We demonstrate dynamic and arbitrary multisite two-photon excitation in three dimensions using the holographic projection method. Rapid response (fourth dimension) is achieved through high-speed noniterative calculation of the hologram using a video graphics accelerator board. We verify that the projected asymmetric spot configurations have sufficient spatiotemporal photon density for localized two-photon excitation. This system is a significant advance and can be applied to time-resolved photolysis of caged compounds in biological cells and complex neuronal networks, nonlinear microfabrication and volume holographic optical storage.
Advanced microscopy and diagnostic techniques require full three-dimensional (3D) access to the sample with fast dynamic control. Developments in array illumination schemes have facilitated simultaneous control and manipulation of multiple micro-particles [1][2][3] . Twodimensional (2D) patterned illumination techniques have also been used for high-speed 3D image rendering of a sample. Techniques based on programmable array microscopy 4 , structured illumination 5 , rotating Nipkow disks [6][7][8] are methods using 2D excitation patterns, confocal detection schemes and post-processing algorithms to render fluorescent samples in 3D. However, some experiments require an intrinsic 3D localized excitation response prior to detection. This can be achieved via non-linear two-photon excitation (2PE) 9 . Such experiments (e.g. photolysis of biomolecules) also require multiple excitation sites at arbitrary positions in 3D. The challenge is therefore to design a system that provides for arbitrary multi-site 2PE and meets the response time of biological tissues and cells, typically ~1 ms.
In this letter, we have expanded and combined the techniques of high-speed holographic beam control and non-linear multi-photon absorption to demonstrate a fully controllable multi-site 2PE in four dimensions. Our system significantly advances the implementation of 3D non-linear microscopy [7][8] , volume holographic storage 10 , microfabrication 11 and nano-surgery 12 . In neuroscience, our system allows for realistic simulation for summating simultaneous synaptic signals from multiple sites within complex dendritic trees of a neuron. Recently, multi-site single-photon (1P) photolysis in neuronal networks has been demonstrated 13 . However, 1P absorption is a linear process and suffers from poor 3D localized excitation.
Highly localized 2PE within a 3D diffraction-limited focal spot is achieved at high spatiotemporal photon densities provided by a focused femtosecond pulsed laser. Timemultiplexed multi-site 2PE has been shown to work with high-speed scanning via acousto-optic modulators (AOM) [14][15] . However, dispersion through an AOM crystal degrades the spatiotemporal quality of the femtosecond pulsed laser, especially when four AOM’s are used to project the focal spot in arbitrary 3D positions 16 . Multi-site 2PE along a plane has also been demonstrated with the holographic method that uses an iterative-adaptive optimization algorithm to produce photon efficient spot arrays 17 . They also incorporate a general lens function to shift the whole plane containing the spot array along the optical axis. On the contrary, we show a fast and arbitrary multi-site 2PE in all three dimensions. Each excitation site has a localized response in 3D. We derive the hologram using a non-iterative method and achieve optimal speeds by taking advantage of the parallel computing capability of a graphics accelerator board.
A phase hologram for 2PE at N arbitrary sites can be calculated with no iterative optimization procedure by the superposition of N fields 1,2 . Each field is a combination of prism and lens phase functions that describe the 3D position of a focal spot. The localized 2PE profile is derived by the square of the intensity distribution of the excitation focal spot. Aberrations disturb the excitation spots when they are arbitrarily positioned around the sample. To visualize these aberrations, we use the non-optimized holograms as input and calculate the 3D intensity profile using the Fresnel diffraction integral 18 . Fig. 1(a) shows the intensity distribution along the xzplane with two spots (N=2) symmetrically positioned (0, 0, f ±5/ξ) with respect to the nominal focus (f) of the lens. The normalized transverse (x,y) and axial (z) coordinates are related to spatial coordinates by
, respectively, where NA is the numerical aperture of the objective lens and λ is the wavelength of the laser. For N=2, the maximum normalized intensity of each spot is 0.405. The axial intensity distribution of the spots is characterized by aberrations with uneven side-lobes along the z-axis. These aberrations increase as the spots are positioned away from the focal plane of the lens. Fig. 1(b) shows N=4 spots positioned at (±2.25/η, 0, 5.25/ξ) at the top layer and (±2/η, 0, -5/ξ) at the bottom layer. For N=4, the maximum normalized intensity of each spot reduces to 0.2. No significant aberrations were observed when the spots are moved along the transverse direction. However, for highly symmetric spot configurations produced from non-optimized holograms, interference from higher diffraction orders affects the uniformity of the maximum spot intensities 19 . Upon implementation, encoding such holograms on a spatial light modulator (SLM) will introduce further losses 20 . Nonetheless, these losses and differences in spot intensities can be accounted for via optical theory.
More uniform spot intensities can be achieved via asymmetric and random spot configur
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