Resolution in the ApoTome and the confocal laser scanning microscope: comparison

. The essential feature of the confocal laser scanning microscope (cid:1) cLSM (cid:2) is the generation of optical sections by the removal of out-of-focus light. About ten years ago, structured illumination microscopy (cid:1) SIM (cid:2) was introduced as an alternative method for obtaining optical sections from biological specimens. Here we compare the resolution of the ApoTome (cid:1) commercial SIM by Zeiss (cid:2) to that achieved by a cLSM (cid:1) Zeiss LSM 510 (cid:2) . If ﬂuorescent beads are used as test objects, then the ApoTome will achieve a lower axial resolution than the cLSM. In contrast to that, its lateral resolution scores slightly better. If subresolution homogeneous ﬂuorescent layers are used as test objects, then the ApoTome will achieve a higher axial resolution than the cLSM. The ApoTome’s axial resolution is homogeneous over the ﬁeld-of-view while that of the cLSM changes markedly. Finally, the anisotropy of the ApoTome’s resolution was found to be negligible for standard applications while its capability to resolve ﬁne structures within stained tissue slices is limited to one or two cell layers and thus worse than in the cLSM. © 2009 Society of Photo-Optical Instrumentation Engineers. (cid:3) DOI: 10.1117/1.3083439 (cid:4)


Introduction
In 1997, a new concept of microscopy appeared that allowed the rejection of out-of-focus light. 1 Differently from confocal optics, this method neither requires a laser as excitation source nor pixelwise scanning of the object. Instead, a single spatial frequency grating placed in the microscope's field stop plane is projected into the focal plane within the specimen so that the excitation intensity I͑x , y͒ is distributed as follows: I͑x,y͒ = I 0 + I s cos͑2 x + 0 ͒, ͑1͒ with I 0 and I s being constants, the normalized grid frequency ͑ = M g / NA͒, M the magnification between object plane and grid, the wavelength, g the grid frequency, NA is the numerical aperture, and 0 is an arbitrary phase. Figure 1 shows the underlying principle. From the three images I 1 , I 2 , and I 3 , taken at grid positions 0 , 0 + ͑2 / 3͒, and 0 + ͑4 / 3͒, the optically sectioned image, I s , is obtained by calculating I s = ͱ 2 3 ͱ ͑I 1 − I 2 ͒ 2 + ͑I 2 − I 3 ͒ 2 + ͑I 3 − I 1 ͒ 2 ,

͑2͒
and the conventional image can be recovered by Variations and refinements of the basic realization include rotation of a grid in order to detect higher spatial frequencies based on Moiré fringes in two 2 and three dimensions, 3 which, if combined with 4Pi-microscopy, yields up to 100 nm axial resolution, 4 and focal intensity modulation through an interference pattern of two laser beams, 5 laser illumination, 6 and stripe-array illumination with light emitting diodes. 7 In a setup with solid-state laser illumination, Cole et al. 8,9 and Webb et al. 10 used linear grid optical sectioning for fluorescence lifetime imaging microscopy measurements. An analysis of specific artifacts was performed by Schaefer et al., 11 and their results were implemented into the Zeiss' AxioVision software. Karadaglić 12 and Karadaglić and Wilson 13 refined the image formation theory in grid illumination, structured illumination microscopy ͑SIM͒, and discussed some sources of error. Lagerholm et al. 14 gave an extended analysis of the proper utilization, potentials, and pitfalls of grid illumination. Chasles et al. 15 quantitatively compared their custom SIM system to commercial SIM and confocal laser scanning microscope ͑cLSM͒ systems at fixed pinhole settings. Taken together, the properties of SIM have thus so far been characterized under various theoretical and practical aspects, but mainly in custom-tailored setups. A comparison of a commercially available SIM systems ͑thus far, Zeiss' ApoTome or Qioptiq's OptiGrid͒ with a standard confocal laser scanning system is as yet lacking.
Here we therefore quantitatively analyze the imaging performance of the ApoTome under various aspects and compare it to that of a commercial confocal microscope ͑LSM 510͒.
For structured illumination measurements, the ApoTomeslider was introduced into the field-stop plane of one of the above microscopes. Thereby, one of two available rectangular-shaped gratings was inserted into the field-stop plane: either a grid with VH = 17.5 lines/ mm or a grid with VL = 35 lines/ mm. "VH" stands for the designated use with "high" magnification objectives, and "VL" stands for the designated use with "low" magnification objectives in an Axiovert microscope. If the 63ϫ / 1.4 Oil Plan-Apochromat objective and = 500 nm are used, the corresponding normalized grid frequencies are VH = 0.15 and VL = 0.29.
Grid phase and focus calibration were performed prior to each experiment. For a z-stack, 60 sectioned images at 100-nm distance were taken. The acquired image stacks were exported as 16-bit TIFF images. For cLSM measurements, the laser scanning unit LSM 510 ͑Zeiss͒ was attached to an Axiovert 100M that was equipped with the same objectives as above. The 488-nm laser line was used for excitation. Pinhole calibration was performed before every experiment. The pixel size was set to 71 nmϫ 71 nm for the measurement of point-spread functions ͑PSFs͒, or to 285 nmϫ 285 nm for measuring subresolution homogeneous fluorescent layers. Sixty images at 100 nm axial distance were taken. The cLSM setup was controlled by the LSM 510 software ͑V 3.2͒. Images were taken at 12 bit and exported as 12-bit TIFF files.

Test Objects: Fluorescent Beads, Layers, and Thin Dendrites
InSpeck Green microspheres ͑175Ϯ 5 nm͒ with a fluorescence coating ͑ ex = 505 nm, em = 515 nm, Invitrogen, Karlsruhe, Germany͒ were used to measure PSFs. The experimentally determined PSFs are the result of the convolution of the test object ͑bead͒ with the imaging system transfer function and thus always affected by the test object's dimension. While the PSFs' axial extensions are nearly unaffected by this convolution, the lateral extensions are slightly higher than the actual microscope's resolution in the given high NA regime. The beads used are hence a compromise with respect to the available signal. The beads were dissolved in 70% ethanol, pipetted onto a cover slip, and allowed to dry. Mounting medium ͑15 L Component E, Invitrogen, Karlsruhe, Germany͒ was then added and gently sealed by covering it with an object slide. In order to measure how a subresolution homogeneous fluorescent layer in the object plane is imaged, we used reference layers fabricated as 100-nm thick fluoresceine/ perylenediimid layers, which had a refractive index of n D Ϸ 1.59. 16 As test objects for anisotropic axial resolution, we prepared cell-cultures with small, straight-grown dendrites. The cell-culture preparation was done as described by Gennerich and Schild. 17 Measurements were carried out within five to ten days after plating. Prior to the experiments, the cultures were loaded for 15 min with 100 M calcein-acetoxymethyl ester ͑Invitrogen, cm = 514 nm at pH 7.8͒, which was dissolved in dimethylsulfoxide ͑DMSO͒ and Pluronic F-127 ͑In-vitrogen͒. The final concentrations of DMSO and Pluronic F-127 did not exceed 0.5 and 0.1%, respectively.  1 ͑a͒ A simplified representation for the ApoTome principle demonstrates how optically sectioned images are obtained. In-focus structures are superposed by the grid pattern ͑red and green sphere͒ and therefore excited only in one or the other image. Thus, they are only visible in a subset of images. Out-of-focus structures appear blurred in both images ͑blue sphere͒. Sensitively depending on the proper grid positions, an alternate subtraction of the raw images readily yields the optically sectioned image. In the actual ApoTome algorithm, three images are taken ͑b͒ Red, green, and blue curve: grid pattern how they are imaged into the specimen for the calculation of one sectioned image. Black curve: intensity pattern that the specimen is exposed to during one sectioned image acquisition.

Tissue Preparation
Larvae of Xenopus laevis ͑stage 54 and older͒ 18 were chilled in a mixture of ice and water and decapitated as approved by the Göttingen University Committee for Ethics in Animal Experimentation. A block of tissue containing the anterior twothirds of the olfactory bulb was extirpated and glued onto the stage of a vibroslicer ͑VT 1000S; Leica, Bensheim, Ger-many͒. A tissue slice of Ϸ300-m thickness containing the glomerular layer was cut out and transferred to a patch clamp setup. The whole cell configuration was established, and the cell was loaded Ϸ1 min with Alexa Fluor 488 biocytin ͑In-vitrogen͒. After another 20 min, the tissue block was turned upside down and imaged under the ApoTome and the cLSM by using an axial stepwidth of 1.5 m ͑overview͒ or 0.45 m ͑selected positions͒.
Multicolour tissue visualization was prepared in four subsequent steps. ͑i͒ For tracing olfactory nerve fibers, some crystals of Alexa Fluor 488 biocytin were placed into the cut olfactory nerve of chilled tadpoles and the lesion was closed with cyanoacrylic glue ͑Roti-Coll 1, Roth, Karlsruhe, Ger-many͒. The tadpole was decapitated 3 h later, as described above, and a block of tissue containing the olfactory nerves and the anterior two-thirds of the brain were cut out and kept in a bath solution. ͑ii͒ A solution containing Alexa Fluor 546 biocytin was injected into the olfactory tract, and the tissue was incubated for another 2 h. Then, the tissue block was fixed in 4% formaldehyde in 0.1 M phosphate buffered saline ͑PBS͒ for Ϸ2 h, washed in PBS ͑3 ϫ 10 min͒, embedded in agarose, glued onto the stage of a vibroslicer ͑VT 1000S; Leica, Bensheim, Germany͒, and cut into slices of 70-m thickness. ͑iii͒ The slices were incubated in PBS containing 1% bovine serum albumin ͑BSA͒ for 30 min at room temperature. Then, they were incubated overnight in Alexa Fluor 647 Phalloidin ͑Invitrogen͒ ͑5 L from methanol stock solu-tion͒ in 200 L of PBS with 1% BSA. ͑iv͒ For further staining with 4Ј,6-diamidino-2-phenylindole ͓͑DAPI͒ Invitrogen͔, the slices were washed 3 ϫ 10 min in PBS and incubated for 15 min in a mixture of 1 mL of PBS and 2 L of DAPI stock solution. After washing in PBS 5 ϫ 10 min, they were mounted on object slides with DAKO Cytomation ͑Hamburg, Germany͒ Fluorescence Mounting Medium S3023.
All chemicals required for the solutions above were purchased at Sigma ͑Deisenhofen, Germany͒.

Analysis
Data analysis was done by using programs written in Matlab. In order to determine the PSFs, single-bead images were cropped. The lateral resolution was obtained from a 2-D-Gaussian fit to the center-of-gravity ͑COG͒ plane. The axial resolution was obtained from a 1-D skewed Gaussian fit to the column containing the COG. R 2 did not improve if the theoretically more precise descriptions for the axial and lateral PSF behavior are used. 20 The cropped PSFs were then aligned to the COG with subpixel precision and summed up.
Our Matlab Sectioned Image Property chart ͑SIPchart͒ analysis 16 allowed freely selectable binning filters and free choice of a number of fit functions. Thus, ApoTome data were fitted by using a skewed Gaussian, where the z coordinate was assumed to follow zЈ = z exp͑−sz͒, with s being the skew factor, and I = I 0 exp͑−zЈ 2 / 2 2 ͒. cLSM data were fitted by using a skewed Lorentzian with I = I 0 ͓ 2 / ͑ 2 +4zЈ 2 ͔͒.

Lateral Resolution
We measured the PSFs of fluorescent beads by using a 63ϫ / 1.4 Oil Plan-Apochromat objective ͑Zeiss͒ in order to compare the resolving power of the ApoTome with epifluorescence and confocal microscopes. 21 The radial and the axial projections of the resulting PSFs are shown in Fig. 2 for epifluorecence ͓Fig. 2͑a͔͒, for the ApoTome with the VH grid or VL grid ͓Figs. 2͑b͒ and 2͑c͔͒, and for the cLSM ͓Fig. 2͑d͔͒. There is no significant difference between the ApoTome and the standard epifluorescence microscope with regard to lateral resolution, whereas the cLSM's PSF was slightly broader. Two noncommercial implementations of structured illumination 2,22 are reported to have a lateral resolution higher than this. Note that SIM as realized in the ApoTome is not a linear-shift invariant system ͓cf. Eq. ͑2͔͒. Thus, it is not possible to describe the process of obtaining an ApoTome image in terms of the PSF for the general case. To this end, a set of fluorescent test samples containing all spatial frequencies in a defined manner would be required. Karadaglic and Wilson 13 showed that in the case of defocus the features around the frequency are enhanced. This effect appears in the interaction between the object's zeroth spatial frequency and the frequencies close to v. The PSF is still a useful measure of the resolution though less informative when imaging complex structures.
The resolution of the cLSM is determined by the size of the emission pinhole, and for maximally closed pinholes, theory predicts an improvement of ͱ 2 over epifluorescence, 23 where 95% of the in-focus light is rejected by the pinhole. A pinhole size of d p =1 Airy unit ͑A.U.͒ is often considered a good compromise between resolution and detected light intensity. 24 If, in this case, the backfocal plane ͑BFP͒ is illuminated homogeneously, then the lateral resolution of the cLSM should outperform epifluorescence by cm / ex . In our measurements, the cLSM's lateral resolution fell behind that of epifluorescence or the ApoTome: d l,EF/VH/VL · 1.1= d l,cLSM . This may be explained, first, by the Gaussian intensity profile in the BFP, which reduced the effective NA. 25 A second explanation is that the axial resolution is distributed spatially inhomogeneous ͑see below͒.

Axial Resolution
It is customary to determine a microscope's axial resolution with fluorescent beads. Fluorescently labelled biological ob-jects are however often rather densely, almost homogeneously stained, so that a fluorescent layer would seem a more adequate test object to determine axial resolution. Here we start by using beads as test objects, and will then use subresolution homogeneous fluorescent layers.
The axial resolution determined with beads differed markedly in the three microscopes analyzed. The full-width-athalf-maximum ͑FWHM͒ values of the axial Gaussian fits ͑Fig. 2, lower row͒ clearly show ͑i͒ that the ApoTome's axial resolution is better than that of the epifluorescence microscope, ͑ii͒ that the ApoTome's axial resolution depends on the grid used, and ͑iii͒ that the ApoTome's axial resolution with the VL grid is about the same as that of the cLSM ͑at a pinhole diameter of d p = 1 A.U.͒. In conventional epifluorescence, the bead images show the characteristic butterflyshaped side lobes as predicted by electromagnetic wave theory. 20 These are clearly reduced in the ApoTome. If the finer grid ͑VL͒ is used, then the ApoTome yields a 33% advantage over conventional epifluorescence and matches the cLSM's resolution. Figure 3 shows the axial resolution ͑i͒ of the cLSM as a function of the pinhole diameter, ͑ii͒ of the ApoTome equipped with the VH grid ͑ VH = 0.15͒, ͑iii͒ of the ApoTome equipped with the VL grid ͑ VH = 0.29͒, and ͑iv͒ of epifluo-  intensity I max has a circular-symmetric shape in both imaging modes, which is ascribed to chromatic and spherical aberration. Without the application of a spatial filter, there remain stripe artifacts induced by improper phase shifts of the grid, intensity fluctuations, and stage movements during acquisition and bleaching. The blots in the Apo-Tome images stem from a residue on the grid, underlining the importance of keeping it perfectly clean. Values ͑insets͒ refer to binned data sets mean± sd over the whole field of view ͑ApoTome: 8 ϫ 2 binning mask to conserve the stripe pattern of the 1388ϫ 1040 pixels image: one period of the grid pattern is sampled by Ϸ23 pixels ͑VH grid͒ or Ϸ11.5 pixels ͑VL grid͒, leading to an artifact stripe pattern of 3ϫ the grid pattern; cLSM: 6 ϫ 6 binning mask for a 512ϫ 512 pixels image͒; objective: 63ϫ / 1.4 Oil Plan-Apochromat. rescence illumination determined with beads ͓Fig. 3͑a͔͒ and layers ͓Fig. 3͑b͔͒. If the axial resolution was determined with beads, then the use of the ApoTome's VH grid corresponds to d p Ϸ 1.5 A.U. in the cLSM, whereas the use of the VL grid corresponds to d p Ϸ 1 A.U. Certainly, with increasingly smaller pinhole sizes, there is a marked increase in resolution ͑e.g., 0.43Ϯ 0.14 m at d p = 0.4 A.U.͒. This outperforms the ApoTome's best bead resolution. It can also be seen from Fig.  3 a that for large pinhole sizes ͑d p ജ 2 A.U.͒, the cLSM shows worse axial resolution than the epifluorescence microscope due to the Gaussian illumination of the BFP in the cLSM ͓i.e., due to the effect that the effective NA in the cLSM is lower than the nominal one, which is indicated on the objective barrel ͑here, 1.4͔͒. If the axial resolution is determined with subresolution homogeneous fluorescent layers, then the VL grid of the Apo-Tome will have about twice the resolution compared to the VH grid. This is expected from the twice-finer-grid structure and the corresponding cutoff frequency. Under these conditions, the ApoTome achieves a better resolution than the cLSM with a pinhole at minimum diameter ͓Fig. 3͑b͔͒. For these comparisons, we took into account the bigger field of view of the cLSM by cropping a field of view corresponding to the size of the ApoTome's field of view from the cLSM image. Because the axial resolution in the cLSM varied with the distance from the optical axis ͑see Section 3.3͒, the centerline of the crop stack was determined by the highest resolution.

Spatial Inhomogeneity of Axial Resolution
To investigate the possibility that the axial resolution was spatially inhomogeneously distributed, one can either measure bead PSFs at multiple distances from the optical axis ͑which is rather impractical͒ or use SIPcharts. 16 These are generated from image stacks of a subresolution homogeneous fluorescent layer.
The SIPchart intensity distribution clearly showed radial symmetry both for the cLSM ͓Fig. 4͑a͔͒ and for the ApoTome ͓Fig. 4͑b͔͒. Moreover, the axial resolution in the cLSM was highly correlated with the radial intensity distribution ͓Fig. 4͑c͔͒. The symmetric shape can be ascribed to spherical and chromatic aberrations, while the off-axis resolution maximum can presumably be attributed to a slightly imperfect pinhole e f adjustment. Remarkably, there is a difference of Ϸ250 nm ͑22% or / 2͒ between the best resolved regions at the intensity maximum and the worst resolved regions ͓see Fig. 4͑c͔͒. Thus, the radial symmetry of and the change in axial resolution indicate that the specific position in the field of view in a cLSM image determines at which precision a subcellular structure can be resolved. Contrary to the cLSM, the Apo-Tome's axial resolution appears to be quite homogeneous, the deviations being ഛ / 10. Interestingly, another feature of the ApoTome can be derived from the SIPcharts shown in Figs. 4͑b͒ and 4͑d͒; both reveal an artifact stripe pattern, which may result from stage vibrations leading to nonstationary imaging of the grid into the sample, imprecise phase shifts of the grid, bleaching of the grid pattern into the sample, or intensity fluctuations of the illumination arc source. The AxioVision software includes a digital filter that removes certain spatial frequencies in the Fourier domain. We found that the so-called weak filter was the best to remove the stripe artifacts under most imaging conditions. But the SIPcharts produced with the "weak filter" setting led to a substantial loss in axial resolution, namely, can be expected that spatial low-pass filtering reduces spatial resolution. Because the AxioVision filtering algorithms are not documented, the user applying a spatial filter to remove the stripe artifacts must find out, empirically, the impact of the filter used on axial resolution.

Anisotropy of Resolution
The ApoTome's grid-shaped illumination being 1-D modulated suggested that its axial resolution might by anisotropic.
To test this, we measured the axial extensions of small and straight fluorescence-labeled neuronal dendrites in cell culture, taking the angle between dendrite and grid pattern as the parameter ͑Fig. 5͒. The lateral extensions of the dendrites were virtually independent of their orientation with respect to the grid ͓350Ϯ 5 nm ͑parallel͒ and 347Ϯ 5 nm ͑orthogonal͒, meanϮ sd͔. In contrast to that, the axial extension of dendrites oriented in a parallel way was significantly larger than that of dendrites oriented in an orthogonal way, with the angle dependency of the axial resolution being rather steep, assuming the value for orthogonal dendrites for less than ␣ = 3 deg ͑Fig. 5͒.

Deep-Tissue Imaging
Because it is of practical relevance how well an optical sectioning technique works within stained biological tissue, we stained mitral cells of the olfactory bulb with Alexa Fluor 488  Fig. 6͒ the ApoTome images show increased blur and noise. In plane b, for instance, the image plane cutting a dendrite is well below the cell's soma. The dendrite cut is clearly seen in both the ApoTome and the cLSM, but in addition, the ApoTome image shows a blurry spot, which is not seen in the cLSM image, reporting the noise originating from the soma above that plane; this is because the ApoTome, though taking into account out-of-focus light while calculating an optical section, does not remove the noise of out-of-focus light. 26 At imaging depths of several cell layers, the noise component becomes dominant in the ApoTome, preventing the acquisition of feature-rich images; at the same depth in the same preparation, the cLSM can still extract tiny structures ͑plane c of Fig.  6͒. This is of course due to out-of-focus photons being confocally suppressed in the cLSM. In the ApoTome in contrast, the grid pattern projected onto the focus plane is increasingly superimposed by scattered light at greater tissue depth. Moreover, its in-focus modulation is correspondingly attenuated with stronger staining; these effects are not taken into account by Eqs. ͑1͒-͑3͒. Figure 7 shows the ApoTome's spectral range of operation, which extends from near ultraviolet ͑UV͒ to near infrared. Commonly, cLSMs are not equipped with UV excitation so that the ApoTome may be preferred in cases where multicolor stainings are to be done. Figure 7 shows images of the olfactory bulb of a X. laevis tadpole stained with four different dyes, taken with a conventional epifluorescence microscope ͓Fig. 7͑a͔͒ or the ApoTome ͓Fig. 7͑b͔͒. Clearly, the ApoTome removes most of the out-of-focus blur seen in epifluorescence mode.

Resolution
The ApoTome can achieve a better lateral resolution than the cLSM. The axial resolution of the ApoTome is in the same range as the confocal one, depending on the particular conditions. If bead PSFs are measured close to the cover slip surface and under standard conditions ͑d p = 1 A.U.͒, then the axial resolution of the cLSM will be superior

Homogeneity of Resolution
Both cLSM and ApoTome show a radial distribution of excitation light intensity in the object plane. In the cLSM, the axial resolution varies markedly with radial symmetry, whereas the axial resolution in the ApoTome is rather constant, the deviations being in the order of / 10.

Penetration Depth
The projection of both grid pattern or laser excitation onto the object plane within a tissue slice is affected by scattering in the tissue. Furthermore, the modulation amplitude of the grid pattern strongly depends on the integrated axial fluorescence intensity. In the cLSM, only the light coming directly from the focal volume is projected through the exit pinhole onto the photon detector. This way, out-of-focus light is mostly rejected. Because this spatial filtering effect is lacking in the ApoTome, images are increasingly deteriorated with increasing tissue depth, depending on the scattering within the tissue and staining intensity. Additionally, in the ApoTome, noise is counted as information. Because the ApoTome is a wide-field technique, the Poissonian noise contribution of any fluorescing probe in the beam path will be present in the optically sectioned image. The cLSM ͑or two-photon excitation mi-croscopy͒ is thus preferred for imaging within slices or tissue blocks.

Acquisition Speed
Both systems, cLSM and ApoTome, are notoriously slow. In the ApoTome, the CCD readout rate, the number of color channels, and the necessity of taking three images for one are the major limiting factors, whereas in the cLSM, the image acquisition rate can be increased by choosing a smaller field of view and a shorter pixel dwell time, both at a certain cost.

Bleaching
The ApoTome is prone to patterned bleaching. In observation mode, the manufacturer tries to avoid patterned bleaching by sinusoidally moving the grid. But once the acquisition has started in the three images equal-phase-shift approach, half of the specimen is illuminated two-third of the three-image acquisition time, whereas the other half is illuminated one-third of the total acquisition time. This creates patterned bleaching with three times the grid frequency. 8,11 This artifact can be reduced at the cost of axial resolution.