Chromatic second harmonic imaging

doi:10.1364/OE.18.023837

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Chromatic second harmonic imaging

Chuan Yang, Kebin Shi, Haifeng Li, Qian Xu, Venkatraman Gopalan, and Zhiwen Liu »View Author Affiliations

Optics Express, Vol. 18, Issue 23, pp. 23837-23843 (2010)
http://dx.doi.org/10.1364/OE.18.023837

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– Abstract
1. Introduction
2. Experimental results
3. Discussion and conclusion
– References and links

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Abstract

We report a non-axial-scanning second harmonic imaging technique, in which the chromatic aberration of a Fresnel lens is exploited to focus different wavelengths of a fundamental beam into different axial positions to effectively realize axial scanning. Since the second harmonic signals at different axial positions are generated by different fundamental wavelengths and hence accordingly have different center wavelengths, they can be resolved and detected in parallel by using a spectrometer without axial mechanical scanning. We have demonstrated a system capable of achieving about 8 μm effective axial scanning range. Proof-of-concept imaging results are also presented.

1. Introduction

The merging of nonlinear optics and microscopy has created new paradigms for optical imaging. Laser-scanning second harmonic generation (SHG) imaging [1

J. N. Gannaway and C. J. R. Sheppard, “Second-harmonic imaging in the scanning optical microscope,” Opt. Quantum Electron. 10(5), 435–439 (1978). [CrossRef]

–5

E. Brown, T. McKee, E. diTomaso, A. Pluen, B. Seed, Y. Boucher, and R. K. Jain, “Dynamic imaging of collagen and its modulation in tumors in vivo using second-harmonic generation,” Nat. Med. 9(6), 796–801 (2003). [CrossRef] [PubMed]

], amongst an array of emerging nonlinear optical imaging modalities, has been extensively investigated in recent times. SHG imaging is unique in that it utilizes the second order nonlinear susceptibility χ⁽²⁾ as an imaging contrast mechanism. It can be used to image samples possessing second order nonlinearity, or the surfaces of specimens with inversion symmetry in which χ⁽²⁾ vanishes in bulk (under electric dipole approximation) [6

R. W. Boyd, Nonlinear Optics (Elsevier, San Diego, CA, 2003).

]. Some significant advantages of SHG imaging include no photobleaching effect, which is a major limitation of fluorescence microscopy (one- or multi-photon excitation [7

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990). [CrossRef] [PubMed]

]), non-blinking steady signal, inherent optical sectioning ability, and minimum photodamage [8

Wikipedia, http://en.wikipedia.org/wiki/Second_harmonic_imaging_microscopy.

C. L. Hsieh, R. Grange, Y. Pu, and D. Psaltis, “Three-dimensional harmonic holographic microcopy using nanoparticles as probes for cell imaging,” Opt. Express 17(4), 2880–2891 (2009). [CrossRef] [PubMed]

]. Despite all these advantages, conventional SHG imaging requires three-dimensional (3D) point-by-point scanning, which can significantly limit the 3D or the x-z and y-z (x, y: lateral directions; z: axial direction) cross-section imaging speed. To address this challenge, here we explore a chromatic SHG imaging technique, which can eliminate mechanical axial scanning by exploiting the chromatic aberration of the Fresnel lens.

The chromatic scanning technique was previously applied to epi-reflection confocal microscopy [10

G. Molesini, G. Pedrini, P. Poggi, and F. Quercioli, “Focus-wavelength encoded optical profilometer,” Opt. Commun. 49(4), 229–233 (1984). [CrossRef]

–13

K. Shi, S. H. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun. 263(2), 156–162 (2006). [CrossRef]

]. Our group has recently extended it to two-photon fluorescence imaging [14

Q. Xu, K. Shi, S. Yin, and Z. Liu, “Chromatic two-photon excitation fluorescence imaging,” J. Microsc. 235(1), 79–83 (2009). [CrossRef] [PubMed]

,15

K. Shi, S. Yin, and Z. Liu, “Wavelength division scanning for two-photon excitation fluorescence imaging,” J. Microsc. 223(2), 83–87 (2006). [CrossRef] [PubMed]

]. To illustrate the underlying principle, let us consider focusing a pulsed fundamental beam by a Fresnel lens. The focal length F of the Fresnel lens is a function of wavelength and satisfies the relationship [16

F. T. S. Yu, Introduction to diffraction, information processing, and holography (MIT Press, Cambridge, MA, 1973).

,17

K. Shi, Supercontinuum imaging and spectroscopy, Penn State Doctoral Dissertation (2007).

]

λ F = λ_{0} F_{0}

(1)

where the λ₀ and F₀ stand for design wavelength and the corresponding design focal length. Consequently, the different wavelength components of the incoming pulse are focused to different axial positions with the shorter wavelength further away from the Fresnel lens. Axial scanning is therefore effectively realized through the chromatic aberration of the Fresnel lens. The focused and chromatically aberrated beam can then be relayed through imaging optics to achieve desired lateral and axial resolutions, and produce second harmonic signal if interacting with a specimen of interest with a non-vanishing χ⁽²⁾. Notice that the SHG signals at different axial positions are generated by different fundamental wavelengths and as a result must have accordingly different wavelengths. A spectroscopic measurement can then resolve the signals (or raw pixel values) generated at different axial positions. In other words, axial imaging can be achieved in parallel without mechanical axial scanning, and 3D images can be obtained by scanning the chromatically aberrated fundamental beam (or the specimen) only in two lateral directions. It should be noted that there is a trade-off between the chromatic scanning range and the required pulse energy. In general, the larger the chromatic aberration the more pulse energy is needed to yield the same signal strength.

2. Experimental results

The schematic diagram of our experimental setup is shown in Fig. 1 . It is similar to that used in our prior chromatic two-photon imaging work. Briefly, femtosecond laser pulses from a Ti:Sapphire mode-locked laser (KMLabs, pulse width ~50 fs, repetition rate ~100 MHz, center wavelength ~820 nm) were delivered to our experimental system through a 40-cm-long photonic crystal fiber (Thorlabs, ESM-12-01). The fiber output was collimated by an objective (20 × , numerical aperture NA 0.4) and subsequently expanded with an imaging system consisting of two lenses with focal lengths of 75.6 mm and 250 mm respectively. A Fresnel lens (design wavelength: λ₀ = 821 nm, design focal length: f₀ = 100 mm) was then utilized to focus the beam. As aforementioned, due to the chromatic aberration different wavelengths of the laser beam were focused to different axial positions, effectively realizing axial scanning. To achieve desired axial and lateral resolutions, the beam was re-collimated by a lens (focal length: 38.1 mm), reflected by a dichroic mirror (Thorlabs DMLP505), and focused by an objective lens (60 × , NA 0.85) onto a sample. The second harmonic signal generated in the sample was then collected in the forward direction by another objective lens (20 × , NA 0.4). After passing through a band-pass filter (Chroma Tech. 405/40BP), which was used to eliminate the fundamental beam, the second harmonic signal was coupled into a five-meter-long multimode fiber. Finally, the output signal from the multimode fiber was detected by a spectrometer (PI/Acton SpectraPro 2500 with a liquid nitrogen cooled charge coupled device detector PI/Acton Spec-10).

Fig. 1 Schematic diagram of the chromatic second harmonic imaging system.

We characterized the effective chromatic scanning range of the system. To this end, we air-dried a thin layer of BaTiO₃ nanocrystal (Nanostructured & Amorphous Materials Inc., Average Particle Size: 200nm, Morphology: Spherical) solution (suspended in water) on a microscope cover slide (VWR Micro Cover Glass). A single cluster of nanocrystals (c.f., the microscope image shown in Fig. 2(a) inset) was identified and placed near the focal plane of the objective L₂ (c.f., Fig. 1) as a second harmonic probe. The cover glass and hence the nanocrystal cluster was scanned vertically by using a computer-controlled motorized translational stage. The generated second harmonic signal was then collected and coupled into a five-meter-long multimode fiber, and detected by the spectrometer. Figure 2 shows our measured results. Each row of the figure represents a spectrum of the second harmonic signal generated by the BaTiO₃ nanocrystal cluster placed at a corresponding axial position as indicated in the vertical axis. As the nanocrystal was moved away from the objective, the center wavelength of the second harmonic signal shifted towards shorter wavelength, as expected from the focal length-wavelength relation of the Fresnel lens (c.f., Eq. (1). This clearly demonstrates the chromatic scanning behavior. An effective chromatic scanning range of about 8 μm in the sample plane is obtained. For each wavelength, we found the corresponding depth position that yielded the maximum second harmonic signal (i.e., where the fundamental wavelength is focused). The obtained depth position (z)-wavelength (λ) relationship is shown in Fig. 2(b), which can be fitted with a linear curve with a slope of about 1.1 µm/nm.

Fig. 2 (a) Second harmonic spectrum generated at different depth positions; A single cluster of nanocrystals (shown in the upper-left inset) was placed near the focal point of the objective lens L₂ (c.f. Fig. 1). A sequence of spectra of the generated second harmonic signal was measured as the nanocrystal cluster was mechanically scanned. (b) Mapping relationship between the depth position and the second harmonic signal wavelength; in the equation, λ represents the signal wavelength in nm while z is the depth position in µm.

To demonstrate the chromatic imaging capability, we utilized our system to image the surface of a LiNbO₃ crystal, which was purposely scratched by silicon carbide sandpaper. An optical microscope image of the crystal is shown in Fig. 3(a) , in which the region of interest (30 µm × 30 µm) is overlaid with a pseudo-color SHG image. Two-dimensional point-by-point lateral scanning of the crystal sample was performed with a scanning step of 1 µm by using computer-controlled translational stages (Newport ESP300 3-Axis Motion Controller with motorized actuator). At each point a second harmonic spectrum was recorded, from which the axial image information is obtained. Figure 3(b) shows a series of second harmonic images at wavelengths from 404 nm to 413 nm with an interval of 0.52 nm. The “X’ shaped grooves on the crystal surface can be observed. The vertical cross section of the grooves can be better visualized in Fig. 3(c), in which the x-λ (z) cross-section images at three different positions (i.e., y = 20 µm, 26 µm, and 30 µm respectively) are shown. It appears that the grooves are tilted with respect to the crystal surface, which is not unexpected considering that the surface was randomly scratched.

Fig. 3 (a) Microscope image of a LiNbO₃ crystal scratched by silicon carbide sandpaper showing an “X” shaped scratch on its surface (b) Chromatic second harmonic imaging results; the crystal was scanned in two lateral dimensions (30 μm × 30 μm). A series of second harmonic images at wavelengths from 404 nm to 413 nm with an interval of 0.52 nm were obtained and shown here. (c) Side cross-sectional imaging results; three images correspond to y = 20 μm, 26 μm, and 30 μm respectively.

In addition, we also imaged a LiNbO₃ microcrystal created by using the same scratching method. A microscope image of the microcrystal is shown in Fig. 4(a) . Similarly, a two-dimensional lateral scan of the sample over an area of 40 µm × 40 µm was performed. The obtained SHG images at wavelengths from 404.2 nm to 410.0 nm with an interval of 0.52 nm is shown in Fig. 4(b). Figure 4(c) shows three x-λ (z) cross-section images at y = 10 µm, 26 µm, and 28µm respectively. Although due to the limited axial scanning range and spatial resolutions the quality of these images needs further improvement, these preliminary proof-of-concept results have clearly demonstrated the 3D imaging capability of the chromatic SHG technique.

Fig. 4 (a) Microscope image of a LiNbO₃ micro-crystal; (b) Chromatic second harmonic imaging results; the sample was scanned in two lateral dimensions (40 μm × 40 μm). The second harmonic images correspond to wavelengths from 404.2 nm to 410.0nm with a step of 0.52 nm; (c) Side cross-sectional imaging results; three images correspond to y = 10 μm, 26 μm, and 28 μm respectively.

3. Discussion and conclusion

In the current work, a multimode fiber was used to collect the SHG signal and deliver it to the spectrometer. Since the second harmonic beam had large chromatic aberration and hence was launched into multiple spatial modes, significant amount of signal power was lost when coupled through the entrance slit of the spectrometer. To improve the overall SHG signal collection efficiency, here we propose a method to collimate the chromatically aberrated second harmonic beam by using chromatic material dispersion. Qualitatively, a shorter-wavelength SHG signal (corresponding to a shorter fundamental wavelength) is nearer to the collecting lens, which implies that the chromatic aberration of the collecting lens should be opposite to that of the Fresnel lens in order to collimate the second harmonic beam. Note that for a singlet lens, the focal length f is given by 1/f = (n − 1)(1/R₁ − 1/R₂) [18

E. Hecht, Optics (Addison Wesley, 2001). [PubMed]

] where n is the index of refraction and R₁ and R₂ are the radius of curvatures of the two facets. For lens material with normal dispersion, the shorter the wavelength the larger the index of refraction is (hence a shorter focal length). Therefore, chromatic material dispersion can compensate for the chromatic aberration produced by the Fresnel lens and result in a better-collimated second harmonic beam. Figure 5(a) shows a schematic diagram of such a chromatic SHG imaging system with improved collection efficiency. For simplicity we assume that lenses L₁ and L₄ are achromatic and have the same focal length, and so do lens L₂ and L₃ (c.f. Fig. 5(a)). Note that the change of focal length of the Fresnel lens as a function of wavelength satisfies

\frac{Δ F}{F} = - \frac{Δ λ_{f}}{λ_{0}} = - \frac{Δ λ_{S H G}}{λ_{0} / 2} = - \frac{Δ λ_{S H G}}{λ_{S H G}}

(2)

where λ₀ is the design wavelength (at fundamental frequency), and the subscript f and SHG stand for the fundamental and SHG wavelength respectively. On the other hand, for a singlet lens the change of focal length as a function of wavelength satisfies

\frac{Δ f}{f} = - \frac{Δ n}{(n - 1)}

(3)

To compensate for the chromatic aberration produced by the Fresnel lens, we require ΔF ≈ −Δf, which leads to

Fig. 5 (a) Schematic diagram of a chromatic SHG microscope with an improved signal collection efficiency (b) an example showing that the material dispersion of a singlet lens (Material: N-SF11 glass, f/F = 3.37) can potentially help improve the SHG signal collection efficiency; the blue curve shows negative of the term on the right hand side of Eq. (4) as a function of the second harmonic wavelength while the green curve shows the term on the left hand side of Eq. (4); the red curve shows the sum of the two.

\frac{f}{F} \frac{Δ n}{(n - 1)} \approx - \frac{Δ λ_{S H G}}{λ_{S H G}}

(4)

The chromatic aberration can be largely compensated in the example shown in Fig. 5(b) if the lens material is N-SF11 [19

S. C. H. O. T. T. Optical Glass Data Sheets, (2010). http://www.us.schott.com/advanced_optics/english/download/schott_optical_glass_june_2010_us.pdf?PHPSESSID=cf27dsjed4tvup6riaj7up87k4.

] glass and a ratio f/F = 3.37 is chosen. One can also use other highly dispersive lens materials and adjust the focal lengths of the two pairs of objectives to optimize the system design.

In summary, we have investigated the feasibility of chromatic second harmonic imaging, in which mechanical axial scanning is eliminated by utilizing the chromatic aberration caused by a Fresnel lens. In our proof-of-concept experiment, an approximately 8μm effective chromatic scanning range (measured in the air) has been achieved. It should be noted that the chromatic scanning range inside a medium differs from that in the air. One can utilize a second harmonic probe buried inside the medium to directly calibrate the system or calculate it from the wavelength-depth mapping relationship measured in the air (e.g., the scanning range in the medium is scaled by the average refractive index). We believe that this new technique has the potential to significantly improve the speed of SHG imaging and therefore useful for real-time applications such as monitoring dynamic biological processes in three dimensions.

Acknowledgement:

This work is supported by the National Science Foundation (Award# DBI0649866, ECCS0547475, DMR-0820404 and DMR-0908718). The Fresnel lens used in our experiments was acquired through the OIDA Photonics Technology Access Program sponsored by the National Science Foundation and the Defense Advanced Research Projects Agency.

References and links

1.	J. N. Gannaway and C. J. R. Sheppard, “Second-harmonic imaging in the scanning optical microscope,” Opt. Quantum Electron. 10(5), 435–439 (1978). [CrossRef]
2.	L. Moreaux, O. Sandre, and J. Mertz, “Membrane imaging by second-harmonic generation microscopy,” J. Opt. Soc. Am. B 17(10), 1685–1694 (2000). [CrossRef]
3.	P. J. Campagnola and L. M. Loew, “Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms,” Nat. Biotechnol. 21(11), 1356–1360 (2003). [CrossRef] [PubMed]
4.	W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100(12), 7075–7080 (2003). [CrossRef] [PubMed]
5.	E. Brown, T. McKee, E. diTomaso, A. Pluen, B. Seed, Y. Boucher, and R. K. Jain, “Dynamic imaging of collagen and its modulation in tumors in vivo using second-harmonic generation,” Nat. Med. 9(6), 796–801 (2003). [CrossRef] [PubMed]
6.	R. W. Boyd, Nonlinear Optics (Elsevier, San Diego, CA, 2003).
7.	W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990). [CrossRef] [PubMed]
8.	Wikipedia, http://en.wikipedia.org/wiki/Second_harmonic_imaging_microscopy.
9.	C. L. Hsieh, R. Grange, Y. Pu, and D. Psaltis, “Three-dimensional harmonic holographic microcopy using nanoparticles as probes for cell imaging,” Opt. Express 17(4), 2880–2891 (2009). [CrossRef] [PubMed]
10.	G. Molesini, G. Pedrini, P. Poggi, and F. Quercioli, “Focus-wavelength encoded optical profilometer,” Opt. Commun. 49(4), 229–233 (1984). [CrossRef]
11.	S. L. Dobson, P. C. Sun, and Y. Fainman, “Diffractive lenses for chromatic confocal imaging,” Appl. Opt. 36(20), 4744–4748 (1997). [CrossRef] [PubMed]
12.	K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic confocal microscopy using supercontinuum light,” Opt. Express 12(10), 2096–2101 (2004). [CrossRef] [PubMed]
13.	K. Shi, S. H. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun. 263(2), 156–162 (2006). [CrossRef]
14.	Q. Xu, K. Shi, S. Yin, and Z. Liu, “Chromatic two-photon excitation fluorescence imaging,” J. Microsc. 235(1), 79–83 (2009). [CrossRef] [PubMed]
15.	K. Shi, S. Yin, and Z. Liu, “Wavelength division scanning for two-photon excitation fluorescence imaging,” J. Microsc. 223(2), 83–87 (2006). [CrossRef] [PubMed]
16.	F. T. S. Yu, Introduction to diffraction, information processing, and holography (MIT Press, Cambridge, MA, 1973).
17.	K. Shi, Supercontinuum imaging and spectroscopy, Penn State Doctoral Dissertation (2007).
18.	E. Hecht, Optics (Addison Wesley, 2001). [PubMed]
19.	S. C. H. O. T. T. Optical Glass Data Sheets, (2010). http://www.us.schott.com/advanced_optics/english/download/schott_optical_glass_june_2010_us.pdf?PHPSESSID=cf27dsjed4tvup6riaj7up87k4.

OCIS Codes
(080.3630) Geometric optics : Lenses
(110.6880) Imaging systems : Three-dimensional image acquisition
(160.4330) Materials : Nonlinear optical materials
(180.6900) Microscopy : Three-dimensional microscopy
(190.2620) Nonlinear optics : Harmonic generation and mixing

ToC Category:
Imaging Systems

History
Original Manuscript: August 4, 2010
Revised Manuscript: September 24, 2010
Manuscript Accepted: October 16, 2010
Published: October 27, 2010

Virtual Issues
Vol. 6, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Chuan Yang, Kebin Shi, Haifeng Li, Qian Xu, Venkatraman Gopalan, and Zhiwen Liu, "Chromatic second harmonic imaging," Opt. Express 18, 23837-23843 (2010)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-23-23837

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References

J. N. Gannaway and C. J. R. Sheppard, “Second-harmonic imaging in the scanning optical microscope,” Opt. Quantum Electron. 10(5), 435–439 (1978). [CrossRef]
L. Moreaux, O. Sandre, and J. Mertz, “Membrane imaging by second-harmonic generation microscopy,” J. Opt. Soc. Am. B 17(10), 1685–1694 (2000). [CrossRef]
P. J. Campagnola and L. M. Loew, “Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms,” Nat. Biotechnol. 21(11), 1356–1360 (2003). [CrossRef] [PubMed]
W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100(12), 7075–7080 (2003). [CrossRef] [PubMed]
E. Brown, T. McKee, E. diTomaso, A. Pluen, B. Seed, Y. Boucher, and R. K. Jain, “Dynamic imaging of collagen and its modulation in tumors in vivo using second-harmonic generation,” Nat. Med. 9(6), 796–801 (2003). [CrossRef] [PubMed]
R. W. Boyd, Nonlinear Optics (Elsevier, San Diego, CA, 2003).
W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990). [CrossRef] [PubMed]
Wikipedia, http://en.wikipedia.org/wiki/Second_harmonic_imaging_microscopy .
C. L. Hsieh, R. Grange, Y. Pu, and D. Psaltis, “Three-dimensional harmonic holographic microcopy using nanoparticles as probes for cell imaging,” Opt. Express 17(4), 2880–2891 (2009). [CrossRef] [PubMed]
G. Molesini, G. Pedrini, P. Poggi, and F. Quercioli, “Focus-wavelength encoded optical profilometer,” Opt. Commun. 49(4), 229–233 (1984). [CrossRef]
S. L. Dobson, P. C. Sun, and Y. Fainman, “Diffractive lenses for chromatic confocal imaging,” Appl. Opt. 36(20), 4744–4748 (1997). [CrossRef] [PubMed]
K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic confocal microscopy using supercontinuum light,” Opt. Express 12(10), 2096–2101 (2004). [CrossRef] [PubMed]
K. Shi, S. H. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun. 263(2), 156–162 (2006). [CrossRef]
Q. Xu, K. Shi, S. Yin, and Z. Liu, “Chromatic two-photon excitation fluorescence imaging,” J. Microsc. 235(1), 79–83 (2009). [CrossRef] [PubMed]
K. Shi, S. Yin, and Z. Liu, “Wavelength division scanning for two-photon excitation fluorescence imaging,” J. Microsc. 223(2), 83–87 (2006). [CrossRef] [PubMed]
F. T. S. Yu, Introduction to diffraction, information processing, and holography (MIT Press, Cambridge, MA, 1973).
K. Shi, Supercontinuum imaging and spectroscopy, Penn State Doctoral Dissertation (2007).
E. Hecht, Optics (Addison Wesley, 2001). [PubMed]
S. C. H. O. T. T. Optical Glass Data Sheets, (2010). http://www.us.schott.com/advanced_optics/english/download/schott_optical_glass_june_2010_us.pdf?PHPSESSID=cf27dsjed4tvup6riaj7up87k4 .

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