Abstract

Optical phase conjugation (OPC) has enabled many optical applications such as aberration correction and image transmission through fiber. In recent years, implementation of digital optical phase conjugation (DOPC) has opened up the possibility of its use in biomedical optics (e.g. deep-tissue optical focusing) due to its ability to provide greater-than-unity OPC reflectivity (the power ratio of the phase conjugated beam and input beam to the OPC system) and its flexibility to accommodate additional wavefront manipulations. However, the requirement for precise (pixel-to-pixel matching) alignment of the wavefront sensor and the spatial light modulator (SLM) limits the practical usability of DOPC systems. Here, we report a method for auto-alignment of a DOPC system by which the misalignment between the sensor and the SLM is auto-corrected through digital light propagation. With this method, we were able to accomplish OPC playback with a DOPC system with gross sensor-SLM misalignment by an axial displacement of up to~1.5cm, rotation and tip/tilt of ~5, and in-plane displacement of ~5mm (dependent on the physical size of the sensor and the SLM). Our auto-alignment method robustly achieved a DOPC playback peak-to-background ratio (PBR) corresponding to more than ~30% of the theoretical maximum. As an additional advantage, the auto-alignment procedure can be easily performed at will and, as such, allows us to correct for small mechanical drifts within the DOPC systems, thus overcoming a previously major DOPC system vulnerability. We believe that this reported method for implementing robust DOPC systems will broaden the practical utility of DOPC systems.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]

2013 (3)

2012 (2)

Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat Commun 3, 928 (2012).
[CrossRef] [PubMed]

I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett. 101(8), 081108 (2012).
[CrossRef] [PubMed]

2011 (1)

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5(3), 154–157 (2011).
[CrossRef] [PubMed]

2010 (4)

C. L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, “Digital phase conjugation of second harmonic radiation emitted by nanoparticles in turbid media,” Opt. Express 18(12), 12283–12290 (2010).
[CrossRef] [PubMed]

E. J. McDowell, M. Cui, I. M. Vellekoop, V. Senekerimyan, Z. Yaqoob, and C. Yang, “Turbidity suppression from the ballistic to the diffusive regime in biological tissues using optical phase conjugation,” J. Biomed. Opt. 15(2), 025004 (2010).
[CrossRef] [PubMed]

M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18(4), 3444–3455 (2010).
[CrossRef] [PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[CrossRef] [PubMed]

2008 (2)

C. Bellanger, A. Brignon, J. Colineau, and J. P. Huignard, “Coherent fiber combining by digital holography,” Opt. Lett. 33(24), 2937–2939 (2008).
[CrossRef] [PubMed]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical Phase Conjugation for Turbidity Suppression in Biological Samples,” Nat. Photonics 2(2), 110–115 (2008).
[CrossRef] [PubMed]

2007 (2)

J. Li, Z. Peng, and Y. Fu, “Diffraction transfer function and its calculation of classic diffraction formula,” Opt. Commun. 280(2), 243–248 (2007).
[CrossRef]

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32(16), 2309–2311 (2007).
[CrossRef] [PubMed]

2003 (1)

1997 (1)

1988 (1)

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
[CrossRef] [PubMed]

1982 (2)

1981 (1)

1980 (1)

1979 (2)

J. Auyeung, D. Fekete, D. M. Pepper, and A. Yariv, “A theoretical and experimental investigation of the modes of optical resonators with phase-conjugate mirrors,” IEEE J Quantum Electron. 15(10), 1180–1188 (1979).
[CrossRef]

A. Yariv, D. Fekete, and D. M. Pepper, “Compensation for channel dispersion by nonlinear optical phase conjugation,” Opt. Lett. 4(2), 52 (1979).
[CrossRef] [PubMed]

1978 (3)

D. M. Pepper, D. Fekete, and A. Yariv, “Observation of amplified phase-conjugate reflection and optical parametric oscillation by degenerate four-wave mixing in a transparent medium,” Appl. Phys. Lett. 33(1), 41 (1978).
[CrossRef]

A. Yariv, “Phase Conjugate Optics and Real-Time Holography,” IEEE J Quantum Electron. 14(9), 650–660 (1978).
[CrossRef]

V. Wang and C. R. Giuliano, “Correction of phase aberrations via stimulated Brillouin scattering,” Opt. Lett. 2(1), 4–6 (1978).
[CrossRef] [PubMed]

1977 (2)

R. Hellwarth, “Generation of time-reversed wave fronts by nonlinear refraction,” JOSA 90007, 1976–1978 (1977).

D. M. Bloom and G. C. Bjorklund, “Conjugate wave-front generation and image reconstruction by four-wave mixing,” Appl. Phys. Lett. 31(9), 592 (1977).
[CrossRef]

1972 (1)

B. Zel’Dovich, V. Popovichev, V. Ragul’skii, and F. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel’shtam-Brillouin scattering,” J. Exp. Theor. Phys. 15, 109–112 (1972).

Auyeung, J.

J. Auyeung, D. Fekete, D. M. Pepper, and A. Yariv, “A theoretical and experimental investigation of the modes of optical resonators with phase-conjugate mirrors,” IEEE J Quantum Electron. 15(10), 1180–1188 (1979).
[CrossRef]

Bellanger, C.

Bjorklund, G. C.

D. M. Bloom and G. C. Bjorklund, “Conjugate wave-front generation and image reconstruction by four-wave mixing,” Appl. Phys. Lett. 31(9), 592 (1977).
[CrossRef]

Bloom, D. M.

D. M. Bloom and G. C. Bjorklund, “Conjugate wave-front generation and image reconstruction by four-wave mixing,” Appl. Phys. Lett. 31(9), 592 (1977).
[CrossRef]

Boccara, A. C.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[CrossRef] [PubMed]

Brignon, A.

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[CrossRef] [PubMed]

Caro, R. G.

Colineau, J.

Cui, M.

I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett. 101(8), 081108 (2012).
[CrossRef] [PubMed]

M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18(4), 3444–3455 (2010).
[CrossRef] [PubMed]

E. J. McDowell, M. Cui, I. M. Vellekoop, V. Senekerimyan, Z. Yaqoob, and C. Yang, “Turbidity suppression from the ballistic to the diffusive regime in biological tissues using optical phase conjugation,” J. Biomed. Opt. 15(2), 025004 (2010).
[CrossRef] [PubMed]

Dimarzio, C. A.

Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat Commun 3, 928 (2012).
[CrossRef] [PubMed]

Dunning, G. J.

Faizullov, F.

B. Zel’Dovich, V. Popovichev, V. Ragul’skii, and F. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel’shtam-Brillouin scattering,” J. Exp. Theor. Phys. 15, 109–112 (1972).

Fekete, D.

A. Yariv, D. Fekete, and D. M. Pepper, “Compensation for channel dispersion by nonlinear optical phase conjugation,” Opt. Lett. 4(2), 52 (1979).
[CrossRef] [PubMed]

J. Auyeung, D. Fekete, D. M. Pepper, and A. Yariv, “A theoretical and experimental investigation of the modes of optical resonators with phase-conjugate mirrors,” IEEE J Quantum Electron. 15(10), 1180–1188 (1979).
[CrossRef]

D. M. Pepper, D. Fekete, and A. Yariv, “Observation of amplified phase-conjugate reflection and optical parametric oscillation by degenerate four-wave mixing in a transparent medium,” Appl. Phys. Lett. 33(1), 41 (1978).
[CrossRef]

Feld, M. S.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical Phase Conjugation for Turbidity Suppression in Biological Samples,” Nat. Photonics 2(2), 110–115 (2008).
[CrossRef] [PubMed]

Feng, S.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
[CrossRef] [PubMed]

Fink, M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[CrossRef] [PubMed]

Fu, Y.

J. Li, Z. Peng, and Y. Fu, “Diffraction transfer function and its calculation of classic diffraction formula,” Opt. Commun. 280(2), 243–248 (2007).
[CrossRef]

Gigan, S.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[CrossRef] [PubMed]

Giuliano, C. R.

Gower, M. C.

Grange, R.

Hellwarth, R.

R. Hellwarth, “Generation of time-reversed wave fronts by nonlinear refraction,” JOSA 90007, 1976–1978 (1977).

Horstmeyer, R.

B. Judkewitz, Y. M. Wang, R. Horstmeyer, A. Mathy, and C. Yang, “Speckle-scale focusing in the diffusive regime with time-reversal of variance-encoded light (TROVE),” Nat. Photonics 7(4), 300–305 (2013).
[CrossRef] [PubMed]

Hsieh, C. L.

Huignard, J. P.

Jang, M.

Judkewitz, B.

B. Judkewitz, Y. M. Wang, R. Horstmeyer, A. Mathy, and C. Yang, “Speckle-scale focusing in the diffusive regime with time-reversal of variance-encoded light (TROVE),” Nat. Photonics 7(4), 300–305 (2013).
[CrossRef] [PubMed]

Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat Commun 3, 928 (2012).
[CrossRef] [PubMed]

Kane, C.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
[CrossRef] [PubMed]

Lai, P.

Lee, P. A.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
[CrossRef] [PubMed]

Lerosey, G.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[CrossRef] [PubMed]

Levenson, M. D.

Li, J.

J. Li, Z. Peng, and Y. Fu, “Diffraction transfer function and its calculation of classic diffraction formula,” Opt. Commun. 280(2), 243–248 (2007).
[CrossRef]

Lind, R. C.

Liu, H.

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5(3), 154–157 (2011).
[CrossRef] [PubMed]

Mathy, A.

B. Judkewitz, Y. M. Wang, R. Horstmeyer, A. Mathy, and C. Yang, “Speckle-scale focusing in the diffusive regime with time-reversal of variance-encoded light (TROVE),” Nat. Photonics 7(4), 300–305 (2013).
[CrossRef] [PubMed]

Matsushima, K.

McDowell, E. J.

E. J. McDowell, M. Cui, I. M. Vellekoop, V. Senekerimyan, Z. Yaqoob, and C. Yang, “Turbidity suppression from the ballistic to the diffusive regime in biological tissues using optical phase conjugation,” J. Biomed. Opt. 15(2), 025004 (2010).
[CrossRef] [PubMed]

Mosk, A. P.

Peng, Z.

J. Li, Z. Peng, and Y. Fu, “Diffraction transfer function and its calculation of classic diffraction formula,” Opt. Commun. 280(2), 243–248 (2007).
[CrossRef]

Pepper, D. M.

A. Yariv, D. Fekete, and D. M. Pepper, “Compensation for channel dispersion by nonlinear optical phase conjugation,” Opt. Lett. 4(2), 52 (1979).
[CrossRef] [PubMed]

J. Auyeung, D. Fekete, D. M. Pepper, and A. Yariv, “A theoretical and experimental investigation of the modes of optical resonators with phase-conjugate mirrors,” IEEE J Quantum Electron. 15(10), 1180–1188 (1979).
[CrossRef]

D. M. Pepper, D. Fekete, and A. Yariv, “Observation of amplified phase-conjugate reflection and optical parametric oscillation by degenerate four-wave mixing in a transparent medium,” Appl. Phys. Lett. 33(1), 41 (1978).
[CrossRef]

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[CrossRef] [PubMed]

Popovichev, V.

B. Zel’Dovich, V. Popovichev, V. Ragul’skii, and F. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel’shtam-Brillouin scattering,” J. Exp. Theor. Phys. 15, 109–112 (1972).

Psaltis, D.

C. L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, “Digital phase conjugation of second harmonic radiation emitted by nanoparticles in turbid media,” Opt. Express 18(12), 12283–12290 (2010).
[CrossRef] [PubMed]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical Phase Conjugation for Turbidity Suppression in Biological Samples,” Nat. Photonics 2(2), 110–115 (2008).
[CrossRef] [PubMed]

Pu, Y.

Ragul’skii, V.

B. Zel’Dovich, V. Popovichev, V. Ragul’skii, and F. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel’shtam-Brillouin scattering,” J. Exp. Theor. Phys. 15, 109–112 (1972).

Schimmel, H.

Senekerimyan, V.

E. J. McDowell, M. Cui, I. M. Vellekoop, V. Senekerimyan, Z. Yaqoob, and C. Yang, “Turbidity suppression from the ballistic to the diffusive regime in biological tissues using optical phase conjugation,” J. Biomed. Opt. 15(2), 025004 (2010).
[CrossRef] [PubMed]

Sentenac, A.

Steel, D. G.

Stone, A. D.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
[CrossRef] [PubMed]

Suzuki, Y.

Vellekoop, I. M.

I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett. 101(8), 081108 (2012).
[CrossRef] [PubMed]

E. J. McDowell, M. Cui, I. M. Vellekoop, V. Senekerimyan, Z. Yaqoob, and C. Yang, “Turbidity suppression from the ballistic to the diffusive regime in biological tissues using optical phase conjugation,” J. Biomed. Opt. 15(2), 025004 (2010).
[CrossRef] [PubMed]

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32(16), 2309–2311 (2007).
[CrossRef] [PubMed]

Wang, L.

Wang, L. V.

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5(3), 154–157 (2011).
[CrossRef] [PubMed]

Wang, V.

Wang, Y. M.

B. Judkewitz, Y. M. Wang, R. Horstmeyer, A. Mathy, and C. Yang, “Speckle-scale focusing in the diffusive regime with time-reversal of variance-encoded light (TROVE),” Nat. Photonics 7(4), 300–305 (2013).
[CrossRef] [PubMed]

Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat Commun 3, 928 (2012).
[CrossRef] [PubMed]

Wyrowski, F.

Xu, X.

Y. Suzuki, P. Lai, X. Xu, and L. Wang, “High-sensitivity ultrasound-modulated optical tomography with a photorefractive polymer,” Opt. Lett. 38(6), 899–901 (2013).
[CrossRef] [PubMed]

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5(3), 154–157 (2011).
[CrossRef] [PubMed]

Yamaguchi, I.

Yang, C.

B. Judkewitz, Y. M. Wang, R. Horstmeyer, A. Mathy, and C. Yang, “Speckle-scale focusing in the diffusive regime with time-reversal of variance-encoded light (TROVE),” Nat. Photonics 7(4), 300–305 (2013).
[CrossRef] [PubMed]

M. Jang, A. Sentenac, and C. Yang, “Optical phase conjugation (OPC)-assisted isotropic focusing,” Opt. Express 21(7), 8781–8792 (2013).
[CrossRef] [PubMed]

I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett. 101(8), 081108 (2012).
[CrossRef] [PubMed]

Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat Commun 3, 928 (2012).
[CrossRef] [PubMed]

M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18(4), 3444–3455 (2010).
[CrossRef] [PubMed]

E. J. McDowell, M. Cui, I. M. Vellekoop, V. Senekerimyan, Z. Yaqoob, and C. Yang, “Turbidity suppression from the ballistic to the diffusive regime in biological tissues using optical phase conjugation,” J. Biomed. Opt. 15(2), 025004 (2010).
[CrossRef] [PubMed]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical Phase Conjugation for Turbidity Suppression in Biological Samples,” Nat. Photonics 2(2), 110–115 (2008).
[CrossRef] [PubMed]

Yaqoob, Z.

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Figures (8)

Fig. 1
Fig. 1

Six misalignment parameters in the alignment of the sensor plane and SLM plane in three-dimensional space. In-plane translation ( Δ x and Δ y ), in-plane rotation ( Δ θ z ), axial translation ( Δ z ), and tip/tilt ( Δ θ x and Δ θ y ) are present. The reference beam is normal to the SLM plane and, thus, it is obliquely incident on the sensor plane.

Fig. 2
Fig. 2

A scheme of the auto alignment of a DOPC system. Flatness between the reference beam wave front and the SLM plane is optimized by the first two steps. Then, the misalignment parameters (three in-plane parameters Δ x , Δ y , Δ θ z , and axial translation Δ z ) are roughly measured. Next, the measured incoming wavefront is digitally propagated to the SLM plane with the roughly measured parameters to virtually achieve the rough alignment. At this step, an initial reconstructed DOPC signal (in our case a low contrast focal spot) can be observed. In the last step, all misalignment parameters are finely tuned around the roughly measured parameters while the intensity of the phase-conjugated focal spot (DOPC performance) is optimized.

Fig. 3
Fig. 3

Experimental scheme of digital OPC. The laser beam is split into two arms: a reference arm and a sample arm. Both arms are spatially filtered with single mode fibers and collimated by plano-convex lens. As the first step of DOPC procedure, the sCMOS camera captures the interferograms created by reference beam and signal beam transmitted through the scattering media (five layers of scattering film). Four-step phase-shifting method is used for the wavefront measurement of the signal beam. EOM, placed on sample arm, shifts the relative phase between two beams. Then, for the time-reversal playback, SLM is used to display the phase-conjugated wavefront, which is measured by the sCMOS camera and digitally propagated. The phase-conjugated light beam (SLM-reflected reference beam) is collimated through the turbid media and creates a focal spot on the CCD camera. Photo diode monitors the back-propagated reference light which is reflected off SLM and propagated back through the single mode fiber (SMF1) for flatness optimization of the reference beam. Microscope cover slip (used due to a high transmission-to-reflection ratio) is placed to sample the back-propagated light. The procedure is detailed in Fig. 4. The Rough Measurement System is used to roughly measure the misalignment between sCMOS camera and SLM in DOPC system. The procedure is described in detail in Fig. 5. Beam blocks stops beam paths to photo diode and the Rough Measurement System during DOPC procedure. SMF, single mode optical fiber; 0.5X TS, 0.5X telescope (from top to bottom); CL, collimation lens; BS, beam splitter; RF, retro reflector; L, lens; M, mirror; BB, beam block; PD, photo diode; EOM, electro-optic phase modulator; SLM, spatial light modulator; sCMOS, scientific CMOS camera; CCD, CCD camera.

Fig. 4
Fig. 4

Iterative searching for an SLM pattern assuring flatness of the reference wavefront to the SLM surface. (a) SLM iteratively displays the phase map that consists of the optimized phase map from the previous step and the “+1” part of a Hadamard pattern ( H n ). For each iteration, four measurements from the PD were obtained by stepping in phase on a Hadamard basis by π/2. An optimized phase map based the Hadamard basis was calculated using these four measurements. The PD signal inset shows the photo diode signal optimized during the iterative procedure. The Hardamad basis inset shows the 2D discrete Hardamad basis used for each iteration step (with the “+1” part in white and “-1” part in black). (b) Acquired phase map after two runs of the iterative procedure. This map optimizes the flatness between the reference wavefront and the SLM surface.

Fig. 5
Fig. 5

Rough measurement of the four major misalignment parameters. (a, b and c) Measurement of in-plane misalignment parameters. (a) Four Fresnel zone patterns are displayed on the SLM so that the mirror-reflected light creates four foci on the sCMOS sensor plane (two are shown here assuming the top view). (b) Four Fresnel zone patterns displayed on the SLM for the measurement of in-plane misalignment parameters. (c) Four foci created on the sCMOS sensor plane (magenta points). The overlaid white points are the ideal position of the four foci that the precisely aligned system is supposed to create. Δ x and Δ y are roughly measured by comparing the distances between the ideal spots and measured spots. Δ θ z is simply estimated by the angle between the horizontal line and the line connecting the bottom left point and the bottom right point (or the upper left point and the upper right point). (d, e, and f) Measurement of the axial displacement. (d) The single zone pattern is displayed. The lens is placed in between the mirror and the SLM so that the focused light is collimated, reflected off the mirror, and focused back on to the same plane with the original focal spot. Then, using the phase-stepping method, the wavefront of the back-propagated light into the sCMOS (by the interference between the red and green light rays) is measured. (e) The zone pattern displayed on the SLM for the measurement of the axial displacement. (f) The zone pattern measured from the sCMOS camera. By comparing the corresponding focal length of the displayed and the measured zone patterns (the focal length of the measured zone pattern is determined by fitted the measured profile along the dotted line to a 1D lens transmission function), the axial translation ( Δ z ) is determined.

Fig. 6
Fig. 6

Auto-alignment based on digital propagation with an angular spectrum method. First, the measured phase map from the sCMOS sensor array is multiplied with the phase gradient of the oblique reference beam (corresponding to Δ θ x and Δ θ y ) and Fourier transformed. Then, the Fourier components are multiplied with the transfer function based on the angular spectrum method (including tip/tilt and in-plane shifts). Thus, the five misalignment parameters ( Δ x , Δ y , Δ z , Δ θ x , and Δ θ y ) are taken account in this step. Then, the map in the Fourier domain is the inverse Fourier transformed to get the phase map on the SLM plane. At the final step, the phase map is rotated ( Δ θ z ) and interpolated at each SLM pixel position.

Fig. 7
Fig. 7

Optimization of the OPC reconstructed spot during the fine-tuning of the misalignment parameters. The peak intensities were measured from the CCD camera while scanning one parameter at a time. (a) and (e) for Δ x (red) and Δ y (blue). (b) and (f) for Δ z . (c) and (g) for Δ θ z . (d) and (h) for Δ θ x (red) and Δ θ y (blue). The upper row shows the signals measured during the rough scanning at the beginning of the fine-tune procedure. The bottom row shows the signals measured during the fine scanning at the end of the fine-tune procedure.

Fig. 8
Fig. 8

(a) Background and (b) DOPC reconstructed spot with roughly measured parameters and (c) optimized parameters (normalized by the optimized peak intensity with the fine-tuned parameter). (a) Without optimization, we observed only background as the misalignment significantly deteriorated the DOPC system. (b) With roughly measured parameters, the OPC peak was observed with low quality (PBR ~61). (c) With fine-tuned parameters, the peak intensity was 870 times increased. A PBR of ~ 52000 was observed, which corresponds to ~0.31 of the ideal PBR.

Tables (1)

Tables Icon

Table 1 Five case studies. An auto-alignment scheme was applied to five different misaligned configurations of the sCMOS sensor array and SLM. The values in between parentheses in the “Fine-tuned parameters” column are the differences between the roughly measured parameters and fine-tuned parameters. Thus, they present the accuracy of measurement on the four measured parameters. The values in between parentheses in the “Optimized PBR” column are the ratio of optimized PBR to the theoretical maximum, 180000 . Misalignment parameters are in units of μ m and degrees. As the control set, the result from a roughly aligned system is presented.

Equations (8)

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ksin( θ sam Δ θ xory )ksin(Δ θ xory )ksin( θ sam )
U S L M ( x , y ) = f x , f y U ^ S A ( f x , f y ) H A S ( f x , f y ) exp ( 2 π i f x x ) exp ( 2 π i f y y ) d f x d f y
H A S ( f x , f y ) = exp [ i k Δ z 1 ( λ f x ) 2 ( λ f y ) 2 ]
( f x , f y, f z ( f x , f y ))=T( f x ' , f y ' , f z ' ( f x ' , f y ' ))
R x =[ 1 0 0 0 cos(Δ θ x ) sin(Δ θ x 0 sin(Δ θ x ) cos(Δ θ x ) ) ]and R y =[ cos(Δ θ y ) 0 sin(Δ θ y ) 0 1 0 sin(Δ θ y ) 0 cos(Δ θ y ) ].
U SLM (xΔx,yΔy)exp(2πiΔx f x )exp(2πiΔy f y ) U ^ SLM ( f x , f y ).
U SLM (x,y)= f x , f y U ^ SA tip/tilt ( T 1 ( f x , f y , f z ( f x , f y ))) H AS ( f x , f y )| J( f x , f y , f z ( f x , f y )) | ×exp(2πi f x (x+Δx))exp(2πi f y (y+Δy))d f x d f y
J( f x , f y , f z ( f x , f y ))=( T 1,2 1 T 2,3 1 T 1,3 1 T 2,2 1 ) f x f z ( f x , f y ) +( T 1,3 1 T 2,1 1 T 1,1 1 T 2,3 1 ) f y f z ( f x , f y ) +( T 1,1 1 T 2,2 1 T 1,2 1 T 2,1 1 )

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