OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 14 — Jul. 2, 2012
  • pp: 15377–15384
« Show journal navigation

SLM-based off-axis Fourier filtering in microscopy with white light illumination

Ruth Steiger, Stefan Bernet, and Monika Ritsch-Marte  »View Author Affiliations


Optics Express, Vol. 20, Issue 14, pp. 15377-15384 (2012)
http://dx.doi.org/10.1364/OE.20.015377


View Full Text Article

Acrobat PDF (2433 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In various microscopy applications spatial light modulators (SLMs) are used as programmable Fourier filters to realize different optical contrast enhancement methods. It is often advantageous to use the SLM in off-axis configuration, where the filtered image wave is sent into the first diffraction order of a blazed grating superposed to the phase mask on the SLM. Because of dispersion this approach is, however, typically limited to spectrally narrowband illumination. Here we suggest a method involving a grating for pre-compensation, which allows one to use spectrally broadband (even thermal) light in SLM-based Fourier filtering. The proposed approach is demonstrated by multicolor imaging of amplitude and phase objects, such as a resolution target, onion epidermal cells and human epithelial cheek cells.

© 2012 OSA

1. Introduction

Optical contrast enhancement methods such as phase contrast, darkfield, differential interference contrast (DIC), spiral phase contrast (SPC), and others have been developed to increase the visibility of nearly transparent objects in optical microscopy. Many of these methods can be emulated by spatial light modulators (SLMs) [1

1. C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5(1), 81–101 (2011). [CrossRef]

]. Using the SLM, for instance, as a programmable Fourier filter has the advantage that switching between different modalities is fast and simple, as it can be performed by simply sending a different image to the SLM [2

2. J. A. Neff, R. A. Athale, and S. H. Lee, “Two-dimensional spatial light modulators: A tutorial,” Proc. IEEE 78(5), 826–855 (1990). [CrossRef]

, 3

3. F. Yaras, H. Kang, and L. Onural, “State of the Art in Holographic Displays: A Survey,” J.Disp. Technol. 6(10), 443–454 (2010). [CrossRef]

]. SLMs acting as pure phase modulators inserted into a Fourier plane in the imaging pathway are often realized by miniaturized high resolution liquid crystal displays, typically with a pixel size of 10 µm x 10 µm and a display diagonal of 2 cm. This type of microscopic setup can be used for optical image processing [4

4. M. Warber, S. Zwick, M. Hasler, T. Haist, and W. Osten, “SLM-based phase-contrast filtering for single and multiple image acquisition,” Proc. SPIE 7442, 74420E (2009). [CrossRef]

, 5

5. S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13(3), 689–694 (2005). [CrossRef] [PubMed]

], aberration correction [6

6. K. D. Wulff, D. G. Cole, R. L. Clark, R. Dileonardo, J. Leach, J. Cooper, G. Gibson, and M. J. Padgett, “Aberration correction in holographic optical tweezers,” Opt. Express 14(9), 4170–4175 (2006). [CrossRef] [PubMed]

], and optical micromanipulation [7

7. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003). [CrossRef] [PubMed]

, 8

8. K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011). [CrossRef]

].

In many respects it is advantageous to use the SLMs in an off-axis configuration, which means that the desired filter function is superposed on a blazed grating in the phase pattern on the SLM, such that the first order diffracted light of the blazed grating, which is spatially separated from the other diffraction orders by its different propagation direction, carries the processed image wave. A major advantage of this method is the fact that it suppresses the background of light unaffected by the SLM, which arises because of the imperfect diffraction efficiency of existing SLMs. Furthermore, in on-axis configuration a “phase-only” SLM can produce only a phase modulation of the wavefront, whereas in off-axis configuration the SLM can also act as an amplitude modulator, by spatially varying the local grating contrast (i.e. modulation depth) and thus the intensity of the diffracted light. Some techniques, such as darkfield imaging, require an off-axis configuration in the case of phase-only modulation, because of the necessary removal of the zero-order Fourier component of the incoming light, which would require an absorptive element in the on-axis variant [9

9. J. Glückstad, “Phase contrast image synthesis,” Opt. Commun. 130(4-6), 225–230 (1996). [CrossRef]

, 10

10. M. Woerdemann, F. Holtmann, and C. Denz, “Holographic phase contrast for dynamic multiple-beam optical tweezers,” J. Opt. A, Pure Appl. Opt. 11(3), 034010 (2009). [CrossRef]

]. Furthermore, the capability to modulate the amplitude to a certain extent is also useful for modifying spiral phase contrast imaging [5

5. S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13(3), 689–694 (2005). [CrossRef] [PubMed]

] to create complex Laguerre-Gaussian filters [11

11. C.-S. Guo, Y.-J. Han, J.-B. Xu, and J. Ding, “Radial Hilbert transform with Laguerre-Gaussian spatial filters,” Opt. Lett. 31(10), 1394–1396 (2006). [CrossRef] [PubMed]

], which obviously requires both amplitude and phase modulations.

2. Experimental section

The experimental setup for realizing various SLM-based contrast enhancement methods in an optical microscope is sketched in Fig. 1
Fig. 1 Schematic setup (not to scale) for the combination of a diffraction grating and a reflective SLM, the latter used as a Fourier filter in imaging, for avoiding dispersion effects due to white light illumination.
. For broadband sample illumination we either use a high power white light emitting diode (LZ4-00MD00, LedEngins Inc., 10 W), or a thermal light source (standard halogen bulb, 4.2 W). The light is coupled into a multimode acrylic fiber (0.4 mm core diameter) by using a focusing lens (L1, f1 = 30 mm). The uniformly illuminated output of the fiber serves as the effective illumination source, defining the spatial coherence of the illumination light. Behind the fiber the beam is collimated by another lens (L2, f2 = 30 mm) and illuminates the sample. The light transmitted through the sample is collected by a microscope objective (10 x magnification, air objective Reichert, Plan 10, NA = 0.2). A set of relay lenses (L3 and L4, with focal lengths of f3 = f4 = 200 mm) images the rear focal plane of the objective (corresponding to a Fourier plane of the optical path) on to the flat side of a ruled blazed glass transmission grating (30 x 30 x 10 mm, 17.5 lines / mm, blaze angle = 2.1°, Newport gratings).

A circular aperture is inserted between lenses L3 and L4 at the position of a sharp image plane, which reduces the field of view. This is necessary in order to limit the angular spread of the image wave in its Fourier plane ( = SLM plane) such that it is smaller than the diffraction angle at the displayed SLM grating. Without the aperture, different residual diffraction orders of the SLM (mainly the zeroth and the first order) would overlap in the camera plane, producing a disturbed image. Due to this restriction the usable field of view becomes
xmax=2λdfob
(1)
where xmax denotes the diameter of the field of view, λ the smallest wavelength in the illumination, d the grating constant of the SLM grating, and fob the effective front focal length of the objective. Using this relation it can be shown that the number of resolvable pixels in the image (given by the field of view divided by the smallest resolvable structure size) in the direction of the SLM grating vector is limited by the number of SLM pixels in the same direction.

Behind the transmission grating the white light beam fans out into a “rainbow” with an angular range depending on the grating constant. Parts of the beam which are scattered into undesired diffraction orders (mainly into the zeroth order corresponding to undiffracted light) are spatially separated at some distance behind the grating, where they are blocked by a beam stop. The light field then passes through a relay system, consisting of two lenses (L5 and L6, f5 = f6 = 250 mm), to the surface of a reflective SLM (HOLOEYE Pluto). The relay system is adjusted such that it produces a sharp image of the transmission grating at the position of the SLM. Thus, also the SLM is located in a Fourier plane of the image field, and - at the same time - in a sharp image plane of the effective illumination source, namely the end face of the fiber.

By using achromatic lenses for the relay optics, the wave field in the SLM plane is not dispersed, and still corresponds to a spatial Fourier transform of the white light image wave. However, now each color within the wave field propagates into another direction. This dispersion is compensated by displaying a blazed phase grating at the SLM which back-diffracts the incoming beam into its original travelling direction (i.e. the direction the beam would have if no gratings, just mirrors and lenses, were in the beam path).

Since the SLM is reflective, this would mean a back-diffraction to the position of the transmissive grating. Therefore, in order to separate the beams, the SLM is slightly tilted (10°), such that the wave is diffracted away from the original optical axis to the camera plane. Note that in the more general case of a relay lens system with a non-unity magnification factor, for optimal dispersion compensation the blazed phase grating displayed at the SLM has to be a phase conjugate copy of the image of the transmission grating in the SLM plane. This means that behind the SLM the sum of the phase modulations produced by the first phase grating, and by the SLM grating, is again spatially flat, and therefore the total diffraction angle is the same for all colors in the beam. The blazed grating displayed at the SLM can be experimentally adjusted such that the incoming “rainbow-beam” is optimally recombined into a white light beam, which then travels through an imaging lens (which performs a Fourier back-transformation, L7, f7 = 200 mm) into the observation plane where a camera chip is located (Canon EOS 1000D).

Here it has to be noted that, in fact, not the first order diffraction of the glass transmission grating (grating period: 58 µm) was used for imaging, but instead the second diffraction order, since this provided the maximal diffraction efficiency in the used wavelength range. Consequently, for compensation the SLM grating (which acted in first diffraction order) was programmed with a doubled line frequency (grating period: 28 µm) for producing the required back-diffraction angle. This has no disturbing effect on the dispersion compensation, as long as the actual diffraction angles of both gratings are the same.

After this kind of adjustment, the SLM phase masks for various image processing applications can be computed as if they were designed for on-axis operation, and then numerically added to the previously optimized blazed grating phase, followed by a modulo 2 π operation. This final modulo 2 π operation of the actual filter mask superposed on the blazed grating assures a fixed “linkage” between the two diffractive structures, i.e. all light diffracted into the first diffraction order of the blazed grating is also “automatically” filtered by the programmed phase mask - independent of the detailed SLM characteristics. For example, a limited phase modulation range of the SLM would affect in this case only the efficiency, but not the precision of the programmed wave front in the first diffraction order.

3. Experimental results

The method described above was tested using both, amplitude and phase objects as specimen for different Fourier contrast enhancing methods, namely darkfield, phase contrast and spiral phase contrast microscopy. The results are shown in Fig. 3
Fig. 3 First row shows the images of a resolution target as an amplitude object, the 2nd and 3rd row show onion epidermal cells and human epithelial cheek cells as phase objects. The insets on the very top of row show the corresponding phase patterns displayed on the SLM. Image illumination was performed with a white light LED.
.

Finally, the image in the last column shows the result of a central phase contrast filter (in off-axis mode) displayed at the SLM. There, a circular area in the center of the SLM surface (where again the zero Fourier component of the image wave is located) contains a phase grating with a shift of its spatial phase by π/2, as compared to the surrounding diffraction grating (see bottom row). This spatial shift of the grating phase is imprinted on the diffracted light, such that the zero Fourier component of the image is shifted also by π/2 with respect to the other components - which is the condition for obtaining a phase contrast image. However, as expected, such a phase contrast operation does not improve the contrast for the absorptive test sample (in fact, it even transforms the amplitude contrast partially to a phase contrast, thus strongly reducing the final image contrast). As shown later for the phase samples below (Fig. 3, row B and C), the usefulness of phase contrast imaging emerges when investigating thin phase samples.

As a further example for off-axis filtering, Figs. 4(A-C)
Fig. 4 Pseudo-relief structures of a resolution target, recorded with a white light LED illumination sorce. It seems that the object is illuminated from three different directions. These shadow-effect images are obtained by filtering with spiral phase holograms on the SLM.
show images obtained with spiral phase contrast filters displaced by a small amount with respect to the optical axis to create a pseudo-relief effect, namely displaced to the top, Fig. 4(A), centered, Fig. 4(B), and displaced to the bottom, Fig. 4(C). Whereas the centered filter, Fig. 4(B), produces an image with isotropic edge enhancement, the displacements in Fig. 4(A) and Fig. 4(C) produce a kind of “shadow” or “pseudo-relief” effect, i.e., the obtained images give the impression of a topographically structured surface which is illuminated from different directions. This kind of shadow-effect resembles the appearance of samples in DIC, and helps the observer to gain a topographic view of the “landscape” of a specimen, for example for distinguishing elevations from depressions in phase samples. Furthermore it has been already shown that a set of images recorded with different apparent illumination directions enables the interferometric reconstruction of complex samples [15

15. S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14(9), 3792–3805 (2006). [CrossRef] [PubMed]

]. The series of images also indicates one advantage of SLM-based image filtering, namely that switching between the different views can be performed purely electronically, and at video rate (refresh rate of the current SLM is 60 Hz). Again, this method can now be extended to operate also with broadband illumination.

4. Conclusions and outlook

We have demonstrated a method to compensate for undesired dispersion effects in SLM-based Fourier filtering microscopy, by implementing a static diffraction grating in the optical path. This allows one to use a multitude of recently developed SLM Fourier filtering applications with standard microscopic illumination, instead of the currently employed narrowband illumination sources. The method is insensitive to slight misalignment of the transmission grating and does not require any additional high prized components. Thus it should be useful for extending the range of applications for SLMs in microscopy. Using optimized blazed gratings for this purpose, the light efficiency of standard microscopy is not reduced.

Similar advantages may be gained for SLM-based light projection [18

18. C. Kohler, X. Schwab, and W. Osten, “Optimally tuned spatial light modulators for digital holography,” Appl. Opt. 45(5), 960–967 (2006). [CrossRef] [PubMed]

, 19

19. T. Ito and K. Okano, “Color electroholography by three colored reference lights simultaneously incident upon one hologram panel,” Opt. Express 12(18), 4320–4325 (2004). [CrossRef] [PubMed]

], for beam steering of optical tweezers, or for display technology. In each case, it is again desirable to program the diffractive structures as off-axis masks, due to the arguments mentioned above (such as the suppression of the background of undiffracted light, the option for amplitude modulation via the local modulation depth in the grating structure, and less sensitivity to imperfections of the SLM). However, off-axis operation also limits the projection systems to narrowband light due to dispersion effects. A similar pre-dispersion method with a static grating as demonstrated here is essential for white light projectors or for illumination by ultra-short pulses.

Acknowledgment

This work was performed within the frame of the Christian Doppler Laboratory CDL-MS-MACH. Financial support by the Federal Ministry of Economy, Family and Youth and the National Foundation for Research, Technology and Development is gratefully acknowledged.

References and links

1.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5(1), 81–101 (2011). [CrossRef]

2.

J. A. Neff, R. A. Athale, and S. H. Lee, “Two-dimensional spatial light modulators: A tutorial,” Proc. IEEE 78(5), 826–855 (1990). [CrossRef]

3.

F. Yaras, H. Kang, and L. Onural, “State of the Art in Holographic Displays: A Survey,” J.Disp. Technol. 6(10), 443–454 (2010). [CrossRef]

4.

M. Warber, S. Zwick, M. Hasler, T. Haist, and W. Osten, “SLM-based phase-contrast filtering for single and multiple image acquisition,” Proc. SPIE 7442, 74420E (2009). [CrossRef]

5.

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13(3), 689–694 (2005). [CrossRef] [PubMed]

6.

K. D. Wulff, D. G. Cole, R. L. Clark, R. Dileonardo, J. Leach, J. Cooper, G. Gibson, and M. J. Padgett, “Aberration correction in holographic optical tweezers,” Opt. Express 14(9), 4170–4175 (2006). [CrossRef] [PubMed]

7.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003). [CrossRef] [PubMed]

8.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011). [CrossRef]

9.

J. Glückstad, “Phase contrast image synthesis,” Opt. Commun. 130(4-6), 225–230 (1996). [CrossRef]

10.

M. Woerdemann, F. Holtmann, and C. Denz, “Holographic phase contrast for dynamic multiple-beam optical tweezers,” J. Opt. A, Pure Appl. Opt. 11(3), 034010 (2009). [CrossRef]

11.

C.-S. Guo, Y.-J. Han, J.-B. Xu, and J. Ding, “Radial Hilbert transform with Laguerre-Gaussian spatial filters,” Opt. Lett. 31(10), 1394–1396 (2006). [CrossRef] [PubMed]

12.

P. Birch, R. Young, C. Chatwin, M. Farsari, D. Budgett, and J. Richardson, “Fully complex optical modulation with an analogue ferroelectric liquid crystal spatial light modulator,” Opt. Commun. 175(4-6), 347–352 (2000). [CrossRef]

13.

S. E. Schausberger, B. Heise, C. Maurer, S. Bernet, M. Ritsch-Marte, and D. Stifter, “Flexible contrast for low-coherence interference microscopy by Fourier-plane filtering with a spatial light modulator,” Opt. Lett. 35(24), 4154–4156 (2010). [CrossRef] [PubMed]

14.

J. Leach and M. J. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys. 5, 154–160 (2003). [CrossRef]

15.

S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14(9), 3792–3805 (2006). [CrossRef] [PubMed]

16.

H. Ding and G. Popescu, “Instantaneous spatial light interference microscopy,” Opt. Express 18(2), 1569–1575 (2010). [CrossRef] [PubMed]

17.

B. Bhaduri, H. Pham, M. Mir, and G. Popescu, “Diffraction phase microscopy with white light,” Opt. Lett. 37(6), 1094–1096 (2012). [CrossRef] [PubMed]

18.

C. Kohler, X. Schwab, and W. Osten, “Optimally tuned spatial light modulators for digital holography,” Appl. Opt. 45(5), 960–967 (2006). [CrossRef] [PubMed]

19.

T. Ito and K. Okano, “Color electroholography by three colored reference lights simultaneously incident upon one hologram panel,” Opt. Express 12(18), 4320–4325 (2004). [CrossRef] [PubMed]

OCIS Codes
(070.6110) Fourier optics and signal processing : Spatial filtering
(170.0180) Medical optics and biotechnology : Microscopy
(230.1950) Optical devices : Diffraction gratings
(230.3720) Optical devices : Liquid-crystal devices
(260.2030) Physical optics : Dispersion

ToC Category:
Microscopy

History
Original Manuscript: April 24, 2012
Revised Manuscript: June 15, 2012
Manuscript Accepted: June 20, 2012
Published: June 25, 2012

Virtual Issues
Vol. 7, Iss. 9 Virtual Journal for Biomedical Optics

Citation
Ruth Steiger, Stefan Bernet, and Monika Ritsch-Marte, "SLM-based off-axis Fourier filtering in microscopy with white light illumination," Opt. Express 20, 15377-15384 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-14-15377


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev.5(1), 81–101 (2011). [CrossRef]
  2. J. A. Neff, R. A. Athale, and S. H. Lee, “Two-dimensional spatial light modulators: A tutorial,” Proc. IEEE78(5), 826–855 (1990). [CrossRef]
  3. F. Yaras, H. Kang, and L. Onural, “State of the Art in Holographic Displays: A Survey,” J.Disp. Technol.6(10), 443–454 (2010). [CrossRef]
  4. M. Warber, S. Zwick, M. Hasler, T. Haist, and W. Osten, “SLM-based phase-contrast filtering for single and multiple image acquisition,” Proc. SPIE7442, 74420E (2009). [CrossRef]
  5. S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express13(3), 689–694 (2005). [CrossRef] [PubMed]
  6. K. D. Wulff, D. G. Cole, R. L. Clark, R. Dileonardo, J. Leach, J. Cooper, G. Gibson, and M. J. Padgett, “Aberration correction in holographic optical tweezers,” Opt. Express14(9), 4170–4175 (2006). [CrossRef] [PubMed]
  7. D. G. Grier, “A revolution in optical manipulation,” Nature424(6950), 810–816 (2003). [CrossRef] [PubMed]
  8. K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics5(6), 335–342 (2011). [CrossRef]
  9. J. Glückstad, “Phase contrast image synthesis,” Opt. Commun.130(4-6), 225–230 (1996). [CrossRef]
  10. M. Woerdemann, F. Holtmann, and C. Denz, “Holographic phase contrast for dynamic multiple-beam optical tweezers,” J. Opt. A, Pure Appl. Opt.11(3), 034010 (2009). [CrossRef]
  11. C.-S. Guo, Y.-J. Han, J.-B. Xu, and J. Ding, “Radial Hilbert transform with Laguerre-Gaussian spatial filters,” Opt. Lett.31(10), 1394–1396 (2006). [CrossRef] [PubMed]
  12. P. Birch, R. Young, C. Chatwin, M. Farsari, D. Budgett, and J. Richardson, “Fully complex optical modulation with an analogue ferroelectric liquid crystal spatial light modulator,” Opt. Commun.175(4-6), 347–352 (2000). [CrossRef]
  13. S. E. Schausberger, B. Heise, C. Maurer, S. Bernet, M. Ritsch-Marte, and D. Stifter, “Flexible contrast for low-coherence interference microscopy by Fourier-plane filtering with a spatial light modulator,” Opt. Lett.35(24), 4154–4156 (2010). [CrossRef] [PubMed]
  14. J. Leach and M. J. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys.5, 154–160 (2003). [CrossRef]
  15. S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express14(9), 3792–3805 (2006). [CrossRef] [PubMed]
  16. H. Ding and G. Popescu, “Instantaneous spatial light interference microscopy,” Opt. Express18(2), 1569–1575 (2010). [CrossRef] [PubMed]
  17. B. Bhaduri, H. Pham, M. Mir, and G. Popescu, “Diffraction phase microscopy with white light,” Opt. Lett.37(6), 1094–1096 (2012). [CrossRef] [PubMed]
  18. C. Kohler, X. Schwab, and W. Osten, “Optimally tuned spatial light modulators for digital holography,” Appl. Opt.45(5), 960–967 (2006). [CrossRef] [PubMed]
  19. T. Ito and K. Okano, “Color electroholography by three colored reference lights simultaneously incident upon one hologram panel,” Opt. Express12(18), 4320–4325 (2004). [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.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited