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Abstract
Computer-generated holography (CGH) has been adopted in two-photon optogenetics as a promising technique for selective excitation of neural ensembles. However, 3D CGH by nonconvex optimization, the state of art method, is susceptible to imprecise axial positioning, due to the quadratic phase approximation in 3D target generation. Even though the misplacement of targets in conventional CGH can be solved by pre-calibration, it still suffers from low efficiency and poor axial resolution of two-photon excitation. Here, we propose a novel CGH method based on non-convex optimization with spherical aberration compensation (SAC-NOVO). Through numerical simulations and two-photon excitation experiments, we verify that SAC-NOVO could achieve precise axial positioning for single and multiple expanded disk patterns, while ensuring high two-photon excitation efficiency. Besides, we experimentally show that SAC-NOVO enables the suppression of dark target areas. This work shows the superiority of SAC-NOVO for two-photon optogenetics.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
By modulating phase distribution at the Fourier surface, CGH can accurately manipulate three-dimensional light field distribution near the image plane. Recently, it has found widespread applications, including three-dimensional display [1–3], optical trapping [4–6], and optogenetics [7–10]. Specially, in the field of two-photon optogenetics [11], using CGH for selective excitation of neural ensembles has been highly desired [12–17]. Compared to single-photon optogenetics, two-photon optogenetics can provide a better spatial specificity and deeper penetration in scattering tissues.
To study the neural circuits, specific excitation of neural ensembles in 3D is necessary, where 3D CGH should be adopted. So far, a variety of algorithms have been proposed for 3D CGH, including superposition algorithm [18,19], GS algorithm [20–22], non-convex optimization (NOVO) algorithm [23], and DeepCGH [24] based on deep learning, etc. Superposition algorithm takes 3D targets as 2D targets distributed at different axial depths which are separate from each other. Then the phase distribution corresponding to each 2D target is superimposed to obtain the final phase distribution on the spatial light modulator (SLM). It takes the shortest calculation time, compared to other algorithms, however, the quality degrades in calculating multi-layer targets as the correlation between different target layers is not introduced. GS algorithm is the most widely adopted algorithm. In each iteration, the amplitude distribution of Fourier plane and image plane are replaced by laser source and 3D targets respectively, while the phase distribution is retained. Through multiple iterations, intensity distribution in the image space is constantly close to that of the 3D target. But GS algorithm could only define target areas where the light is desired, named as bright targets. In optogenetics, except for activating target neurons, it is also necessary to avoid light flowing into other neurons, so as not to cause false activation. Areas where light is not desired to pass through are called dark targets. GS algorithm fails in avoid exciting dark targets (i.e. neurons that are not expected to be excited), which would lead to artifacts. The NOVO method uses an optimization strategy to solve 2D phase searching problem, while defining specific loss functions for different 3D targets. With NOVO method, one can simultaneously define a loss function both containing bright and dark targets, which makes it very suitable for two-photon optogenetic applications. However, in conventional NOVO method, due to the use of quadratic phase approximation in searching phase masks, spherical aberration is introduced, thus leading to problems including imprecise positioning of the generated patterns and poor axial resolution. These drawbacks would reduce the efficiency of optogenetic excitation, or, even worse, lead to false excitation. DeepCGH uses unsupervised learning convolutional neural networks to compute accurate holograms with fixed computational complexity. However, pre-training with a large number of samples is required, which is time consuming. Besides, the quadratic phase approximation is used to describe the axial propagation of light, which would also introduce spherical aberration. Even though the misplacement of targets introduced by quadratic phase approximation in both conventional NOVO and DeepCGH can be solved by pre-calibration, the problem of low two-photon excitation efficiency still exist.
Here, we propose a new algorithm based on non-convex optimization with spherical aberration compensation (SAC-NOVO) for 3D CGH, which is compatible with high NA objectives and ensures precise axial positioning of generated patterns. In section 2, we introduce the experimental setup and the principle of SAC-NOVO. In section 3, to prove the superior performance of SAC-NOVO, we carry out numerical simulations and two-photon excitation experiments in fluorescence-dye on the generation of a single expanded disk pattern and multiple expanded disk patterns. Subsequently, we perform two-photon excitation experiments with sparse fluorescence beads to show the capability of SAC-NOVO in achieving precise and efficient excitation of targets. In section 4, we discuss how to set appropriate loss function according to practical applications.
2. Experimental setup and methods
The diagram of the experimental setup is shown in Fig. 1(a). We use a mode-locked Ti: Sapphire laser (Chameleon Discovery, Coherent) as the excitation source and rotate a half-wave plate (AHWP10M-980, Thorlabs) to ensure the diffraction efficiency of the phase-only SLM (X10468-07, Hamamatsu). Two groups of 4f systems (focal lengths are 100 mm, 200 mm, 60 mm, and 300 mm, respectively) are used to expand the beam to match the size of SLM window, which are shown as a beam expander in Fig. 1(a) for simplification. After the SLM, the beam is relayed and scaled through L1 (AC508-400-B, Thorlabs) and L2 (AC508-500-B, Thorlabs) to fit the rear pupil of the excitation objective 1 (25×, 1.05 NA, XLPLN25XWMP2, Olympus). The excitation wavelength is set to 1040 nm for the two-photon excitation of Sulforhodamine 101. Fluorescent signals are detected in two detection arms. To detect the fluorescence intensity distribution in XY direction generated at the focal plane of the objective 1, the fluorescence emitted from the dye pool is collected by the objective 1, followed by passing through a dichroic mirror (DMSP750B, Thorlabs) and a short-pass filter (ET750SP-2p8, CHROMA), then forms an image on CCD 1 (33UX265, DFK) by a tube lens (TTL200-A, Thorlabs). To detect the axial position of the generated excitation pattern directly, the fluorescence emitted from the dye pool is collected by the objective 2 (4×, 0.13 NA, Nikon, CFI Plan Fluor 4X), followed by passing through a short-pass filter (ET750SP-2p8, CHROMA) and a tube lens (TTL200-A, Thorlabs), then forms images on CCD 2 (72AUC02, DFK). The dye pool consists of a cuvette (1.5 mL, BRAND) and a cover glass (0.13-0.16 mm, CITOGLAS).
Fig. 1. (a) Optical setup of the two-photon 3D CGH excitation and detection system. HWP, half wave plate; BE, beam expander; M, reflective mirror; DM, dichroic mirror; SPF, short-pass filter; TL, tube lens. Inset: Photo of the vertical detection mode. The dye pool and the detection objective are mounted on three-axis translation stages separately. (b) The schematic diagram of SAC-NOVO. Pr, rear pupil plane of the objective (Fourier plane); P1, focal plane of the objective; Pk, a plane with a distance zk away from the focal plane; E, the electric field distribution on Pr; I1, the intensity distribution on P1; Ik, the intensity distribution on Pk; f, focal length of the objective; V+, bright areas in target intensity distribution; V-, dark areas in target intensity distribution. The positive z direction is defined as the beam propagation direction, and z=0 is at the focal plane.
In SAC-NOVO algorithm, 3D CGH is regarded as an optimization problem to solve the best 2D phase distribution $\varphi $ at the Fourier plane, so that the 3D intensity distribution $I(\varphi )$ modulated by the 2D phase is closest to the target intensity V, i.e. user-defined loss function L has the minimum value [23]:
Specifically, in each iteration, the chain rule is used to obtain partial derivative of the loss function to current phase distribution
During the phase searching progress, the 3D intensity distribution I near the focal plane is calculated. However, if the numerical simulation is based on a coarse phase approximation, the 2D phase obtained by the algorithm cannot accurately generate target patterns. Next, we use detailed theoretical analysis to illustrate this problem. As shown in Fig. 1(b), assuming a plane wave A0 is incident on the surface of SLM, the electrical field distribution E after phase modulation is
After being transformed by the objective in 2f configuration, the intensity distribution I1 at focal plane P1 is
where $\cal{F}$ means Fourier transform. In order to calculate intensity distribution Ik at plane Pk with a distance zk away from the focal plane, it is necessary to add an appropriate additional phase on the SLM to simulate divergence (or convergence) of the beam: where $\varPhi_k$ is the additional phase. In conventional NOVO, the additional phase was written as [23] where k is the free-space wavenumber. It is a parabolic phase distribution under paraxial approximation. Actually, for a high NA objective which satisfies the sine condition, the phase distribution on the rear pupil plane from an emitter which has a distance zk away from the nominal focal plane of the objective is [26,27]To this end, we propose to use cosine phase profile, as shown in Eq. (7), instead of second-order approximate phase, to describe the additional phase. In addition, in conventional NOVO, the effect of the refractive index of objective immersion medium was not taken into account, which can also cause the phase to deviate from the physical reality when non-air objectives (n≠1) are used. We correct such phase aberration in our proposed SAC-NOVO method. Our code is available on Github (https://github.com/Jincheng-jcc/SAC-NOVOCGH).
3. Simulation and experiment results
3.1 Single disk pattern generation by SAC-NOVO
In neural stimulation with two-photon optogenetics, as the opsins are on neuron membranes, one can adopt either spiral-scanning of the laser focus or direct targeting with expanded disks to excite enough opsins [28]. With the latter method, the opsins on neuron membranes can be excited at a time, which significantly shortens the response time. Therefore, we set the target of CGH as expanded disk patterns. We first simulate the effects of spherical aberration compensation on single expanded disk patterns with different target axial positions and different radii. In Figs. 2(a) and 2(b), we use SAC-NOVO and NOVO methods to calculate the required phase masks for a disk pattern with a radius of 5 µm (targeted axial position = 50 µm, lateral offset = 10 µm) at the rear pupil plane of the objective, respectively. The phase distributions in the low frequency region are similar, however, the phase mask calculated by SAC-NOVO has more high frequency details. The reason is that in low frequency region, the parabolic phase approximation could accurately describe the phase introduced by actual physical transmission, but as the aperture angle increases, it fails. As shown in Fig. 2(d), without spherical aberration compensation in CGH, lateral and axial resolutions of the generated the two-photon intensity distribution near the image plane are deteriorated, meanwhile, the axial position of the generated pattern deviates from the target. We then quantitatively characterize the quality of the disk patterns of different radii with conventional NOVO method in Figs. 2(e) and 2(f). Two-photon intensity falling into the target intensity region in each lateral section is integrated to obtain axial intensity distribution curve [7]. The full width at half maximum (FWHM) and the peak position of the Gaussian fitting curve are used to characterize the axial resolution and actual axial position of the expanded disk pattern [29], respectively. In Fig. 2(e), as the target axial position deviates from the focal plane (z = 0 µm), the axial resolution of expanded disk pattern without spherical aberration compensation becomes worse. Moreover, the spherical aberration has a great influence on the axial positioning of generated patterns. We define the axial positioning error δz as the difference between actual and target axial positions of the disk pattern. As shown in Fig. 2(f), δz increases as the targeted axial position leaving away from the focal plane (z = 0 µm), resulting from the increasing spherical aberration. Besides, δz increases as the radius of targeted disk increases. For example, for a disk pattern with a radius of 10 µm, an axial offset of ∼20 µm occurs when the targeted axial position is 100 µm, which cannot be tolerated in practical two-photon optogenetic excitation.
Fig. 2. Simulation results of single disk pattern generation by SAC-NOVO and conventional NOVO. (a, b) Phase masks for generating a disk pattern with a radius of 5 µm, an offset of 10 µm away from the original focus without phase modulation in x direction and a targeted z position at 50 µm, using SAC-NOVO and NOVO method, respectively. (c,d) 3D stack (upper), XZ cross sections (middle, at y=0) and XY cross sections (lower, at z=50 µm for (c) and z=40 µm) of the generated two-photon intensity distributions corresponding to phase masks (a) and (b), respectively. Stack size: 50×50×50 µm3. Scale bar: 10 µm. The central position of the focal point is considered as the origin without additional phase. (e) The relationship between the axial resolution of single disk patterns and the target axial positions for different disk radii (labelled in the legend), based on conventional NOVO method. FWHM: full width at half maximum. (f) The relationship between the axial positioning error δz of single disk patterns and the target axial positions for different disk radii (labelled in the legend), based on conventional NOVO method.
We further experimentally verify the improvement of SAC-NOVO in single disk generation. We first test the PSFs of the system at z = 100 µm before and after spherical aberration compensation, as shown in Fig. 3(a). The axial resolutions (in FWHMs) are 12.03 µm and 7.20 µm, before and after spherical aberration compensation, respectively. The axial resolution is increased by ∼40%. Then, we generate phase masks corresponding to single disk patterns at different target axial positions with different extended radii, based on SAC-NOVO and NOVO algorithms, respectively. We load them on the SLM for two-photon excitation in the fluorescence-dye pool. In Figs. 3(c)-(j), we show four pairs of patterns in XZ planes of the generated disks of different radii, detected by CCD2 in Fig. 1(a). In each pair, we show the results at different targeted axial positions, based on SAC-NOVO and NOVO algorithms, respectively. We merge a group of single patterns with different depths into a single image by maximum intensity projection. The axial intensity distribution of each pattern is fitted by the Gaussian function, and the actual axial position of the pattern is regarded as the peak position of the Gaussian curve. As shown in Fig. 3(l), SAC-NOVO can significantly reduce the axial positioning error of generated patterns as it introduces spherical aberration compensation in phase generation process. For example, compared with NOVO, SAC-NOVO can reduce the positioning error from 18 µm to 1.5 µm when the targeted axial offset is 100 µm. Indeed, the misplacement of targets in conventional CGH can be solved by pre-calibration [30]. When NOVO is used, the mapping relationship between actual excitation positions and target positions can be calibrated in advance. However, it can be seen from Fig. 3 that the spots generated by the NOVO suffer from low axial resolutions, leading to pour excitation efficiency.
Fig. 3. Experimental results of single disk pattern generation by SAC-NOVO and conventional NOVO. (a) PSFs of our system before (upper) and after (lower) spherical aberration compensation at z=100 µm. Scale bar: 5 µm. (b) The axial intensity distribution of PSFs before and after spherical aberration compensation. ‘o’ indicates the original data, while ‘-’ indicates the Gaussian fitting data. (c, d), (e, f), (g, h) and (i, j) show the two-photon fluorescence intensity in XZ section for target positions from -100 µm to 100 µm, when the radii of targeted single disks are 0.5 µm, 2 µm, 5 µm and 10 µm, respectively. Results from SAC-NOVO are labeled with blue boxes, and results from conventional NOVO are labeled with red boxes. Scale bar: 10 µm. The target axial position range in (c-j) is -100 to 100 µm. The axial interval is 25 µm in (c-h), while it is 50 µm in (i, j). (k) The relationship between the axial positioning error δz and the target axial positions of single disk patterns, for different disk radii. Circles: data from SAC-NOVO, asterisks: data from NOVO. (l) Intensity contrast comparison of SAC-NOVO and NOVO. Radii of target patterns are 0.5 µm and 5 µm, respectively.
As shown in Figs. 3(c)-(j), the pattern generated by SAC-NOVO usually has higher peak intensity than that generated by conventional NOVO at axial positions away from z = 0. It is necessary to quantitatively compare the energy changes of these two methods. Here, we select two typical target sizes for comparison, as shown in Fig. 3(l). The contrast ratio metric is defined as the ratio of the peak energy of the current pattern to the peak energy of the pattern with the highest intensity. The maximal axial-range is defined as where the contrast ratio is >0.6. For patterns generated by SAC-NOVO, the maximal axial-ranges are 190.33 µm (R = 0.5 µm) and 171.84 µm (R = 5 µm), respectively. For patterns generated by NOVO, the maximal axial-ranges are 82.9 µm (R = 0.5 µm) and 140.91 µm (R = 5 µm), respectively. Therefore, SAC-NOVO can effectively increase the maximal axial-range, and the smaller the pattern size is, the more obvious the increase of axial-range is.
3.2 Simultaneous generation of multiple disk patterns by SAC-NOVO
In practical photo-stimulation of neural activities based on two-photon optogenetics, many complex neural circuits and behaviors are based on the orchestrated interaction of multiple neurons [31,32]. Here we generate multiple disks simultaneously based on both NOVO and SAC-NOVO algorithms, and show two-photon fluorescence patterns excited in the dye pool in Fig. 4. In Figs. 4(a) and 4(b), we generate 5 vertically-aligned disks simultaneously, based on SAC-NOVO and NOVO algorithms, respectively. It can be seen that as the axial displacement increases, the pattern energy of disks generated by NOVO algorithm [Fig. 4(b)] decreases significantly, and the axial resolution deteriorates. In comparison, the pattern energy of disks generated by SAC-NOVO algorithm decreases slightly with the increase of axial displacement [Fig. 4(a)], which is mainly caused by the decrease of diffraction efficiency [33]. Figures 4(c) and 4(d) suggest that multiple disk patterns generated by the SAC-NOVO algorithm have better axial positioning precision. In Figs. 4(e) and 4(f), 4(g) and 4(h), we also generate 3 and 4 disks simultaneously, aligned in 3D, based on SAC-NOVO and NOVO algorithms, respectively. Similar conclusions can be achieved as above.
Fig. 4. Experimental results of simultaneous generation of multiple disk patterns by SAC-NOVO and NOVO, respectively. The two-photon fluorescence patterns excited in the dye pool are shown (detected by CCD2). (a,b) Simultaneous generation of 5 vertical-aligned disks, based on SAC-NOVO and NOVO, respectively. Targeted axial positions of the disks: from -100 to 100 µm, with axial interval of 50 µm. These disks are targeted at 10 µm away laterally from the original focus without phase modulation in x direction. (c) Axial intensity distribution curves, obtained by integrating intensity along x direction in (a, b). (d) The relationship between the axial positioning error δz and the targeted axial positions of multiple disk patterns shown in (a, b). (e,f) Simultaneous generation of 3 disk patterns in 3D. Targeted axial positions of the disks: from -50 to 50 µm, with axial interval of 50 µm, and lateral offsets are set as 30 µm and 10 µm. (g,h) Simultaneous generation of 4 disk patterns in 3D. Targeted axial positions of the disks: from -75 to 75 µm, with axial interval 25 µm, and lateral offsets are set as 30 µm and 10 µm. Circled with blue are obtained by SAC-NOVO, while circled with red are obtained by NOVO. Radius of target disk: 0.5 µm. Scale bar: 5 µm.
We also compare the performance of global GS, NOVO, and SAC-NOVO algorithms in the simultaneous generation of multiple disk patterns. As an example, we set the targeted intensity distribution of three-disk pattern (radius = 5 µm) with an axial interval of 50 µm and a lateral interval of 20 µm. In Fig. 5, we show the simulation and experimental results. From Figs. 5(d), (g) ,(j), it can be seen that high intensity distribution in non-targeted areas exists based on the phase calculated by GS algorithm. This is due to the fact that GS algorithm could only define bright target areas, while causing the search result to fall into a local optimal solution. In Figs. 5(e), (h), (k), NOVO algorithm can define dark areas so as to optimize the light field distribution, but the issues of axial positioning exists. In comparison, SAC-NOVO can define dark areas and compensate the spherical aberration, thereby improving the axial positioning precision and the resolution of generated patterns [Figs. 5(f), (i), (l)].
Fig. 5. Simulation and experimental results of multiple disk pattern generation, based on global GS, NOVO and SAC-NOVO algorithms, respectively. Targeted radius of patterns: 5 µm. Targeted axial positions: from -50 to 50 µm, with an axial interval of 50 µm, and lateral offsets of 30 µm and 10 µm. (a-c) Phase masks generated by global GS, NOVO, and SAC-NOVO algorithms, respectively. (d-f) Simulation results of the two-photon intensity distribution of targeted 3 disks, corresponding to phase masks (a-c), respectively. Stack size: 50×50×150 µm3. (g-i) Maximum intensity projections in XZ plane corresponding to (d-f), respectively. Scale bar: 10 µm. (j-l) Experimental results of the two-photon fluorescence patterns excited in the dye pool (detected by CCD2), corresponding to phase masks (a-c), respectively.
3.3 Two-photon selective excitation of fluorescent beads based on 3D CGH
To mimic the photo-stimulation in two-photon optogenetics, we selectively excite fluorescent beads based on 3D CGH of different algorithms. Fluorescent beads of 2 µm diameter are diluted in 2% agarose as sparse excitation targets, and we use CCD 2 to detect the excitation of fluorescent beads at XZ cross sections.
We first perform two-photon excitation experiments of a single bead. By loading a flat phase on the SLM, we move the 3D translation stage to get a bead at the excitation focus. Then we move the fluorescence bead to a targeted position, and load corresponding phase masks, generated by SAC-NOVO and NOVO, respectively, onto the SLM. We check if the fluorescence bead can be excited with these two phase masks. When the targeted axial displacement is 100 µm or -100 µm, the phase mask generated by SAC-NOVO enables precise excitation of the fluorescence bead, as shown in Fig. 6(c). In contrast, the fluorescent bead cannot be excited with the corresponding phase mask generated by NOVO. Then we move the bead axially to find the actual excitation position (defined as the position where the highest excitation efficiency is achieved) by NOVO. As shown in Fig. 6(d), z = 92 µm (or z =-91 µm) is the actual excitation position when the targeted axial displacement is 100 µm (or -100 µm). It should be noted that the imprecise positioning in NOVO methods not only reduces the excitation efficiency, but also has a risk of stimulating neighboring beads by mistake.
Fig. 6. Two-photon selective excitation of fluorescent beads based on 3D CGH. (a) Schematic diagram of exciting a single fluorescent bead. The solid yellow star shows the excitation pattern, while the blue bead shows the fluorescent bead. The dashed plane represents the original focal plane. (b) The excitation of a single bead at focal plane, with flat phase on SLM. (c) The excitation of a single bead by loading the phase generated by SAC-NOVO. The images of the beads at targeted bead positions: z = -100 µm and z = 100 µm are overlaid. (d) The excitation of a single bead by loading the phase generated by NOVO. To get the images of the beads, stage offset Δz = 9 µm and Δz = -8 µm are carried out to get the brightest position of the bead. The images at two positions are overlaid. Scale bar: 10 µm. (e) Schematic diagram of exciting multiple fluorescent beads. (f) The excitation of two beads by loading the phase generated by SAC-NOVO. Targeted bead positions: bead 1, x = -49.5 µm, y = 14 µm, z = -102.5 µm; bead 2, x = 49.5 µm, y = -14 µm, z = 102.5 µm. (g) The excitation of two beads by loading the phase generated by NOVO. Same target information as in c. (h, i) The excitation of two beads with same phase mask as in (g) generated by NOVO, by moving the beads position to make a single bead reach the brightest. Δz = 8 µm and Δz = -8 µm for (h) and (i), respectively. Scale bar for (f-i): 20 µm.
Then, we also perform two-photon excitation of multiple beads simultaneously. By loading a flat phase on the SLM, we search for two beads at different depths. Then we move the 3D stage to a position to make these two beads being symmetric about the original focus with the flat phase mask [Fig. 6(e, left)]. By loading the corresponding phase masks, generated by the SAC-NOVO and NOVO with targeted positions, onto the SLM, we can check their excitation effects [Fig. 6(e, right)]. As shown in Figs. 6(f) and (g), the pattern generated by SAC-NOVO enables simultaneous excitation of the two target beads, while the pattern generated by NOVO could not. Moreover, by fine-tuning the 3D stage, we verify that the pattern generated by NOVO can only excite one of the two beads with low excitation efficiency [Figs. 6(h) and (j)]. It suggests the advantages of SAC-NOVO in simultaneous two-photon excitation of multiple targets.
4. Discussions and conclusions
We show that, with the proposed SAC-NOVO, spherical aberration introduced by parabolic phase approximation in 3D CGH could be compensated. When using SAC-NOVO to generate a phase mask, it is necessary to reasonably define loss function according to the characteristics of the actual patterns. More specifically, how to define the target intensity restriction in loss function is important. In this work, for single expanded pattern generation, we only limit the intensity distribution inside each disk, while the intensity distribution outside the disk is not considered. Compared with restricting the entire space, this way could relax search conditions and obtain search results of higher diffraction efficiency in the target area. In generating multiple expanded disk patterns, both bright field restriction on the target disk and the dark field restriction on the non-target area are used, so as to achieve the suppression of non-target intensity distribution.
In SAC-NOVO, the computation speed is similar to that in NOVO, because only the transfer function is modified. We use CPU (Intel Core I5-6200U CPU @2.30GHz) as the processor, to generate holograms of size 600 × 600, with 50 iterations. When a single pattern is generated, it takes ∼110s for NOVO and SAC-NOVO, while it costs only ∼6s for GS. Of course, GPU will be beneficial in improving the computing speed [23,24]. Compared with SAC-NOVO, deepCGH [24] would be much faster once the neural network is pre-trained. It is expected that the spherical aberration compensation method proposed in SAC-NOVO can also improve the accuracy and efficiency of the pattern generation by deepCGH.
In summary, we systematically demonstrate the performance of SAC-NOVO in generating two-photon extended patterns through theoretical analysis, simulation, and experiments. Compared with conventional CGH methods, SAC-NOVO has the capability in precise axial positioning and giving dark field limitation simultaneously, which is promising in two-photon optogenetics.
Funding
National Natural Science Foundation of China (61831014, 61771287, 32021002); “Bio-Brain+X” Advanced Imaging Instrument Development Seed Grant; Tsinghua University Initiative Scientific Research Program (Tsinghua University - Cambridge University Joint Research Initiative Fund); Graduate Education Innovation Grants, Tsinghua University (201905J003).
Acknowledgments
LK thanks the support from Tsinghua University, the “Thousand Talents Plan” Youth Program, and Beijing Frontier Research Center for Biological Structure.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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