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This paper addresses optical super-resolution in the far field. We will describe the use of a novel optical component, which we call the proximity projection grating (PPG), that can provide different intensity patterns for sample illumination. These different illumination patterns allow the optical system to perform various modes of imaging, all are capable of resolution beyond the Abbe diffraction limit. Results will be shown to demonstrate the operations of some of these imaging modes. The potential of the PPG unit will also be discussed.
©2013 Optical Society of America
1. Introduction
It was widely accepted that the resolution of an optical microscope operating in the far field was determined by diffraction, with the limit given by half of the wavelength of the light used. Although a small value, optical resolution is often not adequate for many applications. In the recent decades there has been extensive effort to improve the resolving power of optical systems, and different approaches have been proposed to overcome the conventional limit. These techniques include the confocal, I5, 4pi, structured illumination, stimulated depletion (STED) microscopy among others [1–6]. It is interesting to observe that the illumination patterns for some of the techniques are quite complicated. Another type of microscope that has achieved extremely high imaging resolution is based on an entirely different concept: these operate by determining accurately the locations of isolated particles, either temporally or spatially. This type of system includes the stochastic optical reconstruction microscope (STORM) [7], and fluorescence photoactivation localized microscopy (PALM) [8]. Resolution as low as 20nm has been reported with these systems [9]. Another technique that has attained very high lateral resolution is the near field scanning optical microscopy. However we will not discuss this technique here as we are confining ourselves to non-scanning far-field imaging systems in this article.
In a recent publication [10] the Authors reported the use of a novel proximity projection grating (PPG) in an optical microscope. The motivation behind the used of the PPG was to extend the imaging resolution attained by the original, linear, structured illumination microscope (SIM). With a linear SIM, because of the need to image the optical grating onto the sample, the resolution improvement is limited to a factor of two compared to that of a conventional microscope. The use of the PPG circumvents this constraint and allows greater improvement to be achieved. Figure 1 is a sketch of the grating unit. The key element is the dielectric thin film between the sample and the grating. It allows the k-vector of the illumination at the sample to be increased by the refractive index n of the thin film. With the availability of high index material, such as As2O3 [11], (As2O3 is a chalcogenide glass that can be evaporated onto substrates. Its refractive index is around 2.5 at λ = 600nm as deposited, and will increase to 2.6 after photo-polymerization), a significant improvement in imaging resolution can be achieved. It should be emphasised that evanescent field created by the grating is not used in our system, as the thickness of the thin film ranges from a couple to ten’s of microns. This point will be made clear in the next section.
In this paper, we will present experimental results obtained with a triangular shape grating, showing their superior imaging performance as compared to those obtained using the square grating as described in the previous publication. We will discuss how the PPG can be used to produce different imaging modes. Finally, we will consider in detail the full potential of the technique, in terms of both the resolution attainable and the quality of the image obtained.
2. System principle
The principle behind the technique has been described in [10]. Figure 2 shows the system configuration which is similar to the one used in [10]. The system consists of an illumination section, a sample unit and an imaging section. The light source is a frequency doubled Nd-YAG laser (λ = 532nm), which is focused onto the back focal plane of the condenser lens Lc. The collimated light beam from Lc illuminates the sample unit as shown. The imaging lens is a Zeiss CP Achromat × 100 1.25 oil Phase 3 objective, which is followed by a set of relay lenses. The overall magnification of the system is x110. The camera (Andor iXON EMCCD) has 1002 x 1002 pixels with pixel size 8 x 8 μm2. The effective pixel size at the sample plane is therefore 73x73 nm2. An optical bandpass filter (Chroma Technology Corp. Z488/532m) can be inserted in the imaging arm to allow for fluorescent operation.
The incident laser beam, after passing through the grating, will form an intensity pattern at the upper surface of the optical thin film (see Fig. 1). The shape of this pattern depends on the grating, the optical properties of the thin film and the wavefront of the incoming laser beam. As this intensity pattern illuminates the sample directly, its distribution has significant effect on the operation of the system. A set of experiments has been performed to demonstrate this point. For purpose of illustration, the variable aperture in the system was stopped down to provide an overall imaging NA of 0.2.
The grating used for the experiment is depicted in Fig. 3. The substrate is a 100µm thick microscope slide. The grating consists of 60nm thick Cr tracks, deposited on the substrate, forming an equilateral triangle pattern (as opposed to a square one used in [10]). The height h of the triangle is 3µm with the track width 0.6µm. Microscope immersion oil (nc = 1.512) is used as the thin film. A glass slide is placed on top of the oil film and acts as the sample. The glass slide is mounted on a PI P-611.3 NanoCube XYZ Piezo Stage so that the thickness of the oil film d can be controlled. The interface between the top surface of the immersion oil and the glass slide is therefore the object plane, which is imaged onto the camera with d set at different values. For this experiment the optical bandpass filter has been removed.
Figure 4 shows the resulting patterns obtained with different values of d. Also shown are computer simulated patterns with the model used based on scalar diffraction theory [12], and the Fourier spectra of the simulated patterns. In the figure TD is the so called Talbot distance of the grating [13] and is given by 2nT2/λ . One feature of the Talbot effect is that the intensity pattern should repeat itself at multiple values of TD, giving rise to the Talbot images. It should be pointed out, however, that the Talbot effect is valid only when the Fresnel diffraction approximation is applicable. This imposes constraints on the values of the grating period and the observation distance d. For our grating unit, TD is 51µm. Figures 4(a) and 4(e) are two repeated Talbot images. Note that if the grating period is reduced to 2µm, the Talbot effect will become less accurate and the patterns will not repeat exactly. As we change the separation d, the relative phase of the spatial frequency components from the grating will change, thus resulting in different intensity patterns at the top of the thin film. This effect can also be observed from the third column of the figure, where the relative magnitude of the Fourier components changes as d is changed. As can be seen, the experimental and the simulated results show remarkable agreement. Noted that the frequency components of the illumination patterns are formed from the cross terms arising from the interference between the different, propagating orders, as described in Eq. (1).
where M and N are the propagating orders, bpq the relative amplitude, and ϕpq the phase shift suffered by the orders when propagate through thin film. The incident light beam is assumed to be normal to the grating. In general if our aim is to enhance the lateral resolution, then Fig. (d) should be the illumination of choice because its spectral components have the furthermost extent, and would give the greatest image bandwidth with good signal to noise ratio [14].
Fig. 4 Illumination patterns at the sample surface for different oil film thickness. Left column: simulated results; mid column: experimental results and right column: normalised spectra of simulated patterns. Note that for clarity the vertical scales of the spectra have been truncated to 0.4. Oil film thickness: (a) Td; (b) Td + 3µm; (c) Td + 23µm; (d) Td + 27µm and (e) Td + 51µm. The widths of the patterns shown are 15.5μm.
3. The use of the PPG for different imaging modalities
In this section we will present experimental results to demonstrate the characteristics of the technique and images obtained with different imaging modalities. The system used for the experiment is the one shown in Fig. 3, except that the objective lens is replaced with an Olympus RMS100X – x100 Plan Fluorite Oil Objective. This objective has a built in iris to allow its NA to be varied between 0.6 - 1.3. The test object is a layer of 40nm diameter fluorescent beads on a glass substrate, with the beads in contact with the optical thin film, which is a layer of microscope immersion oil. The shifting of the illumination pattern, required for the reconstruction purpose, is achieved by translating the illumination unit in the x-y plane. This will result in the incident angle of the light beam at the grating to change, causing a lateral shift of the position of the intensity pattern at the sample as required.
The thickness of the immersion oil d is set to 33µm. the resulting illumination pattern at the sample is shown in Fig. 5(a), and is an array of tightly focused light spots. Figures 5(b) and 5(c) show details of one of the spots and its profiles along the x and y directions. The measured FWHM of the spot is 0.45µm. Figure 5(d) is the spectrum of the illumination pattern.
Fig. 5 Illumination pattern showing (a) an array of light spots; (b) 2D distribution of one light spot; (c) profile of the light spot in (b) and (d) spectrum of the illumination pattern.
To obtain the fluorescent image, the optical bandpass filter is inserted in the imaging arm and the light pattern is scanned in the x-y directions, with each light spot scanning an area of 3.5µm x 3µm, which is indicated with the rectangle in Fig. 5(a). This scan area is expanded and shown in Fig. 6(a). Ls are the light spots at the sample surface and Sp, given by the intersections of the crosshairs, are the scan positions. The number of scan points within the area is 15 (horizontal) x 13 (vertical). The image at each scan point is captured and saved for processing. Denoting this set of images by A, with A = {aij} and aij the individual images at scan location (i,j). Figures 6(b) and 6(c) are two images captured at different scan points. The effect of the illumination pattern moving across the sample can be seen clearly as the brightness of the images of the various particles changes from Fig. 6b to Fig. 6c. The particle at the top left corner of the picture is a good example.
Fig. 6 (a) scan locations with Ls representing the light spots and the scan locations are at the intersections of the crosshair, represented by Sp. (b) & (c) are two images obtained at two different scan positions, showing different particles lighting up and fading.
In the next section we will show, by applying three different procedures, to obtain images from the same data set A, corresponding to three different imaging modes.
Scanningoptical microscope(SOM): in a scanning optical microscope an image is formed by scanning a focused light spot relative to the sample, and the transmitted or reflected light is collected with a photodetector. With the present system, an SOM image is obtained by summing 15x13 images in the set A. The result is shown in Fig. 7.
Parallel scanning confocal microscope (PSCM): by using a point detector instead of a large area detector, a SOM is converted into a confocal microscope. With the present setup, confocal operation is realised by 1) using a detector array consisting of many small pixels; and 2) the illumination light spots are well separated thus minimising any overlap of the light spots. Figure 8 shows a CCD array with some light spots at a particular scan location. To effect the confocal operation for a sparse array of points, the illuminating spots are scanned and the read out from the CCD is matched to the conjugate position of the illumination spots. This means that, for each aij, the outputs of the pixels directly underneath the light spots are retained, with the rest set to zero. Summation of these images will result in a confocal image. Figure 9 shows the resulting image.
Referring back to Fig. 5, the separations of the light spots are 3.5µm and the FWHM of the light spot is 0.45µm, confirming that overlap between any neighbouring confocal detectors would be insignificant. Note that as in a scanning confocal microscope where the detector used is not truly a point detector, we also use more than one CCD pixel under each light spot, and Fig. 9 is obtained by using 7 x 7 pixels.
Figure 10 shows the effect of the size of the confocal detector on the confocal response. The pinhole size is expressed as the number of pixels at the detector plane. The diameter of the psf is 1.12µm, equivalent to 15.4 detector pixels, and is marked in the figure by the dashed line. The vertical axis is the FWHM of the confocal image of an isolated fluorescent bead. The response is similar to that in [15], although the overshoot is relatively large. This is attributable to the large sidelobes of the light spots created using the grating unit [10].
Proximity projection grating structured illumination microscope: in this section we will show images reconstructed with the data set A but using the structured illumination approach. Since the algorithm has been described elsewhere [10], only the reconstructed images will be shown here. Figure 11 is a schematic showing the main illumination orders generated from a hexagonal structure. Note that the relative magnitudes of the different orders depend on the thickness d of the optical thin film, and the width of the metal tracks with respect to the period of the grating. It is of interest to note that, if a square grating is used instead of the triangular one, the main illumination orders will be along the vertical and horizontal axes only. This will lead to a loss in the coverage in the frequency domain, and a loss in the object information. In addition the resulting psf will have larger sidelobes, as described in [10]. Figure 12 shows two reconstructed images with one using only the zero, ± 1 and ± 2 orders, and the other using orders up to and including the fifth.
Fig. 12 Image formed with the PPG-SIM. (a) using only the zero, ± 1 and ± 2 orders, (b) using orders up to and including ± 5.
From one data set A we now have three images, corresponding to SOM, confocal and SIM. Figure 13 shows the profiles of particle P in Fig. 7, obtained with these methods. Table 1 contains the FWHMs of a number of particles in Fig. 7, reconstructed using the different methods. The headings SIM2 - SIM7 represent the PPGSIM method, with the final digit indicating the number of orders used in the reconstruction. The headings CON7 – CON11represent the confocal method, and the final digit shows the number of pixels used as the confocal detector (7 means 7 × 7 pixels). Also included in the table are the averaged FWHM of the seven particles. The lower half of Table 1 contains the equivalent system NA required to produce those FWHM values, if the imaging system used has a transfer function corresponding to a conventional fluorescence microscope. The NA values are calculated using a scalar diffraction program that we developed and has been described in [10]. The table shows clearly the NA value increases with the order of the PPGSIM. It also increases as the confocal detector size decreases. It should be noted that the NA for SIM7 is more than a factor of 2 greater than that of the SOM.
Fig. 13 Line profiles of reconstructed images, (a) i. SOM, ii – iv. PPGSIM2 reconstructed with up to ± 2, ± 4, and ± 6 orders; (b) i. SOM, ii. Confocal formed with 9 x 9 pixels as detector pinhole.
Table 1. FWHM of particles obtained with the various techniques, and the corresponding system NA. P: particles; SOM: scanning optical microscope; SIMn: PPGSIM with up to ± n reconstruction orders; CONm: confocal with m × m number of detector pixels.
4. Discussions and conclusions
In the last two sections we have demonstrated the use of the proximity projection grating in an optical imaging system. We have shown that, depending on the configuration of the grating unit, different intensity patterns can be generated for sample illumination, resulting in images corresponding to different imaging modalities. For some of these imaging modes resolution improvement of more than 2 times that afforded by the underlying optical system can be achieved. In this section we will consider factors that influence the resolution improvement. We will also investigate arrangements that may potentially provide greater resolution improvement.
The factors that can influence the resolution include the index of the thin film, the period of the grating and the width of the grating track relative to its period. Figure 14 shows a typical spectrum of an image reconstructed using PPGSIM. The parameters kn represent the locations of the illumination orders, similar to those in Fig. 5(d). Bw is the intensity bandwidth of the underlying imaging system, and is given by 4NAimg/λ [13] with NAimg the numerical aperture of the imaging section of the system and λ the wavelength in the object space. With a conventional fluorescent system, only the zero order k0 exists and the system bandwidth is thus Bw. For linear SIM and PPGSIM, there is, in theory, no limit to the number of illumination orders. The crucial difference is, for linear SIM, |Km |≤ Bw /2 where Km represents the highest illumination order supported by the system. This constraint is due to the need to image an optical grating onto the sample. The imaging NA for a linear SIM, therefore, is 2Bw, or twice the bandwidth of the conventional fluorescent system. For PPGSIM, the value of Km is limited by the refractive index n of the optical thin film used, and is given by 2n/λ (corresponding to the grating order that is propagating at 90 degrees from the surface normal). The maximum imaging NA of the system is therefore 4n/λ + Bw, or 4(n + NAimg) /λ [10].
Fig. 14 Example of the spectrum of a reconstructed image with the PPGSIM method. Kn represents the locations of the illumination orders and Bw the bandwidth of the intensity imaging system.
We now consider the confocal imaging mode as implemented using the proximity projection grating . The intensity point spread function (PSF) for a confocal microscope is given by [1]
where the three parameters are the intensity PSF’s of the system, the illumination section and the imaging section respectively. The transfer function Ĥ of the system iswhere the caret denotes the Fourier transform, and * is the convolution operator. Ĥill is the illumination orders at the sample (see Fig. 5(d)). Ĥimg is the optical transfer function (OTF) of the imaging section. Performing the convolution will yield a picture similar to the one in Fig. 14. The transfer function of the confocal imaging mode is therefore the same as that of the PPGSIM. This is not a surprising conclusion as the illumination patterns used for the two reconstructions are the same, as shown in Fig. 5(a). The reasons behind the difference between the two techniques, as shown in Table 1, are the number of illumination orders used in the SIM reconstruction and the number of detector pixels used for the confocal system.The illumination pattern can also be altered by changing the source wavelength, which can lead to other important applications. One possibility is to implement STED with the present setup. In a STED microscope, two lasers of appropriate wavelengths are used. One is focused onto the sample to excite the fluorescent dye in it. This is followed by the second laser, which has an intensity distribution at the sample resembling a doughnut. This laser is chosen such that it would deplete the excited fluorescent state. The net effect is a greatly reduced PSF, and a much improved imaging resolution.
This process can be accomplished using the projection grating. By using appropriate grating structures, the two required intensity patterns can be effected. To demonstrate this operation, computer simulations have been performed and the results are shown in Fig. 15. It is assumed that the dye used has a excitation wavelengths λE = 495nm and a depletion wavelength λS = 600nm. The parameters of the grating unit are: period = 0.96µm, grating track width = 0.192µm, refractive index of thin film = 1.52, and thickness of thin film = 5.67µm. Figure 15(a) shows the distribution of the psf for the excitation laser on its own and Fig. 15(b) shows the intensity distribution corresponding to the second laser. Figure 15(c) is the pattern after the application of the two and is therefore the psf of the STED microscope. 15(d) shows the line profiles of the three, superposed for ease of comparison. The reduction in the widths between Fig. 15(a) and Fig. 15(c) is obvious. The intensity pattern in Fig. 15(b) has a minimum value of around 2% of the peak value and is comparable to the figure published in [16]. It should be mentioned that this set of results is purely for demonstration purpose, and no attempt has been made to optimise the parameters used in the simulation. By selecting different parameters for the grating structure, or by changing the grating shape, the minimum value of pattern Fig. 15(b) may be further suppressed. It should also be pointed out that, apart from the improvement afforded by the STED operation, the resolution of the system is further improved due to the use of high index material as the thin film, which would lead to more tightly focused light spots at Fig. 15(a). It is sufficient to note at this point that the above simulation has demonstrated the potential of the technique in realizing optical imaging with very high resolution. Further research in this area is therefore warranted.
Fig. 15 simulated results showing the STED operation. Grating structure: triangle; period: 0.96μm; thin film: BK7, 5.67μm thick. (a) intensity pattern obtained using λ = 495nm; (b): intensity pattern obtained using λ = 600nm; (c) STED focal distribution; and (d) line profiles of (a), (b) and (c), showing the narrowing of the light spot. Widths of simulated patterns = 4.2μm.
Apart from changing the structure of the grating unit and using different wavelength of light as the source, the illumination pattern can be altered by using light beam of appropriate wavefront to illuminate the grating unit. Changing the latter will change k-vectors of the diffracted orders emerged from the grating. The advantage of modifying the illumination pattern in this manner is that it is achieved with the grating unit in situ. By using a spatial light modulator to condition the wavefront of the light beam, the operation of the system would become more flexible and its function more powerful. This aspect of the system will merit further investigation.
In conclusion, we have described the principle behind the proximity projection grating microscope. We have shown the change of the illumination pattern at the sample surface as a function of the thickness of the thin film. Using a set of scanned data, we have reconstructed images corresponding to three different imaging modes: SOM, SIM and confocal, with the last two exhibiting resolution considerably better than that afforded using conventional approach. The potential of the technique in terms of the resolution achievable, and the possibility of implementing other imaging modes such as STED, have also be discussed. Results obtained from these investigations will be presented in future publications.
Acknowledgments
The authors gratefully acknowledge the financial support of the Engineering and Physical Sciences Research Council (EPSRC) for a platform grant, ‘Strategies for Biological Imaging’. Feng Hu would like to thank the University of Nottingham and China Scholarship Council (CSC) for sponsoring his PhD study.
References and Links
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