Adsorption of human plasma fibrinogen (HPF) on 6 differently treated titanium samples (polished, polished and etched, and 4 titanium carbide coatings samples produced by using plasma-enhanced chemical vapour deposition (PECVD) method) is investigated by using diffractive optical element (DOE) sensor. Permittivity (susceptibility) change and fluctuation in optical roughness (Ropt) of treated titanium surface in the presence of background electrolyte without and with HPF molecules are sensed by using DOE sensor and optical ellipsometry. Correlation between transmitted light and thickness of molecule layer was found. The findings allow to sense temporal organization and severity of adsorption of nano-scale HPF molecules on polished, on polished and etched, and on titanium carbide surface.
© 2008 Optical Society of America
The investigation of the interactions of blood plasma proteins at different surfaces is a challenging task in biomedicine. Titanium is frequently used as a biomaterial for hard tissue replacement, such as dental and orthopaedic implants. Thus the understanding of the protein adsorption on titanium surface is of great importance [1, 2, 3, 4]. Biomaterial devices made of titanium give a satisfactory performance. The surface morphology, which can be varied by different processing methods influence the final interactions of the implant with the surrounding environment. Rough surfaces promote better oseointegration than smooth surfaces [5, 6, 7, 8].
Soon after implantation - within a few seconds - the biomaterial surface becomes coated with a film of adsorbed proteins, which mediate the interaction between the implant and the body environment. Since most implants are exposed to blood during implantation, the initial protein film is mainly composed of plasma proteins. Human plasma fibrinogen (HPF) is one of the most relevant proteins that are adsorbed on biomaterial surfaces. HPF takes part in blood coagulation, facilitates adhesion and aggregation of platelets [9, 10]. The structure and composition of the adsorbed protein layer determine the type and extent of the subsequent biological reactions, such as activation of coagulation and immune response and oseointegration . Thus the initially adsorbed protein layer is a factor conditioning the biocompatibility [12, 13, 14]. The mechanisms and the factors important for protein adsorption and desorption are still subject of scientific research and not very well understood. Therefore it is important to investigate how different titanium surfaces influence the formation and properties of adsorbed protein layers.
The need to develop novel methods for the investigation of biopolymer adsorption at surfaces is arisen from the observation that conventional surface characterization methods and tools (as Scanning Electron Microscopy - SEM, Transmission Electron Microscopy - TEM, Environmental Scanning Electron Microscopy - ESEM, diamond stylus and optical profilometer) can be used in most of the case only for the dry surfaces. There are a restricted number of methods, which can be applied for the investigation of surfaces immersed into a liquid (like Atomic Force Microscopy AFM with a special liquid cell). The optical method described in this paper can provide information on the optical roughness (contrary to the mechanical roughness obtained from AFM profilometer) and reflectance of the surfaces immersed into a liquid. This method can be thus used for the study of the interactions of the molecules dissolved in the liquid with the surface. Previously we have applied diffractive optical element (DOE) based sensor for inspection of different type of bulk and fragile materials , and later the same principle is applied to investigate quality of electrode surface used in electrochemistry [16, 17].
In this paper we report results from our recent DOE sensor investigations concerning the organisation of biopolymers as human blood plasma fibrinogen adhered on polished, on chemically etched titanium surfaces, and on titanium carbide coatings. The titanium carbide coated surfaces were realized by using plasma-enhanced chemical vapour deposition (PECVD) method [18, 19, 20]. The data is gained by using the DOE sensor through optical window of a cuvette to sense permittivity change and fluctuation in optical roughness (R opt) of treated titanium surface, when the surface is subjected to the absorption of the ions of electrolyte without and with HPF molecules on these treated surfaces.
2.1. A diffractive optic sensor setup
In the DOE sensor measurements we investigated the permittivity change and fluctuation in optical roughness R opt of polished, polished and chemically etched titanium surfaces, and surfaces with titanium carbide coatings (denoted by complex refractive index N 4) in the presence of buffer (N 2) without and with HPF molecules (N 3) (see Fig. 1). The DOE sensor utilizes expanded and focused laser beam (λ=632.8nm) realized by using the lens system L1–L2 to hit treated titanium surface N 4 locating in liquid of cuvette via beam splitter BS and cuvette window N 1.
Backscattered laser light is directed by using BS on DOE aperture, which analyzes if the wavefront is distorted by adsorbed HPF molecules denoted by N 3 from buffer N 2 on treated Ti surface. Distorted 4×4 light spot DOE image is grabbed from two-dimensional (2D) photo-array of the charge coupled device (CCD) and analyzed by using a personal computer (PC). The DOE sensor utilizes non-coherent response for permittivity changes and coherent response for R opt changes, which relate to surface roughness R a .
2.2. Non-coherent response of DOE sensor
Although the DOE sensor principle and procedure is described in the reference 15 and in the chapter 8 of the reference 27, we show how the reflectance of normal incidence from the treated Ti interface depends both on n and κ if the interface is immersed in the electrolyte solution (Fig. 2). The complex permittivity ε and complex refractive index Nnκ=n-iκ is assumed to relate to each other as follows ε=ε′+iε″=(n-iκ)2, where ε′=n 2+κ 2,ε″=2nκ. The loss angle δ denotes the relation tan(δ)=ε″/ε′. The reflectance R is calculated from the relation R=|(1-Nnκ)/(1+Nnκ)|2. Next we demonstrate how to utilize the pseudo-dielectric function shown in Fig. 2 to draw out information from a treated Ti interface. In Fig. 2 is also shown a locus of contour line, which is now an example projection of a contour line from the reflectance surface on the level of . The locus of reflectance value of 0.30 includes also the Ti0.82-C0.18 reflectance at the complex refractive index at 632.8 nm. The origin of the radius of the curvature of the projected circular locus locates on the n-axis. When the adsorption of HPF molecules from background electrolyte on the Ti0.82-C0.18 surface starts, the reflectance from that interface will also change. This will change the curvature and the origin of the projected locus.
By sensing the reflectance value by the DOE sensor at single wavelength (632.8nm) it is possible to gain information to plot the reflectance contour line and project it into (n, κ) -plane to be CLx. The data for the reflectance value is captured by using the 2D photo array of the CCD camera from the DOE image window, which locates at the focal plane of DOE element and is shown in the inset including the 4×4 light spot matrix of Fig. 1. The image window shown in the inset of Fig. 1 includes the non-coherent and coherent image portions. The non-coherent image portion appears outside the 4×4 light spot matrix whereas the coherent components perform the spots. The reflectance value is calculated from the non-coherent irradiance INC by utilizing Eq. (1) as follows
where nw and mw are the dimensions of the DOE image window and is the image irradiance observed by the (iw, jw)th element of the CCD camera array. To be sure that the irradiance of peaks (coherent response) do not make any uncertainties, the irradiance portion of peaks denoted by subscript pk are subtracted from the total irradiance of that DOE image. Here we point out that the non-coherent response obeys the following procedure for each pixel INC=∑|Aj|2, where Aj=Aojexp(iϕj) is the jth complex wavefront amplitude, i denotes the imaginary unit and ϕj=2πrj/λj is the respective phase angle, where rj is the optical path and λ is the wavelength used.
To find out the changes in n and κ values really caused by the HPF adsorption from electrolyte solution on treated Ti surface, we measured first the fluctuations in optical density (OD) respecting the optical path length (OPL), which is used in our DOE experiments. The OD value respecting the wavelength of 632.8 nm was observed to be negligible being 0.004±0.001, which respects the accuracy limit of the spectrophotometer used in the measurements. On the other hand, basing on the data reported in the literature, optical properties of soft-tissue  as well as HPF molecules [23, 24] do not have strong absorption anomalies in the visible VIS regime, which may in turn if the absorption anomalies are strong affect changes in extinction coefficient κ according to Kramers-Kronig relation [25, 26]. Mainly however the strong absorption appears in ultraviolet UV regime [23, 24]. In the final detection of the changes in n and κ values of Nx caused by the molecules attached on the Titreat surface we made projection from located on via it’s curvature origin onto CLx just compensating the shift of the curvature origin of .
2.3. Coherent response of DOE sensor
To sense the thickness of the adsorbed portion on treated titanium surface immersed background electrolyte in the absence or presence of HPF molecules we utilize the coherence response of DOE sensor. The data to calculate the thickness of adsorbed layer on treated titanium surfaces is calculated utilizing the captured DOE image data of the 4×4 light spot matrix as already described in the section 2.2. To calculate the irradiance of the peaks we utilize Eq. (2) as follows
where npk and mpk are the dimensions of each 16 peaks in DOE image and is the image irradiance observed by the (ipk, jpk)th element of the peak in DOE image captured by CCD camera. Caused by the fact that DOE aperture consist of 16 different diffractive lenses obeying coherent response for each pixel as follows IC=|∑Aj|2, which satisfies the principle of compact and phase sensitive interferometer. Moreover the DOE images the 4×4 light spot matrix in its focal plane. If the reconstructing wavefront do not satisfy the terms of hologram imaginary, the spot image matrix do not appear in the image plane. The same holds e.g. for the case, where the radiant exitance from the laser resonator in TEM00 mode start to suffer from appearance of side modes, and DOE will spatially filter out those images from its original 4×4 light spot image. After tedious numerical simulations it is showed that the irradiance of the 4×4 spots will decrease as a function of OPL and disappears when the OPL exceeds λ/4. This response is published and appears in the Fig. 8.21(b) of the reference . It is also observed that this response resembles the response of Beckmann-Spizzichino model . To consider the thickness of the adsorbed portion on treated titanium surface immersed background electrolyte in the absence or presence of HPF molecules we first measure the irradiance of the peaks and after that the optical path difference Δr, which is also understood as an optical roughness (R opt), is solved inversely by utilizing this response. In our previous measurements we have noted that the accuracy of 0.2nm can be achieved by using this one arm interferometric technique . The similar accuracy limits is also reported recently for the coupling dynamics of lasers of self-mixing interferometers in vibrometer applications ranging from 0.1 nm to 100µm , whereas the accuracy of conventional two arm interferometers used in optical diagnostics of random phase objects  as well as in optical diagnostics of rough surfaces  are estimated to be ~0.005µm, which is not reasonable for sensing of adsorption of HPF molecules on treated titanium surface.
2.4. DOE sensor and ellipsometric measurements of treated titanium surfaces
In the experiments six different types of treatments for titanium were used as follows: polishing, polishing and chemical etching with surface material loss of 0.03mm, and plasma-enhanced chemical vapour deposition (PECVD) method to produce titanium carbide surfaces with four different concentrations of carbon: Ti0.82-C0.18; Ti0.38-C0.62; Ti0.09-C0.91 and Ti0.00-C1.00 (diamond). The experiments were repeated three times for each treated titanium surfaces immersed in water and in background electrolyte without and with HPF molecules.
The thickness of titanium oxide layer was measured to be down 220 nm of the polished, and polished and chemically etched titanium surface. The thickness of Tix-C1-x coatings produced by using plasma-enhanced chemical vapour deposition (PECVD) were ranged from 2.5µm–3.5µm, which is thick enough in optical sense to consider it as solid bulk layer .
In the begin of all measurements the DOE sensor images for reference signal level from test surface were made in water for 100 seconds, and during that time frame 1000 reference samples were grabbed. After that the water was removed by syringe from cuvette and the buffer solution, in turn, was injected in the cuvette. Immediately after injection of buffer, grabbing of the DOE images was started, and the image grabbing was repeated after two minutes interval. Before HPF measurement, the cuvette was washed, and after washing the new treated titanium sample was installed in the sample holder inside the cuvette. The water was injected in the cuvette, and the DOE image references from the new sample surface were taken. Before adding the HPF solution in the cuvette, the immersion water was removed, and grabbing process of DOE images was started. The image grabbing was repeated two times consecutively after two minutes interval. The diameter of the laser beam waist on the all surfaces was 1mm.
Immediately after the DOE sensor measurements in buffer and HPF solutions the samples were subjected for ellipsometric measurements, which were made during a half hour time frame (in room temperature) when surface sample is taken out from the solution. The measurements were performed by using Woollam spectroellipsometer working in the wavelength range from 200nm to 1700nm. The ellipsometric measurements were performed in aim to gain information about the adsorbability and compare the values caused by the adsorption of the ions of electrolyte without and with HPF molecules on the Titreat surface already drawn out by the DOE sensor. The corroborative ellipsometric measurements were performed at the incidence angle of 75° for probe beam to avoid the harmful effects caused by the possible appearance of surface roughness [33, 34]. Here we measured the complex refractive index Nnκ of each treated titanium surfaces (polished, chemically etched and titanium carbide surfaces) used in our experiments in dry environment. We point out that it is also possible to measure complex refractive index values from the interface of treated titanium with adsorbed short molecules in dry environment, and calculate the effective thickness value of adsorbed molecule volume from the extinction coefficient κ obtained by ellipsometric measurement. However, in the case of HPF molecules, which are long molecules, the strong scattering of light will disturb the determination of thickness of the absorbed HPF molecule volume on treated titanium surface in dry environment.
Human plasma fibrinogen (HPF), fraction I, type III was purchased from Sigma. In all experiments the HPF was dissolved in phosphate buffer solution (PBS) +0.136 M sodium citrate, which serve as a background electrolyte at a concentration of 500 nM. Measurements were performed at room temperature.
3. Results and discussion
In Fig. 3 are shown six respective reflectance bar sets from the polished titanium, from the polished and chemically etched titanium and from the four titanium carbide Tix-C1-x surfaces immersed in background electrolyte without and with HPF molecules. The mutual concentrations of titanium and carbon are consecutively from left to right as follows: Ti0.82-C0.18, Ti0.38-C0.62, Ti0.09-C0.91 and Ti0.00-C1.00, which respects the diamond structure of carbon.
The responses were calculated from the n and κ data (at 632.8nm) sensed with the aid of the DOE sensor and corroboratively by using ellipsometry. The DOE sensing was performed in cuvette, which procedure respects the n and κ sensing in wet environment and the ellipsometric measurements were drawn out after DOE measurements in air respecting the sensing in dry environment. The reflectance responses show decreasing tendency in treated titanium surfaces from NIF=1 to NIF=5, whereas diamond surface (NIF=6) makes exception from the decreasing evolution of reflectance. The attachment of electrolyte fractions on the treated titanium surfaces seems to have insignificant influences to the reflectance. In R DOE responses the attachment of HPF molecules from electrolyte has extra decreasing influences to reflectance, whereas in R EM reflectance performed by ellipsometry this trend is even higher when the carbon concentration in titanium exceeds 18 per cent. The strong decrease in R EM reflectance is believed to be caused from the higher scattering of light from HPF molecules in air than in electrolyte solution, where the refractive index matching is more dominate than in air.
Thereafter we compared the optical roughness R opt values measured by DOE sensor as a function of time from the treated titanium surface - electrolyte interface in the absence or presence of HPF molecules. The threshold of optical roughness of the treated titanium surface was cancelled out by measuring the base line of R opt in distilled water, which refractive index (n=1.3334) was close to electrolyte . As an example we present here two temporal responses for the optical roughness R opt responses from a polished titanium surface in background electrolyte with the presence of HPF molecules (Fig. 4(a)), and respectively from a titanium carbide (Fig. 4(b)).
The temporal response from polished titanium surface in background electrolyte (t 1=0-100s) shows almost two times higher R opt level than that from titanium carbide surface (Ti0.38-C0.62) as also shown in Table 1. When the polished titanium is immersed in electrolyte with HPF molecules, the R opt levels show rather strong fluctuation as a function of time (Fig. 4(a)). The temporal increase of R opt, which is greater than average of R opt from the base of polished titanium surface in background electrolyte, indicates that the HPF molecules are attaching to the polished titanium surface but temporally the R opt become lower than the average of R opt of polished titanium surface in background electrolyte, which may indicate that the molecule volume get unstuck from the surface as a consequence of the appearance of huge amount of nanobubbles . For the appearance of huge amount of nanobubbles the DOE sensor will sense the decrease of optical roughness less than the average of R opt obtained from treated titanium surfaces in background electrolyte. The R opt values from (Ti0.38-C0.62) surface in background electrolyte with HPF molecules indicate that the HPF molecules are attaching to the titanium carbide surface but the molecule volume do not get unstuck from the surface, only some remodelling in molecule volume appears as a function of time (Fig. 4(b)). The severity of the attachments of fractions on treated titanium surfaces in background electrolyte in the absence or presence of HPF molecules was estimated from the six R opt bar sets from the polished titanium, from the polished and chemically etched titanium and from the four titanium carbide Tix-C1-x surfaces (Fig. 5).
The estimates were performed by comparing the differences of the average R opt values with their standard deviations from surfaces in background electrolyte in the absence or presence of HPF molecules.
From Fig. 5 we can observe that the averaged R opt values in background electrolyte in the absence or presence of HPF molecules falls inside the limits of standard deviations in polished titanium (NIF=1), in titanium carbide Ti0.82-C0.18 surface (NIF=3) and in diamond (NIF=6) surface, and thus do not differ significantly. This can be understood to implicate weak attachments of the HPF molecules on polished titanium, on Ti0.82-C0.18 surface and on diamond surfaces, whereas the polished and chemically etched (with 0.03mm material loss) (NIF=2) surface and titanium carbide (NIF=4-5) surfaces indicate strong attachments of the HPF molecules on their surfaces. It is quite interesting that the HPF adsorption at the titanium carbide surface depends on the mutual concentration of titanium and carbon. The HPF adsorption is weak at low (sample NIF=3) or high (“diamont like” sample NIF=6) carbon concentrations.
In the progress of this work we noted that the DOE sensor is effective in sensing of permittivity changes, which bear also information from temporal fluctuations of optical roughness R opt of treated titanium surface, when the HPF molecules modify the surface in wet environment. The reflectance results related to permittivity changes are also in accordance with the ellipsometer results, which are gained from the same surfaces in dry environment. Moreover, the observation of the magnitude of temporal R opt evolution, which relates to the porosity of the molecule layer or volume revealed information from the dynamic processes of organization of the molecules on the biomaterial surface. Optical roughness measurements have shown that the surface treatment of titanium affect the adsorption of HPF molecules. HPF is best adsorbed at the polished and chemically etched titanium as well as at the titanium carbide surfaces Ti0.38-C0.62 and Ti0.09-C0.91.
This work was supported by the Ministry of Education and Sport of the Czech Republic (1M0528 to J. V.), the Academy of Sciences of the Czech Republic (KAN200040651 to S. H.), the grant agency of the Czech Republic (202/08/1688 to V. V.), the Ministry of Education of the Czech Republic (LC06035), and by an institutional research plan (AVOZ 50040507, AVOZ 50040702).
References and links
1. B. Walivaara, B. O. Aronsson, M. Rodahl, J. Lausmaa, and P. Tengvall, “Titanum with different oxides-in-vitro studies of protein adsorption and contact activation,” Biomaterials 15, 827–834 (1994). [CrossRef] [PubMed]
2. M. I. Jones, I. R. McColl, D. M. Grant, K. G. Parker, and T. L. Parker, “Protein adsorption and platelet attachment and activation, on TiN, TiC, and DLC coatings on titanium for cardiovascular applications,” J. Biomed. Mater. Res. 52, 413–421 (2000). [CrossRef] [PubMed]
3. N. Juany, P. Yang, Y. X. Leng, J. Y. Chen, H. Sun, J. Wang, G. J. Wang, P. D. Ding, T. F. Xi, and Y. Leng, “Hemocompatibility of titanium oxide films,” Biomaterials 24, 2177–2187 (2003). [CrossRef]
4. F. Hook, J. Voros, M. Rodahl, R. Kurrat, P. Boni, J. J. Ramsden, M. Textor, N. D. Spenser, P. Tengvall, J. Gold, and B. Kasemo, “A comparative study of protein adsorption on titanium oxide surfaces using in situ ellipsometry, optical waveguide lightmode spectroscopy, and quartz crystal microbalance/dissipation,” Colloid Surf. B 24, 155–170 (2002). [CrossRef]
8. E. Jansoon and P. Tengvall, “Adsorption of albumin and IgG to porous and smooth titanium,” Colloid Surf. B 35, 45–51 (2004). [CrossRef]
9. P. Cacciafesta, A. D. L. Humphris, K. D. Jandt, and M. J. Miles, “Human Plasma Fibrinogen Adsorption on Ultraflat Titanium Oxide Surfaces Studied with Atomic Force Microscopy,” Langmuir 16, 8167–8175 (2000). [CrossRef]
10. P. Cacciafesta, K. R. Hallam, A. C. Watkinson, G. C. Allen, M. J. Miles, and K. D. Jandt, “Visualisation of human plasma fibrinogen adsorbed on titanium implant surfaces with different roughness,” Surf. Sci. 491, 405–420 (2001). [CrossRef]
11. H. Nygren, P. Tengvall, and I. Lundstrom, “The initial reactions of TiO2 with blood,” J. Biomater. Res. 34, 487–492 (1997). [CrossRef]
12. S. Kidoaki and T. Matsuda, “Adhesion forces of the blood plasma proteins on self-assembled monolayer surfaces of alkanethiolates with different functional groups measured by an Atomic Force Microscope,” Langmuir 15, 7639–7646 (1999). [CrossRef]
13. A. G. Hemmersam, M. Foss, J. Chevallier, and F. Besenbacher, “Adsorption of fibrinogen on tantalum oxide, titanium oxide and gold studied by the QCM-D technique,” Colloid Surf. B 43, 208–215 (2005). [CrossRef]
14. M. Rouahi, E. Champion, O. Gallet, A. Jada, and K. Anselme, “Physico-chemical characteristics and protein adsorption potential of hydroxyapatite particles: Influence on in vitro biocompatibility of ceramics after sintering,” Colloid Surf. B 47, 10–19 (2006). [CrossRef]
15. R. Silvennoinen, K.-E. Peiponen, and T. Asakura, “Diffractive optical elements in materials inspection”: in T. Asakura (ed.) The International Trends in Optics and Photonics ICO IV, Part VI Optical Metrology (Optical Systems), pp. 281–293 (Springer-Verlag, Berlin Heidelberg, 1999).
16. S. Hason, S.-P. Simonaho, R. Silvennoinen, and V. Vetterl, “On the adsorption and kinetics of phase transients of adenosine at the different carbon electrodes modified with a mercury layer,” Electrochim. Acta 48, 651–668 (2003). [CrossRef]
17. S. Hason, S.-P. Simonaho, R. Silvennoinen, and V. Vetterl, “Detection of phase transients in two-dimensional adlayers of adenosine at the solid amalgam electrode surfaces,” J. Electroanal. Chem. 568(1), 65–77 (2004). [CrossRef]
18. Y. L. Su and W. H. Kao, “Tribological behaviour and wear mechanisms of Ti-C:H/TiC/TiCN/TiN/Ti coatings when sliding against steel, bronze and alumium alloy rods” J. Mater. Sci. 36, 189–199 (2001). [CrossRef]
19. V. Kulikovsky, A. Kuzmichev, P. Bohaca, Z. Hubicka, K. Jurek, and L. Jastrabik, “Composition of Ti-C:H films obtained by pulsed and continuous magnetron sputtering,” Surf. Coat. Technol. 200, 620–624 (2005). [CrossRef]
20. T. Vitu, T. Polcar, L. Cvrcek, R. Novak, J. Vyskocil, and A. Cavaleiro, “Structure and Tribology of Biocompatible Ti-C:H Coatings,” Surf. Coat. Technol. (in press).
21. J. Räsänen, M. Savolainen, R. Silvennoinen, and K. E. Peiponen, “Optical sensing of surface roughness and waviness by computer generated hologram,” Opt. Eng. 34, 2574–2580 (1995). [CrossRef]
23. W. W. Layne, D. J. Hnatowich, P. W. Doherty, R. L. Childs, D. Lanteigne, and J. Ansell, “Evaluation of the Viability of In-111-Labeled DTPA Coupled to Fibrinogen,” J. Nucl. Med. 23, 627–630 (1982). [PubMed]
24. S. N. Roy, R. Procyk, B. J. Kudryk, and C. M. Redman, “Assembly and Secretion of Recombinant Human Fibrinogen,” J. Biol. Chem. 266, 4758–4763 (1991). [PubMed]
25. H. A. Kramers, “Some remarks on the theory of absorption and refraction of x-rays,” Nature 117, 775–778 (1926).
26. V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. Vartiainen, Kramers-Kronig Relations in Optical Materials Research, (Springer, Berlin, 2005).
27. R. Silvennoinen, K.-E. Peiponen, and K. Myller, Specular gloss (Elsevier, Amsterdam, 2007).
28. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surface, (Pergamon Press, Oxford, 1963).
29. R. Silvennoinen, S. Hason, and V. Vetterl, “Organization of nano-scale synthetic oligonugloetides on immersed electrode surface: an optical study,” Technical digest of the Seventh Finnish-Japanese Joint Symposium on Optics in Engineering, K.-E. Peiponen, R. Hernberg, and T. Yatagai eds., (8–10 August, Tampere, Finland, 2007), pp. 101–102.
30. S. Donati, “Coupling dynamics in lasers and applications in self-mixing interferometry,” Summaries of the 2nd International Meeting on Optical Sensing and Artificial Vision (OSAV’2008), p. 67, 2008.
32. O. V. Angelsky, A. P. Maksimyak, P. P. Maksimyak, and S. G. Hanson, “Optical correlation diagnostics of rough surfaces with large surface inhomogeneities,” Opt. Express 14, 7299–7311 (2006). [CrossRef] [PubMed]
33. R. A. M. Azzam and N. M. Bashra, Ellipsometry and Polarized Light, (North-Holland, Amsterdam, 1977).
34. S.-M. F. Nee and T.-W. Nee, “Principal Mueller matrix of reflection and scattering measured for a one-dimensional rough surface,” Opt. Eng. 41, 994–1001 (2002). [CrossRef]
35. X. H. Zhang, A. Quinn, and W. A. Ducker, “Nanobubbles at the Interface between Water and a Hydrophobic Solid,” Langmuir, ASAP Article; DOI: 10.1021/la703475q (2008). [PubMed]