The wide-field optical sectioning of microlens array and structured illumination-based plane-projection multiphoton microscopy

doi:10.1364/OE.21.002097

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The wide-field optical sectioning of microlens array and structured illumination-based plane-projection multiphoton microscopy

Jiun-Yann Yu, Daniel B. Holland, Geoffrey A. Blake, and Chin-Lin Guo »View Author Affiliations

Optics Express, Vol. 21, Issue 2, pp. 2097-2109 (2013)
http://dx.doi.org/10.1364/OE.21.002097

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Abstract

We present a theoretical investigation of an optical microscope design that achieves wide-field, multiphoton fluorescence microscopy with finer axial resolution than confocal microscopy. Our technique creates a thin plane of excitation light at the sample using height-staggered microlens arrays (HSMAs), wherein the height staggering of microlenses generate temporal focusing to suppress out-of-focus excitation, and the dense spacing of microlenses enables the implementation of structured illumination technique to eliminate residual out-of-focus signal. We use physical optics-based numerical simulations to demonstrate that our proposed technique can achieve diffraction-limited three-dimensional imaging through a simple optical design.

1. Introduction

Fluorescence is one of the most important optical contrasts in biological imaging, for it offers high molecular sensitivity and specificity. The general desire for obtaining three-dimensional (3D) information of dynamic biological systems has spurred the development of several fluorescence microscopies [1

J. B. Pawley, Handbook of Biological Confocal Microscopy , 3rd ed. (Springer, 2006). [CrossRef]

–4

D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express 13, 1468–1476 (2005). [CrossRef] [PubMed]

] with the ability to selectively image thin sections of an intact sample. This ability of optical sectioning can be categorized into two general regimes - intrinsic and extrinsic. Intrinsic optical sectioning utilizes an axially peaked excitation profile along the imaging path to obtain optical sectioning; examples include two-photon excitation microscopy (2PE) [2

W. Denk, J. Strickler, and W. Webb, “2-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990). [CrossRef] [PubMed]

] and selective plane illumination microscopy (SPIM) [3

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305, 1007–1009 (2004). [CrossRef] [PubMed]

]. Extrinsic optical sectioning is performed post-excitation and primarily relies on a far-field imaging principle: the higher spatial-frequency components of the images decay more rapidly with defocusing [5

T. Wilson, Confocal Microscopy (Academic Press, 1990).

]. As a result, one can create a high-spatial-frequency excitation pattern and use appropriate spatial filters to selectively extract the in-focus signal. Confocal microscopy (CFM) [5

T. Wilson, Confocal Microscopy (Academic Press, 1990).

] and structured illumination microscopy (SIM) are two examples that use physical and numerical spatial filters, respectively, to achieve equivalent optical sectioning [6

M. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett. 22, 1905–1907 (1997). [CrossRef]

Present imaging techniques, however, have important drawbacks. For CFM and 2PE, phototoxicity and photothermal damages are noted [1

J. B. Pawley, Handbook of Biological Confocal Microscopy , 3rd ed. (Springer, 2006). [CrossRef]

, 7

B. Masters, P. So, C. Buehler, N. Barry, J. Sutin, W. Mantulin, and E. Gratton, “Mitigating thermal mechanical damage potential during two-photon dermal imaging,” J. Biomed. Opt. 9, 1265–1270 (2004). [CrossRef] [PubMed]

], and are exacerbated if video-rate acquisition is required. To reduce these effects, spatially/temporally parallelized CFM/2PE systems, such as spinning disk confocal [8

I. Akira, T. Takeo, I. Katsumi, S. Yumiko, K. Yasuhito, M. Kenta, A. Michio, and U. Isao, “High-speed confocal fluorescence microscopy using a nipkow scanner with microlenses for 3-d imaging of single fluorescent molecule in real time,” Bioimaging 4, 57–62 (1996-06).

], multifocal multiphoton microscopy (MMM) [9

J. Bewersdorf, R. Pick, and S. Hell, “Multifocal multiphoton microscopy,” Opt. Lett. 23, 655–657 (1998). [CrossRef]

], and time-multiplexed multifocal multiphoton microscopy (TM-MMM) [10

V. Andresen, A. Egner, and S. Hell, “Time-multiplexed multifocal multiphoton microscope,” Opt. Lett. 26, 75–77 (2001). [CrossRef]

] were developed. In these techniques, multiple foci are created as independent, parallel channels for excitation in and detection from the sample. To reduce crosstalk among parallel channels, however, the foci spacing has to be sufficiently sparse (typically <1 foci per 10²-focus area, see Appendix A, B), which limits the degree of parallelization. SIM and SPIM do not suffer from parallelization issues; however both techniques have their own limitations. SIM can lead to significant photobleaching and low signal-to-noise ratio (SNR) in the processed images, because it excites fluorophores and receives fluorescence over a wide axial range at each acquisition. SPIM requires a compromise between axial resolution and the size of the field of view. Moreover, SPIM raises design issues and challenges in sample handling and manipulation for its separate excitation and imaging objectives in close proximity.

In principle, intrinsic and extrinsic optical sectioning can be combined to take the advantages of both. For example, it has been shown that a SPIM system can incorporate SIM to improve its optical sectioning when a reasonably large field of view is desired [11

P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. K. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods 7, 637–U55 (2010). [CrossRef] [PubMed]

]. Here, we propose a hybrid optical microscope design (Fig. 1) incorporating SIM and temporal focusing [4

D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express 13, 1468–1476 (2005). [CrossRef] [PubMed]

], a wide-field, intrinsic sectioning technique. Our design utilizes height-staggered microlens arrays (HS-MAs) having periodic patterns (Fig. 1(b)) to precisely control the time staggering for temporal focusing, and to provide an excitation pattern for SIM to further suppress residual out-of-focus signal. We herein refer to this approach as Microlens Array and Structured Illumination-based Plane-Projection Multiphoton Microscopy (MASI-PPMP).

Fig. 1 (a) Setup of MASI-PPMP. L₁ is the microscope objective lens. L₂ and L₃ are tube lenses of focal length f_T. XY stage performs the lateral translations for SIM. The specimen plane is defined as the focal plane of the objective lens L₁. (b) Illustration of a spiral HSMA used in this study.

2. MASI-PPMP: integrating (intrinsic) temporal focusing and (extrinsic) SIM

We have previously demonstrated a new technique, plane-projection multiphoton microscopy (PPMP) [12

J.-Y. Yu, C.-H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C.-L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt. 16, 116009 (2011). [CrossRef] [PubMed]

], in which temporal focusing with randomized excitation patterns is achieved through the randomly staggered light pulses (in the time domain) created by the surface roughness of a ground-glass optical diffuser. The randomized excitation patterns, as suggested by a previous report [13

C. Ventalon and J. Mertz, “Quasi-confocal fluorescence sectioning with dynamic speckle illumination,” Opt. Lett. 30, 3350–3352 (2005). [CrossRef]

], could be used for SIM. However, mitigating the excitation patterns in the processed images requires considerable effort. For simplicity, periodic excitation patterns are commonly used [6

M. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett. 22, 1905–1907 (1997). [CrossRef]

], and chosen for the present study. Further, the design control afforded in the HSMA allows for optimization of the intrinsic sectioning.

The combination of the microlens arrays and temporal masks, as used in TM-MMM [14

A. Egner and S. Hell, “Time multiplexing and parallelization in multifocal multiphoton microscopy,” J. Opt. Soc. Am. A 17, 1192–1201 (2000). [CrossRef]

], can provide equivalent functions of the proposed HSMAs, although additional precision alignment and positioning are required. Notably, the step sizes of time staggering Δt in TM-MMM and MASI-PPMP are different. In TM-MMM, Δt is set to be much larger than the pulse duration τ₀ to reduce temporal inter-foci interferences [14

A. Egner and S. Hell, “Time multiplexing and parallelization in multifocal multiphoton microscopy,” J. Opt. Soc. Am. A 17, 1192–1201 (2000). [CrossRef]

], by which individual foci can be considered as independent, parallel channels. In contrast, MASI-PPMP allows Δt < τ₀ for practical reasons detailed below and in Supplementary Materials.

We begin the design of MASI-PPMP with consideration of the physical limitations of HS-MAs. The dimensions of HSMAs are limited by fabrication technologies as well as diffractive losses. Existing techniques cannot straightforwardly engineer micro-optics of depth variation >1 mm [15

J. Jahns and K.-H. Brenner, Microoptics: from Technology to Applications , vol. v. 97 (Springer, 2004).

]. In addition, when we consider the HSMA as an array of time-delay channels, a light pulse propagating in one channel can leak into its neighboring channels due to the nature of diffraction. A simple estimation of the appropriate dimensions of HSMAs is given in Appendix A. In short, to have negligible inter-channel light leakage, the spatial parameters of the HSMAs should satisfy

d \geq \sqrt{λ_{0} Δ h_{\max}},

(1)

where d is the aperture diameter of a single time-delay channel, λ₀ is the central wavelength of the excitation light (here ∼ 800 nm), and Δh_max is the height staggering between the longest and shortest time-delay channels. Accordingly, we restrict Δh_max to ∼ 300 μm and 36 μm ≥ d ≥ 18 μm, via Eq. (1). These dimensions make the HSMA fabrication feasible through existing techniques, and can create up to ∼ 10⁶ foci within a 2-inch aperture, thereby providing the periodic, high-spatial-frequency pattern for SIM. For a simple analysis, we assume that the total amount of time delay Δt_tot is separated equally into N_t distinct time-delay steps (with step size Δt, Eq. (2)). These time-delay steps are then arranged in a prescribed periodic pattern in the HSMA (Fig. 1(b)). Considering the propagation speed of light in a material, we have

Δ t_{tot} \equiv (N_{t} - 1) \times Δ t = \frac{Δ h_{\max} (n - 1)}{c},

(2)

where c and n are the speed of light in vacuum and the refractive index of the material of the HSMAs (set to be 1.5), respectively.

Because of the limitation of Δh_max, the estimated Δt in Eq. (2) can be around or shorter than the pulse duration of conventional ultrafast oscillators or amplifiers above certain values of N_t. In such cases, we should take into account the temporal interferences among light pulses of different time delays. Notably, temporal masks with much larger Δt_tot have been proposed to avoid temporal interferences and to achieve scanningless TM-MMM [14

A. Egner and S. Hell, “Time multiplexing and parallelization in multifocal multiphoton microscopy,” J. Opt. Soc. Am. A 17, 1192–1201 (2000). [CrossRef]

]. However, Eqs. (1) and (2) indicate that the required Δh_max falls far beyond the limits of existing fabrication techniques, and the aperture sizes of these temporal masks could be too large for standard biomedical microscopes (see Appendix B).

To have fabrication-feasible HSMAs and to improve the SNR of the SIM post-processed images, we turn to optimizing the parameters of HSMAs. In the following sections, we first construct a model that considers the temporal interferences (§3); through this model we investigate how intrinsic optical sectioning depends on the choice of N_t (and Δt) for a given Δt_tot (§4), and the arrangement of time delays in the HSMA (Appendix C). Then, we couple HSMAs with SIM to enhance optical sectioning (§5).

3. Construct a physical optics-based model taking into account temporal interferences

Given the temporal focusing effect in the proposed technique, and with the non-negligible temporal interferences among the light pulses, a time-independent model such as that previously used for TM-MMM [14

A. Egner and S. Hell, “Time multiplexing and parallelization in multifocal multiphoton microscopy,” J. Opt. Soc. Am. A 17, 1192–1201 (2000). [CrossRef]

] is no longer sufficient for analyzing the performances of our setup. Thus, we develop a new model taking into account the time-dependent optical phase of multiple spectral components in an ultrafast pulse. For simplicity, we use a Gaussian-pulse approach, i.e., in the excited area, the electric field E(r, z, t) at position (r, z) (z = 0 at the specimen plane) and time t is approximated as the Gaussian-weighted sum of a series of constant-interval (in k–space), in-phase light waves,

E (r, z, t) = \sum_{j} e^{\frac{- {(k_{j} - k_{0})}^{2}}{2 σ_{k}^{2}}} E_{k_{j}} (r, z) e^{- i ω_{j} t},

(3)

where k₀ is the central wavenumber of the pulse spectrum, and E_{k_j} is the scalar field of the light wave of wavenumber k_j. To approximate the ultrafast pulse train generated by the amplified laser system we used previously [12

], we set k₀ ≈ 7.85 × 10⁴ cm⁻¹ and a pulse duration τ₀ of ≈ 30 fs (by using an appropriate σ_k). We then employ the amplitude point spread function (PSF) derived previously for high numerical-aperture (NA) lenses [14

A. Egner and S. Hell, “Time multiplexing and parallelization in multifocal multiphoton microscopy,” J. Opt. Soc. Am. A 17, 1192–1201 (2000). [CrossRef]

, 16

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light , 6th ed. (Cambridge University Press, 1997).

], E_{k_j}, as

E_{k_{j}} (r, z) \approx k_{j} \int_{0}^{α} \sqrt{\cos θ} \sin θ J_{0} (k_{j} r \sin θ) e^{i k_{j} z \cos θ} d θ,

(4)

where α is the maximal focusing angle θ of the objective lens, and J₀ is the zero-order Bessel function of the first kind. The objective lens used in all the simulations presented here is a 60X oil-immersion lens of NA 1.42.

Through Eqs. (3) and (4) we can numerically evaluate the time-dependent amplitude PSF of an ultrafast pulse focused by a well-corrected objective lens, E_PSF (r,z,t). Having solved E_PSF numerically, we estimate the electric field near the specimen plane, E_SP(r,z,t), as the linear superposition of the E_PSF from the individual microlenses,

E_{S P} (r, z, t) = \sum_{m} E_{P S F} (r - r_{m}, z, t - Δ t_{m}),

(5)

where r_m and Δt_m are the central position and time delay of the ultrafast pulse going though the m-th HSMA channel, respectively. An example of numerically simulated E_SP(r,z,t) is shown in Media 1, which also reveals the dynamic process of temporal focusing (see Appendix D). Notably, to fulfill the wide-field illumination condition and to simplify the simulations, our model assumes that a ’unit’ microlens array is infinitely replicated in the transverse coordinates, as shown in Fig. 1(b). Under such a periodic condition, the physical optics properties in the projected region of one unit microlens array is sufficient to represent the entire system (the validity and details of this model are given in Appendix E).

Through Eq. (5), the excitation intensity profiles I_SP(r, z) can be derived by integrating the excitation intensity over time, as

I_{S P} (r, z) = \int {| E_{S P} (r, z, t) |}^{2 n_{p}} d t,

(6)

where n_p is the number of photons required in single excitation event (here n_p = 2).

4. Optimize intrinsic optical sectioning through tuning N_t and Δt

To quantify the intrinsic optical sectioning created by a particular design of HSMA, we calculate the total fluorescence signal at a depth z, S(z), through integration of I_SP(r, z) in Eq. (6) over the transverse coordinates, as

S (z) = \int I_{S P} (r, z) d^{2} r .

(7)

Experimentally, S(z) corresponds to the detected fluorescence signal from a thin fluorescent film placed at a depth z.

To determine the choice of (N_t, Δt) that produces the most efficient optical sectioning, we evaluate S(z) and the ratio of out-of-focus and in-focus signal, S_out / S_in, for various sets of N_t and Δt (constrained by Eq. (2)) with two inter-foci spacings, d_foci(≡ d/M, where M is the magnification of the microscopy system) ≈ 0.4 and 0.8 λ₀, corresponding to ∼ 56 and ∼ 14 foci per 10²-focus area, respectively (Fig. 2). Because of the square geometry of our HSMAs, we examine N_t = 2², 3², 4², ... and 9². Analyzing S_out /S_in reveals that the decay of the out-of-focus excitation significantly slows down between N_t = 25 and 64, corresponding to Δt ≈ 20-8 fs (i.e., 2/3τ₀-1/4τ₀) (Fig. 2(c)). We observe similar trends of S_out / S_in for various geometrical arrangements of the distinct time-delay steps (see Appendix C). This result suggests that the intrinsic optical sectioning for a fixed Δt_tot is optimized when Δt is slightly smaller than τ₀. Further reducing Δt (equivalent to increasing N_t (Eq. (2))) can complicate the fabrication of the HSMAs without major improvement of the intrinsic optical sectioning. In addition, increasing d_foci leads to weaker out-of-focus excitation and a less complex axial excitation profile S(z) (Fig. 2(b)).

Fig. 2 (a) Left panel: the intensity distribution I_SP at several depths from the focal plane. d_foci is the distance between adjacent foci. The intensity profiles indicated by the yellow line segments are plotted in the right panel. The full widths at half maximum of the intensity peaks are similar to those of conventional 2PE (≈ 0.36λ₀/NA). (b) Fluorescence signal S(z) of various (N_t, Δt) sets. (c) Upper panel: definition of in-focus signal (S_in) and out-of-focus signal (S_out). z_HM is the position where half-maximum excitation occurs in 2PE (≈ 0.375λ₀); Lower panel: S_out /S_in as a function of N_t.

5. Obtain extrinsic optical sectioning via implementing SIM

Next, we implement SIM to extrinsically remove the residual out-of-focus signal of the optimized HSMA. SIM relies on the post processing of multiple images, each noted as I_IM. Because the emitted fluorescence (wavelength assumed to be ∼ 0.56λ₀) from the specimen is generally incoherent, we can estimate I_IM from a convolution of the excitation intensity profile I_SP and the intensity PSF of the microscopy system, I_SYS[5

T. Wilson, Confocal Microscopy (Academic Press, 1990).

], as

I_{I M} (r^{'}) = \int I_{S P} (r, z) f (r, z) I_{S Y S} (r^{'} + M r, M^{2} z) d^{2} r d z,

(8)

where f is the concentration distribution of the fluorophore in the specimen. To quantify the optical-sectioning effect, we assume that the specimen is an ideal thin fluorescent film placed at z = z_f, i.e., f(r,z) = δ(z − z_f). Eq. (8) then becomes

I_{I M} (r; z_{f}) = \int I_{S P} (r^{'}, z_{f}) I_{S Y S} (r + M r^{'}, M^{2} z_{f}) d^{2} r^{'} .

(9)

Conventional SIM takes 3 shifts of the 1-dimension periodic pattern; each step is 1/3 of the period of the pattern [6

M. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett. 22, 1905–1907 (1997). [CrossRef]

]. In our case, the periodicity of I_SP is 2-dimensional. We thus use 3-by-3 shifts (I_IM₁, I_IM₂, ..., I_IM₉ denote the obtained images) and apply SIM post-processing to extract the optically sectioned images,

I_{S I M} = \sqrt{\sum_{i = 1}^{9} \sum_{j = 1}^{9} {(I_{I M i} - I_{I M j})}^{2}} .

(10)

We then substitute I_SP in Eq. (7) with I_SIM to evaluate the overall strength of optical sectioning (Fig. 3).

Fig. 3 S(z) of MA-PPMP (i.e., without SIM post-processing, red), CFM (green) and MASI-PPMP (blue) in linear and log scales. The S(z) of confocal microscopy is simulated as the diameter of the confocal pinhole equal to 1 Airy unit×M, where M is the magnification of the microscopy system. The log-scale plot shows that the optical sectioning of MASI-PPMP is better than CFM. The wavelengths of both the emitted fluorescence and the excitation light of CFM are set to be ∼ 0.56λ₀.

The results show that MASI-PPMP can achieve a better optical sectioning than CFM. Such results are reasonable because the fundamental mechanisms of intrinsic and extrinsic optical sectioning are independent from each other and can be combined. We further simulate the images of a virtual 3D object obtained by the different imaging techniques (Fig. 4) to illustrate the optical sectioning of MASI-PPMP. Compared with conventional epifluorescence microscopy (Fig. 4(b)), the images obtained before SIM post-processing (denoted as MA-PPMP) shows the ability of intrinsic optical sectioning. In the log-scale intensity plot (Fig. 4(c)), MASI-PPMP has the highest signal contrast between fluorescent and non-fluorescent areas, consistent with the results in Fig. 3. Moreover, the reconstructed 3D views show that MASI-PPMP successfully reproduces the details of the object (Fig. 4(d)).

Fig. 4 Image analysis of conventional epifluorescence microscopy (Epi), CFM, MA-PPMP (i.e., without SIM post-processing), and MASI-PPMP. (a) The object. (b) The sectioned images obtained by various techniques at the corresponding depth of the virtual slice. The intensity profiles indicated by the yellow line segments are plotted in (c). (d) 3D-view reconstructed from the z-stacked images of Epi and MASI-PPMP.

We should note that the SIM process introduced here, i.e., the 9-frame imaging procedure and Eq. (10), is not the only way to remove out-of-focus signal from the obtained images I_IM. Other methods using a high-spatial-frequency illumination pattern to distinguish in-focus and out-of-focus signals, such as HiLo microscopy [17

D. Lim, K. K. Chu, and J. Mertz, “Wide-field fluorescence sectioning with hybrid speckle and uniform-illumination microscopy,” Opt. Lett. 33, 1819–21 (2008). [CrossRef] [PubMed]

, 18

D. Lim, T. N. Ford, K. K. Chu, and J. Mertz, “Optically sectioned in vivo imaging with speckle illumination hilo microscopy,” J. Biomed. Opt. 16, 016014 (2011). [CrossRef] [PubMed]

], may also be applied to the proposed optical setup. These methods use different imaging procedures and post-processing algorithms, which may lead to different imaging properties such as speed and spatial resolutions, such that different methods may be most suitable for different imaging applications. For example, the HiLo method, whose algorithms are more complicated than Eq. 10, requires only 2 frames to retrieve in-focus signal, one frame each with uniform and non-uniform illumination; the reduced number of frames may therefore shorten the imaging time. However, such an advantage exists only when the frame rate of the camera is much lower than the repetition rate of the ultrafast pulse train. If these two rates fall in the same order of magnitude, one will need to increase the exposure time to shift the structural illumination pattern around the sample so as to mimic the effect of uniform illumination, and the overall imaging time will eventually be similar to SIM.

6. Conclusion

In conclusion, our numerical modeling shows that MASI-PPMP can efficiently provide intrinsic optical sectioning via temporal focusing effect generated by the HSMAs, and achieve an axial resolution finer than CFM via the implementation of extrinsic optical-sectioning technique. Our analysis provides the design guide of HSMAs with small time-delay increments; the dimensions of the proposed HSMAs are compatible with standard biomedical microscopes, and feasible for existing fabrication methods. In contrast to conventional SIM, the intrinsic sectioning of our method can reduce photobleaching and increase the SNR of the processed images.

Compared with parallelized CFM and 2PE, MASI-PPMP has a denser spacing of foci (> 10 foci per 10²-focus area), and thus has greater potential in high-speed imaging. In addition to the finer axial resolution than CFM, the lateral resolution can be enhanced via utilization of the periodic excitation structures and Fourier analysis of the obtained images [19

R. Heintzmann and P. A. Benedetti, “High-resolution image reconstruction in fluorescence microscopy with patterned excitation,” Appl. Opt. 45, 5037–5045 (2006). [CrossRef] [PubMed]

]. Moreover, MASI-PPMP can use the pulse train generated by ultrafast amplifiers, thereby yielding a sufficient signal level and moderate impact on the specimen at high acquisition rates, as demonstrated in our previous PPMP setup [12

]. Taken together, we have shown that MASI-PPMP has the potential to achieve (better-than-conventional) diffraction-limited, high-frame-rate 3D imaging with a simple, wide-field optical design.

Appendices

Appendix A: Determining the dimensions of the time-delay channels

In this section we discuss the appropriate dimensions of the height-staggered microlens arrays (HSMAs) utilized in our technique. As mentioned in the main article, the light waves propagating along one particular time-delay channel can leak into the neighboring channels due to diffraction. In the microscope, this leakage appears as stray light, which induces multiphoton excitation at all depths and thus increases out-of-focus excitation.

To quantify such an effect, we use a simple model consisting of two adjacent microlenses with height staggering Δh, as shown in Fig. 5. When the light of wavelength λ₀ exits from channel 1 (Ch1) and propagates to distance z, diffraction theory predicts the beam size, d_B, as a function of λ₀ and z. With this regard, we consider the inter-channel leakage to be non-negligible if d_B before propagating to z = Δh is larger than the diameter of the microlens, d. In other words, the inter-channel leakage is negligible if

d_{B} \leq d for z \leq Δ h .

(11)

A reasonable design, as shown in Fig. 5, is to set the focus of Ch1 at z = Δh, so that the d_B decreases upon exiting Ch1 and reaches its minimum, d_f, at z = Δh. Based on the diffraction-limited spot size of an ideal thin lens, we can estimate d_f as

d_{f} = 1.22 λ_{0} \times f_{#},

(12)

where f_# is defined as f/d[20

E. Hecht, Optics , 4th ed. (Addison-Wesley, 2002).

]. Combining Eqs. (11), (12) and the geometry, we have

d \geq 1.22 λ_{0} \times \frac{f}{d} \approx λ_{0} \times \frac{Δ h}{d},

(13)

and the criterion of negligible inter-channel light leakage is thus

d \geq \sqrt{λ_{0} Δ h} .

(14)

To ensure the inter-channel light leakage is negligible regardless of the geometrical arrangements of distinct time-delay steps, we can substitute the largest height difference in the HSMA, Δh_max, for Δh in Eq. (14), and thus derive

d \geq \sqrt{λ_{0} Δ h_{\max}} .

(15)

Fig. 5 A model of two adjacent microlenses. d: aperture of the microlenses. f : focal length of the microlens. d_f : the diameter of the focal spot. Δh: height difference between two microlenses.

The argument here also applies to the design of the combination of temporal masks and microlens arrays used in TM-MMM [14

A. Egner and S. Hell, “Time multiplexing and parallelization in multifocal multiphoton microscopy,” J. Opt. Soc. Am. A 17, 1192–1201 (2000). [CrossRef]

]. In such a case, the ends of the time-delay channels are flat surfaces, and one can use the single-slit diffraction to approximate the beam size with propagation. Such an approach yields a similar criterion.

Appendix B: Size of the microlens arrays to achieve scanningless imaging using conventional time-multiplexing approach

In this section we estimate the size of the HSMAs for scanningless TM-MMM, using the criterion derived in the previous section. To achieve a complete, gap-less plane of illumination for a truly scanningless wide-field imaging requires the placement of adjacent foci no more than one focal spot diameter apart. However, to preserve the intrinsic optical sectioning of conventional multiphoton microscopy, the foci (of the same timing) have to be spatially separated by a certain distance, d₀, which is commonly much larger than the size of the focal spot of the objective lens, d_fs. As a result, there will be substantial un-illuminated area between the foci. For example, take an oil-immersion, NA 1.42 objective lens: the resultant d₀ and d_fs is approximately 5 λ[14

A. Egner and S. Hell, “Time multiplexing and parallelization in multifocal multiphoton microscopy,” J. Opt. Soc. Am. A 17, 1192–1201 (2000). [CrossRef]

] and 0.3 λ, which makes the fraction of un-illuminated area approximately

1 - {(\frac{d_{f s}}{d_{0}})}^{2} \approx 99.6 %

, equivalent to ∼0.4 foci per 10²-focus area. To cover the un-illuminated area, Egner et al. [14

A. Egner and S. Hell, “Time multiplexing and parallelization in multifocal multiphoton microscopy,” J. Opt. Soc. Am. A 17, 1192–1201 (2000). [CrossRef]

] proposed to use foci that are largely separated in time, so that the interferences among these foci is negligible even though they partially overlap in space. Consequently, the number of distinct time-delay steps required to cover the un-illuminated area, N_t, can be estimated as

N_{t} \approx {(\frac{d_{0}}{d_{f s}})}^{2} \approx 280.

(16)

Given N_t, and using the propagation speed of light in the HSMA material, we can estimate the difference of height between the longest and shortest time channels, Δh_max, as:

Δ h_{\max} = \frac{(N_{t} - 1) c Δ t}{(n - 1)},

(17)

where Δt, c and n are the step size of the distinct time-delay steps, speed of light in vacuum and the refractive index of the material of the HSMAs, respectively. The appropriate values of Δt for negligible temporal interferences, as suggested in the previous study of TM-MMM [14

A. Egner and S. Hell, “Time multiplexing and parallelization in multifocal multiphoton microscopy,” J. Opt. Soc. Am. A 17, 1192–1201 (2000). [CrossRef]

], are equal to or larger than twice the pulse duration of the light pulse, τ₀, i.e., Δt ≥ 2τ₀ (where τ₀ was set as ≈ 100 fs for conventional ultrafast oscillators) [14

A. Egner and S. Hell, “Time multiplexing and parallelization in multifocal multiphoton microscopy,” J. Opt. Soc. Am. A 17, 1192–1201 (2000). [CrossRef]

]. Accordingly, we find that Δh ≈ 33 mm and d ≈ 0.15 mm using Eqs. (15)–(17), wherein λ and n are assumed to be ∼ 800 nm and 1.5, respectively. As a result, if one needs 1000-by-1000 foci in the field of view (FOV), the typical aperture of the entire HSMA will be as large as 1000×d ≈ 150 mm, which is considerably larger than the optical elements of a standard biomedical microscope. Furthermore, when an ultrafast pulse propagates in a long, narrow glass cylinder, both group velocity dispersion and modal dispersion broaden the pulse width, and thus reduce the axial resolution as well as excitation efficiency. From Eqs. (15), (17) and the requirement of Δt ≥ 2τ₀, we can derive that Δh ∝ τ₀ and

d \propto \sqrt{τ_{0}}

, indicating that Δh and d can be scaled down via using small τ₀. However, commonly available ultrafast systems typically achieve τ₀ ≥ 10 fs, such that the resultant Δh and d remain considerably large. Moreover, the ultrafast pulses of smaller τ₀ (and thus greater spectral bandwidth) will suffer more from group velocity dispersion and modal dispersion while propagating in the HSMA materials.

Appendix C: Various geometrical arrangements of distinct time-delay steps show a similar trend of S_out / S_in

Figure 6 shows the simulation results of the ratio between out-of-focus and in-focus signal, S_out / S_in, using various geometrical arrangements of distinct time-delay steps. As concluded in the main article, these S_out / S_in curves show that the decays of the out-of-focus excitation slow down significantly when N_t = 25–64, (Δt ≈ 2/3 τ₀-1/4 τ₀), although the curves from different patterns of time delays show slight differences in the values of S_out / S_in.

Fig. 6 S_out /S_in curves of distinct time-delay steps arranged in various patterns: jumping-sprial (left), raster (middle), and diagonal (right) geometry.

Appendix D: Simulation of the dynamic E_SP in space reveals temporal focusing

In Media 1 (a static frame shown in Fig. 7), we show an example of the numerically simulated E_SP. In particular, we plot the distributions of the real part of the electric field (Re(E_SP), upper panel) and intensity (|E_SP|², lower panel). The geometrical arrangement of the distinct time-delay steps used for this simulation is a spiral pattern (Fig. 1(b) of main article) with N_t = 49 and d_foci ≈ 0.4 λ₀. Media 1 shows that at most of the area, except for the in-focus region (z ≈ 0), the intensity is moderate during nearly the entire time course (100–700 fs). On the other hand, at in-focus region the intensity is high in a relatively short period of time (450–540 fs). Such a phenomenon is commonly recognized as temporal focusing [4

D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express 13, 1468–1476 (2005). [CrossRef] [PubMed]

Fig. 7 A static frame of Media 1: the time-dependent E_SP near the specimen plane (top: Re(E_SP); bottom: |E_SP|²). The geometrical arrangement of the distinct time-delay steps used for this simulation is a spiral pattern (Fig. 1(b) of main article) with N_t = 49 and d_foci ≈ 0.4λ₀. Both plots are normalized to their maximal values.

Appendix E: Validity of the assumption of infinitely replicated unit HSMA in a wide-field microscope

In this section, we validate the model of infinitely replicated unit HSMAs for conventional wide-field biomedical microscopes. As described in the main article, the analysis of the properties of the proposed system can become simpler if we assume that the whole HSMA consists of infinitely, laterally repeated unit HSMAs. This is because the system is laterally periodic under such an assumption (referred to as the inf-HSMA model herein) and thus the physical properties (ex. the distribution of electric field) of one unit region can be used to describe the entire system. Although the infinite replication of unit HSMAs is not realistic for either experiments or numerical simulations, the inf-HSMA model is made tractable by assuming that, for the multiphoton excitation intensity I_SP at arbitrary positions, the contributions from very distant foci are negligible. In other words, one can approximate the results of using the infinitely replicated unit HSMAs via consideration of only the contributions from the foci within a certain range. To justify such an approach, we need to examine if the computed I_SP becomes stationary (i.e., converging to a certain value) as the range of foci considered to contribute, defined by r_tot (Fig. 8(a)), is expanded.

Fig. 8 (a) The time-integrated intensity I at a particular position is numerically obtained by taking into account the contributions of foci within distance r_tot. The dark area with an array of bright spots indicates the calculated intensity distribution. The faded grid patterns shows the locations of microlenses when projected to the specimen plane of the microscope. (b) The convergence of I for 100 randomly picked positions (upper panel: log scale; lower panel: linear scale). Each curve represents I/I_end as a function of r_tot (see text) at a particular position. The analysis has been repeated 10 times; all results show similar convergence. (c) The area for the inf-HSMA model is valid can be determined by r_inf and the size of the whole FOV of the microscope.

To proceed, we compute time-integrated intensity I using Eq. (6) of the main article, with only the contributions to E_SP from the foci within a distance r_tot considered (Fig. 8(a)). Here we use I_end, the intensity at a given position as derived with a relatively large r_tot (≈ 375 λ₀, where λ₀ is the central wavelength of the light pulse), as a reference value, and plot I/I_end as r_tot increases from 0 to 125 λ₀. Fig. 8(b) shows that values of I at all of the 100 randomly chosen positions converge to their corresponding I_end as r_tot increases. In particular, we note that when r_tot ≥ 62.5 λ₀ (equivalent to 50 μm in physical dimensions), the error of I, defined as |I − I_end |/I_end, is less than 0.1%. Such results suggest that, for a given error tolerance in numerical simulations, we can use the inf-HSMA model by considering only the contributions of foci within a certain distance r_inf. Here, we have r_inf ≈ 50 μm for a 0.1% error tolerance. In the physical microscopy system, we can also use r_inf to determine the region wherein the inf-HSMA assumption is valid, as shown in Fig. 8(c). For conventional biomedical microscopes using M = 60X objective lenses, the diameter of the full FOV is typically lager than 300 μm. Thus, the inf-HSMA model is valid in the central region of diameter larger than 200 μm. At the image plane, this region corresponds to a disk of diameter ∼ 12 mm (200 μm×M) or larger, which is able to cover most conventional imaging devices.

Acknowledgment

We gratefully acknowledge Dr. Alexander Egner of Laser-Laboratorium Gttingen e.V. for his kind advices on algorithm development. We are indebted to Mr. Yu-Hang Chen of National Taiwan University (NTU) for his assistance with the simulations, and we thank Dr. Chien-Cheng Chen of NTU for helpful comments. The support from Ellison Medical Foundation is acknowledged.

References and links

1.	J. B. Pawley, Handbook of Biological Confocal Microscopy , 3rd ed. (Springer, 2006). [CrossRef]
2.	W. Denk, J. Strickler, and W. Webb, “2-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990). [CrossRef] [PubMed]
3.	J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305, 1007–1009 (2004). [CrossRef] [PubMed]
4.	D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express 13, 1468–1476 (2005). [CrossRef] [PubMed]
5.	T. Wilson, Confocal Microscopy (Academic Press, 1990).
6.	M. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett. 22, 1905–1907 (1997). [CrossRef]
7.	B. Masters, P. So, C. Buehler, N. Barry, J. Sutin, W. Mantulin, and E. Gratton, “Mitigating thermal mechanical damage potential during two-photon dermal imaging,” J. Biomed. Opt. 9, 1265–1270 (2004). [CrossRef] [PubMed]
8.	I. Akira, T. Takeo, I. Katsumi, S. Yumiko, K. Yasuhito, M. Kenta, A. Michio, and U. Isao, “High-speed confocal fluorescence microscopy using a nipkow scanner with microlenses for 3-d imaging of single fluorescent molecule in real time,” Bioimaging 4, 57–62 (1996-06).
9.	J. Bewersdorf, R. Pick, and S. Hell, “Multifocal multiphoton microscopy,” Opt. Lett. 23, 655–657 (1998). [CrossRef]
10.	V. Andresen, A. Egner, and S. Hell, “Time-multiplexed multifocal multiphoton microscope,” Opt. Lett. 26, 75–77 (2001). [CrossRef]
11.	P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. K. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods 7, 637–U55 (2010). [CrossRef] [PubMed]
12.	J.-Y. Yu, C.-H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C.-L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt. 16, 116009 (2011). [CrossRef] [PubMed]
13.	C. Ventalon and J. Mertz, “Quasi-confocal fluorescence sectioning with dynamic speckle illumination,” Opt. Lett. 30, 3350–3352 (2005). [CrossRef]
14.	A. Egner and S. Hell, “Time multiplexing and parallelization in multifocal multiphoton microscopy,” J. Opt. Soc. Am. A 17, 1192–1201 (2000). [CrossRef]
15.	J. Jahns and K.-H. Brenner, Microoptics: from Technology to Applications , vol. v. 97 (Springer, 2004).
16.	M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light , 6th ed. (Cambridge University Press, 1997).
17.	D. Lim, K. K. Chu, and J. Mertz, “Wide-field fluorescence sectioning with hybrid speckle and uniform-illumination microscopy,” Opt. Lett. 33, 1819–21 (2008). [CrossRef] [PubMed]
18.	D. Lim, T. N. Ford, K. K. Chu, and J. Mertz, “Optically sectioned in vivo imaging with speckle illumination hilo microscopy,” J. Biomed. Opt. 16, 016014 (2011). [CrossRef] [PubMed]
19.	R. Heintzmann and P. A. Benedetti, “High-resolution image reconstruction in fluorescence microscopy with patterned excitation,” Appl. Opt. 45, 5037–5045 (2006). [CrossRef] [PubMed]
20.	E. Hecht, Optics , 4th ed. (Addison-Wesley, 2002).

OCIS Codes
(170.0110) Medical optics and biotechnology : Imaging systems
(180.6900) Microscopy : Three-dimensional microscopy
(260.1960) Physical optics : Diffraction theory
(180.4315) Microscopy : Nonlinear microscopy

ToC Category:
Microscopy

History
Original Manuscript: October 31, 2012
Revised Manuscript: December 23, 2012
Manuscript Accepted: December 26, 2012
Published: January 18, 2013

Virtual Issues
Vol. 8, Iss. 2 Virtual Journal for Biomedical Optics

Citation
Jiun-Yann Yu, Daniel B. Holland, Geoffrey A. Blake, and Chin-Lin Guo, "The wide-field optical sectioning of microlens array and structured illumination-based plane-projection multiphoton microscopy," Opt. Express 21, 2097-2109 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-2-2097

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References

J. B. Pawley, Handbook of Biological Confocal Microscopy, 3rd ed. (Springer, 2006). [CrossRef]
W. Denk, J. Strickler, and W. Webb, “2-photon laser scanning fluorescence microscopy,” Science248, 73–76 (1990). [CrossRef] [PubMed]
J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science305, 1007–1009 (2004). [CrossRef] [PubMed]
D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express13, 1468–1476 (2005). [CrossRef] [PubMed]
T. Wilson, Confocal Microscopy (Academic Press, 1990).
M. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett.22, 1905–1907 (1997). [CrossRef]
B. Masters, P. So, C. Buehler, N. Barry, J. Sutin, W. Mantulin, and E. Gratton, “Mitigating thermal mechanical damage potential during two-photon dermal imaging,” J. Biomed. Opt.9, 1265–1270 (2004). [CrossRef] [PubMed]
I. Akira, T. Takeo, I. Katsumi, S. Yumiko, K. Yasuhito, M. Kenta, A. Michio, and U. Isao, “High-speed confocal fluorescence microscopy using a nipkow scanner with microlenses for 3-d imaging of single fluorescent molecule in real time,” Bioimaging4, 57–62 (1996-06).
J. Bewersdorf, R. Pick, and S. Hell, “Multifocal multiphoton microscopy,” Opt. Lett.23, 655–657 (1998). [CrossRef]
V. Andresen, A. Egner, and S. Hell, “Time-multiplexed multifocal multiphoton microscope,” Opt. Lett.26, 75–77 (2001). [CrossRef]
P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. K. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods7, 637–U55 (2010). [CrossRef] [PubMed]
J.-Y. Yu, C.-H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C.-L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16, 116009 (2011). [CrossRef] [PubMed]
C. Ventalon and J. Mertz, “Quasi-confocal fluorescence sectioning with dynamic speckle illumination,” Opt. Lett.30, 3350–3352 (2005). [CrossRef]
A. Egner and S. Hell, “Time multiplexing and parallelization in multifocal multiphoton microscopy,” J. Opt. Soc. Am. A17, 1192–1201 (2000). [CrossRef]
J. Jahns and K.-H. Brenner, Microoptics: from Technology to Applications, vol. v. 97 (Springer, 2004).
M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Cambridge University Press, 1997).
D. Lim, K. K. Chu, and J. Mertz, “Wide-field fluorescence sectioning with hybrid speckle and uniform-illumination microscopy,” Opt. Lett.33, 1819–21 (2008). [CrossRef] [PubMed]
D. Lim, T. N. Ford, K. K. Chu, and J. Mertz, “Optically sectioned in vivo imaging with speckle illumination hilo microscopy,” J. Biomed. Opt.16, 016014 (2011). [CrossRef] [PubMed]
R. Heintzmann and P. A. Benedetti, “High-resolution image reconstruction in fluorescence microscopy with patterned excitation,” Appl. Opt.45, 5037–5045 (2006). [CrossRef] [PubMed]
E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

The wide-field optical sectioning of microlens array and structured illumination-based plane-projection multiphoton microscopy

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Abstract

1. Introduction

2. MASI-PPMP: integrating (intrinsic) temporal focusing and (extrinsic) SIM

3. Construct a physical optics-based model taking into account temporal interferences

4. Optimize intrinsic optical sectioning through tuning N_t and Δt

5. Obtain extrinsic optical sectioning via implementing SIM

6. Conclusion

Appendices

Appendix A: Determining the dimensions of the time-delay channels

Appendix B: Size of the microlens arrays to achieve scanningless imaging using conventional time-multiplexing approach

Appendix C: Various geometrical arrangements of distinct time-delay steps show a similar trend of S_out / S_in

Appendix D: Simulation of the dynamic E_SP in space reveals temporal focusing

Appendix E: Validity of the assumption of infinitely replicated unit HSMA in a wide-field microscope

Acknowledgment

References and links

References

Appl. Opt.

Bioimaging

J. Biomed. Opt.

J. Opt. Soc. Am. A

Nat. Methods

Opt. Express

Opt. Lett.

Science

Other

Cited By

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OpticsInfoBase

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

The wide-field optical sectioning of microlens array and structured illumination-based plane-projection multiphoton microscopy

Article Tools

Article Navigation

Abstract

1. Introduction

2. MASI-PPMP: integrating (intrinsic) temporal focusing and (extrinsic) SIM

3. Construct a physical optics-based model taking into account temporal interferences

4. Optimize intrinsic optical sectioning through tuning Nt and Δt

5. Obtain extrinsic optical sectioning via implementing SIM

6. Conclusion

Appendices

Appendix A: Determining the dimensions of the time-delay channels

Appendix B: Size of the microlens arrays to achieve scanningless imaging using conventional time-multiplexing approach

Appendix C: Various geometrical arrangements of distinct time-delay steps show a similar trend of Sout / Sin

Appendix D: Simulation of the dynamic ESP in space reveals temporal focusing

Appendix E: Validity of the assumption of infinitely replicated unit HSMA in a wide-field microscope

Acknowledgment

References and links

References

Appl. Opt.

Bioimaging

J. Biomed. Opt.

J. Opt. Soc. Am. A

Nat. Methods

Opt. Express

Opt. Lett.

Science

Other

Cited By

Figures

Multimedia

4. Optimize intrinsic optical sectioning through tuning N_t and Δt

Appendix C: Various geometrical arrangements of distinct time-delay steps show a similar trend of S_out / S_in

Appendix D: Simulation of the dynamic E_SP in space reveals temporal focusing