Optical transducer exploiting time-reversal symmetry

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1 Optical transducer exploiting time-reversal symmetry Seungwoo Shin 1,2, KyeoReh Lee 1,2, YoonSeok Baek 1,2, and YongKeun Park 1,2,3* 1 Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea. 2 KAIST Institute for Health Science and Technology, KAIST, Daejeon 34141, Republic of Korea. 3 Tomocube, Daejeon 3451, Republic of Korea. *Correspondence: Prof. YongKeun Park, Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea. Tel: (82) , yk.park@kaist.ac.kr One of the fundamental limitations in photonics is the lack of a transducer that can convert optical information into electronic signals or vice versa. In acoustics or at microwave frequencies, wave signals can be simultaneously received and transmitted by a single transducer. In optics, however, optical fields are generally measured via reference-based interferometry or holography using silicone-based image sensors, whereas they are modulated using spatial light modulators (SLMs). Here, we propose a scheme for an optical transducer using an SLM, without the need for an image sensor and interferometry. By exploiting time-reversal symmetry of light scattering, twodimensional optical fields can be received as well as transmitted by the optical transducer. We experimentally demonstrated the optical transducer for optical information consisting of spatial modes at visible and short-wave infrared wavelengths. The ability to measure or modulate both the amplitude and phase information of a light field is central to optical metrology, with potential applications in materials science, nanotechnology, and biophotonics 1, 2, 3, 4, 5. Optical phase information can be obtained indirectly by recording the patterns that are formed as a result of the interference of a sample beam with a well-defined reference beam. Interference-based holographic imaging techniques 6, 7, 8 have led to the emergence of various research disciplines, and their applications have been further expanded with recent advances in the development of silicon image sensors, such as charge-coupled devices and complementary metal-oxide-semiconductor devices. However, conventional holographic imaging techniques require both of an interferometer and an image sensor, and this requirement greatly restricts realization of an optical transducer. Radio or acoustic waves can be received and transmitted using bidirectional transducers such as an antenna (Figs. 1a b) 9, 1. On the contrary, the measurement and modulation of optical fields are achieved using separate principles: silicon-based image sensors are used to measure the interference patterns of the sample and reference beams that are generated in interferometry 2, 3, whereas spatial light modulators (SLMs) are used to modulate optical fields through the reorientation of liquid crystal molecules or the actuation of deformable surfaces or micro reflective elements 5, 11. The simultaneous reception and transmission of optical fields using a single electronic device or an optical transducer have not yet been demonstrated (Fig.1c). Here, we propose and experimentally demonstrate a scheme for an optical transducer using an SLM (Fig.1d). Instead of employing an interferometer and an image sensor, the proposed optical transducer receives and transmits optical fields by exploiting time-reversal symmetry of light scattering and the original functionality of an SLM, respectively.

2 The principle of receiving optical information is based on time-reversal symmetry of light scattering 12, 13. After a light-matter interaction, plane-wave illumination results in a scattered field S (Fig.1d). If the scattered field is propagated back to the sample in a time-reversed manner, the beam will become a plane wave after a light-matter interaction 12, 13. To use this time-reversal symmetry for receiving an incident field, we exploited time-reversal nature of optical phase conjugation. The optical phase conjugation of a monochromatic wave in the spatial domain is identical to the time reversal of the wave, E ( r, t) E( r, t) 12, 14. Thereby, a scattered field S can be rewound to a plane wave by modulating the scattered field using its optical phase conjugation S (Fig. 1d). By sequentially displaying complex-valued patterns on an SLM, the intensities of the modulated fields are measured by a point detector. Then, from the time-reversal discussion, the displayed pattern corresponding to the maximum intensity is uniquely determined as the optical phase conjugation of the incident field, from which both amplitude and phase images of the field can be produced (See the Supplementary Information). a radio waves b ultrasonic waves c optical waves optical field image electronic signal antenna electronic signal ultrasonic transducer (virtual) optical transducer d S S plane wave optical transducer transmitter receiver sample imaging optics spatial light modulator lens single point imaging by optical phase conjugation Figure 1 Bidirectional transducers in various waves and the proposed scheme for an optical transducer. a, b, Schematic illustrations of transducers in radio waves and ultrasonic waves. Using the transducers, radio (a) and ultrasonic (b) waves can be converted into electronic signals or vice versa. c, Schematic illustration of a virtual optical transducer: optical waves can be converted into optical field images or vice versa. d, The proposed scheme for an optical transducer. By exploiting time-reversal symmetry of light scattering, incident optical field information can be received using a spatial light modulator (SLM) and a point detector, without the need for an image sensor and construction of an interferometer. For transmission of optical waves, an SLM converts optical field images into optical waves, which is an original function of an SLM. For receiving optical fields in practice, it is crucial to effectively find the pattern which gives the maximum focused intensity after a lens. Recently, several algorithms have been developed to achieve point optimization 15, 16, 17. In this work, we utilized basis transformation. When an incident field S is modulated by a complex-valued map Dn, the intensity measured by a singlepoint detector located at the focus of a lens can be expressed as I D S D S da 2 2, n n k n where represents element-wise multiplication or the Hadamard product, k is a spatial frequency vector, and da denotes a surface integral. For effective working, we construct a i p set of displaying patterns using phase shifts and an arbitrary basis H as follows: e

3 i p Dn e Hq H1, where i,, and q 1 N, where N represents number of basis vectors in the basis H. Then, the intensity measured by the single-point detector is equal to 1 p 1,2,3 2 2 i p i p n q 1 q, (1) I e H S da H S da e s r where sq H q S da represents the decomposition coefficient of S calculated on a basis vector Hq and r H1 S da is a constant. By regarding the constant value r as a global phase and using the known phase shifts, the complex values sq for all q are obtained (see the Methods). The incident field in the standard basis can be expressed via a basis transformation. Note that the modulation patterns are combinations of the reference and basis vectors; therefore, our method for receiving fields inherently has the geometry of common-path interferometry. For experimental demonstrations, we used three optical components: a digital micromirror device (DMD) as an SLM, a lens, and a single-mode fibre (Fig. 2a). A DMD consists of up to a few million micromirrors, which are individually switchable between the on and off states at a speed of tens of khz. We utilized a DMD rather than a liquid-crystal SLM to achieve fast modulation of the light field and broadband operation. However, the proposed method is not limited only to this specific type of light modulator; any type of SLM, regardless of its amplitude or phase modulation, can be used. The workflow of an optical transducer when receiving optical fields are presented in Fig. 2. An incident field is sequentially modulated by multiple binary patterns displayed on a DMD (Figs. 2a b). The intensities of the modulated fields are then measured by a single-point detector (Fig. 2c). To construct the set of displaying patterns, Hadamard basis was used (Fig. 2d) 18. In addition, for displaying complex values on the DMD, we employed the superpixel method 19 (see the Methods). From the measured intensities by the single-point detector, the incident field can be retrieved as described below Eq. (1) (Fig. 2e). We first experimentally validated the optical transducer for receiving optical fields (Fig.3). An interconvertible set-up was used for the direct comparison of the proposed optical transducer as a receiver and conventional digital holography using an off-axis Mach-Zehnder interferometer (see the Methods and Supplementary Information). To demonstrate the feasibility of our method for various types of samples, we measured the fields diffracted by a phase object (a polystyrene bead with a diameter of 1 m, Figs. 3a b) and an amplitude object (the number 7 representing group 7 from the United States Air Force (USAF) resolution test chart, Figs. 3c d). Both the amplitude and phase images of the samples that were measured using the proposed method were well consistent with those obtained via conventional holographic imaging, thereby serving as a proof of principle for the optical transducer as a receiver. For an experimental demonstration of the proposed optical transducer, we designed an experiment as presented in Fig. 4. The optical transducer first receives a diffracted field from a cluster of 1m diameter polystyrene beads immersed in oil (Figs. 4a b). To verify the ability of reception and transmission of optical information using a single device, the optical transducer transmits the phase conjugation of the received field to the same cluster of the beads (Fig. 4c). By the time-reversal symmetry of light scattering, the transmitted wave becomes a plane wave after diffraction from the cluster. Then, the plane wave is measured and verified using an interferometer, which clearly shows the successful working of the optical transducer (Fig. 4d). In addition, for purposes of comparison, a diffracted field by the cluster of the beads under plane-wave illumination is measured by the conventional interferometer (Figs. 4e f). In

4 this work, to transmit optical fields using a DMD, amplitude holograms are displayed using time-multiplexing method2 (see Methods). a Dn S DMD photodiode single-mode fibre In (Dn S )k= 2 lens sample field, S b c D1 D2 d intensity (In ) D3N D3 e [e i ]-1 [I ] S pattern index (n ) Im -4 (rad) 4-1 p Re /2 3 /2 1 superpixel Dn D p 3 q on off (a.u.) e i p Hq H1 Figure 2 Working principle of the proposed optical transducer when receiving optical field information. a, The optical field S that is diffracted by a sample is modulated by a binary pattern Dn displayed on a digital micromirror device (DMD). The intensity of the modulated field at a single point is measured by a photodiode after passing through a lens and a single-mode fibre. b, Multiple binary patterns that are sequentially displayed on the DMD. c, Measured intensities corresponding to the displayed pattern index. d, Construction of binary i patterns using phase shifts and a Hadamard basis. e p and Hq denote the phase shift ( p {1, 2, 3} )and the qth basis vector of the Hadamard basis (q 1 N), respectively. The superpixel method of displaying a complexvalued map using a DMD is illustrated in the inset. e, The received incident field. The narrow arrows indicate the entire sequence of an optical transducer for receiving incident optical field information.

5 Figure 3 Experimental demonstrations of receiving optical fields diffracted from various samples. a-b, The field diffracted by a phase object, namely, a 1- m-diameter polystyrene bead immersed in oil, is received by the optical transducer (a) and conventional holography (b). c-d, The field diffracted by an amplitude object, namely, the numeral 7 representing group 7 in the United States Air Force (USAF) resolution test chart, is received by the optical transducer (c) and conventional digital holography (d). The amplitude and phase images are labeled with the symbols A and, respectively, in the bottom right corner of each figure. a optical transducer (receiver) b sample c DMD imaging optics lens SMFC photodiode optical transducer (transmitter) interferometer d A 1 m image sensor reference beam A e optical transducer (transmitter) f amplitude (a.u.) phase (rad) Figure 4 Experimental demonstrations of the optical transducer. a, The optical transducer receives an optical field diffracted by a cluster of 1- m-diameter polystyrene beads immersed in oil. SMFC; single-mode fibre coupler. b, The amplitude and phase images of the received field. c, The optical transducer transmits an optical A

6 amplitude (a.u.) depth (nm) depth (nm) depth (nm) field which is the phase conjugation of the received field. After a light matter interaction, the transmitted wave becomes a plane wave which can be verified using a conventional interferometer. d, The amplitude and phase images of the plane wave measured by the interferometer. e, For comparison, the optical transducer transmits a plane wave, and a diffracted field is measured by the interferometer. f, The amplitude and phase images of the diffracted field. The proposed scheme for an optical transducer offers several advantages. Because it does not require interferometry for measuring optical fields, the optical transducer allows to robustly receive and transmit optical information using a single device, without undesired fluctuations in interferometry. In addition, the fast operating speed of a DMD and high SNR achieved using the Hadamard basis ensure high-quality field measurements by significantly reducing the image deterioration caused by dark-current and read-out noise 21. Most importantly, the principle presented in this work can be readily applied to electromagnetic waves of other wavelengths, ranging from X-ray and deep ultraviolet wavelengths to infrared and terahertz wavelengths. To further demonstrate the applicability of the proposed method at other wavelengths, we used the optical transducer for receiving fields in the short-wave infrared (SWIR) at a wavelength of 1.55 m (Fig. 5). At SWIR wavelengths, silicon image sensors are blind; as an alternative, indium gallium arsenide (InGaAs) image sensors can be utilized, but their applications are highly limited because of their limited response and pixel resolution as well as their high price. A silicon wafer etched with patterns was used as the phase object for the SWIR experiment (Fig. 5a). A laser with a wavelength of 1.55 m and an InGaAs photodiode were employed (Fig. 5b), and the field diffracted from the wafer was measured using the optical transducer (Figs. 5c d). The height map d of the wafer was calculated from the measured phase image (x,y) (Fig. 5d) as d( x, y) x, y / 2 n, where n represents the difference between the refractive indices of silicon and air. To verify the SWIR field reception using the optical transducer, a topographic map of the letter P was measured via atomic force microscopy (AFM). For direct comparison, a magnified image of the height map obtained using the proposed method is shown alongside the topographic map measured via AFM (Fig. 5e). To systematically compare these images, the measured profiles are presented on the same plot (Fig. 5f); the results serve as validation of the field image measured in the SWIR. a b etched silicon wafer 1.55 m wafer sample (side view) imaging optics DMD lens InGaAs photodiode SWIR transducer (receiver) c d e f SWIR transducer AFM 1 2 m -2 AFM -2-2 along the profile Figure 5 Optical transducer in the short-wave infrared, where conventional silicon detectors are blind. a, A photograph of a silicon wafer, which acts as a phase object at a wavelength of 1.55 m. On the wafer,

7 repetitive patterns are etched to a depth of 2 nm in the form of the word PHASE. b, A beam whose wavelength is 1.55 m transmitted through the wafer is projected onto a DMD. The field diffracted by the pattern is received by the optical transducer. For visualization purposes, the DMD, which is in fact a reflective modulator, is depicted as a transmissive modulator. c, The amplitude image of the received field. d, The depth map of the wafer produced from the phase image of the received field. e, A magnified view of the portion of the depth map indicated by the dotted red box in d (upper) and a topographic map of the letter P (lower) as measured via atomic force microscopy. f, The depths along the profiles indicated in e. Recently, several studies have reported holographic imaging methods using single-pixel cameras in reference-based interferometry 22, 23, 24, 25, 26, 27. Due to the fluctuations of interferometers, these prior techniques have shown inferior performance for measuring phase images compared to the proposed optical transducer (see Supplementary Information). Also, unlike existing methods of wavefront measurement and shaping 5, 16, 28, 29 and digital optical phase conjugation 3, 31, 32, 33, our method does not require an interferometer and an image sensor, and thus, its applicability is significantly broader. From a technical perspective, the proposed method can be combined with illumination engineering methods to realize holographic imaging with sub-diffraction resolution using the synthetic aperture method 34, 35 or 3-D refractive index (RI) tomography exploiting optical diffraction tomography 36, 37, 38. Moreover, the optical transducer as a receiver can be extended to spectroscopic holography using the linear dispersion of a DMD and a spectrometer. In this work, 49,152 patterns were displayed on the DMD with a display rate of 1 khz, from which we acquired an optical field in 4.9 seconds. Although the present method has limitations with regard to dynamic studies because of the need for sequential measurements, algorithms for compressive sensing 21, 23 can be adapted to improve the image acquisition rate. In conclusion, we have proposed and experimentally demonstrated an optical transducer that can convert optical information into electronic images or vice versa. By exploiting timereversal symmetry of light scattering, a diffracted field from a sample can be precisely received and transmitted without the need for an interferometer and an image sensor. Furthermore, the applicability of the proposed method in the SWIR was verified by measuring complex field images at the wavelength of 1.55 m. We expect that the proposed method may offer solutions for wavefront shaping, adaptive optics, and high-fidelity holographic imaging at wavelengths where the applicability of high-quality image sensors is limited. Methods Field retrieval using a matrix representation In terms of the three different phase shifts, equation (1) can be represented in matrix form as [I] [e i ] [S], i 1 i I1 I3N 2 1 e e s1 r sn r i 2 i 2 I2 I3N 1 1 e e s1r snr, i 3 i 3 I3 I 3N 1 e e s1 r sn r where [I] and [S] are 3 N matrices constructed in the orders of the phase shifts and the basis vectors. The phaseshifting matrix [e i ] is a 3 3 invertible matrix. By multiplying the inverse of the phase-shifting matrix by the measured intensity matrix, the matrix [S] can be obtained as follows: [S] [e i ] 1 [I]. Then, from the second row of the obtained matrix [S], the complex values s q r can be obtained for q 1 N. Since the constant complex value r can be regarded as a global phase factor, we can then obtain the values s q for all q, which correspond to the incident field S represented in the Hadamard basis. Through a basis transformation, the incident optical field S can be represented in the standard basis. Superpixel method and the construction of binary patterns

8 To display a complex-valued map on the DMD, we utilized the superpixel method proposed by the Mosk group 19. With the appropriate placement of the single lens, linearly varying phase shifts can be assigned to each micromirror of the DMD, increasing by and /2 along the horizontal and vertical directions, respectively (inset of Fig. 2d). Thus, the phase shifts of the 4 neighbouring micromirrors in a rectangular region will be equally divided between and 2, allowing superpixels to be defined as 2 2 arrays of DMD micromirrors. To allow the phase shifts in a superpixel to be combined, the set-up should be designed such that the micromirrors in each superpixel are unable to be resolved by optics. Thus, by turning on different combinations of the micromirrors in a superpixel, 9 different complex values can be displayed. The addition of e i p H q, the phase-shifted q-th basis vector of the N-dimensional Hadamard basis, to H 1, the first basis vector, generates a complex-valued map, e i p H q + H 1, where and q 1 N. Then, a binary pattern D n is generated from the complex-valued map via the superpixel method. Since a superpixel must be able to modulate 9 different complex values, the phase shifts are set to, /2, and for p = 1, 2, and 3, respectively. For the construction of the binary patterns, we used the Hadamard basis method with N 128. With three phase shifts, patterns were displayed on the DMD with a display rate of 1 khz, from which we acquired an optical field in 4.9 seconds. The image acquisition rate depends on the number of spatial modes N and the display rate f of the DMD as f / 3N 2. Superpixels consisting of 2 2 arrays of DMD micromirrors were chosen; altogether, micromirrors were used to display binary patterns in the visible wavelength range. The numerical aperture of OL1 and the focal length of TL1 were appropriately selected to ensure that all micromirrors were unresolvable. In the SWIR range, because of the larger diffraction limit, each superpixel was chosen to consist of 4 4 DMD micromirrors, and in total, an array of micromirrors was used to display the binary patterns. p 1,2,3 Experimental set-up To experimentally validate the optical transducer for receiving optical fields, we constructed an interconvertible set-up for the direct comparison of two imaging methods: optical transducer as a receiver and conventional digital holography using a Mach-Zehnder interferometer (Figs. S2a-S2c). For a systematic comparison, a flip mirror and a 2 2 single-mode fibre optic coupler (2 2 SMFC; FC532-9B-FC, Thorlabs Inc.) were used to share the optical set-up between the two methods. To allow both conjugate planes of the sample plane to be used as the image planes for the two different imaging methods, the optical set-up was constructed symmetrically. The same visible laser ( 532 nm; LSS-532, Laserglow Inc.) was used as the source for both imaging methods. For the measurement of an optical field using the optical transducer, a plane wave was introduced into the optical set-up by the flip mirror (Fig. S2b). The plane wave impinged on the sample, and the beam diffracted by the sample was projected onto the DMD (maximum switching rate = 22.7 khz; V-71, Vialux Inc.) by an objective lens (OL1,.7 NA; LUCPLFLN6X, Olympus) and a tube lens (TL1, f 25 mm). Then, the optical field of the diffracted beam could be retrieved using the matrix representation as described. The optical field was sequentially modulated by multiple binary patterns, and an avalanche photodiode then measured the intensity of the light passing through a single lens and one arm of the 2 2 SMFC. Finally, by multiplying the inverse phase-shifting matrix by the measured intensity matrix, the optical field can be retrieved. For comparison, the optical field diffracted by the same sample was measured via Mach-Zehnder interferometry (Fig. S2c). The laser beam was split into two arms (sample and reference arms) by the 2 2 SMFC. To illuminate the sample with a plane wave, the optical transducer transmitted a planar wavefront. An objective lens (OL2,.7 NA; LUCPLFLN6X, Olympus) and a tube lens (TL2, f 18 mm) were used to project the beam diffracted by the sample onto a camera (FL3-U3-13Y3M-C, FLIR Inc.), where the sample beam interfered with a reference beam at a slightly tilted angle to generate an off-axis hologram. From the measured hologram, the optical field diffracted by the sample was retrieved via the Fourier transform method 39. To demonstrate the broadband capability of our method, a SWIR laser beam ( 1.55 m; SFL155P, Thorlabs Inc.) was directed onto an etched wafer sample by a 4-f telescopic system comprising a tube lens (TL2) and an objective lens (OL2,.3 NA; LCPNL1XIR, Olympus). The beam diffracted from the wafer was collected and projected onto the DMD by another 4-f telescopic system comprising a tube lens (TL1) and an objective lens (OL1,.65 NA; LCPNL5XIR, Olympus). The intensity of the light passing through a single-mode fibre (P3- SMF28E-FC-2, Thorlabs Inc.) was measured by an InGaAs switchable gain-amplified detector (PDA1CS-EC, Thorlabs Inc.). Time multiplexing method To transmit optical fields using a DMD, amplitude holograms are displayed using time-multiplexing method 2. Since the DMD can display only binary images, several binary images are sequentially displayed onto a sample. To effectively display an 8-bit image, the DMD displays 8 binary images with different temporal weightings, I 2 (8 n) b n, where I is an 8-bit image, 2 (8 n) is temporal weighting for displaying time, and b n are binary

9 images for n 1 8. In addition, since the objective lens (OL1) and a tube lens (TL1) are chosen for the superpixel method, the displayed amplitude holograms are spatially filtered and projected onto the sample plane. Sample preparation We used polystyrene beads with a diameter of 1 m (n at 532 nm, Sigma-Aldrich Inc.) immersed in index-matching oil (n at 532 nm, Cargille Laboratories). To separate aggregated beads, the beads in the immersion oil were sandwiched between coverslips before measurement. To measure the complex field diffracted by a phase object in the SWIR, we prepared a double-sided polished wafer on which repetitive patterns were dry etched. Data availability The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Acknowledgements The authors acknowledge H. S. Yeo in Korea Advanced Institute of Science and Technology for help in using AFM. This work was supported by KAIST, BK21+ program, Tomocube, and National Research Foundation of Korea (215R1A3A26655, 214M3C1A352567, 214K1A3A1A96327). Author contributions S.S. designed and performed the experiments. K.L. and Y.B. contributed analytic tools. Y.P. conceived and supervised the project. S.S and Y.P wrote the manuscript, which was revised by all authors. Correspondence and requests for materials should be addressed to Y.P. Competing financial interests The authors declare no competing financial interests. References 1. Hariharan P. Optical Holography: Principles, techniques and applications. Cambridge University Press (1996). 2. Popescu G. Quantitative phase imaging of cells and tissues. McGraw Hill Professional (211). 3. Lee K, et al. Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications. Sensors 13, (213). 4. Horstmeyer R, Ruan H, Yang C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature photonics 9, (215). 5. Yu H, et al. Recent advances in wavefront shaping techniques for biomedical applications. Current Applied Physics 15, (215). 6. Gabor D. A new microscopic principle. Nature 161, (1948). 7. Gabor D. Microscopy by reconstructed wave-fronts. In: Proc. R. Soc. A (ed^(eds). The Royal Society (1949). 8. Frauel Y, Naughton TJ, Matoba O, Tajahuerce E, Javidi B. Three-dimensional imaging and processing using computational holographic imaging. Proceedings of the IEEE 94, (26). 9. Fink M. Time reversal of ultrasonic fields. I. Basic principles. IEEE transactions on ultrasonics, ferroelectrics, and frequency control 39, (1992). 1. Lerosey G, De Rosny J, Tourin A, Fink M. Focusing beyond the diffraction limit with far-field time reversal. Science 315, (27). 11. Mosk AP, Lagendijk A, Lerosey G, Fink M. Controlling waves in space and time for imaging and focusing in complex media. Nature photonics 6, (212). 12. Potton RJ. Reciprocity in optics. Reports on Progress in Physics 67, 717 (24). 13. Born M, Wolf E. Principles of optics: electromagnetic theory of propagation, interference and diffraction of light. Elsevier (213). 14. Carminati R, Saenz J, Greffet J-J, Nieto-Vesperinas M. Reciprocity, unitarity, and time-reversal symmetry of the S matrix of fields containing evanescent components. Physical review A 62, (2). 15. Vellekoop IM, Mosk A. Phase control algorithms for focusing light through turbid media. Optics communications 281, (28). 16. Cui M. Parallel wavefront optimization method for focusing light through random scattering media. Optics letters 36, (211). 17. Yoon J, Lee K, Park J, Park Y. Measuring optical transmission matrices by wavefront shaping. Optics Express 23, (215).

10 18. Tao X, Bodington D, Reinig M, Kubby J. High-speed scanning interferometric focusing by fast measurement of binary transmission matrix for channel demixing. Optics express 23, (215). 19. Goorden SA, Bertolotti J, Mosk AP. Superpixel-based spatial amplitude and phase modulation using a digital micromirror device. Optics express 22, (214). 2. Lee K, Kim K, Kim G, Shin S, Park Y. Time-multiplexed structured illumination using a DMD for optical diffraction tomography. Optics Letters 42, (217). 21. Duarte MF, et al. Single-pixel imaging via compressive sampling. IEEE signal processing magazine 25, (28). 22. Clemente P, Durán V, Tajahuerce E, Torres-Company V, Lancis J. Single-pixel digital ghost holography. Physical Review A 86, 4183 (212). 23. Clemente P, Durán V, Tajahuerce E, Andrés P, Climent V, Lancis J. Compressive holography with a singlepixel detector. Optics letters 38, (213). 24. Sun B, et al. 3D computational imaging with single-pixel detectors. Science 34, (213). 25. Zhang Z, Ma X, Zhong J. Single-pixel imaging by means of Fourier spectrum acquisition. Nature communications 6, (215). 26. Stockton PA, Bartels R, Field JJ. Simultaneous fluorescent and quantitative phase imaging through spatial frequency projections. In: Frontiers in Optics 216 (ed^(eds). Optical Society of America (216). 27. Martínez-León L, Clemente P, Mori Y, Climent V, Lancis J, Tajahuerce E. Single-pixel digital holography with phase-encoded illumination. Optics Express 25, (217). 28. Vellekoop IM, Mosk A. Focusing coherent light through opaque strongly scattering media. Optics letters 32, (27). 29. Booth MJ. Wavefront sensorless adaptive optics for large aberrations. Optics Letters 32, 5-7 (27). 3. Yaqoob Z, Psaltis D, Feld MS, Yang C. Optical phase conjugation for turbidity suppression in biological samples. Nature photonics 2, (28). 31. Lee K, Lee J, Park J-H, Park J-H, Park Y. One-wave optical phase conjugation mirror by actively coupling arbitrary light fields into a single-mode reflector. Physical review letters 115, (215). 32. Park J, Park C, Lee K, Cho Y-H, Park Y. Time-reversing a monochromatic subwavelength optical focus by optical phase conjugation of multiply-scattered light. Scientific Reports 7, (217). 33. Hillman TR, et al. Digital optical phase conjugation for delivering two-dimensional images through turbid media. Scientific Reports 3, 199 (213). 34. Alexandrov SA, Hillman TR, Gutzler T, Sampson DD. Synthetic aperture Fourier holographic optical microscopy. Physical review letters 97, (26). 35. Lee K, et al. Synthetic Fourier transform light scattering. Optics express 21, (213). 36. Wolf E. Three-dimensional structure determination of semi-transparent objects from holographic data. Optics Communications 1, (1969). 37. Shin S, Kim K, Yoon J, Park Y. Active illumination using a digital micromirror device for quantitative phase imaging. Optics Letters 4, (215). 38. Kim K, Yoon J, Shin S, Lee S, Yang S-A, Park Y. Optical diffraction tomography techniques for the study of cell pathophysiology. Journal of Biomedical Photonics & Engineering 2, (216). 39. Takeda M, Ina H, Kobayashi S. Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry. J Opt Soc Am 72, (1982).