On 2020-04-23 10:47:43, user Dora Mahecic wrote:
Response to the main comments from the review by Andrew G York:
Comment 1<br />
I found the paper well organized and well written. I found the figures made clear, convincing arguments that their method greatly improves on the original iSIM design. I was impressed by the combination with expansion microscopy and particle averaging, especially the comparison to estimated speeds of STED and/or SMLM alternatives. I suspect their technique would also compare favorably to a normal-resolution microscope and a 2x larger expansion factor. I assume it's hard/annoying to expand 2x more? If the authors are comfortable doing so, I recommend adding this comparison (no additional figures, just a description of what they'd expect).<br />
We agree that it is important to offer comparisons to other methods yielding similar resolutions. The effective resolution improvement X is determined by the resolution improvement of the method (Xres) and the expansion factor (Xexp) such that X = Xres * Xexp. Therefore, in the case of iSIM (Xres = 2) and U-ExM (Xexp = 4-5), the effective improvement in resolution is in the range of 8-10-fold (X = 8-10). <br />
Achieving the same improvement is therefore possible on a standard diffraction-limited microscope (Xres = 1), if the sample has an 8-10-fold expansion factor (Xexp = 8-10), but raises several issues. Firstly, while methods for achieving larger expansion factors are available1,2, they are generally more complicated than the U-ExM protocol and have not been demonstrated for expanding multi-molecular complexes such as the centriole. Secondly, assuming a larger expansion factor Xexp is achievable, the field-of-view (FOV) would be reduced along each dimension by Xexp and would therefore require stitching together Xexp^2 individual images. This would in turn reduce the throughput by Xexp^2, and result in a 4-fold lower throughput than combining iSIM and U-ExM (assuming that both methods start with similar FOV sizes). The same applies to a spinning disk microscope, which could achieve a ?2 improvement in resolution and hence require an expansion factor of 5.5-7, and a decreased throughput by a factor of 2. <br />
Overall there are specific advantages to prioritizing Xres, since Xexp increases the physical sample size effectively reducing the size of the FOV. Furthermore, achieving Xexp beyond the traditional factor of 4-5 involves more complicated expansion protocols. On the other hand, additional advantages of increasing Xexp come from the fact that sample expansion also improves other optical (sectioning, aberrations) and mechanical (drift) features of the method. Therefore combining fast super-resolution techniques with moderate expansion is likely to provide the best of both worlds. <br />
A sentence addressing this issue has been added to the main manuscript lines 359-362, and a similar more detailed discussion has been included in the supplemental information lines 363-387.<br />
1. Truckenbrodt, S. et al. X10 expansion microscopy enables 25-nm resolution on conventional microscopes. EMBO Rep. e45836 (2018). doi:10.15252/embr.201845836<br />
2. Chang, J.-B. B. et al. Iterative expansion microscopy. Nat. Methods 14, 593–599 (2017).
Comment 2<br />
I don't fully understand how their optics work. Perhaps this is my fault; I have a decent background in optics, but a short attention span. If the authors want people like me to understand their optics better than I did, perhaps they can change the paper to convey this more completely. For example, it's not obvious to me exactly what effect the rotating diffuser has. What does the illumination look like with no diffuser, or with a static diffuser? How does the illumination change as the diffuser moves? Does motion of the diffuser change the position of each illumination spot, or the size, or the intensity? How fast does the diffuser have to move, compared to the galvo scanning? <br />
We thank the reviewer for bringing up this important question, which seems unlikely due to any lack of attention span.<br />
With no diffuser, the homogenization plane will not produce a flat-field but instead a highly inhomogeneous interference pattern making up a periodic array of spots1,2. The rotating diffuser serves to scramble the incoming wavefront and produce an extended partially coherent source. However, when the rotating diffuser is static, it produces a speckle pattern in the homogenization plane that is not homogeneous, but spatially random with respect to the interference pattern without the rotating diffuser.<br />
https://uploads.disquscdn.c...
Rotating the diffuser causes different, spatially random, scrambled wavefronts to be projected in the homogenization plane where the excitation microlens array (MLA) is located. In the front focal plane of the excitation MLA, each incoming scrambled wavefront will in turn produce spots with varying intensities, and might cause variations in the size and position of the spots (Supplemental Movie 2). However, if many different, spatially random, scrambled wavefronts are averaged over time (by a rapidly rotating diffuser), they will produce a homogeneous flat-field in the homogenizing plane and therefore a homogeneous array of excitation points in the front focal plane of the excitation MLA (Supplemental Movie 1, Supplemental Movie 3). <br />
How fast does the diffuser need to rotate to achieve homogeneity in the scanned spots? To characterize the scrambling speed of the rotating diffuser, we perform a back of the envelope calculation given the characteristics of the rotating diffuser and the imaging process. We then use the simulation platform and real data to quantify the relationship between the scrambling speed of the rotating diffuser and the variations in position, width and amplitude of the excitation points at different timescales. For a quick visual, please see Supplementary Movie 3, which shows how homogeneity of excitation points emerges experimentally as more and more wavefronts are averaged.
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Back-of-the-envelope calculation<br />
This aims to estimate how fast the rotating diffuser averages out the incoming wavefronts during imaging. We characterize the rotating diffuser by its rotation speed ?, distance of the rotation axis from the optical axis r and a grain size d:<br />
Rotation speed ??6000 rpm=100 rps<br />
Distance from optical axis r?10 mm<br />
Diffuser grain size d?10 um<br />
Therefore we can approximate that as the diffuser is rotating, it will average out over n grains per unit time, and therefore produce at least n random wavefronts per unit time.<br />
n=2?r/d•??6.28•10^5 s^(-1)<br />
This is a conservative estimate of the scrambling rate, since changing sub-grain position on the diffuser is likely to produce a differently spatially distributed wavefront.<br />
Now, given an imaging frame rate f and assuming that on the sample each point needs to scan a distance s, we can approximate how many scan positions p this requires given a diffraction limited spot size on the sample s_PSF.<br />
Imaging frame rate f=10-100 Hz<br />
Scan distance s?10 um<br />
Diffraction limited spot size s_PSF?0.25 um<br />
Number of scan positions on sample p?s/s_PSF ?100<br />
Finally, we can estimate the number of wavefront iterations over which each point is averaged at each scan position on the sample as N:<br />
N=n/(p•f)<br />
At the fastest imaging rate f_max =100 Hz this results in N_max?62.8 iterations<br />
At the imaging rate used in the majority of this work f_real=10 Hz this results in N_real?628 iterations<br />
We would like to highlight that these numbers represent a purely technical limitation, and that higher scrambling rates can be easily achieved by increasing the distance of the axis of rotation of the rotating diffuser from the optical axis, finding a rotating diffuser with a faster rotation speed or smaller grain size, placing two rotating diffusers in series but rotating in opposite directions2 or switching to speckle reducers with higher operating frequencies such as the Optotune Speckle Reducers sold by Edmund Optics (https://www.edmundoptics.co... "https://www.edmundoptics.com/f/optotune-laser-speckle-reducers/14335/)"). Nevertheless, we thank the reviewer for helping us improve the characterization of the setup and highlight this important technical consideration.
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Simulation <br />
To test whether the numbers of iterations from the calculation are sufficient to provide homogeneous spots during scanning, we use our extended simulation platform to address how the position, size and intensity of the spots is changing when averaged out over different numbers of iterations. <br />
To test whether the numbers of iterations from the calculation are sufficient to provide homogeneous spots during scanning, we use our extended simulation platform to address how the position, size and intensity of the spots change when averaged over different numbers of iterations. To do this, we generated 8000 random wavefronts using our extended simulation platform, before bootstrapping over different numbers of iterations and examining how the intensity of the same point varies between the different averages and their realizations. Specifically, we measured the position of the maximum of each peak, its FWHM and maximal value representing the amplitude, and compared the same parameters across 10 different realizations of bootstrapping together a varying number of iterations N. Each realization contained ~90-110 excitation spots. A visualization of how the flat-profile is built up by averaging over many realizations in the simulation is shown in Supplementary Movie 1.
https://uploads.disquscdn.c...
We then quantified how these parameters varied between 10 different realizations, by computing their difference for each excitation point between the 10 different realizations for each N. Plotting the variation distributions allowed us to measure their FWHM and reported those values as function of the number of iterations over which the illumination is averaged out. Similarly, we can study how the intensity of a single point varies between different scrambled wavefronts (without temporal averaging). All of these results are now reported in the Supporting information and compared with the experimental results.
- Experimental results<br />
Since the rotating diffuser rotates too fast to capture the individual wavefronts corresponding to different positions of the diffuser, we manually rotated the diffuser by random amounts to acquire 2064 images of the resulting scrambled wavefronts, analogous to the simulated data. How the excitation spots change at different positions of the rotating diffuser is represented in Supplementary Movie 2. We then repeated a similar analysis as for the simulated data, by comparing the variation in spot position, size and intensity by bootstrapping over different numbers of iterations. This is represented in Supplementary Movie 3.<br />
https://uploads.disquscdn.c...
By measuring the FWHM of the variation profiles, we could study how the spot localization, width and amplitude varied as function of the number of iterations. Specifically, we measured the subpixel localization of each spot by fitting it to a 2D Gaussian profile, from which we also extracted the FWHM of each spot. There were generally ~472 spots in different frames and bootstrapped realizations. The amplitude was measured by taking the raw pixel value at the peak location. <br />
https://uploads.disquscdn.c...
Similarly, by not bootstrapping over multiple iterations, we could compare how a single point varies between individual scrambled wavefronts.<br />
https://uploads.disquscdn.c...
The results show that the simulation is conservative compared to the real data. This could be because the simulation is performed in one dimension, while the real data is two-dimensional, and that averaging over an additional dimension could produce better results. Nevertheless, the simulated and real results show that averaging over an order of magnitude of 10 iterations produces excitation spots with <20% variation in intensity, while averaging on the order of 100 provides <10% variation in intensity. Interestingly, the values appear to plateau at ~2-3% which could be due to the limited size of the simulated and experimental datasets, or suggests that averaging out further does not bring additional improvement to the homogeneity. <br />
The variation in spot localization and width also decreases as the excitation is averaged over more iterations. The plotted variations in localization and width are represented before magnification (x116). Therefore, on the sample these represent ~10 nm variation in localization and width, which does not compromise the ability to focus the excitation to a diffraction-limited spot. In fact, the slight variation in localization of the excitation spot might be beneficial in reducing the striping artefact often present in scanning methods. <br />
We briefly summarized this analysis in the main manuscript lines 194-198 and a similar more detailed discussion has been included in the supplemental information lines 221-334 and Supplemental Figure 4.<br />
1. Zimmermann, M., Lindlein, N., Voelkel, R. & Weible, K. J. Microlens laser beam homogenizer: from theory to application. 666302, 666302 (2007).<br />
2. Voelkel, R. & Weible, K. J. Laser beam homogenizing: limitations and constraints. 71020J (2008). doi:10.1117/12.799400
Comment 3<br />
For another example, it's not obvious to me what the second flat-fielding MLA is doing. Naively, it seems to me that I could remove it from Figure 1i without changing the beam path, but presumably I'm wrong. Perhaps fine details of the optics may not be the point of the paper, but if they are, I'd like to see more details. I apologize in advance if these details are present, and I simply missed them.<br />
We thank the reviewer for pointing out this lack of clarity. Briefly, the second MLA serves to cancel the quadratic phase curvature introduced by the first MLA1,2.<br />
In detail, the primary components of a Köhler integrator are a collimating lens, a pair of microlens arrays (MLAs) and a Fourier lens1,2. The collimating lens serves to collimate the light from the inhomogeneous light source. The first MLA takes the incoming collimated beam and samples the different parts of the angular spectrum through the individual microlenses. Each microlens channel serves as a parallel Köhler illumination channel for different sections of the angular spectrum of the beam. The second MLA, identical to the first one and positioned one focal length away from the first MLA, serves to cancel the quadratic phase curvature introduced by the first MLA. The Fourier lens then combines the light from the different microlens channels at its front focal plane, causing any variations in the spatial and angular distributions of the light source to be averaged out into a flat-top beam. <br />
For incoherent light sources, this would be sufficient to produce a homogeneous flat-top profile. However, for coherent light sources such as lasers, the homogenization plane would produce an inhomogeneous interference pattern. Therefore a focusing lens and a rotating diffuser are needed to scramble the incoming light and create a partially coherent extended source. <br />
We added a sentence further describing the Köhler integrator to the manuscript lines 93-96 and an extended description in the supplemental information lines 22-37.<br />
1. Zimmermann, M., Lindlein, N., Voelkel, R. & Weible, K. J. Microlens laser beam homogenizer: from theory to application. 666302, 666302 (2007).<br />
2. Voelkel, R. & Weible, K. J. Laser beam homogenizing: limitations and constraints. 71020J (2008). doi:10.1117/12.799400
Comment 4<br />
I found the first video striking and beautiful. The second video, in contrast, emphasizes the striping artifact in a way I found jarring. Your stripes are certainly improved compared to my iSIM, but I suspect this movie will alarm at least some of your readers. On the other hand, I applaud your honesty in showing both the good and the bad. If your iSIM is like my iSIM, the highly visible stripes are due to out-of-focus objects in a thick sample. If so, I recommend adding a brief discussion of striping to the text, to manage expectations for your reader. It might also be worth (briefly) discussing methods to mitigate this artifact (for example, extra scanning mirrors like the Visitech Ingwaz, or computational methods).<br />
We agree with the reviewer, that striping artifacts should be better described as well as how to mitigate them. <br />
iSIM imaging can produce substantial striping artefacts due to its scanning mechanism, especially in thick samples with significant out of focus light. While careful alignment can diminish the intensity of the stripes, there are also mechanical solutions that mitigate the striping on the sample, or computational tools for filtering out the effect during post-processing. For example, the commercial Visitech Ingwaz system introduces extra scanning mirrors to fluctuate the position of the beam and hence reduce the striping artefact. Furthermore, a similar effect might be introduced by mfFIFI due to the slight fluctuation in the localization of the excitation spots, although this might not be sufficient to fully overcome this effect.<br />
We have added a similar discussion to the supplemental information lines 353-362.
Finally, I believe your method is novel, inventive, and potentially commercially important. Therefore perhaps you should patent your method. If you choose to file a patent, I recommend disclosing this (reasonable) conflict of interest.<br />
We thank the reviewer for this comment and have revised the conflict of interest section accordingly, found in the manuscript linse 665-669.