition system with an ion beam source 6-cm in diameter was employed to prepare a broadband antireflection coating (AR). Ta2O5 (n = 2.16 at 510nm) and SiO2 (1.49 at 510nm) were used as the high and low refraction index materials, respectively. The monitoring light passed through the substrate (BK7 glass, n = 1.52@ 510nm). Its intensity was then measured by a spectrometer. For an AR coating, according to Eq. (5), we should let the equivalent optical admittance of the fabricated film stack be as close to the optical admittance of the incident medium as possible. In general, the incident medium is air, for which the refraction index is 1.0. The equivalent optical admittance loci of a typical 4-layer AR coating for the visible ranges are shown in Fig. 6 . The reference wavelength is 510nm.

 

Fig. 6 Admittance loci of the AR coating in 510nm.

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During the monitoring process, like the transmittance locus, the equivalent optical admittance would not proceed along the expected (designed) locus. The corresponding errors can be compensated for by terminating the deposition at the new cross point with the expected admittance locus of the next layer. Thus, the deviating locus will be corrected to the expected locus in the next layer, and the final spectrum of the fabricated thin films can be kept as originally designed [7,10]. If the reflection phase shift technique for improving the monitoring sensitivity described in the previous section is applied, the phase shift should be added not only in the current layer, but also in the next layer, to provide correct error compensation.

For the layer where the admittance locus is designed to end on the real axis, the deviating locus should still terminate on the real axis instead of at the intersection point with the designed locus for the next layer. Figure 7 shows the corresponding simulated spectra for an AR coating with an excess thickness of 7nm in the second layer. The green indicates the results calculated with Method 1, in which the third layer locus terminates on the real axis. The red indicates the results calculated with Method 2, in which the third layer locus terminates at the intersection point with the designed locus in the next layer. The results show that Method 1 is better than Method 2. In other types of quarter-wave stack filter fabrication, such as narrow-band pass filter fabrication, the admittance loci should also end on the real axis [11].

 

Fig. 7 Comparison between two optical admittance monitoring.

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For the broadband monitor, T for wavelengths of 450 to 700 nm was calculated. For our Equivalent Optical Admittance Monitor (EOAM), the Simplex Algorithm is employed to find the minimum of Eq. (4) and the corresponding Equivalent Optical Admittance. A Cauchy Equation is used to calculate the refraction index dispersion. The physical thicknesses from the first to forth layer were 14nm, 33nm, 130nm, and 85nm. To fabricate the third and forth layers, a phase of π was added to the reflection phase, to improve the monitoring sensitivity. The experimental results are shown in Fig. 8 . It can be seen that the EOAM performs better than the other methods.

 

Fig. 8 Spectra of the AR coatings fabricated with various monitor methods.

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Another experiment was carried out to evaluate the error compensation abilities, in which an excess thickness of 7nm (around 20% of the layer thickness) was added to the second layer. The first two layers in the AR coating are very thin, and the spectrum of the fabricated coating is very sensitive to any thickness errors in these two layers. The experiment results are shown in Fig. 9 . The results show that, under the excessive deposition in the 2nd layer, the spectrums of the coatings fabricated by LM and BM have larger shifts in wavelengths. EOAM has better performance on maintaining the coating spectrum shape. It shows that, compared to other monitoring methods, EOAM obviously has higher error compensation ability.

 

Fig. 9 Spectra of the AR coatings with 20% thickness excess in the 2nd layer fabricated with various monitoring methods.

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4. Conclusions

A novel monitoring method with good error compensation and monitoring sensitivity for the fabrication of optical coatings is proposed. Not only do we offer a clear rule to predict the termination point, but broadband information is also employed to achieve higher monitoring precision. This method combines the advantages of the broadband and single-wave monitoring methods without their drawbacks. A phase-adding technique is also proposed to increase the monitoring sensitivity. This should greatly improve the fabrication precision and decrease the defection rate of optical filters, especially for the fabrication of multilayer filters where good error compensation and higher monitoring precision are needed. Such filters are used for DWDM in optical communication, mirrors in laser systems, etc.

Acknowledgment

The authors would like to thank the National Science Council of Taiwan under project No. NSC 099-2221-E-008-046-MY3.

References and links

1. C. J. van der Laan, “Optical monitoring of nonquarterwave stacks,” Appl. Opt. 25(5), 753–760 (1986). [CrossRef]   [PubMed]  

2. H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin-film optical filters,” Opt. Acta (Lond.) 19(1), 1–28 (1972). [CrossRef]  

3. C. C. Lee, K. Wu, C. C. Kuo, and S. H. Chen, “Improvement of the optical coating process by cutting layers with sensitive monitor wavelengths,” Opt. Express 13(13), 4854–4861 (2005). [CrossRef]  

4. B. Badoil, F. Lemarchand, M. Cathelinaud, and M. Lequime, “Interest of broadband optical monitoring for thin-film filter manufacturing,” Appl. Opt. 46(20), 4294–4303 (2007). [CrossRef]   [PubMed]  

5. S. Wilbrandt, N. Kaiser, and O. Stenzel, “In-situ broadband monitoring of heterogeneous optical coatings,” Thin Solid Films 502(1-2), 153–157 (2006). [CrossRef]  

6. H. A. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitor systems,” Opt. Acta (Lond.) 24(9), 907–930 (1977). [CrossRef]  

7. C. C. Lee and Y. J. Chen, “Multilayer coatings monitoring using admittance diagram,” Opt. Express 16(9), 6119–6124 (2008). [CrossRef]   [PubMed]  

8. K. Wu, Research on optical monitor through optical admittance analysis and dynamic interferometry, Ph. D. Dissertation, (Department of Optics and Photonics, National Central University 2005), Chap. 5.

9. C. C. Lee, K. Wu, S. H. Chen, and S. J. Ma, “Optical monitoring and real time admittance loci calculation through polarization interferometer,” Opt. Express 15(26), 17536–17541 (2007). [CrossRef]   [PubMed]  

10. B. Chun, C. K. Hwangbo, and J. S. Kim, “Optical monitoring of nonquarterwave layers of dielectric multilayer filters using optical admittance,” Opt. Express 14(6), 2473–2480 (2006). [CrossRef]   [PubMed]  

11. C. C. Lee and K. Wu, “In situ sensitive optical monitoring with proper error compensation,” Opt. Lett. 32(15), 2118–2120 (2007). [CrossRef]   [PubMed]  

12. H. A. Macleod, Thin Film Optical Filters, 3rd ed. (Inst. of Physics Publishing 2001), Chap. 2.

13. K. Wu, M. C. Li, J. C. Wyant, N. J. Brock, B. Kimbrough, and C. C. Lee, “Optical admittance monitor through a dynamic interferometer,” Optical Interference Coating, USA TuC5 (2010).

References

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  1. C. J. van der Laan, “Optical monitoring of nonquarterwave stacks,” Appl. Opt. 25(5), 753–760 (1986).
    [Crossref] [PubMed]
  2. H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin-film optical filters,” Opt. Acta (Lond.) 19(1), 1–28 (1972).
    [Crossref]
  3. C. C. Lee, K. Wu, C. C. Kuo, and S. H. Chen, “Improvement of the optical coating process by cutting layers with sensitive monitor wavelengths,” Opt. Express 13(13), 4854–4861 (2005).
    [Crossref]
  4. B. Badoil, F. Lemarchand, M. Cathelinaud, and M. Lequime, “Interest of broadband optical monitoring for thin-film filter manufacturing,” Appl. Opt. 46(20), 4294–4303 (2007).
    [Crossref] [PubMed]
  5. S. Wilbrandt, N. Kaiser, and O. Stenzel, “In-situ broadband monitoring of heterogeneous optical coatings,” Thin Solid Films 502(1-2), 153–157 (2006).
    [Crossref]
  6. H. A. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitor systems,” Opt. Acta (Lond.) 24(9), 907–930 (1977).
    [Crossref]
  7. C. C. Lee and Y. J. Chen, “Multilayer coatings monitoring using admittance diagram,” Opt. Express 16(9), 6119–6124 (2008).
    [Crossref] [PubMed]
  8. K. Wu, Research on optical monitor through optical admittance analysis and dynamic interferometry, Ph. D. Dissertation, (Department of Optics and Photonics, National Central University 2005), Chap. 5.
  9. C. C. Lee, K. Wu, S. H. Chen, and S. J. Ma, “Optical monitoring and real time admittance loci calculation through polarization interferometer,” Opt. Express 15(26), 17536–17541 (2007).
    [Crossref] [PubMed]
  10. B. Chun, C. K. Hwangbo, and J. S. Kim, “Optical monitoring of nonquarterwave layers of dielectric multilayer filters using optical admittance,” Opt. Express 14(6), 2473–2480 (2006).
    [Crossref] [PubMed]
  11. C. C. Lee and K. Wu, “In situ sensitive optical monitoring with proper error compensation,” Opt. Lett. 32(15), 2118–2120 (2007).
    [Crossref] [PubMed]
  12. H. A. Macleod, Thin Film Optical Filters, 3rd ed. (Inst. of Physics Publishing 2001), Chap. 2.
  13. K. Wu, M. C. Li, J. C. Wyant, N. J. Brock, B. Kimbrough, and C. C. Lee, “Optical admittance monitor through a dynamic interferometer,” Optical Interference Coating, USA TuC5 (2010).

2008 (1)

2007 (3)

2006 (2)

S. Wilbrandt, N. Kaiser, and O. Stenzel, “In-situ broadband monitoring of heterogeneous optical coatings,” Thin Solid Films 502(1-2), 153–157 (2006).
[Crossref]

B. Chun, C. K. Hwangbo, and J. S. Kim, “Optical monitoring of nonquarterwave layers of dielectric multilayer filters using optical admittance,” Opt. Express 14(6), 2473–2480 (2006).
[Crossref] [PubMed]

2005 (1)

1986 (1)

1977 (1)

H. A. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitor systems,” Opt. Acta (Lond.) 24(9), 907–930 (1977).
[Crossref]

1972 (1)

H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin-film optical filters,” Opt. Acta (Lond.) 19(1), 1–28 (1972).
[Crossref]

Badoil, B.

Cathelinaud, M.

Chen, S. H.

Chen, Y. J.

Chun, B.

Hwangbo, C. K.

Kaiser, N.

S. Wilbrandt, N. Kaiser, and O. Stenzel, “In-situ broadband monitoring of heterogeneous optical coatings,” Thin Solid Films 502(1-2), 153–157 (2006).
[Crossref]

Kim, J. S.

Kuo, C. C.

Lee, C. C.

Lemarchand, F.

Lequime, M.

Ma, S. J.

Macleod, H. A.

H. A. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitor systems,” Opt. Acta (Lond.) 24(9), 907–930 (1977).
[Crossref]

H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin-film optical filters,” Opt. Acta (Lond.) 19(1), 1–28 (1972).
[Crossref]

Pelletier, E.

H. A. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitor systems,” Opt. Acta (Lond.) 24(9), 907–930 (1977).
[Crossref]

Stenzel, O.

S. Wilbrandt, N. Kaiser, and O. Stenzel, “In-situ broadband monitoring of heterogeneous optical coatings,” Thin Solid Films 502(1-2), 153–157 (2006).
[Crossref]

van der Laan, C. J.

Wilbrandt, S.

S. Wilbrandt, N. Kaiser, and O. Stenzel, “In-situ broadband monitoring of heterogeneous optical coatings,” Thin Solid Films 502(1-2), 153–157 (2006).
[Crossref]

Wu, K.

Appl. Opt. (2)

Opt. Acta (Lond.) (2)

H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin-film optical filters,” Opt. Acta (Lond.) 19(1), 1–28 (1972).
[Crossref]

H. A. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitor systems,” Opt. Acta (Lond.) 24(9), 907–930 (1977).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Thin Solid Films (1)

S. Wilbrandt, N. Kaiser, and O. Stenzel, “In-situ broadband monitoring of heterogeneous optical coatings,” Thin Solid Films 502(1-2), 153–157 (2006).
[Crossref]

Other (3)

H. A. Macleod, Thin Film Optical Filters, 3rd ed. (Inst. of Physics Publishing 2001), Chap. 2.

K. Wu, M. C. Li, J. C. Wyant, N. J. Brock, B. Kimbrough, and C. C. Lee, “Optical admittance monitor through a dynamic interferometer,” Optical Interference Coating, USA TuC5 (2010).

K. Wu, Research on optical monitor through optical admittance analysis and dynamic interferometry, Ph. D. Dissertation, (Department of Optics and Photonics, National Central University 2005), Chap. 5.

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Figures (9)

Fig. 1
Fig. 1

Multilayer thin films.

Fig. 2
Fig. 2

Admittance and transmittance loci of two quarter wave layers.

Fig. 3
Fig. 3

Equivalent optical admittance loci of a quarter-wave stack (ns = 1.52, nH = 2.18, nL = 1.46).

Fig. 4
Fig. 4

Optical thickness phase distribution on the optical admittance loci.

Fig. 5
Fig. 5

Phase shifting technique for the optical admittance to increase monitoring sensitivity (1 dot/ nm).

Fig. 6
Fig. 6

Admittance loci of the AR coating in 510nm.

Fig. 7
Fig. 7

Comparison between two optical admittance monitoring.

Fig. 8
Fig. 8

Spectra of the AR coatings fabricated with various monitor methods.

Fig. 9
Fig. 9

Spectra of the AR coatings with 20% thickness excess in the 2nd layer fabricated with various monitoring methods.

Equations (5)

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[ B C ]=[ E a E k H a E k ]= j=1 m [ cos δ j i y j sin δ j i y j sin δ j cos δ j ] [ 1 H k E k ]= j=1 m [ cos δ j i y j sin δ j i y j sin δ j cos δ j ] [ 1 y s ]= j=1 m [ cos δ j i n j y v sin δ j i n j y v sin δ j cos δ j ] [ 1 n s y v ]
y E = H a E a = C B
T= 4 n 0 y V n s ( n 0 y V B+C) ( n 0 y V B+C) * R=( n 0 y V BC n 0 y V B+C ) ( n 0 y V BC n 0 y V B+C ) *
M= i [ T measured ( λ i ) T cal ( n j ( λ i ), d j , λ i )] 2
r e iδr = y 0 y E y 0 + y E

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