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In this paper, we present a modified SOFI algorithm with enhanced temporal resolution: the required number of raw images for SOFI is reduced from hundreds to tens. The modification is intended to eliminate the low-frequency fluctuation and readout noise from the raw image stack, and is achieved by separately utilizing two wavelet-based filters in the temporal and spatial domains of the raw image stack. The high-frequency stochastic fluctuating signal could be extracted effectively, and the efficiency of SOFI could be enhanced. The modified SOFI image could be generated with 25 frames of raw images, and the corresponding acquisition time was 1.25 s.
© 2016 Optical Society of America
1. Introduction
Far-field super-resolution optical Microscopy has experienced tremendous improvement in the last two decades. STimulated Emission Depletion (STED) [1–3], Single Molecular Localization (SML) [4,5] and Structured Illumination Microscopy (SIM) [6,7] are the major super-resolution microscopy techniques [8]. However, more efforts are needed to realize widespread application of super-resolution microscopy in biology laboratories. In addition to high spatial resolution, the major goals for the super resolution microscopy are lower phototoxicity, higher temporal resolution, vibration immunity, maintenance-free, and less complexity and cost of the system.
In 2009, Dertinger et al. [9] demonstrated Super-resolution Optical Fluctuation Imaging (SOFI), which could obtain microscopic images beyond the optical diffraction limit with the fluctuating signals emitted from semiconductor Quantum Dots (QD). SOFI microscopy only needs a wide-field fluorescence microscope coupled with a fast frame detector (Electron-Multiplying Charge-Coupled Device (EMCCD) or scientific Complementary Metal Oxide Semiconductor (sCMOS)). For now, SOFI is not confined to wide-field epi-fluorescence microscope [9–12], and there are also reports utilizing Total Internal Reflection Fluorescence Microscope (TIRFM) [13–15] and Spinning-disk confocal microscope [16]. On the other hand, QDs [10,11,17,18], organic dyes [19,20] and Fluorescent Proteins (FP) [19] could be utilized in SOFI. The notable features of SOFI are lower illumination intensity, 3D super-resolution, and less complexity of the system.
However, the conventional SOFI algorithm requires hundreds or even thousands of raw images, and this could constrain the temporal resolution of the SOFI algorithm. Theoretically, there is no limit for the number of raw images for SOFI. The large number of raw images required is attributed to the readout noise and the instability of QDs in experiments. The SOFI algorithm inherently removes noise, but the Signal-to-Noise Ratio (SNR) of raw images determines the required number of raw images [9]. Conventionally, the quality of a SOFI image could be enhanced by utilizing more raw images or a longer exposure time for each image. Meanwhile, these measures reduce the temporal resolution of SOFI. Higher illumination intensity could increase the SNR of the raw image, but results in more phototoxicity.
For now, novel experimental modifications could improve the temporal resolution of SOFI. By enhancing the labeling density with 3 different types of QDs, Xi et al. [18] has generated a SOFI image with 100 images from each type of QDs. To the best of our knowledge, the temporal resolution of 4.5 s is the highest temporal resolution of SOFI with commercially available QDs [18]. Watanabe et al. [17] has utilized Blinking Enhanced QDs (BEQ) in experiments, and a SOFI image was generated with 10 raw images. The fluctuation and the stability of BEQs are enhanced with respect to commercially available QDs. Recently, Geissbuehler et al. [19] realized a 1.5 s temporal resolution SOFI image of the sample labeled with Dreiklang, and a SOFI image with an acceptable SNR was generated with at least 500 raw images.
There is no report on reducing the required number of raw images with modification of the SOFI algorithm. For now, most modifications for the SOFI algorithm are post process, such as Fourier reweighting [10]. This measure will reduce the size of the Point Spread Function (PSF) and improve image quality. There are only two papers on the pre processing of the fluctuating signals for SOFI. Dertinger et al. [13] and Stein et al. [12] mentioned that the fluctuating signals could be influenced by the bleaching effect of the organic dyes or the QDs. They both proposed that combining SOFI images of sub-stacks of raw images could reduce the influence of photo bleaching, and thousands of raw images are needed with this algorithm.
In this study, we have improved the fluctuating signal extraction process for the SOFI algorithm, and the required number of raw images for SOFI is reduced to tens. First, we demonstrated the modified SOFI algorithm with simulated raw images of QDs. The results show that an enhanced resolving ability could be achieved with respect to conventional SOFI algorithm while using tens of raw images. Then, we excited the commercially available QDot 525 labeled on the microtubule network inside the Hela cell with a mercury vapour lamp, in the experiment. The SOFI image could be generated with at least 25 raw images (50 ms per frame), and the corresponding acquisition time was 1.25 s.
2. Experiment setup
Microtubule networks inside the Hela cell were immunostained with commercially available quantum dots (QDot 525, Invitrogen). And the QDs were excited with a mercury-vapour lamp, which was filtered with a band-pass filter (325-375 nm). The illuminated intensity was estimated less than 100 W/cm2 on the sample. And a filter was used to extract the fluorescence emitted from the sample. A standard wide-field epi-fluorescence microscope was utilized in the experiment. An 1.4 numerical aperture oil-immersion objective (UPLSAPO 100 x, Olympus) was coupled with the microscope. An sCMOS camera (C11440, Hamamatsu) was utilized as the detector, and the pixel size was 6.5 μm × 6.5 μm.
3. Theory
In the theory of SOFI, QDs are identified with their independent fluctuation of fluorescence [9]. For conventional SOFI, the zero-mean like fluctuating signal could be obtained by subtracting the mean value from the time series. This is based on the assumption that the average intensity of QD fluorescence is stable over observation [9].
Figure 1(a) and (b) presents two time series of fluorescence intensity from adjoining pixels recorded with the experimental setup mentioned above. These two pixels are close to the center of a Gaussian-shaped PSF generated from an isolated quantum dot. In Fig. 1(c) and (d), two time series of adjoining pixels from the background are presented as references. The dotted lines feature the mean values of each time series.
Fig. 1 Raw time series in four individual pixels from 500 frames of raw images. (a) and (b) are from two adjoining pixels inside an isolated QDs, and (c) and (d) are from two adjoining pixels in the non-blinking background
According to the theory of SOFI, two time series inside a single PSF should possess two characteristics. First, the optical fluctuating signal should be like a zero mean random signal. Second, the optical fluctuating signals from the same QD should be highly correlated. In Fig. 1(a) and (b), because of the instability of the QD fluorescence, both of the raw signals possessed low frequency background. In this case, neither of the mean value subtracted fluctuating signals is not zero mean random signals. On the other hand, the amplitude of readout noise is so intense that there are almost no similarities between two fluctuating signals.
Unfortunately, as shown in Fig. 1, the optical fluctuating signals of QDs could be influenced by two aspects: the instability of QDs fluorescence (such as long time intensity fluctuation, bleaching time, and dark time) and the readout noise of CCD / sCMOS [9,10,12], in the experiments.
First, the low frequency background will remain in the fluctuating signal, when it is extracted by subtracting the mean value of the time series. Then the converging rate of the SOFI algorithm over the number of raw images will be slowed down, and more raw images are needed. The instability of QD fluorescence could be more severe in the case of reducing illumination intensity, and even more raw images are required. Second, the readout noise from the detector was reduced in the SOFI image by increasing the number of raw images [17], and this could compromise the temporal resolution. Furthermore, if there is noise in the raw images, the enhancement of spatial resolution could not reach the theoretical limit of the SOFI algorithm [9]. Therefore, the low frequency fluctuation and the noise could reduce the temporal and spatial resolution of the SOFI image.
In order to enhance the temporal resolution of SOFI, the extraction process of a fluctuating signal has been modified in this study. This modification is intended to eliminate the low frequency background and the readout noise from the time series, and the actual fluctuating signals could then be extracted.
First, because of the frequency differences between the stochastic fluctuating signal and the low frequency background fluctuating signal, a high-pass filter is feasible to extract the stochastic fluctuating signal from the time series. Furthermore, considering the stochastic property of the fluorescence intensity, an 1-Dimensional wavelet-based filter was employed to eliminate the low frequency background fluctuating signal [21].
On the other hand, the readout noise could not be simply eliminated in the temporal frequency domain, because the frequencies of the readout noise are high and equal to that of some components of the stochastic fluctuating signal. If a low-pass frequency filter is applied to the temporal frequency domain, a large fraction of the stochastic fluctuating signals of QDs will be eliminated as well as the readout noise. Obviously, the SOFI results could be compromised by utilizing this filter. However, the frequencies of the readout noise are significantly higher than that of the Optical Transfer Function (OTF) in the spatial frequency domain. Therefore, the readout noise could be removed in the spatial frequency domain, and the stochastic fluctuating signal will be almost intact in the temporal domain. Considering the randomness of the distributed locations of QDs and the stochastic property of the stochastic fluctuating signal, a 2-Dimensional wavelet-based denoising filter was utilized to eliminate the high frequency readout noise [22].
Figure 2 presents the fluctuating signals obtained using this modified extracting process with the time series presented in Fig. 1. After the modified extraction of the fluctuating signals, all of the time series in Fig. 1 are transformed into zero mean random signals. The higher frequency components of fluctuation have been properly preserved in the filtered signals. Furthermore, the two signals in Fig. 2(a) and (b) are almost identical with each other. Only minor differences between Fig. 2(a) and (b) could be distinguished after a close examination. On the other hand, in Fig. 2(c) and (d), the fluctuating signals are still distinct from each other, and the amplitudes of oscillation are much lower than those of Fig. 2(a) and (b). Apparently, the QD signals in Fig. 2(a) and (b) are highly correlated, and the background signals in Fig. 2(c) and (d) are less correlated. Thus, the second-order cross covariance of the QDs will be much higher than that of the background.
Fig. 2 Fluctuating signals extracted from time series presented in Fig. 1 with modified algorithm. Figure 2(a) and (b) are from two adjoining pixels inside an isolated PSF of QDs, and Fig. 2(c) and (d) are from two adjoining pixels in the background.
In order to evaluate the convergence rate of SOFI with the mean value subtraction and the modified algorithm, the ratios of cross covariance of background to signal (B/S) over the amount of raw images are shown in Fig. 3. The evolution of the ratios in Fig. 3(a) and (b) were calculated with data presented in Fig. 1 and Fig. 2, respectively. In theory, an algorithm with higher efficiency should converge with fewer raw data. In Fig. 3(a), intense oscillation of the background to signal ratio could be observed under 100 frames, and the result is approximately converged above ~400 frames. This is consistent with reports that a SOFI result could only be obtained with at least hundreds of raw images.
Fig. 3 The evolution of the ratio of background to signal (B/S) cross covariance over the number of raw images, (a) Mean subtracting algorithm, (b) Modified algorithm
On the other hand, the result is converged with tens of frames with the modified algorithm in Fig. 3(b), and the B/S ratio is almost stationary with more than 50 frames. Results indicate that the convergence rate of the modified SOFI has been enhanced, and it is possible to obtain a SOFI result with tens of raw images. Furthermore, the ratio of B/S is more stable than that of the conventional algorithm after convergence. The enhanced convergence rate and stable ratio of B/S could contribute to a flattened background in the SOFI image, especially for fewer than 100 raw images. Less background will then be left after a linear contrast stretching, and the background elimination ability of SOFI could be enhanced.
4. Results and discussion
This modified algorithm was then evaluated with the simulated and experimental raw images. First, we simulated the raw images of QDs with considering the stochastic fluctuation and the long time background fluctuation. The dimensions of the images are 128 pixels × 128 pixels, and the size of each pixel is 19.5 nm × 19.5 nm. The intensities of the PSFs are set as Gaussian distributions. The Full Width at Half Maximum (FWHM) of the PSF is 9 pixels, corresponding to ~180 nm.
As shown in Fig. 4(a), there are four rows in the images, and each row has 4 or 5 pairs of QDs. The distances between each pair of QDs are equal in the same row. In the first and second row, the distances between the centers of pixels are 5 pixels in the horizontal and diagonal directions, respectively, which correspond to 97.5 nm. In the third row, the horizontal distances are 6 pixels, corresponding to 117 nm. The distances between QDs are 5.6 pixels in the fourth row, corresponding to 110 nm. The amplitude ratio between the QDs and noise is 4:1.
Fig. 4 Simulated QD raw images and SOFI images. (a) The centers of the simulated QDs. (b) A typical frame of the simulated raw images. (c) Averaged image of 50 simulated raw images. (d) The 2nd-order SOFI image with 50 raw images using publicly available software [23]. (e) The 2nd-order modified SOFI image without deconvolution or background subtraction. (f) Histogram of FWHM for conventional SOFI and modified SOFI
Obviously, a typical raw image is noisy, as shown in Fig. 4(b), and there are 4 rows which can be resolved. In Fig. 4(c), the SNR of the averaged image of 50 simulated frames is still low in SNR. There are obviously 4 rows of QDs in Fig. 4(c). However, not a single pair of QDs could be resolved.
Figure 4(d) presents the 2nd-order SOFI using publicly available software [23] with 50 simulated frames. With the conventional 2nd-order SOFI, the averaged FWHM of the PSFs is reduced to ~97 nm, corresponding to a nearly two fold increase in resolution. Comparing Fig. 4(c) and (d), the SNR was increased with the conventional 2nd-order SOFI. Because of the noise in the background and the deconvolution after the SOFI algorithm, there are noticeable ring shape artifacts around each QDs.
Figure 4(f) presents the 2nd-order SOFI using the modified algorithm with the same 50 simulated frames as in Fig. 4(d). With the modified 2nd-order SOFI, the averaged FWHM of the PSFs is ~130 nm, which is much larger than those shown in Fig. 4(d). However, the resolving ability is enhanced especially in rows 1 and 4, and the distances between the centers of QDs are 97.5 nm and 110 nm respectively. In the case of background noise in the modified SOFI result, most of the intensities are in the range of 0-2, which are nearly 100-200 times dimmer than the peak intensities of QDs. This result indicates the ability of background elimination has been enhanced with the modification. It should be noted that the resulting image in Fig. 4(e) didn't processed by deconvolution or background subtraction.
Figure 5 presents the intensity profiles of line 1 and 2 in Fig. 4(c), (d) and (e) as shown in Fig. 4(a). In Fig. 5(a), distinct noise could be detected in the line profile of the averaged 50 raw images. In Fig. 5(a), there are clearly two peaks in the modified SOFI result, and the central position of the left peak is exactly the same as the simulated center of the QD. In Fig. 5(a), the distance is 108 nm between the 2 peaks, and the simulated distance is 97.5 nm. On the other hand, the distance between 2 peaks is 130 nm in Fig. 5(b), and the simulated distance is 110 nm. The resultant distance is 20 nm larger than that of the simulation, which is approximately the length of 1.5 pixels in the diagonal direction. These results show that the resolving ability of SOFI was not only determined by the size of the PSF. Because of the more effective extraction of optical fluctuating signal, the resolving ability of SOFI has been enhanced.
Fig. 5 Intensity profiles of line 1 and 2 in Fig. 4(c), (d), and (e) as marked in Fig. 4 (a). (a). Intensity profiles of line 1 in Fig. 4 (c), (d), and (e). (b) Intensity profile of line 2 in Fig. 4 (c), (d), and (e).
Comparing with the conventional algorithm, there are almost no artifacts or noise around the QDs in the modified 2nd-order SOFI result with the simulated images. These results are consistent with Fig. 3 in that the stability of the B/S ratio is improved with the modified algorithm. The low-level noise in the modified 2nd-order SOFI image indicates that nearly no artifacts could be generated with higher order SOFI or deconvolution [9,10]. We attribute these improvements to the efficient extraction of fluctuating signal from the raw images.
Then, the modified SOFI algorithm is evaluated in the experiment. The sample of microtubule network inside Hela cell was labeled with QDot 525. In Fig. 6(a), averaged image of 25 raw frames is shown. The dimensions of the raw images are 765 pixels × 765 pixels, and the size of each pixel is 32.5 nm × 32.5 nm. The exposure time for each frame is 50 ms, and 25 raw images are corresponding to 1.25 s. Figure 6(b) presents the modified 4th-order SOFI results with 25 frames of raw images. The modified SOFI image in Fig. 6(b) was not processed by deconvolution or background subtraction. Comparing Fig. 6(a) and (b), the background is almost eliminated with the modified 4th-order SOFI. Obviously, the enhanced resolution could be discovered by comparing Fig. 6(a), (c) and Fig. 6(b), (d). As showed in Fig. 6 (f), the center of Gaussian fitted FWHM is less than 100 nm. In Fig. 6(e), the distance between the two peaks is 130 nm, which could not be resolved in the averaged image. And the FWHM of PSF could be further reduced by utilizing deconvolution or higher order SOFI. There are some QDs missed in the SOFI image, and this is caused by the intermittent fluorescence of QD [16] and the large dynamic range of SOFI result [9]. The computational time for a single image using 25 frames of 765 pixels × 765 pixels raw images is ~2 min, while utilizing a desktop PC equipped with a conventional CPU (Intel Core i7).
Fig. 6 Comparison between averaged raw image and the modified 4th-order SOFI results of the microtubule network of immunostained Hela cell. (a) Averaged wide-field microscopy image. (b) The modified 4th-order SOFI results with 25 frames of raw images. (c), (d) Magnified views in areas marked in (a) and (b). (e) Profiles of line 1 and 2 marked in (c) and (d). (f) Histogram of FWHMs of PSF in the modified 4th-order SOFI image.
This research is conducive to enhancing the temporal resolution of SOFI. Furthermore, this modification could reduce the requirement for the SNR of raw images, and it is especially important in reducing the intensity of illumination and the phototoxicity in biology samples. In the future, the performance of fluctuating signal extraction and SOFI image will be further improved with superior mathematical models. At the same time, the spatial-temporal resolution could also be enhanced with improved QD/FP and detectors. The major drawback of this modification is a higher computational load.
5. Conclusion
In conclusion, we have enhanced the temporal resolution of the SOFI algorithm by modification of the extraction process of fluctuating signals. The low frequency fluctuation and the readout noise are eliminated by two wavelet-based filters applied on the temporal and spatial frequency domain of the raw image stack. Consequently, the stochastic fluctuating signal could be extracted effectively. In the case of the simulated images, the resolution and the background eliminating ability have been enhanced with the modified SOFI algorithm while utilizing only 50 simulated images. In the experiments, the required number of raw images has been reduced to 25, corresponding to total acquisition time of 1.25 s. The FWHM of the PSF in the SOFI image is 98 nm. Therefore, this research is conducive to enhancing the performance of SOFI, and it is important for widespread biological applications of SOFI.
Acknowledgments
We thank Xiaomei Liu and Wenjun Lan from Suzhou Institute of Biomedical Engineering and Technology for preparing the sample. This work is supported by the Key Program for the National key scientific and research equipment development Foundation of China under Grant No.ZDYZ2013-1, the Six Talent Peaks Project of Jiangsu Province under Grant No. 2012-swyy-020, and the Basic Research Project in Suzhou under Grant No. SYG201510.
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