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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 2 — Mar. 4, 2013
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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.

© 2013 OSA

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

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

4

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

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

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

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

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

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

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

, 7

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

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

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

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

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

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 fT. 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

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

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

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

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
dλ0Δhmax,
(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 Δhmax is the height staggering between the longest and shortest time-delay channels. Accordingly, we restrict Δhmax 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 Δttot is separated equally into Nt 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
Δttot(Nt1)×Δt=Δhmax(n1)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 Δhmax, 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 Nt. In such cases, we should take into account the temporal interferences among light pulses of different time delays. Notably, temporal masks with much larger Δttot have been proposed to avoid temporal interferences and to achieve scanningless TM-MMM [14

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 Δhmax 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 Nt (and Δt) for a given Δttot (§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

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)=je(kjk0)22σk2Ekj(r,z)eiωjt,
(3)
where k0 is the central wavenumber of the pulse spectrum, and Ekj is the scalar field of the light wave of wavenumber kj. To approximate the ultrafast pulse train generated by the amplified laser system we used previously [12

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]

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

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

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

], Ekj, as
Ekj(r,z)kj0αcosθsinθJ0(kjrsinθ)eikjzcosθdθ,
(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, EPSF (r,z,t). Having solved EPSF numerically, we estimate the electric field near the specimen plane, ESP(r,z,t), as the linear superposition of the EPSF from the individual microlenses,
ESP(r,z,t)=mEPSF(rrm,z,tΔtm),
(5)
where rm and Δtm are the central position and time delay of the ultrafast pulse going though the m-th HSMA channel, respectively. An example of numerically simulated ESP(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 ISP(r, z) can be derived by integrating the excitation intensity over time, as
ISP(r,z)=|ESP(r,z,t)|2npdt,
(6)
where np is the number of photons required in single excitation event (here np = 2).

4. Optimize intrinsic optical sectioning through tuning Nt 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 ISP(r, z) in Eq. (6) over the transverse coordinates, as
S(z)=ISP(r,z)d2r.
(7)
Experimentally, S(z) corresponds to the detected fluorescence signal from a thin fluorescent film placed at a depth z.

Fig. 2 (a) Left panel: the intensity distribution ISP at several depths from the focal plane. dfoci 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 (Nt, Δt) sets. (c) Upper panel: definition of in-focus signal (Sin) and out-of-focus signal (Sout). zHM is the position where half-maximum excitation occurs in 2PE (≈ 0.375λ0); Lower panel: Sout /Sin as a function of Nt.

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 IIM. Because the emitted fluorescence (wavelength assumed to be ∼ 0.56λ0) from the specimen is generally incoherent, we can estimate IIM from a convolution of the excitation intensity profile ISP and the intensity PSF of the microscopy system, ISYS[5

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

], as
IIM(r)=ISP(r,z)f(r,z)ISYS(r+Mr,M2z)d2rdz,
(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 = zf, i.e., f(r,z) = δ(zzf). Eq. (8) then becomes
IIM(r;zf)=ISP(r,zf)ISYS(r+Mr,M2zf)d2r.
(9)
Conventional SIM takes 3 shifts of the 1-dimension periodic pattern; each step is 1/3 of the period of the pattern [6

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 ISP is 2-dimensional. We thus use 3-by-3 shifts (IIM1, IIM2, ..., IIM9 denote the obtained images) and apply SIM post-processing to extract the optically sectioned images,
ISIM=i=19j=19(IIMiIIMj)2.
(10)
We then substitute ISP in Eq. (7) with ISIM 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 IIM. Other methods using a high-spatial-frequency illumination pattern to distinguish in-focus and out-of-focus signals, such as HiLo microscopy [17

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

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.

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, dB, as a function of λ0 and z. With this regard, we consider the inter-channel leakage to be non-negligible if dB before propagating to z = Δh is larger than the diameter of the microlens, d. In other words, the inter-channel leakage is negligible if
dBdforzΔh.
(11)
A reasonable design, as shown in Fig. 5, is to set the focus of Ch1 at z = Δh, so that the dB decreases upon exiting Ch1 and reaches its minimum, df, at z = Δh. Based on the diffraction-limited spot size of an ideal thin lens, we can estimate df as
df=1.22λ0×f#,
(12)
where f# is defined as f/d[20

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

]. Combining Eqs. (11), (12) and the geometry, we have
d1.22λ0×fdλ0×Δhd,
(13)
and the criterion of negligible inter-channel light leakage is thus
dλ0Δh.
(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, Δhmax, for Δh in Eq. (14), and thus derive
dλ0Δhmax.
(15)

Fig. 5 A model of two adjacent microlenses. d: aperture of the microlenses. f : focal length of the microlens. df : 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

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

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

Figure 6 shows the simulation results of the ratio between out-of-focus and in-focus signal, Sout / Sin, using various geometrical arrangements of distinct time-delay steps. As concluded in the main article, these Sout / Sin curves show that the decays of the out-of-focus excitation slow down significantly when Nt = 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 Sout / Sin.

Fig. 6 Sout /Sin 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 ESP in space reveals temporal focusing

In Media 1 (a static frame shown in Fig. 7), we show an example of the numerically simulated ESP. In particular, we plot the distributions of the real part of the electric field (Re(ESP), upper panel) and intensity (|ESP|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 Nt = 49 and dfoci ≈ 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

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 ESP near the specimen plane (top: Re(ESP); bottom: |ESP|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 Nt = 49 and dfoci ≈ 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 ISP 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 ISP becomes stationary (i.e., converging to a certain value) as the range of foci considered to contribute, defined by rtot (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 rtot. 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/Iend as a function of rtot (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 rinf 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 ESP from the foci within a distance rtot considered (Fig. 8(a)). Here we use Iend, the intensity at a given position as derived with a relatively large rtot (≈ 375 λ0, where λ0 is the central wavelength of the light pulse), as a reference value, and plot I/Iend as rtot 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 Iend as rtot increases. In particular, we note that when rtot ≥ 62.5 λ0 (equivalent to 50 μm in physical dimensions), the error of I, defined as |IIend |/Iend, 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 rinf. Here, we have rinf ≈ 50 μm for a 0.1% error tolerance. In the physical microscopy system, we can also use rinf 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) 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

  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,” Science248, 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,” Science305, 1007–1009 (2004). [CrossRef] [PubMed]
  4. D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express13, 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,” Bioimaging4, 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. Methods7, 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. A17, 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).

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