## GPC Light Shaper for speckle-free one- and two-photon contiguous pattern excitation |

Optics Express, Vol. 22, Issue 5, pp. 5299-5311 (2014)

http://dx.doi.org/10.1364/OE.22.005299

Acrobat PDF (1623 KB)

### Abstract

Generalized Phase Contrast (GPC) is an efficient method for generating speckle-free contiguous optical distributions useful in diverse applications such as static beam shaping, optical manipulation and recently, for excitation in two-photon optogenetics. To fully utilize typical Gaussian lasers in such applications, we analytically derive conditions for photon efficient light shaping with GPC. When combined with the conditions for optimal contrast developed in previous works, our analysis further simplifies GPC’s implementation. The results of our analysis are applied to practical illumination shapes, such as a circle and different rectangles commonly used in industrial or commercial applications. We also show simple and efficient beam shaping of arbitrary shapes geared towards biophotonics research and other contemporary applications. Optimized GPC configurations consistently give ~84% efficiency and ~3x intensity gain. Assessment of the energy savings when comparing to conventional amplitude masking show that ~93% of typical energy losses are saved with optimized GPC configurations.

© 2014 Optical Society of America

## 1. Introduction

1. D. Palima, A. R. Bañas, G. Vizsnyiczai, L. Kelemen, P. Ormos, and J. Glückstad, “Wave-guided optical waveguides,” Opt. Express **20**(3), 2004–2014 (2012). [CrossRef] [PubMed]

2. E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods **7**(10), 848–854 (2010). [CrossRef] [PubMed]

3. E. Papagiakoumou, “Optical developments for optogenetics,” Biol. Cell **105**(10), 443–464 (2013). [PubMed]

4. D. Palima, C. A. Alonzo, P. J. Rodrigo, and J. Glückstad, “Generalized phase contrast matched to Gaussian illumination,” Opt. Express **15**(19), 11971–11977 (2007). [CrossRef] [PubMed]

5. T. R. M. Sales, R. P. C. Photonics, C. Road, and R. Ny, “Structured Microlens Arrays for Beam Shaping,” Proc. SPIE **5175**, 109–120 (2003). [CrossRef]

6. C. Kopp, L. Ravel, and P. Meyrueis, “Efficient beamshaper homogenizer design combining diffractive optical elements, microlens array and random phase plate,” J. Opt. A, Pure Appl. Opt. **1**(3), 398–403 (1999). [CrossRef]

7. J. A. Hoffnagle and C. M. Jefferson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt. **39**(30), 5488–5499 (2000). [CrossRef] [PubMed]

8. S. K. Case, P. R. Haugen, and O. J. Løkberg, “Multifacet holographic optical elements for wave front transformations,” Appl. Opt. **20**(15), 2670–2675 (1981). [CrossRef] [PubMed]

10. W. B. Veldkamp, “Laser beam profile shaping with interlaced binary diffraction gratings,” Appl. Opt. **21**(17), 3209–3212 (1982). [CrossRef] [PubMed]

11. M. R. Wang, “Analysis and optimization on single-zone binary flat-top beam shaper,” Opt. Eng. **42**(11), 3106 (2003). [CrossRef]

13. J. Glückstad and P. C. Mogensen, “Optimal phase contrast in common-path interferometry,” Appl. Opt. **40**(2), 268–282 (2001). [CrossRef] [PubMed]

14. S. Tauro, A. Bañas, D. Palima, and J. Glückstad, “Experimental demonstration of Generalized Phase Contrast based Gaussian beam-shaper,” Opt. Express **19**(8), 7106–7111 (2011). [CrossRef] [PubMed]

15. A. W. Lohmann and D. P. Paris, “Binary fraunhofer holograms, generated by computer,” Appl. Opt. **6**(10), 1739–1748 (1967). [CrossRef] [PubMed]

16. W. H. Lee, “Sampled fourier transform hologram generated by computer,” Appl. Opt. **9**(3), 639–643 (1970). [CrossRef] [PubMed]

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

19. M. A. Go, C. Stricker, S. Redman, H.-A. Bachor, and V. R. Daria, “Simultaneous multi-site two-photon photostimulation in three dimensions,” J Biophotonics **5**(10), 745–753 (2012). [CrossRef] [PubMed]

20. L. Ge, M. Duelli, and R. Cohn, “Enumeration of illumination and scanning modes from real-time spatial light modulators,” Opt. Express **7**(12), 403–416 (2000). [CrossRef] [PubMed]

21. T. Matsuoka, M. Nishi, M. Sakakura, K. Miura, K. Hirao, D. Palima, S. Tauro, A. Bañas, and J. Glückstad,D. L. Andrews, E. J. Galvez, and J. Glückstad, eds., “Functionalized 2PP structures for the BioPhotonics Workstation,” in *Proceedings of SPIE*, D. L. Andrews, E. J. Galvez, and J. Glückstad, eds. (2011), Vol. 7950, p. 79500Q. [CrossRef]

3. E. Papagiakoumou, “Optical developments for optogenetics,” Biol. Cell **105**(10), 443–464 (2013). [PubMed]

1. D. Palima, A. R. Bañas, G. Vizsnyiczai, L. Kelemen, P. Ormos, and J. Glückstad, “Wave-guided optical waveguides,” Opt. Express **20**(3), 2004–2014 (2012). [CrossRef] [PubMed]

22. P. J. Rodrigo, L. Gammelgaard, P. Bøggild, I. Perch-Nielsen, and J. Glückstad, “Actuation of microfabricated tools using multiple GPC-based counterpropagating-beam traps,” Opt. Express **13**(18), 6899–6904 (2005). [CrossRef] [PubMed]

23. Y. Tanaka, S. Tsutsui, M. Ishikawa, and H. Kitajima, “Hybrid optical tweezers for dynamic micro-bead arrays,” Opt. Express **19**(16), 15445–15451 (2011). [CrossRef] [PubMed]

2. E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods **7**(10), 848–854 (2010). [CrossRef] [PubMed]

1. D. Palima, A. R. Bañas, G. Vizsnyiczai, L. Kelemen, P. Ormos, and J. Glückstad, “Wave-guided optical waveguides,” Opt. Express **20**(3), 2004–2014 (2012). [CrossRef] [PubMed]

22. P. J. Rodrigo, L. Gammelgaard, P. Bøggild, I. Perch-Nielsen, and J. Glückstad, “Actuation of microfabricated tools using multiple GPC-based counterpropagating-beam traps,” Opt. Express **13**(18), 6899–6904 (2005). [CrossRef] [PubMed]

24. S. Tauro, A. Bañas, D. Palima, and J. Glückstad, “Dynamic axial stabilization of counter-propagating beam-traps with feedback control,” Opt. Express **18**(17), 18217–18222 (2010). [CrossRef] [PubMed]

25. D. Palima and J. Glückstad, “Multi-wavelength spatial light shaping using generalized phase contrast,” Opt. Express **16**(2), 1331–1342 (2008). [CrossRef] [PubMed]

2. E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods **7**(10), 848–854 (2010). [CrossRef] [PubMed]

3. E. Papagiakoumou, “Optical developments for optogenetics,” Biol. Cell **105**(10), 443–464 (2013). [PubMed]

26. J. Glückstad, L. Lading, H. Toyoda, and T. Hara, “Lossless light projection,” Opt. Lett. **22**(18), 1373–1375 (1997). [CrossRef] [PubMed]

4. D. Palima, C. A. Alonzo, P. J. Rodrigo, and J. Glückstad, “Generalized phase contrast matched to Gaussian illumination,” Opt. Express **15**(19), 11971–11977 (2007). [CrossRef] [PubMed]

## 2. GPC with Gaussian beams

### 2.1 Optimizing GPC for output contrast

*f*setup depicted in Fig. 1. The field at the input plane can be described aswhere

*a*(

*x*,

*y*) is an amplitude profile that arises either due to the illumination beam, or from a limiting aperture and

*θ*-phase shifting region has the form,where

*f*,

_{x}*f*and

_{y}*f*are respectively the abscissa, ordinate and radial spatial frequency coordinates. Note that we have dropped the absorption factors originally present in the wavefront sensing filter [27

_{r}27. F. Zernike, “How I Discovered Phase Contrast,” Science **121**(3141), 345–349 (1955). [CrossRef] [PubMed]

*f*, is the radius of the PCF’s phase shifting region. At the output plane, the low-pass-filtered image of the input phase variations, scaled by a multiplicative complex factor, [exp(i

_{r}*θ*)–1], serves as a reference wave for the directly imaged input pattern. Thus the synthesized intensity pattern at the output plane is formed from the interference of an inverted copy of the original input and the low passed image acting as an SRWHere, we have used an approximation for the SRW,

4. D. Palima, C. A. Alonzo, P. J. Rodrigo, and J. Glückstad, “Generalized phase contrast matched to Gaussian illumination,” Opt. Express **15**(19), 11971–11977 (2007). [CrossRef] [PubMed]

^{th}order,

### 2.2 GPC with Gaussian illumination

^{2}waist,

*w*To exploit the symmetry, we would, for now, assume that the phase mask is circular. We also assume that both phase mask pattern and PCF imparts π-phase shifts on the transmitted light. This allows us to conveniently express the phase modulation as a change in sign in the amplitude and deal with only real numbers.

_{0}*g*(

*r’*) is a Fourier transform of a truncated Gaussian. Evaluating this Fourier transform is not straightforward, thus different approximations have been presented in the literature [28

28. V. Nourrit, J.-L. de Bougrenet de la Tocnaye, and P. Chanclou, “Propagation and diffraction of truncated Gaussian beams,” J. Opt. Soc. Am. A **18**(3), 546 (2001). [CrossRef]

*η*as the ratio of the PCF phase shifting radius to the Gaussian waist at the Fourier plane,

*w*, when the wavelength is

_{f}*λ*and the focal length is

*f*.For a π-phase shifting circular phase mask with radius Δ

*r*, the modulated input could be expressed asSince this also involves a truncated Gaussian, the evaluation of

*g*(

*r*´ = 0)where we defined the dimensionless

*ζ*as the ratio between the phase mask radius and input Gaussian waist,On the optical axis, we can express Eq. (6) using Eqs. (8) and (11) giving the condition for optimal contrastAlthough this derivation is for a circular phase mask, extending to any shape is a matter of finding the corresponding

## 3. Optimizing GPC for photon efficiency

*f*≤ Δ

_{r}*f*. At this region, the Fourier transform of Eq. (10) is approximatelyThis is illustrated in Fig. 2(b), where the displaced Gaussian (blue plot), approximates the Fourier transform (red plot) at low frequencies. To make the PCF radius coincide with the first zero crossing, we thus impose

_{r}### 3.1 Optimizing contrast and efficiency

*ζ*and

*η*from Eqs. (13) and (16) gives us the optimal parameters for a circular phase mask Numerically evaluating the GPC output from this

*ζ*-

*η*pair gives an efficiency of ~84% and a gain of ~3x relative to the input Gaussian’s central intensity (see Table 1). To generalize to arbitrary shapes Eqs. (13) and (16) can be expressed in terms of

*ζ*, giving These can be simplified further by solving for

*η*, resulting in These two equations summarize the conditions for an optimally performing GPC system under Gaussian illumination. The phase mask’s geometry is embodied in

*η*in Eq. (22) means that a reconfigurable GPC system with a fixed PCF will still perform optimally with different phase masks satisfying Eq. (21). The succeeding sections use these two equations to optimize Gaussian GPC with rectangular and arbitrary patterns.

## 4. Extending to rectangular apertures

*W*×

*H*can be expressed as (

*cf.*Eq. (10))To optimize a GPC system using rectangular phase apertures, we first identify

*x*and

*y*dependence are separable and that the rect functions can be treated as integration limits, results in an expression for

*x*),Here we defined the aspect ratio,

*ζ*

_{Rect}for rectangular phase apertures as half the width divided by the input Gaussian waist,

*ζ*

_{Rect}to get

*A*= 1, which givesFor other aspect ratios,

_{R}*ζ*

_{Rect}can be found numerically or by graphically looking for the intersection of the plots of Eqs. (13) and (16) which we will show here. Using the form of

*η*in terms of

*ζ*

_{Rect}Figure 3 shows the plots of Eq. (28) in solid lines and Eq. (29) in dashed lines.

*A*is chosen from common video display aspect ratios. The plot is zoomed at the intersections which occur at

_{R}*η*= 1.1081, as implied by Eq. (22). The numeric values of

*ζ*

_{Rect}at these intersections are listed in Table 1 (to 4 decimal places).

## 5. Numerical experiments with circular and rectangular phase apertures

*w*

_{0}= 240.7957 samples such that Δ

*f*is an integer value,

_{r}*ηw*= 12 samples. GPC efficiency is defined as in Eq. (14) and the gain is defined as the central intensity at the output (input central intensity is unity). Since discretization errors prevent

_{f}*ζ*or

*ζ*

_{Rect}from being represented accurately, we also list their effective values when integer rectangle sizes are used.

## 6. Efficient generation of arbitrary intensity patterns

### 6.1 Optimally scaled arbitrary patterns

*b*(

*x*,

*y*), having values 0 and 1, as our aperture. Assuming the binary image is mapped to 0 and π phase shifts on an incident Gaussian, we can numerically evaluate and scale

*b*(

*x*,

*y*) such thatIn our simulations we first start with a large bitmap and optimize

*w*

_{0}which is easier to change. Once (31) is satisfied, we revert to the original

*w*

_{0}and then scale the image preserving its optimal proportion with

*w*

_{0}. Results for various optimized patterns are shown in Fig. 6.

### 6.2 Dynamic and arbitrarily sized excitation patterns

**7**(10), 848–854 (2010). [CrossRef] [PubMed]

*w*

_{0}can be applied (obtained by dropping the inner integral). We note however that the intensity beyond this radius is considerably lower than that in the utilized region. Results for ring compensated neuron shaped patterns are shown in Fig. 7. Figures 7(d)–7(f) show the possibility to optimally illuminate a cell that is branching out. We observe that the gain tends to be higher with a less efficiency-optimized GPC setup. This counteracting behavior of intensity gain and photon efficiency helps keep the energy savings at around ~85-93%.

## 7. Summary and outlook

31. D. Palima and J. Glückstad, “Gaussian to uniform intensity shaper based on generalized phase contrast,” Opt. Express **16**(3), 1507–1516 (2008). [CrossRef] [PubMed]

## Acknowledgment

## References

1. | D. Palima, A. R. Bañas, G. Vizsnyiczai, L. Kelemen, P. Ormos, and J. Glückstad, “Wave-guided optical waveguides,” Opt. Express |

2. | E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods |

3. | E. Papagiakoumou, “Optical developments for optogenetics,” Biol. Cell |

4. | D. Palima, C. A. Alonzo, P. J. Rodrigo, and J. Glückstad, “Generalized phase contrast matched to Gaussian illumination,” Opt. Express |

5. | T. R. M. Sales, R. P. C. Photonics, C. Road, and R. Ny, “Structured Microlens Arrays for Beam Shaping,” Proc. SPIE |

6. | C. Kopp, L. Ravel, and P. Meyrueis, “Efficient beamshaper homogenizer design combining diffractive optical elements, microlens array and random phase plate,” J. Opt. A, Pure Appl. Opt. |

7. | J. A. Hoffnagle and C. M. Jefferson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt. |

8. | S. K. Case, P. R. Haugen, and O. J. Løkberg, “Multifacet holographic optical elements for wave front transformations,” Appl. Opt. |

9. | I. Gur and D. Mendlovic, “Diffraction limited domain flat-top generator,” Opt. Commun. |

10. | W. B. Veldkamp, “Laser beam profile shaping with interlaced binary diffraction gratings,” Appl. Opt. |

11. | M. R. Wang, “Analysis and optimization on single-zone binary flat-top beam shaper,” Opt. Eng. |

12. | R. Voelkel and K. J. Weible, “Laser beam homogenizing: limitations and constraints,” in |

13. | J. Glückstad and P. C. Mogensen, “Optimal phase contrast in common-path interferometry,” Appl. Opt. |

14. | S. Tauro, A. Bañas, D. Palima, and J. Glückstad, “Experimental demonstration of Generalized Phase Contrast based Gaussian beam-shaper,” Opt. Express |

15. | A. W. Lohmann and D. P. Paris, “Binary fraunhofer holograms, generated by computer,” Appl. Opt. |

16. | W. H. Lee, “Sampled fourier transform hologram generated by computer,” Appl. Opt. |

17. | J. Glückstad and D. Z. Palima, |

18. | D. G. Grier, “A revolution in optical manipulation,” Nature |

19. | M. A. Go, C. Stricker, S. Redman, H.-A. Bachor, and V. R. Daria, “Simultaneous multi-site two-photon photostimulation in three dimensions,” J Biophotonics |

20. | L. Ge, M. Duelli, and R. Cohn, “Enumeration of illumination and scanning modes from real-time spatial light modulators,” Opt. Express |

21. | T. Matsuoka, M. Nishi, M. Sakakura, K. Miura, K. Hirao, D. Palima, S. Tauro, A. Bañas, and J. Glückstad,D. L. Andrews, E. J. Galvez, and J. Glückstad, eds., “Functionalized 2PP structures for the BioPhotonics Workstation,” in |

22. | P. J. Rodrigo, L. Gammelgaard, P. Bøggild, I. Perch-Nielsen, and J. Glückstad, “Actuation of microfabricated tools using multiple GPC-based counterpropagating-beam traps,” Opt. Express |

23. | Y. Tanaka, S. Tsutsui, M. Ishikawa, and H. Kitajima, “Hybrid optical tweezers for dynamic micro-bead arrays,” Opt. Express |

24. | S. Tauro, A. Bañas, D. Palima, and J. Glückstad, “Dynamic axial stabilization of counter-propagating beam-traps with feedback control,” Opt. Express |

25. | D. Palima and J. Glückstad, “Multi-wavelength spatial light shaping using generalized phase contrast,” Opt. Express |

26. | J. Glückstad, L. Lading, H. Toyoda, and T. Hara, “Lossless light projection,” Opt. Lett. |

27. | F. Zernike, “How I Discovered Phase Contrast,” Science |

28. | V. Nourrit, J.-L. de Bougrenet de la Tocnaye, and P. Chanclou, “Propagation and diffraction of truncated Gaussian beams,” J. Opt. Soc. Am. A |

29. | R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Stuttg.) |

30. | A. Bañas, D. Palima, and J. Glückstad, “Matched-filtering generalized phase contrast using LCoS pico-projectors for beam-forming,” Opt. Express |

31. | D. Palima and J. Glückstad, “Gaussian to uniform intensity shaper based on generalized phase contrast,” Opt. Express |

**OCIS Codes**

(070.0070) Fourier optics and signal processing : Fourier optics and signal processing

(070.6110) Fourier optics and signal processing : Spatial filtering

(120.5060) Instrumentation, measurement, and metrology : Phase modulation

(140.3300) Lasers and laser optics : Laser beam shaping

**ToC Category:**

Fourier Optics and Signal Processing

**History**

Original Manuscript: January 17, 2014

Revised Manuscript: February 19, 2014

Manuscript Accepted: February 20, 2014

Published: February 27, 2014

**Virtual Issues**

Vol. 9, Iss. 5 *Virtual Journal for Biomedical Optics*

**Citation**

Andrew Bañas, Darwin Palima, Mark Villangca, Thomas Aabo, and Jesper Glückstad, "GPC Light Shaper for speckle-free one- and two-photon contiguous pattern excitation," Opt. Express **22**, 5299-5311 (2014)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-22-5-5299

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### References

- D. Palima, A. R. Bañas, G. Vizsnyiczai, L. Kelemen, P. Ormos, J. Glückstad, “Wave-guided optical waveguides,” Opt. Express 20(3), 2004–2014 (2012). [CrossRef] [PubMed]
- E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010). [CrossRef] [PubMed]
- E. Papagiakoumou, “Optical developments for optogenetics,” Biol. Cell 105(10), 443–464 (2013). [PubMed]
- D. Palima, C. A. Alonzo, P. J. Rodrigo, J. Glückstad, “Generalized phase contrast matched to Gaussian illumination,” Opt. Express 15(19), 11971–11977 (2007). [CrossRef] [PubMed]
- T. R. M. Sales, R. P. C. Photonics, C. Road, R. Ny, “Structured Microlens Arrays for Beam Shaping,” Proc. SPIE 5175, 109–120 (2003). [CrossRef]
- C. Kopp, L. Ravel, P. Meyrueis, “Efficient beamshaper homogenizer design combining diffractive optical elements, microlens array and random phase plate,” J. Opt. A, Pure Appl. Opt. 1(3), 398–403 (1999). [CrossRef]
- J. A. Hoffnagle, C. M. Jefferson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt. 39(30), 5488–5499 (2000). [CrossRef] [PubMed]
- S. K. Case, P. R. Haugen, O. J. Løkberg, “Multifacet holographic optical elements for wave front transformations,” Appl. Opt. 20(15), 2670–2675 (1981). [CrossRef] [PubMed]
- I. Gur, D. Mendlovic, “Diffraction limited domain flat-top generator,” Opt. Commun. 145(1-6), 237-248 (1998).
- W. B. Veldkamp, “Laser beam profile shaping with interlaced binary diffraction gratings,” Appl. Opt. 21(17), 3209–3212 (1982). [CrossRef] [PubMed]
- M. R. Wang, “Analysis and optimization on single-zone binary flat-top beam shaper,” Opt. Eng. 42(11), 3106 (2003). [CrossRef]
- R. Voelkel and K. J. Weible, “Laser beam homogenizing: limitations and constraints,” in Proc. of SPIE, A. Duparré and R. Geyl, eds. (2008), Vol. 7102, p. 71020J–71020J–12.
- J. Glückstad, P. C. Mogensen, “Optimal phase contrast in common-path interferometry,” Appl. Opt. 40(2), 268–282 (2001). [CrossRef] [PubMed]
- S. Tauro, A. Bañas, D. Palima, J. Glückstad, “Experimental demonstration of Generalized Phase Contrast based Gaussian beam-shaper,” Opt. Express 19(8), 7106–7111 (2011). [CrossRef] [PubMed]
- A. W. Lohmann, D. P. Paris, “Binary fraunhofer holograms, generated by computer,” Appl. Opt. 6(10), 1739–1748 (1967). [CrossRef] [PubMed]
- W. H. Lee, “Sampled fourier transform hologram generated by computer,” Appl. Opt. 9(3), 639–643 (1970). [CrossRef] [PubMed]
- J. Glückstad and D. Z. Palima, Generalized Phase Contrast: Applications in Optics and Photonics (Springer Series in Optical Sciences, 2009).
- D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003). [CrossRef] [PubMed]
- M. A. Go, C. Stricker, S. Redman, H.-A. Bachor, V. R. Daria, “Simultaneous multi-site two-photon photostimulation in three dimensions,” J Biophotonics 5(10), 745–753 (2012). [CrossRef] [PubMed]
- L. Ge, M. Duelli, R. Cohn, “Enumeration of illumination and scanning modes from real-time spatial light modulators,” Opt. Express 7(12), 403–416 (2000). [CrossRef] [PubMed]
- T. Matsuoka, M. Nishi, M. Sakakura, K. Miura, K. Hirao, D. Palima, S. Tauro, A. Bañas, and J. Glückstad,D. L. Andrews, E. J. Galvez, and J. Glückstad, eds., “Functionalized 2PP structures for the BioPhotonics Workstation,” in Proceedings of SPIE, D. L. Andrews, E. J. Galvez, and J. Glückstad, eds. (2011), Vol. 7950, p. 79500Q. [CrossRef]
- P. J. Rodrigo, L. Gammelgaard, P. Bøggild, I. Perch-Nielsen, J. Glückstad, “Actuation of microfabricated tools using multiple GPC-based counterpropagating-beam traps,” Opt. Express 13(18), 6899–6904 (2005). [CrossRef] [PubMed]
- Y. Tanaka, S. Tsutsui, M. Ishikawa, H. Kitajima, “Hybrid optical tweezers for dynamic micro-bead arrays,” Opt. Express 19(16), 15445–15451 (2011). [CrossRef] [PubMed]
- S. Tauro, A. Bañas, D. Palima, J. Glückstad, “Dynamic axial stabilization of counter-propagating beam-traps with feedback control,” Opt. Express 18(17), 18217–18222 (2010). [CrossRef] [PubMed]
- D. Palima, J. Glückstad, “Multi-wavelength spatial light shaping using generalized phase contrast,” Opt. Express 16(2), 1331–1342 (2008). [CrossRef] [PubMed]
- J. Glückstad, L. Lading, H. Toyoda, T. Hara, “Lossless light projection,” Opt. Lett. 22(18), 1373–1375 (1997). [CrossRef] [PubMed]
- F. Zernike, “How I Discovered Phase Contrast,” Science 121(3141), 345–349 (1955). [CrossRef] [PubMed]
- V. Nourrit, J.-L. de Bougrenet de la Tocnaye, P. Chanclou, “Propagation and diffraction of truncated Gaussian beams,” J. Opt. Soc. Am. A 18(3), 546 (2001). [CrossRef]
- R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).
- A. Bañas, D. Palima, J. Glückstad, “Matched-filtering generalized phase contrast using LCoS pico-projectors for beam-forming,” Opt. Express 20(9), 9705–9712 (2012). [CrossRef] [PubMed]
- D. Palima, J. Glückstad, “Gaussian to uniform intensity shaper based on generalized phase contrast,” Opt. Express 16(3), 1507–1516 (2008). [CrossRef] [PubMed]

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