OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 20 — Oct. 7, 2013
  • pp: 23963–23977
« Show journal navigation

Three-beam interference with circular polarization for structured illumination microscopy

Hsiao-Chih Huang, Bo-Jui Chang, Li-Jun Chou, and Su-Yu Chiang  »View Author Affiliations


Optics Express, Vol. 21, Issue 20, pp. 23963-23977 (2013)
http://dx.doi.org/10.1364/OE.21.023963


View Full Text Article

Acrobat PDF (6161 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Three-dimensional structured illumination microscopy (3D-SIM) is a wide-field technique that can provide doubled resolution and improved image contrast. In this work, we demonstrate a simple approach to 3D-SIM − using three-beam interference with circular polarization to generate the pattern of structured illumination, so that the modulation contrast is routinely maintained at all orientations without a complicated polarization rotator or mechanical motion. We derive the resultant intensity distribution of the interference pattern to confirm the modulation contrast independent of orientation, and compare the result with those using interfering beams of linear polarization. To evaluate the influence of the modulation contrast on imaging, we compare the simulated SIM images of 100-nm beads. Experimental results are presented to confirm the simulations. Our approach requires merely a λ/4-wave plate to alter the interfering beams from linear to circular polarization. This simplicity together with the use of a spatial light modulator to control the interference pattern facilitates the implementation of a 3D-SIM system and should broaden its application.

© 2013 OSA

1. Introduction

Structured illumination microscopy (SIM) is a wide-field technique that doubles the spatial resolution of a fluorescent image beyond the classical diffraction limit [1

1. R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185–196 (1999). [CrossRef]

7

7. R. Heintzmann, “Saturated patterned excitation microscopy with two-dimensional excitation patterns,” Micron 34(6-7), 283–291 (2003). [CrossRef] [PubMed]

]. The use of a structured pattern to illuminate samples enables undetectable information of large spatial frequency to be encoded into a detectable region of small frequency, and then computationally extracted to extend the region of the optical-transfer function (OTF) of a wide-field microscope, so doubling the resolution [8

8. M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008). [CrossRef] [PubMed]

]. Although this improvement is less than that of other super-resolution fluorescence microscopic methods [9

9. T. A. Klar and S. W. Hell, “Subdiffraction resolution in far-field fluorescence microscopy,” Opt. Lett. 24(14), 954–956 (1999). [CrossRef] [PubMed]

13

13. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006). [CrossRef] [PubMed]

], SIM with its wide-field characteristics requires no special emitters for fluorescence, and enables imaging a live entire cell labeled with multiple colors [14

14. P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009). [CrossRef] [PubMed]

17

17. R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. L. Gustafsson, “Time-lapse two-color 3D imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5311–5315 (2012). [CrossRef] [PubMed]

]. To improve further the resolution below 100 nm, SIM is combined with other imaging techniques [18

18. E. Chung, D. Kim, and P. T. So, “Extended resolution wide-field optical imaging: objective-launched standing-wave total internal reflection fluorescence microscopy,” Opt. Lett. 31(7), 945–947 (2006). [CrossRef] [PubMed]

20

20. L. Shao, B. Isaac, S. Uzawa, D. A. Agard, J. W. Sedat, and M. G. L. Gustafsson, “I5S: wide-field light microscopy with 100-nm-scale resolution in three dimensions,” Biophys. J. 94(12), 4971–4983 (2008). [CrossRef] [PubMed]

] or uses a nonlinear structured illumination pattern [21

21. M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A. 102(37), 13081–13086 (2005). [CrossRef] [PubMed]

23

23. E. H. Rego, L. Shao, J. J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution,” Proc. Natl. Acad. Sci. U.S.A. 109(3), E135–E143 (2012). [CrossRef] [PubMed]

]; the scheme for nonlinear illumination can, in principle, provide unlimited resolution. Furthermore, SIM-based contrast imaging methods, developed recently, allow one to observe metal nanoparticles and features without labels inside native samples with improved resolution and image contrast [24

24. B. J. Chang, S. H. Lin, L. J. Chou, and S. Y. Chiang, “Subdiffraction scattered light imaging of gold nanoparticles using structured illumination,” Opt. Lett. 36(24), 4773–4775 (2011). [CrossRef] [PubMed]

26

26. J. Chen, Y. Xu, X. Lv, X. Lai, and S. Zeng, “Super-resolution differential interference contrast microscopy by structured illumination,” Opt. Express 21(1), 112–121 (2013). [CrossRef] [PubMed]

].

An achievement of the doubled resolution depends greatly on the lateral period and modulation contrast of the structured pattern [8

8. M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008). [CrossRef] [PubMed]

]. The lateral period of that pattern determines mainly the extension of the OTF region and is therefore set near the diffraction limit. To achieve that, the full numerical aperture (NA) of a microscope objective is applied to maximize the interaction angles of the excitation beams; the use of a large NA objective is accordingly crucial. The modulation contrast mainly boosts the components of large spatial frequency to improve the resolution and the image quality. Beams of s-linear polarization (SLP) produce a maximal contrast, and a λ/2-wave plate on a rotating stage or a polarization rotator based on liquid crystal (LC) maintains the modulation contrast at varied orientations − at least three at 0°, 60° and 120° − to achieve isotropically lateral resolution [14

14. P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009). [CrossRef] [PubMed]

17

17. R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. L. Gustafsson, “Time-lapse two-color 3D imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5311–5315 (2012). [CrossRef] [PubMed]

]. That λ/2-wave plate requires mechanical means and an additional polarizer on a rotating stage to clean the polarization [15

15. L. M. Hirvonen, K. Wicker, O. Mandula, and R. Heintzmann, “Structured illumination microscopy of a living cell,” Eur. Biophys. J. 38(6), 807–812 (2009). [CrossRef] [PubMed]

]. Although a polarization rotator prevents mechanical motion, it requires two custom-made LC switchable retarders that impede implementation [14

14. P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009). [CrossRef] [PubMed]

].

The original SIM setup is complicated, involving mechanical motions of great precision to shift and to rotate the pattern [8

8. M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008). [CrossRef] [PubMed]

]. Moreover, a small rate of acquisition limits the capability to image live samples. A LC-based spatial light modulator (SLM) has replaced a transmission phase grating [14

14. P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009). [CrossRef] [PubMed]

,15

15. L. M. Hirvonen, K. Wicker, O. Mandula, and R. Heintzmann, “Structured illumination microscopy of a living cell,” Eur. Biophys. J. 38(6), 807–812 (2009). [CrossRef] [PubMed]

,19

19. R. Fiolka, M. Beck, and A. Stemmer, “Structured illumination in total internal reflection fluorescence microscopy using a spatial light modulator,” Opt. Lett. 33(14), 1629–1631 (2008). [CrossRef] [PubMed]

,27

27. B. J. Chang, L. J. Chou, Y. C. Chang, and S. Y. Chiang, “Isotropic image in structured illumination microscopy patterned with a spatial light modulator,” Opt. Express 17(17), 14710–14721 (2009). [CrossRef] [PubMed]

] to enable a rapid and precise control of the structured pattern in phase and orientation on varying the phases of the LC, which not only prevents mechanical motion but also provides a large rate of imaging to allow study of the dynamics of living cells. 2D- and 3D-SIM images of cellular structures and motions in live cells have been demonstrated [14

14. P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009). [CrossRef] [PubMed]

17

17. R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. L. Gustafsson, “Time-lapse two-color 3D imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5311–5315 (2012). [CrossRef] [PubMed]

]. To simplify the system further, one can avoid the polarization rotation that maintains the polarization states of beams. One simple approach is to use beams of circular polarization (CP) to generate a structured pattern. We expect the modulation contrast to be independent of the orientation but it becomes weaker; to derive the intensity distribution of the modulation and to understand the influence on image quality requires further investigation.

2. Theory

2.1 Three polarized beams for interference

In a 3D-SIM system, three diffracted beams of orders 0 and ± 1 generate an interference pattern. Their electric fields are described as
Ej=Pjfjeikjr,
(1)
with j = 1, 0 and −1, polarization vector Pj, amplitude fj and propagation vector kj of beam j ; r(x, y, z) denotes the position within the beam. As the zero-order beam is focused at the center of the back focal plane of the objective and the two first-order beams at opposite edges, we define the incident plane xz at orientation θ = 0°, with the central zero-order beam propagating along the z direction and the two first-order beams propagating in the xz plane to interact respectively with the zero-order beam at angle β from opposite directions in the sample focal plane. Moreover, to generate an orientated interference pattern, the central beam is fixed, but the two first-order beams are rotated with the pattern orientation θ in plane xy. Figure 1
Fig. 1 (a) Side (xz plane) and (b) top (xy plane) views of propagation and polarization vectors of three interfering beams to generate interference patterns in the sample focal plane at θ = 0°, 45° and 90° with interaction angle β = 44°; black arrows represent the propagation vectors, and red arrows and circles represent the polarization states for the fixed linear polarization case; the red circle with a central dot or a cross indicates that the polarization vector is out of the plane in a forward or backward direction.
shows (a) side (xz plane) and (b) top (xy plane) views of the propagation vectors, indicated as black arrows, for the three beams propagating from the exit of the microscope objective to the sample focal plane to generate interference patterns at three orientations − 0°, 45° and 90°. The three propagation vectors are accordingly described as

{k1=cosθsinβx^+sinθsinβy^+cosβz^k0=z^k1=cosθsinβx^sinθsinβy^+cosβz^.
(2)

The polarization vector of a beam is perpendicular to its propagation vector, but its direction depends on the polarization state and the orientation of the beam. Two cases for three beams of s-linear polarization relative to each other at orientation θ = 0° are considered, one with and the other without a polarization rotator. The former is called maintained SLP because beams of s-linear polarization are maintained at all pattern orientations. Without a polarization rotator, the linear polarization (LP) states of the beams are not rotated with grating orientation; beams of s-linear polarization occurs only at θ = 0°. Accordingly, we abbreviate this case as fixed LP. The polarization vectors at θ = 0°, 45° and 90° indicated as red arrows and circles for the fixed LP case are shown in Fig. 1. We use arrows to indicate the relative phase and amplitude of the polarization vectors in the plane; the circle with a dot or a cross further indicates that the polarization vector is out of the plane in a forward or backward direction. Accordingly, the polarization vectors of the three beams of s-linear polarization at θ = 0° are in phase on the y axis. At θ = 90°, the two first-order beams are rotated to plane yz and their polarization vectors become out of phase.

To derive the polarization states as a function of orientation, we begin with the use of three elliptically polarized (EP) beams, as a general case for fixed LP and CP. The central zero-order EP beam that is independent of orientation but varies in the xy plane is described as
P0=12(21+e2y^i2e21+e2x^),
(3)
with ellipticity e = x/y; x and y correspond to the lengths of the semi-major and semi-minor axes; e = 0 and 1 correspond to fixed LP and circular polarization, respectively. We describe the first-order beam in a general form as
P1=12[21+e2(xrx^+yry^+zrz^)+i2e21+e2(xix^+yiy^+ziz^)].
(4)
Six unknowns (xr, yr, zr, xi, yi, and zi) require six equations for their evaluation, which we derive based on the normalization and orthogonal properties of the vectors, such as P1k1=0, and the β dependence of the z components with zr2 + zi2 = sin2β. It is not straightforward to derive the solutions because a cross term results from orthogonality, xrxi + yryi + zrzi = 0. For simplicity, we derive the z components based on geometric considerations. According to Fig. 1, the two first-order beams are rotated θ clockwise along the z axis to generate a correspondingly orientated interference pattern. The real and imagery parts of the z component thus comprise factors of sinθ and cosθ, respectively. The z component also has a factor of sinβ involving interaction angle β that marks the tilt of the first-order beams from the z axis. Combining both factors, we describe the z component as zr = -sinθsinβ and zi = cosθsinβ, and then use them to derive the x and y components from equations. The solution of Eq. (4) is
P1=12{21+e2[cosθsinθ(cosβ1)x^+(sin2θcosβ+cos2θ)y^sinθsinβz^)]i2e21+e2[(cos2θcosβ+sin2θ)x^+cosθsinθ(cosβ1)y^cosθsinβz^)]}.
(5)
With a similar procedure we derive P1except that the interaction angle is :
P1=12{21+e2[cosθsinθ(cosβ1)x^+(sin2θcosβ+cos2θ)y^+sinθsinβz^)]i2e21+e2[(cos2θcosβ+sin2θ)x^+cosθsinθ(cosβ1)y^+cosθsinβz^)]}.
(6)
According to Eqs. (3)-(6), the polarization states for the fixed LP case are
{P1=cosθsinθ(cosβ1)x^+(sin2θcosβ+cos2θ)y^sinθsinβz^P0=y^P1=cosθsinθ(cosβ1)x^+(sin2θcosβ+cos2θ)y^+sinθsinβz^.
(7)
Calculations of the polarization states at θ = 45° and 90° are shown in Fig. 1. The interaction angle β for calculations, about 44°, is calculated from the lateral period 293 nm of the measured 0° interference pattern. As expected, the maximal contrast occurs at θ = 0° and decreases to a minimum at θ = 90° due to the polarization vectors of the two-first order beams becoming out of phase. Analogously, with e = 1, we obtain the polarization states for three CP beams as

{P1=12[cosθsinθ(cosβ1)x^+(sin2θcosβ+cos2θ)y^sinθsinβz^)]i2[(cos2θcosβ+sin2θ)x^+cosθsinθ(cosβ1)y^cosθsinβz^)]P0=12(y^ix^)P1=12[cosθsinθ(cosβ1)x^+(sin2θcosβ+cos2θ)y^+sinθsinβz^)]i2[(cos2θcosβ+sin2θ)x^+cosθsinθ(cosβ1)y^+cosθsinβz^)].
(8)

2.2 Intensity distribution of three-beam interference

The intensity distribution of three-beam interference is described as
I(r)=(E0+E1+E1)(E0+E1+E1).
(9)
Substituting Eqs. (1)-(6) into Eq. (9), we obtain the intensity distribution for the interference of three EP beams as
I[r(x,y,z),θ,β]E(e)=I0+2I1+12[(21+e2)(cos2β2+cos2θsin2β2)+(2e21+e2)(cos2β2cos2θsin2β2)]4I0I1cos(kxcosθsinβ+kysinθsinβ)cos[kz(1cosβ)]+12[(21+e2)(cos2β+cos2θsin2β)+(2e21+e2)(cos2βcos2θsin2β)]2I1cos(2kxcosθsinβ+2kysinθsinβ),
(10)
in which intensity Ij = fj2, j = 0, 1 and −1, and I1 = I-1. With e = 0, the intensity distribution for the fixed LP case is explicitly described as
I[r(x,y,z),θ,β]s=I0+2I1+(cos2θ+sin2θcosβ)4I0I1cos[ksinβ(xcosθ+ysinθ)]cos[kz(1cosβ)]+(cos2θ+sin2θcos2β)2I1cos[2ksinβ(xcosθ+ysinθ)],
(11)
in which cos2θ+sin2θcosβ = cos2β2+cos2θsin2β2. Similarly, with e = 1, the intensity distribution for the CP case is
I[r(x,y,z),θ,β]c=I0+2I1+(cos2β2)4I0I1cos[ksinβ(xcosθ+ysinθ)]cos[kz(1cosβ)]+(cos2β)2I1cos[2ksinβ(xcosθ+ysinθ)].
(12)
According to Eq. (10), the first and second terms correspond to uniform illumination in a wide-field microscope; the third and fourth terms correspond to the interferences of the zero- and first-order beams and the two first-order beams to improve the axial and lateral resolutions, respectively. Although the third term also improves the lateral resolution, the improvement is only one half that of the fourth term and thus becomes unimportant. Figure 2
Fig. 2 Modulation contrasts for interferences of the (a) zero- and first-order beams and (b) two first-order beams in orientations 0°−180° for the cases of fixed linear polarization (LP), circular polarization (CP) and maintained SLP; the interaction angle β for the calculations is 44°.
shows the results of calculations of modulation contrasts for the interferences of (a) the zero- and first-order beams and (b) the two first-order beams in orientations 0°−180° for the cases of fixed LP, CP and maintained SLP. The modulation contrasts of circular polarization are seen to be independent of the pattern orientation. With maintained SLP as a reference, the modulation contrast from the interference of the zero- and first-order beams remains over 85%, but that of the two-first order beams is only about 50%. Regarding the fixed LP case, the modulation contrast varies significantly with the pattern orientation, with a minimum at θ = 90°. Considering an interaction angle 2β = 88° between the two first-order beams, the nearly zero contrast at θ = 90° is rational as the two beams are nearly orthogonal in the sample to make radial polarized interference impossible.

3. Microscope setup and image reconstruction

3.1 Microscope setup

The setup of our 3D-SIM microscope is similar to that for imaging of light scattering reported previously [23

23. E. H. Rego, L. Shao, J. J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution,” Proc. Natl. Acad. Sci. U.S.A. 109(3), E135–E143 (2012). [CrossRef] [PubMed]

]. Briefly, the system consists of a standard upright microscope (Nikon 80i) with a He-Ne laser (Lasos, LGK7786 P100) operating at 543 nm. Figure 3(a)
Fig. 3 (a) Optical setup to generate three diffracted beams of circular polarization for interference in a 3D-SIM system. (b) Portions of 0°, 45°, and 60° SLM patterns and (c) corresponding interference patterns of nearly the same lateral period − 293 nm (0°), 290 nm (45°) and 295 nm (60°); the black pixels indicate no phase retardation and the white pixels indicate a phase retardation 7π/8 of the liquid crystal; the periodicity for each SLM pattern is indicated by coloring one pixel in each unit cell red.
shows a simple scheme of the optical setup to generate the interference patterns and to detect fluorescence. A phase-only SLM (Hamamatsu, X10468–04) was used to diffract the incident laser beam mainly into zero and ± 1 order beams at a selected orientation. Three lenses collected and focused the three diffracted beams, with the zero-order beam at the center and the two first-order beams near the edges, on the back focal plane (pupil) of a water-immersion objective (Nikon, Plan Apochromat VC, 60x, NA = 1.2) to form an interference pattern on the sample. Because the linear polarization of the laser light must orient along the director axis of the liquid crystal to ensure effective phase modulation, a λ/4-wave plate (CVI Laser, ACWP) was placed after the SLM to alter the three diffracted beams from linear to circular polarization for interference. Fluorescence from the sample was selected with an emission filter (Chroma, HQ600/75) and then detected with an electron-multiplying CCD camera (Andor, DU885). To collect images in a stack at a selected focus step, we controlled the axial position of the sample with a stage driven with a piezoelectric transducer (PI, P-562.3CD). All imaging processes were conducted with programs (LabVIEW).

The interference pattern had its orientation altered or its phase shifted for imaging with a design of SLM patterns. The SLM served as a two-level phase grating; the white pixels represent a phase modulation of the liquid crystal at an input grey level whereas the black pixels represent no phase modulation. According to the nearly linear curve for phase modulation (calibrated by the manufacturer), a π phase shift was set at grey level 120; the 7/8 π phase shift corresponded to level 110. To increase the intensity ratio of the zero- and first-order beams, the white pixels were set at level 110 in our designed SLM patterns. We designed SLM patterns for imaging at orientations 0°, 45°, 90° and 135°, or at orientations 0°, 60°, and 120°. Figure 3(b) shows portions of 0°, 45° and ~60° SLM patterns designed in periods of length 7.0, 5√2 ( = 7.1) and 7.0 pixels and Fig. 3(c) shows corresponding interference patterns with a nearly identical lateral period − 293 nm (0°), 290 nm (45°) and 295 nm (60°); the interference patterns were measured from reflections with a silicon wafer on the sample stage. The SLM patterns are classified into three sets − (0°, 90°), (45°, 135°), and (60°, 120°); those of 90°, 120° and 135° are therefore omitted.

3.2 Image reconstruction

4. Results

4.1 Interference patterns

The modulation contrasts for the fixed LP and CP cases were calculated according to Eqs. (11) and (12), respectively, with the system parameters I0/I1 = 0.75 and β = 44°. The modulation contrast for maintained SLP is identical to that of fixed LP at θ = 0°. Figure 4(a)
Fig. 4 Simulations of (a) lateral modulations at the sample focal plane (upper) at θ = 0°, 45°, 60° and 90°, and the corresponding axial modulations (bottom) for fixed linear polarization and circular polarization, and (b) corresponding lateral and axial profiles, indicated in yellow lines in (a). The axial modulation for each orientation is projected on its oriented plane, such as plane x’z at θ = 45° to simplify the view; the parameters for calculations are I0/I1 = 0.75 and β = 44°.
shows the lateral modulations at the sample focal plane at θ = 0°, 45°, 60° and 90°, and the corresponding axial modulations projected on the orientated plane for a simple view. The corresponding lateral and axial profiles indicated as yellow lines in Fig. 4(a) are shown in Fig. 4(b); the profiles of CP correspond to those of fixed LP at θ = 45° and are thus omitted.

As expected, the maintained SLP corresponding to fixed LP at θ = 0° provides a maximal contrast. For the fixed LP case, the contrast of the lateral and axial modulations varies greatly at the four orientations, and attains a minimum with a greater bandwidth. According to Fig. 2(a), the contrast of the strong lateral modulation at θ = 45°, 60° and 90° relative to θ = 0° decrease about 14%, 21% and 28%, respectively; the decrease of the corresponding weak lateral modulation in Fig. 2(b) is more significant, about 48%, 72% and 96%, respectively. This result indicates that fixed LP provides a highly anisotropic illumination; moreover, the use of four orientations − 0°, 45°, 90° and 135° − to reconstruct a high-resolution image is inappropriate because the component at θ = 90° is too weak to be observed.

In contrast, the use of circular polarization achieves the objective − to avoid rotational components or a complicated polarization rotator, but to produce an identical modulation contrast at varied orientation for imaging. As seen in Fig. 4(a), the modulation contrasts are identical at the four orientations to provide an isotropic illumination. The modulating contrast of CP corresponds to that of fixed LP at θ = 45°, and is therefore greater than those of fixed LP at θ = 60° and 90°. Alternatively, a comparison of fixed LP at θ = 0° and 45° indicates that the modulation contrast from the two-first order beams is only about 50% with circular polarization instead of maintained SLP. This decrease mainly weakens the spatial-frequency components in the lateral direction, and might therefore influence the improvement of lateral resolution and image quality.

4.2 Simulations

To evaluate the influence of modulation contrast on imaging, we simulated the reconstructed SIM component images of 100-nm beads for the fixed LP case at SNR = 10 and 40 as a reference; the results of fixed LP at θ = 0° and 45° correspond to those of circular polarization and maintained SLP, respectively. In the simulation, we generated a raw image stack of 31 layers by adding beads of identical signals but randomly distributed in one layer to a noisy background. The noise in each layer was also randomly generated on a basis pixel by pixel with a mean value about 3, selected based on the experimentally modulated images. Figure 5
Fig. 5 Simulations of reconstructed component images of 100-nm beads at the focal plane at θ = (a) 0°, (b) 45°, (c) 60° and (d) 90° for fixed linear polarization with the raw images at the ratio of signal to noise about 10; each 8-bit image is rescaled with the maximal signal to 255 for display.
shows the reconstructed and normalized SIM component images at the focal plane at θ = (a) 0°, (b) 45°, (c) 60° and (d) 90° with the raw images at SNR about 10. As seen, the image contrast decreases with decreased pattern contrast but the effect is much less at θ = 45° and 60° than that at θ = 90°. The image at θ = 90° reveals indiscernible beads in a large background; this large effect is attributed to a diminutive contrast from the interference of the two first-order beams, as seen in Fig. 4(b). With SNR increased to 40, the image contrasts are improved to become comparable for θ ≤ 60° and are thus not shown. Accordingly, the use of maintained SLP and circular polarization results in merely a small difference in imaging at SNR ≥10.

We further compared the Wiener-deconvoluted 3D-SIM images of 100-nm beads reconstructed from three orientations − 0°, 60°, and 120°. Because of the severely deteriorated image for fixed LP at θ = 90°, four pattern orientations were not used. Figure 6
Fig. 6 Simulations of lateral and axial projections of reconstructed images of 100-nm beads from three orientations − 0°, 60° and 120° for (a) fixed linear polarization, (b) circular polarization and (c) maintained s-linear polarization with raw images at the ratio of signal to noise about 10; each image is 8-bit with the maximal signal rescaled to 255 for display.
shows the lateral (xy) and axial (xz) projections of the reconstructed 3D-SIM images of 100-nm beads with the raw images at SNR about 10 for the cases of (a) fixed LP, (b) circular polarization and (c) maintained SLP. Evidently, the image contrast increases from fixed LP to circular polarization to maintained SLP through an increased modulation contrast. With SNR increased to 40, all image contrasts are improved, as expected, and are thus not shown. To quantify, we calculated the SNR of the lateral and axial projections of 3D-SIM images. The noise is determined from a region 17 by 17 pixels containing no beads; the values of five regions are averaged. For the raw images at SNR about 10 and 40, the SNR of 3D-SIM images from the lateral projections are 13 ± 1 and 27 ± 2 for fixed LP, 16 ± 1 and 34 ± 2 for CP, and 23 ± 2 and 45 ± 2 for maintained SLP, respectively. The corresponding SNR of axial projections are 16 ± 1 and 31 ± 3 for fixed LP, 24 ± 3 and 45 ± 9 for CP, and 31 ± 3 and 56 ± 16 for maintained. Maintained SLP is evidently superior to provide the best image quality. The use of circular polarization provides a satisfactory image quality, about SNR 70−80% SNR. The use of fixed LP is less required with SNR about 50−60%.

4.3 Experimental results

To confirm the simulation, we performed measurements of 100-nm fluorescent beads with our 3D-SIM system. We used linear polarization lying on the x axis rather than the y axis because the setup of the SLM for diffractions in our system. We abbreviate this case as fixed LP-x. The result is expected to be the same for that of fixed LP lying on the y axis except a difference 90° in pattern orientation. Figure 7
Fig. 7 Reconstructed component images of 100-nm fluorescent beads at the focal plane at 0°, 60° and 120° with beams of (a) fixed s-linear polarization on the x axis and (b) circular polarization; the ratio of signal to noise in the measured raw image is about 250.
shows the reconstructed and normalized SIM component images at the focal plane at θ = 0°, 60°, and 120° using beams of (a) fixed LP-x and (b) circular polarization. The raw image stack has 31 layers at z-step 100 nm; the SNR of the raw image is about 250. In Fig. 7(a), the image of fixed PL-x at θ = 0° that reveals fluorescent beads vaguely due to a diminutive contrast is consistent with the simulation of fixed LP at θ = 90° shown in Fig. 5. The image contrasts at θ = 60° and 120° that are nearly the same also confirm that their modulation contrasts are comparable. In Fig. 7(b), the use of circular polarization reveals identical image contrast at the three orientations, confirming that the modulation contrast is independent of the pattern orientation.

To demonstrate the resolution and image contrast with the use of CP, Fig. 8(a)
Fig. 8 (a) Lateral and axial projections of the wide-field (WF) and 3D-SIM images of 100-nm fluorescent beads and (b) corresponding profiles of an individual bead marked in lines; the solid curve corresponds to a Gaussian fit.
shows the lateral (xy) and axial (xz) projections of the wide-field (WF) and 3D-SIM images of 100-nm fluorescent beads; the corresponding lateral and axial profiles of a single bead are shown in Fig. 8(b), with the solid line for a Gaussian fit. The 3D-SIM image shows improved resolution and image contrast. From the full width at half maximum (FWHM) of a single bead and averaged FWHM of five beads, the lateral and axial resolutions obtained are 280 ± 8 nm and 766 ± 47 nm in the WF image and 127 ± 7 nm and 425 ± 20 nm in the 3D-SIM image. The improving factors are about 2.2 laterally and 1.8 axially.

To demonstrate the ability of our 3D-SIM system in biological applications, we acquired a 3D image of Alexa-488-labeled microtubules inside a HeLa cell. The cell was fixed with paraformaldehyde (4%) on the glass slide before immersion in deionized water for imaging. The fluorescence emits at ~520 nm upon excitation at 473 nm. Figure 9
Fig. 9 Lateral (xy) and yz views of (a) wide-field (WF) and (b) 3D-SIM images of Alexa-488-labeled microtubules inside a HeLa cell; the xy view is at a selected z position; the three dash lines indicate the positions for yz views. The image size is about 16.4 x 16.4 x 5 μm3 in the x, y and z directions.
shows the lateral xy view at a selected z position and yz views at three x positions of (a) wide-field and (b) 3D-SIM images of microtubules; the x positions are indicated with dash lines in the xy plane. The wide-field image was obtained from the retrieved conventional OTF spectra. Evidently, the 3D-SIM image reveals the improved resolution and contrast to enable individual microtubules to be well-resolved in a low background. We estimate the resolution from 10 microtubules; the averaged lateral and axial FWHM are about 128 ± 11 and 430 ± 37 nm, respectively.

5. Conclusion

Acknowledgments

NSRRC and National Science Council (NSC-99-2113-M-213-005) in Taiwan provided financial support.

References and links

1.

R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185–196 (1999). [CrossRef]

2.

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000). [CrossRef] [PubMed]

3.

M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Doubling the lateral resolution of wide-field fluorescence microscopy using structured illumination,” Proc. SPIE 3919, 141–150 (2000). [CrossRef]

4.

B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366(6450), 44–48 (1993). [CrossRef] [PubMed]

5.

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97(13), 7232–7236 (2000). [CrossRef] [PubMed]

6.

J. T. Frohn, H. F. Knapp, and A. Stemmer, “Three-dimensional resolution enhancement in fluorescence microscopy by harmonic excitation,” Opt. Lett. 26(11), 828–830 (2001). [CrossRef] [PubMed]

7.

R. Heintzmann, “Saturated patterned excitation microscopy with two-dimensional excitation patterns,” Micron 34(6-7), 283–291 (2003). [CrossRef] [PubMed]

8.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008). [CrossRef] [PubMed]

9.

T. A. Klar and S. W. Hell, “Subdiffraction resolution in far-field fluorescence microscopy,” Opt. Lett. 24(14), 954–956 (1999). [CrossRef] [PubMed]

10.

T. A. Klar, S. Jakobs, M. Dyba, A. Egner, and S. W. Hell, “Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97(15), 8206–8210 (2000). [CrossRef] [PubMed]

11.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006). [CrossRef] [PubMed]

12.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006). [CrossRef] [PubMed]

13.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006). [CrossRef] [PubMed]

14.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009). [CrossRef] [PubMed]

15.

L. M. Hirvonen, K. Wicker, O. Mandula, and R. Heintzmann, “Structured illumination microscopy of a living cell,” Eur. Biophys. J. 38(6), 807–812 (2009). [CrossRef] [PubMed]

16.

L. Shao, P. Kner, E. H. Rego, and M. G. L. Gustafsson, “Super-resolution 3D microscopy of live whole cells using structured illumination,” Nat. Methods 8(12), 1044–1046 (2011). [CrossRef] [PubMed]

17.

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. L. Gustafsson, “Time-lapse two-color 3D imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5311–5315 (2012). [CrossRef] [PubMed]

18.

E. Chung, D. Kim, and P. T. So, “Extended resolution wide-field optical imaging: objective-launched standing-wave total internal reflection fluorescence microscopy,” Opt. Lett. 31(7), 945–947 (2006). [CrossRef] [PubMed]

19.

R. Fiolka, M. Beck, and A. Stemmer, “Structured illumination in total internal reflection fluorescence microscopy using a spatial light modulator,” Opt. Lett. 33(14), 1629–1631 (2008). [CrossRef] [PubMed]

20.

L. Shao, B. Isaac, S. Uzawa, D. A. Agard, J. W. Sedat, and M. G. L. Gustafsson, “I5S: wide-field light microscopy with 100-nm-scale resolution in three dimensions,” Biophys. J. 94(12), 4971–4983 (2008). [CrossRef] [PubMed]

21.

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A. 102(37), 13081–13086 (2005). [CrossRef] [PubMed]

22.

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy--a concept for optical resolution improvement,” J. Opt. Soc. Am. A 19(8), 1599–1609 (2002). [CrossRef] [PubMed]

23.

E. H. Rego, L. Shao, J. J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution,” Proc. Natl. Acad. Sci. U.S.A. 109(3), E135–E143 (2012). [CrossRef] [PubMed]

24.

B. J. Chang, S. H. Lin, L. J. Chou, and S. Y. Chiang, “Subdiffraction scattered light imaging of gold nanoparticles using structured illumination,” Opt. Lett. 36(24), 4773–4775 (2011). [CrossRef] [PubMed]

25.

S. Chowdhury, A. H. Dhalla, and J. Izatt, “Structured oblique illumination microscopy for enhanced resolution imaging of non-fluorescent, coherently scattering samples,” Biomed. Opt. Express 3(8), 1841–1854 (2012). [CrossRef] [PubMed]

26.

J. Chen, Y. Xu, X. Lv, X. Lai, and S. Zeng, “Super-resolution differential interference contrast microscopy by structured illumination,” Opt. Express 21(1), 112–121 (2013). [CrossRef] [PubMed]

27.

B. J. Chang, L. J. Chou, Y. C. Chang, and S. Y. Chiang, “Isotropic image in structured illumination microscopy patterned with a spatial light modulator,” Opt. Express 17(17), 14710–14721 (2009). [CrossRef] [PubMed]

28.

J. J. M. Braat, http://www.nijboerzernike.nl/.

OCIS Codes
(100.6640) Image processing : Superresolution
(180.0180) Microscopy : Microscopy
(260.5430) Physical optics : Polarization

ToC Category:
Microscopy

History
Original Manuscript: June 19, 2013
Revised Manuscript: August 8, 2013
Manuscript Accepted: September 9, 2013
Published: October 1, 2013

Citation
Hsiao-Chih Huang, Bo-Jui Chang, Li-Jun Chou, and Su-Yu Chiang, "Three-beam interference with circular polarization for structured illumination microscopy," Opt. Express 21, 23963-23977 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-23963


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE3568, 185–196 (1999). [CrossRef]
  2. M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc.198(2), 82–87 (2000). [CrossRef] [PubMed]
  3. M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Doubling the lateral resolution of wide-field fluorescence microscopy using structured illumination,” Proc. SPIE3919, 141–150 (2000). [CrossRef]
  4. B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature366(6450), 44–48 (1993). [CrossRef] [PubMed]
  5. J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A.97(13), 7232–7236 (2000). [CrossRef] [PubMed]
  6. J. T. Frohn, H. F. Knapp, and A. Stemmer, “Three-dimensional resolution enhancement in fluorescence microscopy by harmonic excitation,” Opt. Lett.26(11), 828–830 (2001). [CrossRef] [PubMed]
  7. R. Heintzmann, “Saturated patterned excitation microscopy with two-dimensional excitation patterns,” Micron34(6-7), 283–291 (2003). [CrossRef] [PubMed]
  8. M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J.94(12), 4957–4970 (2008). [CrossRef] [PubMed]
  9. T. A. Klar and S. W. Hell, “Subdiffraction resolution in far-field fluorescence microscopy,” Opt. Lett.24(14), 954–956 (1999). [CrossRef] [PubMed]
  10. T. A. Klar, S. Jakobs, M. Dyba, A. Egner, and S. W. Hell, “Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A.97(15), 8206–8210 (2000). [CrossRef] [PubMed]
  11. E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313(5793), 1642–1645 (2006). [CrossRef] [PubMed]
  12. S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J.91(11), 4258–4272 (2006). [CrossRef] [PubMed]
  13. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3(10), 793–796 (2006). [CrossRef] [PubMed]
  14. P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods6(5), 339–342 (2009). [CrossRef] [PubMed]
  15. L. M. Hirvonen, K. Wicker, O. Mandula, and R. Heintzmann, “Structured illumination microscopy of a living cell,” Eur. Biophys. J.38(6), 807–812 (2009). [CrossRef] [PubMed]
  16. L. Shao, P. Kner, E. H. Rego, and M. G. L. Gustafsson, “Super-resolution 3D microscopy of live whole cells using structured illumination,” Nat. Methods8(12), 1044–1046 (2011). [CrossRef] [PubMed]
  17. R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. L. Gustafsson, “Time-lapse two-color 3D imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. U.S.A.109(14), 5311–5315 (2012). [CrossRef] [PubMed]
  18. E. Chung, D. Kim, and P. T. So, “Extended resolution wide-field optical imaging: objective-launched standing-wave total internal reflection fluorescence microscopy,” Opt. Lett.31(7), 945–947 (2006). [CrossRef] [PubMed]
  19. R. Fiolka, M. Beck, and A. Stemmer, “Structured illumination in total internal reflection fluorescence microscopy using a spatial light modulator,” Opt. Lett.33(14), 1629–1631 (2008). [CrossRef] [PubMed]
  20. L. Shao, B. Isaac, S. Uzawa, D. A. Agard, J. W. Sedat, and M. G. L. Gustafsson, “I5S: wide-field light microscopy with 100-nm-scale resolution in three dimensions,” Biophys. J.94(12), 4971–4983 (2008). [CrossRef] [PubMed]
  21. M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A.102(37), 13081–13086 (2005). [CrossRef] [PubMed]
  22. R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy--a concept for optical resolution improvement,” J. Opt. Soc. Am. A19(8), 1599–1609 (2002). [CrossRef] [PubMed]
  23. E. H. Rego, L. Shao, J. J. Macklin, L. Winoto, G. A. Johansson, N. Kamps-Hughes, M. W. Davidson, and M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy with a photoswitchable protein reveals cellular structures at 50-nm resolution,” Proc. Natl. Acad. Sci. U.S.A.109(3), E135–E143 (2012). [CrossRef] [PubMed]
  24. B. J. Chang, S. H. Lin, L. J. Chou, and S. Y. Chiang, “Subdiffraction scattered light imaging of gold nanoparticles using structured illumination,” Opt. Lett.36(24), 4773–4775 (2011). [CrossRef] [PubMed]
  25. S. Chowdhury, A. H. Dhalla, and J. Izatt, “Structured oblique illumination microscopy for enhanced resolution imaging of non-fluorescent, coherently scattering samples,” Biomed. Opt. Express3(8), 1841–1854 (2012). [CrossRef] [PubMed]
  26. J. Chen, Y. Xu, X. Lv, X. Lai, and S. Zeng, “Super-resolution differential interference contrast microscopy by structured illumination,” Opt. Express21(1), 112–121 (2013). [CrossRef] [PubMed]
  27. B. J. Chang, L. J. Chou, Y. C. Chang, and S. Y. Chiang, “Isotropic image in structured illumination microscopy patterned with a spatial light modulator,” Opt. Express17(17), 14710–14721 (2009). [CrossRef] [PubMed]
  28. J. J. M. Braat, http://www.nijboerzernike.nl/ .

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited