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Beversluis et al. Vol. 25, No. 6 /June 2008/J. Opt. Soc. Am. A 1371

Effects of inhomogeneous fields in superresolvingstructured-illumination microscopy

Michael R. Beversluis, Garnett W. Bryant, and Stephan J. Stranick*

The National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA*Corresponding author: stranick@nist.gov

Received December 4, 2007; accepted March 20, 2008;posted April 8, 2008 (Doc. ID 90467); published May 21, 2008

The increased resolution attained by structured illumination is based on the degree to which high spatial fre-quencies can be down converted into the passband of the imaging system. To effectively do this, a high contrasthigh-frequency illumination pattern is required. We show how the use of high numerical aperture (1.42 NA and1.65 NA) microscope objectives in structured-illumination microscopy can provide relatively high-frequency il-lumination patterns. However, a consequence of this is that the resulting illumination pattern can become eva-nescently decaying and thus becomes inhomogeneous within a microscopically extended sample medium. Wedemonstrate how these inhomogeneous fields impact the superresolved imaging of the microscope and howthese adverse effects can be avoided.

OCIS codes: 100.6640, 180.2520.

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. INTRODUCTIONtructured-illumination microscopy is a technique thatan extend the resolution of fluorescence microscopy be-ond the Rayleigh diffraction limit �0.61 � /NA� to what isommonly referred to as superresolution. The use of mov-ng gratings or structured illumination to achieve super-esolution in a microscope was first described by Lukoszn 1966 [1]. Lukosz suggested placing a transmissionrating between the sample and the microscope pupil toreate a modulated-illumination pattern or fringes. Thisould result in spatial-frequency sidebands that are com-rised of the high frequencies that were normally outsidef the microscope’s passband, a concept similar to theoiré interference effect. These sidebands can then be de-odulated to extend the frequency range of the micro-

cope’s optical transfer function (OTF), thereby improvinghe microscope’s spatial resolution to superresolution. Inodern implementations of structured-illumination mi-

roscopy a superresolved image results when a series ofatterned illumination images are recorded under differ-nt modulation conditions, e.g., modulation angle andelative phase of the standing wave pattern. Next, the se-ies is digitally demodulated to extract the downshiftedigh spatial-frequency components; then these frequencyomponents are digitally restored to their original fre-uency. The resolution advantage can be realized bothxially for optical sectioning [2] and laterally for super-esolution [3–5]. In comparison to the low-frequencyodulation patterns used in optical sectioning

tructured-illumination microscopes, superresolvingtructured-illumination microscopes use as high a modu-ation frequency as possible to maximize the resolutiondvantage. Such microscopes have been shown to nomi-ally offer twice the lateral spatial resolution of a conven-ional fluorescence microscope and when combined withnterferometric techniques many times higher axial spa-ial resolution [6,7]. The resolution can be further im-

roved when structured illumination is combined withonlinear saturation effects; this results in harmonics ofhe modulation frequency being generated within the im-ge [8,9].With linear and even nonlinear techniques it is advan-

ageous to use the highest possible modulation frequency.he maximum modulation frequency depends in largeart on the numerical aperture (NA) of the illuminationptics. This leads to the use of ultrahigh NA total internaleflectance fluorescence (TIRF) objectives for structured-llumination microscopy [10]. By using 1.78 refractive in-ex coverslips, TIRF objectives can achieve 1.65 NA com-ared to 1.30 NA water-immersion and 1.42 NA oil-mmersion Plan-Apo objectives. By design, excitationrom the maximum NA of these objectives results in totalnternal reflection (TIR) of the structured illumination athe coverslip/sample interface that evanescently decaysnto the sample. The evanescent field is inhomogeneousith the planes of constant intensity and the planes of

onstant phase no longer coincident [11]. In this paper, weemonstrate the adverse effects of using these inhomoge-eous illumination fields and outline the conditions nec-ssary to avoid them.

. STRUCTURED-ILLUMINATION THEORYND ANALYSIS

he theory for demodulation of structured-illuminationuorescence images has been covered in detail in [2–4].or the purpose of discussion, demodulation begins byodeling the excitation intensity pattern across the focal

lane,

I�r� = I0�M cos�u · r + �� + 1�, �1�

here r is the position vector, I0 is the excitation irradi-nce, M is the modulation amplitude, u=2� /du is therating lattice vector determined by its pitch d and orien-

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1372 J. Opt. Soc. Am. A/Vol. 25, No. 6 /June 2008 Beversluis et al.

ation u in the xy plane, and � is its phase relative to themage origin. Typically, the intensity pattern in Eq. (1) isreated by the interference of two plane waves incident atngles ±� with respect to the optic axis; therefore, d�ex/2n1 sin �, where �ex is the excitation vacuum wave-

ength and n1 is the coverslip refractive index. The phaseof the fringe pattern is a critical element because it will

e used to separate the conventional and superresolvingmages. It is determined by the relative phase betweenhe two incident fields, which can be defined as �12=�2�1.Figure 1 shows that two possible illumination condi-

ions exist when an immersion objective illuminates aample region surrounded by a medium with refractivendex n2; in Fig. 1(A) the incident angle �0 is less than theritical angle �c=sin−1�n2 /n1�; therefore, the refractedngle across the interface �1 is real, and the transmittedelds homogeneously propagate into the sample. Therehey interfere to form an intensity modulation patterniven by Eq. (1), and since this condition is fulfilled a su-erresolving image can be demodulated from a series ofeasurements. The second illumination condition is illus-

rated in Fig. 1(B), where the incident angle is greaterhan the critical angle. Then the incident light undergoesIR at the coverslip interface, and only evanescent fieldsre present in the sample region. These fields are inhomo-eneous because the refracted angle is complex. Takingn appropriate choice in the sign of the complex root thehase of the evanescent field takes on the form

k · r − �12 =2�n1

�ex�iz�sin2 � − n21

2 + � sin �� − �12, �2�

here n21=n2 /n1 and � is the projection of the in-planeomponent � of r along the in-plane component of k. Theerm proportional to �sin2 �−n21

2 is purely imaginary, andonsequently, the intensity pattern within the sample willow depend on z, unlike the expected z coordinate inde-endence that is assumed in the normal derivation oftructured-illumination image demodulation.

The importance of the intensity pattern in Eq. (1) cane seen when we consider in detail the image processingnd demodulation used to extract the superresolving im-ges. If we assume that the sample consists of randomlyistributed fluorophore dipoles, the fluorescence rate is

n2 = 1.0

θ0

θ1

θ0

Plane ofConstant Phase

Plane ofConstant Amplitude

(A) (B)

z z

x x

n1 = 1.515

Planes of ConstantPhase and Amplitude

ig. 1. Propagating and TIR illumination at an air–glass inter-ace. (A) If the incident angle of the illumination is less than theritical angle, the light will refract into a propagating transverseeld. (B) If the incident angle is greater than the critical angle,he incident light undergoes TIR. Above the interface the evanes-ent field is inhomogeneous and has disjoint planes of constantmplitude and phase.

roportional to the product of I�r� and the local sampleuorophore density ��r�. The image is given by the con-olution ��� of this product with the microscope’s incoher-nt point spread function (PSF), PSF�r�:

w�r� = �I�r� � ��r�� � PSF�r�. �3�

he product of I�r� and ��r� is the source of moiré fringesn the structured-illumination image, which can be writ-en in frequency space by first taking the Fourier trans-orm of I�r�:

I�k� = I0/2�Me−i���k − u� + 2��k� + Me+i���k + u��. �4�

hen, by twice applying the convolution theorem the im-ge’s Fourier transform is

w�k� = �I�k� � ��k�� � OTF�k�, �5�

here ��k� is the complex-valued Fourier transform of�r� and OTF�k� is the microscope’s OTF. The convolu-

ion of ��k� with the three delta functions present in I�k�esults in

w�k� = I0/2�Me−i���k − u� + 2��k�

+ Me+i���k + u�� � OTF�k�. �6�

he PSF convolution has a multiplicative low-pass filter-ng effect. To account for this frequency dependent at-enuation, a high-frequency boosting filter (described inore detail herein) is applied to the raw images. This re-

tores the downshifted spectral components to their origi-al magnitudes.Fluorescence results in an incoherent image; thus the

hree spectral components in Eq. (5) add together throughheir intensity. This means that they can be separated us-ng three or more structured-illumination measurements,

n, with different illumination phases �n. If N3 is theotal number of phase steps taken for each grating orien-ation u then it is convenient to use a value of �n2��q /N�n for integers q�N /2 (to avoid degeneracy) forach image wn. To synthesize the superresolved image weegin by writing the structured-illumination images ashe superposition of a conventional image and the super-esolving image:

wn = w + wSR cos� − �n�. �7�

n general, depending on the image and grating phaseshe spectrum of each measured image has an additionallobal phase that varies for each grating vector u.herefore, the data for each needs to be incoherentlydded together to produce the final image. The conven-ional image is then formed by averaging the data sets,

w =1

m�n=1

m

wn, �8�

here the sum is performed for each pixel in the image.As previously mentioned, to form the superresolved im-

ge it is necessary to correct for the high-frequency at-enuation of the incoherent OTF and image edge artifacts.o correct for image edge artifacts, each wn was filteredround the edges using a two-pixel Gaussian blur to re-

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Beversluis et al. Vol. 25, No. 6 /June 2008/J. Opt. Soc. Am. A 1373

ove image edge discontinuities and then convolved withn empirically derived inverse OTF:

OTF−1�k� = �a + b�k�3�c

1 + ��k�/k0�p . �9�

he first factor accounts for the high-frequency decay ofhe OTF with experimentally determined parameters and b chosen to give a flat response over the microscope’supported frequencies. The second factor is a p-order low-ass filter with cutoff frequency k0, which was set to theaximum frequency supported by the OTF. The value of cas set to renormalize the total power to its originalalue.

The spectral components can be separated in frequencypace using a least-squares solution; however, there areeveral ways to calculate the superresolved image in real-pace. We can first calculate the superresolving image us-ng the formula

wSR =2

m��

n=1

m

ei�nwn� . �10�

s previously mentioned, the calculation must be doneeparately for each grating orientation to avoid distortionue to global phase . The results are then added togethero produce the final synthetic image. A second approach iso calculate

wSR = �n=1

m

�wn − wn+j�2/m�1 + cos�2�qj/m��1/2

, �11�

here j is a positive integer and the index n+ j is under-tood to cycle modulo m. Either Eq. (9) or Eq. (10) willive the correct result for wSR.

Next, we look at the issues involved with the inhomo-eneous fields resulting from TIR illumination. It is illu-ination from above the critical angle that creates the

argest values of u in the xy plane at the interface andherefore the highest modulation frequency and reso-ution enhancement. The evanescently decaying electriceld vector of the two incident fields produced within theample/medium can be written as

E1,2�r� = Re�F1,2 exp�±i�k · r − �1,2���, �12�

here F1 and F2 are the complex field amplitudes whoseagnitude and phase will depend on the polarization

elative to the plane of incidence and k ·r is a complexumber given by Eq. (2). The real part of k ·r is given by

���� =2�n1

�exsin � �13�

hile the imaginary part, which gives the evanescent de-ay length into the sample medium, is given by

���� = �ex/�4��n12 sin2 � − n2

2�1/2�. �14�

epending on the electric field polarization vector, the ex-ression for the resulting interference pattern will beomplicated; assuming that the two beams are-polarized, the resulting irradiance pattern will appearithin the medium:

Is��,z� = I0s�1 + cos��� − �12��exp�− z/��. �15�

ntroducing p-polarized components will result in addi-ional phases and a reduction in the illumination pat-ern’s modulation contrast. In either polarization case,he inhomogeneous intensity dependence on both � and zeans that the relative intensity of the fringe pattern

hrough the sample will strongly depend on z, leading tortifacts during image reconstruction.The extent to which the evanescent field decay and re-

ulting inhomogeneity of the modulation pattern affectshe imaging strongly depends on the relative scale be-ween the sample thickness and the field decay factor �.igure 2 shows plots of the illumination pattern’s pitch asfunction of the incidence angle and decay factors at air

nd water interfaces. For both objectives, illuminationbove the critical angle will adversely affect thetructured-illumination imaging of samples thicker thanhe decay length: approximately one-tenth of the excita-ion wavelength. A further complication will occur if theample is strongly absorbing within the field decay re-ion. In this case, the refracted angle will be partiallymaginary instead of purely imaginary, and the directionf the wavenormals [given by Eq. (12)] will vary between° and 90° from the planes of constant amplitude.

. EXPERIMENTAL ARRANGEMENThe experimental arrangement is schematically shown inig. 3. The starting point for these experiments was aide-field imaging fluorescence microscope that used anrgon ion laser operating at a 488 nm wavelength forllumination/excitation and a 512�512 pixel 16 biteltier-cooled CCD camera for fluorescence detection. The

aser light was filtered with a 10 nm bandpass filter cen-ered at 488 nm and directed into the microscope objectivesing a 500 nm long-pass dichroic mirror. Laser light waslocked from the camera using an additional 500 nm

2

1

0 00 9030 60

Length

λex488

[nm]

Incident Angle θ [degrees]

βair βwater

IlluminationPitch d

θmax

2

1

0 00 9030 60Incident Angle θ [degrees]

IlluminationPitch d

βair βwater900 900

1.65 NAObjective1.42 NAObjective

300

600

300

600

θmaxLength[λex]

244 nm 183 nm

172 nm

244 nm 183 nm

147 nm

EvanescentDecay Parameters

(A) (B)

ig. 2. (Color online) Illumination grating period d as a func-ion of the incident angle for (A) 1.42 and (B) 1.65 NA objectives.he dotted curves at �=�max show the maximum incident angle,nd the right-hand axis has been scaled to the 488 nm wave-ength excitation used in the experiment. The evanescent decayurves �air and �water are plotted versus the incident angle for thelass–air and glass–water interfaces. The minimum propagatingllumination fringe periods in air (d=244 nm, refractive index.00) and water (d=183 nm, refractive index 1.33) are shown.he minimum fringe periods supported by the 1.42 NA objectivef 172 nm and by the 1.65 NA objective of 147 nm fall well belowhe cutoff for propagating fields and are accessible only within aew nanometers of the interface.

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1374 J. Opt. Soc. Am. A/Vol. 25, No. 6 /June 2008 Beversluis et al.

avelength long-pass filter. An additional magnificationens within the microscope produced an image on theCD such that the pixel size was close to the Nyquistampling limit: 85.7 nm per pixel for the 60�1.42 NAlan-Apo objective and 51.3 nm per pixel for the 1001.65 objective. To avoid aliasing in the superresolving

mage the digital images were resampled (from 512512 to 1024�1024) by zero-padding their Fourier

ransforms and then renormalized to their original valuess outlined by Gustafsson [5]. We used a liquid crystalpatial light modulator (SLM) to project sinusoidal illumi-ation patterns onto the sample with predeterminedhases and orientations. This is accomplished by generat-ng a sinusoidal phase grating on the SLM surface thatiffracted the laser beam into several orders. Three relayenses symmetrically focused the +1 and −1 orders intohe objective pupil. Residual zero-order light was blockedn the external Fourier transform plane using a small

etal sphere glued to a glass window to form a high-passpatial filter.

The spatial-frequency, orientation, and position (phase)f the excitation pattern was given by the pitch, orienta-ion, and phase of the SLM grating. A series of illumina-ion patterns of predetermined pitch, orientation, andhase were created and optimized for each objective pu-il: 24 images in a series comprised of six relative pitchhases (0°, 60°, 120°, 180°, 240°, and 300°) repeated forour pitch orientations (0°, 45°, 90°, and 135°). An optimi-ation procedure corrected the SLM wavefront errors andny inhomogeneous response of the SLM [12]. The poweriffracted into the +1 and −1 orders depends on the phaserating modulation depth m and is proportional to1�m /2�, where J1 is the first Bessel function. In general,

was set to maximize the diffraction efficiency into the1/−1 orders and then fine-tuned for the different grat-

ngs so that all orientations and phases had equal powero within 1%. As a practical note the SLM works besthen the pitch represents an integer number of pixels.his avoids artifactual frequency sidebands that other-ise result from the discrete nature of the SLM.To characterize the effects of inhomogeneous fields on

he resolving power of a structured-illumination micro-cope a series of experiments were carried out using 40nd 100 nm diameter yellow-green fluorescent beads withpeak emission wavelength at 530 nm. The samples used

n this paper were prepared by placing a drop of a solutionontaining the beads onto a clean coverslip that was thenlown dry to create semidilute coverages.The integration time for each image in a given series

as 100 ms. The average total power illuminating the

Liquid CrystalSpatial Light Modulator

(SLM)

+1-1

Diffracted beams

DichroicMirror

Em.Filter

CCD CameraArgon Ion Laser

High-pass Spatial Filter

λex = 488 nm

ig. 3. Experimental schematic of the structured-illuminationuorescence microscope used in our experiments. A liquid crystalLM is used to project sinusoidal patterns onto the sample.

ample was set to 5 W, which typically resulted in 5000ounts for the maximum pixel value of a single bead.umming the 24 raw images of a series together to formhe conventional image resulted in a typical peak inten-ity of 120,000 counts per pixel.

. STRUCTURED ILLUMINATION WITHHE ULTRAHIGH NUMERICAL APERTUREBJECTIVES

he 60�1.42 NA objective used borosilicate coverslipsith refractive index n=1.515. At the glass–air interface

his results in a critical angle of 41.3°. The objective’saximum collection angle specified by the 1.42 NA is

9.7°. At the excitation wavelength of 488 nm thesengles correspond to illumination patterns with periods of44 and 172 nm, respectively. Sinusoidal illuminationatterns with periods greater than 244 nm will be of highontrast and transmitted through the glass interface. Pat-erns with periods between 244 and 172 nm will be totallynternally reflected at the glass interface and thus becomeonpropagating and more importantly inhomogeneous.Figure 4 compares the results for conventional

iffraction-limited imaging with superresolved imagingsing propagating (310 nm period) and nonpropagating205 nm period) fringes. Figures 4(A) and 4(B) show im-ges of the objective pupil taken with a Bertrand lens forhe propagating and nonpropagating cases, respectively.n Fig. 4(A) the two spots within the disk show the laserllumination locations (below the critical angle) for a sinu-oidal excitation with a 310 nm fringe period. The edge ofhe darker center disk marks the location of the criticalngle for this objective, and it can be seen in Fig. 4(B)hat the illumination location for the 205 nm period pat-ern lies above the critical angle. Additionally, it can beeen in Figs. 4(A) and 4(B) that most of the fluorescencebright ring region) appears above the critical angle dueo the nature of dipole emission close to a dielectric inter-ace [13].

The images in Figs. 4(C) and 4(D) show that the con-entional mode (derived from the structured-illuminationeries) does not fully resolve the individual beads withinhe strands and clusters. Although Fig. 4(C) was takenith illumination from below the critical angle and Fig.(D) was taken with illumination above the critical angle,he normalized intensities of each image were similar toithin a root-mean-square difference of 3.7%. However,

he superresolved images produced by these two data setsppeared very different. Figure 4(E) shows the image thatesults from illumination with 310 nm period patternsith individual beads resolved as is expected for a

tructured-illumination microscope operating at thisavelength and NA. Figure 4(F) shows the image that re-

ults when the experiment is repeated with an illumina-ion period of 205 nm (above the critical angle for TIR).his frequency is supported by the microscope. However,s a result of TIR the illumination field is inhomogeneous,nd the resulting image of the beads is blurred with onlylusters of two or three beads resolvable.

To further assess the impact of the inhomogeneouselds brought about by TIR, the 200 nm fluorescent beadample was covered with immersion oil �n=1.515�. The

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Beversluis et al. Vol. 25, No. 6 /June 2008/J. Opt. Soc. Am. A 1375

eads are located at the interface of two media with simi-ar refractive indices; under these conditions there is noIR for any of the illumination periods supported by theicroscope. Figures 5(A) and 5(B) show the resulting con-

entional images of a 10 m area; similar to those shownn Figs. 4(A) and 4(B) the beads are not individually re-olved. Figures 5(C) and 5(D) show the resulting superre-olved images taken with 310 and 205 nm fringes, respec-ively. Now within the homogeneous environment createdy the immersion oil, both superresolution images resolvehe individual beads with the beads appearing slightlyarger and more distinctly separated in Fig. 5(D).

Next, the 1.42 NA objective was replaced with a.65 NA objective. This objective achieves its high NA bysing 1.78 refractive index coverslips. At a glass–air in-erface this index results in a critical angle of 34.2° com-ared to the objective’s maximum illumination angle ofearly 68°. An illumination pattern with a 147 nm fringeeriod can be produced from this maximum illuminationngle when using a 488 nm wavelength light.Figures 6(A) and 6(B) show images acquired with a

ertand lens of the 1.65 NA objective pupil when illumi-

(A)

2 μm

(E)

(B)

2 μm

(F)

2 μm

(D)(C)

2 μm

ux= 20.1 rad/μm(Period = 310 nm)

Critical Angle (BK7-Air)

ux= 30.6 rad/μm(Period = 205 nm)

ig. 4. (A) and (B) Bertrand lens image of the pupil of a 1.42 NAbjective showing the fluorescence from 200 nm fluorescent beadsnd the two laser illumination points. In (A) the sample is beinglluminated with a 310 nm period fringe while in (B) the samples illuminated from above the critical angle with a 205 nm periodringe. (C) and (D) Resulting diffraction-limited conventional im-ges and (E) an (F) resulting superresolution image taken underach illumination condition, respectively.

ated from below and above the critical angle with 260nd 160 nm fringe patterns, respectively. Figures 6(C)nd 6(E) show the resulting conventional and superre-olved image when a 260 nm fringe period was used, andigs. 6(D) and 6(F) show the resulting conventional anduperresolved image when a 160 nm fringe period wassed. As was the case with the 1.42 NA objective, the00 nm beads are not individually resolved in the conven-ional image, resolved by the superresolution image whensing a fringe period that lies below the critical angle andhen distorted by the inhomogeneous fields that resulthen the fringe period lies above the critical angle forIR. Again, the addition of the indexing matching fluidould remove the conditions for TIR and create a homo-eneous field.

Imaging of fluorescently stained biological samples isn important application area for superresolvingtructured-illumination microscopy. In biological applica-ions the sample and surrounding medium’s refractive in-ex is similar to that of water. To assess the degree tohich inhomogeneous fields would impact applications inn aqueous environment, the final experiments measuredhe superresolving capability of the microscope when theeads were immersed in water. From Fig. 2(B) we wouldxpect better resolution in an aqueous environment thant the glass–air interface because of the larger criticalngle and smaller fringe period that can propagate acrosshe interface. Structured-illumination microscopy usinghe minimum propagating illumination fringe period for a.65 NA objective and an excitation wavelength of 488 nmhould nominally yield a PSF full width at half-maximumFWHM) of 90 nm. With a critical angle at the glass–ater interface of 48.3°, the minimum propagating illu-ination fringe period corresponds to 183 nm. Therefore195 nm fringe period was used to avoid the TIR and in-

2 µm2 µm

2 µm

(C)

(B)

(D)

(A)

2 µm

ig. 5. Imaging performance of the 1.42 NA microscope whenhe 200 nm fluorescent beads are surrounded with index-atching fluid �n=1.515�. (A) and (B) Resulting conventional im-

ge and (C) and (D) resulting superresolution images taken with10 and 205 nm period fringes, respectively.

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1376 J. Opt. Soc. Am. A/Vol. 25, No. 6 /June 2008 Beversluis et al.

omogeneous fields. Images of a dilute sample of 40 nmeads were used to determine the PSF of the two modes.igures 7(A) and 7(B) show the resulting PSF measure-ents of the conventional and superresolving microscopeodes with a nominal FWHM of 300 and 100 nm, respec-

ively. Although the conventional PSF is larger than ex-ected, the structured-illumination PSF was close to theest case. To further assess the resolution enhancement ailute 100 nm bead sample was imaged. Figures 7(C) and(D) show the conventional and superresolution images ofhe 100 nm bead sample. As expected, the superresolvingtructured-illumination image is considerably better re-olved with individual beads evident.

. CONCLUSIONShe increased resolution that is afforded by structured il-

umination arises from its ability to down convert highpatial frequencies into the passband of the imaging sys-em. To effectively do this, a high modulation frequencyllumination pattern is required. Additionally, the con-rast and uniformity of the illumination pattern must re-

(A)

2 μm

(E)

(B)

2 μm

(F)

2 μm

(C)

ux= 24.0 rad/μm(Period = 260 nm)

Critical Angle (TIR Coverslip-Air)

ux= 39.3 rad/μm(Period = 160 nm)

(D)

2 μm

ig. 6. (A) and (B) Bertrand lens image of the pupil of a 1.65 NAbjective showing the fluorescence from 200 nm fluorescent beadsnd the two laser illumination points. In (A) the sample is beinglluminated with a 260 nm period fringe while in (B) the samples illuminated from above the critical angle with a 160 nm periodringe. (C) and (D) Resulting diffraction-limited conventional im-ges and (E) and (F) resulting superresolution image taken un-er each illumination condition, respectively.

ain high over the microscopic extent of the sample. Inhis paper, we have shown how the apparent advantage ofn ultrahigh NA objective (higher passband) is nullifiedhen the illumination conditions result in a decrease in

he modulation pattern’s contrast and uniformity. Thisecrease results when TIR illumination conditions areet and the modulation fields become largely evanescent

nd inhomogeneous (in phase and amplitude) within aew tens of nanometers of a glass–air interface. Whenhese illumination conditions are avoided, the increasedptical passband of the ultrahigh NA illumination andollection can be realized, making it possible to achieve a00 nm resolution at an excitation wavelength of 488 nm.ur current work in this area is focused on the further de-elopment of the theory of TIR-structured illumination14] that accounts for the evanescent decay and resultingrtifacts.

EFERENCES1. W. Lukosz, “Optical systems with resolving powers

exceeding the classical limit,” J. Opt. Soc. Am. 56,1463–1472 (1966).

2. M. A. A. Neil, R. Juskaitis, and T. Wilson, “Method ofobtaining optical sectioning by using structured light in aconventional microscope,” Opt. Lett. 22, 1905–1907 (1997).

3. M. G. L. Gustafsson, “Extended resolution fluorescencemicroscopy,” Curr. Opin. Struct. Biol. 9, 627–634 (1999).

4. J. T. Frohn, H. F. Knapp, and A. Stemmer, “True opticalresolution beyond the Rayleigh limit achieved by standingwave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97,7232–7236 (2000).

5. M. G. L. Gustafsson, “Surpassing the lateral resolutionlimit by a factor of two using structured illuminationmicroscopy,” J. Microsc. 198, 82–87 (2000).

6. B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni,“Enhancement of axial resolution in fluorescencemicroscopy by standing-wave excitation,” Nature 366,44–48 (1993).

100 nm300 nm

2 μm

-1 -1 11

2 μm

x [mm] x [mm]

(A) (B)

(C) (D)

ig. 7. Performance of the 1.65 NA TIRF objective at a glass–ater interface. The glass coverslip’s refractive index is 1.78 and

he water’s refractive index is taken as 1.33. (A) and (B)iffraction-limited and resulting superresolution images of a0 nm fluorescent bead taken in water with 195 nm periodringes along with associated cross sections. (C) and (D) Result-ng conventional and superresolving images, respectively, of00 nm fluorescent beads taken under the same conditions asbove.

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