Microscope 3D Point Spread Function Evaluation Method on a Confirmed Object Plane Perpendicular to the Optical Axis

Round 1

Reviewer 1 Report

The reviewer fully agrees with the authors that the experimental determination of PSF gives much better results than numerical calculation. This happens because, inter alia, the calculation model should take into account the actual parameters of the measurement path, the values of which we do not know exactly enough. The more complex the optical system, the more parameters should be taken into account, and thus the PSF calculation result is less accurate. Another important reason for a large calculation error are influential conditions not accounted for in the model, such as e.g. installation inaccuracies, temperature, which also affect its value.
The authors present the original method of determining the PSF of the microscope based on a dual PSD-based unit. They provide the theoretical analysis of the method and the experimental results of its application. Important information for the reader wishing to use the proposed method is a description of the full procedure for its application.

Author Response

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Reviewer 2 Report

Accurate knowledge of the point spread function (PSF) of an imaging system is of high importance in super-resolution microscopy, where small mismatches between the assumed and the true PSF shape can lead to significant errors in the data analysis and thereby to a degradation of the image quality. Mao, Wang and Pan report on a method to adjust the orientation of a PSF calibration system with respect to the optics of a fluorescence microscope, such that fluorescent beads can be moved laterally in an object plane perpendicular to the optical axis.

The approach might help increase the accuracy of PSF measurements. Unfortunately, the manuscript lacks clarity and detail, which prevents a full appreciation of the results. Before an eventual publication, a major revision is required to address the concerns below. I suggest discussing the manuscript with a colleague to improve its readability and clarity.

 

1. It is necessary to describe the method in sufficient detail and clarity to understand and implement it. Only the most critical parts are listed below:

Section 3.1 cites reference 15, in particular its figure 3 and equation (11), but does not define the parameters E, F and P_2. Please clarify and introduce the relevant parameters in figure 3.

In optics, “paraxial” commonly refers to rays that propagate at small angles with respect to the optical axis. Figure 4 suggests that “paraxial region” stands for the focused image region, i.e. the region of the lateral plane that lies within the depth of focus. Please clarify “paraxial” early in the main text or use common expressions.

Lines 124 to 156 should be rewritten. It is not clear what a “two division Gaussian function” is (line 132); what is meant by “each of the two parts” (line 124); what “differences between two FWHMs” (line 134) or “series” (line 133) and “normalization” (line 142) thereof are; what a “polynomial combining logistic curve” is; and what the parameters l_0, l_1, l_2 and s are (Eq. 2).

Please label all axes in Figure 6. Are the measured points of the two panels equal? If the green fit in the left panel is a second-order polynomial, it should look like a parabola. Please indicate and label the paraxial region.

Please specify the shape of the paraxial region determined by “the four end points of the two lines” (elliptical? Line 155).

Please define “pitching” (line 159) and “rolling” (line 160), e.g. by adding the angles alpha and beta (line 230) to figure 2 and using the angles’ names.

Equation (3) yields half of the particles thickness assuming a bead centered at the coordinate origin. Its fluorescence intensity is proportional to its thickness, but not normalized to it (line 174), because the bead’s diameter is much smaller than the depth of focus.

Equation (5) defines the bead’s image as the convolution of its thickness with the lateral PSF. The bead image might approach a Gaussian profile, but less so the underlying diffraction-limited PSF. Why was a Gaussian PSF used anyway?

What kind of objective has been used (1.15 NA oil immersion? Line 258)?

2. The report does not show any measured PSF profile. I strongly recommend including a figure with cross-sections through the measured PSF.

3. The report would also benefit by comparing the new results with other PSF measurements.

For instance, in fluorescence microscopy, the PSF can be measured by imaging a fluorescent bead with a diameter smaller than a quarter wavelength. Then, the fluorescence image approximates the PSF and a deconvolution with the bead’s geometric image allows measuring it precisely. If several beads are distributed sufficiently sparse within the image region, their individual images can be distinguished and analyzed separately to obtain the PSFs at different positions. Imaging this sample several times for different sample displacements allows assessing the magnification and the image distortion as well. The three-dimensional tracking of the displacements in the images further allows measuring the angular orientation of the sample stage, such that displacements can be aligned with respect to the optical axis for a second, more accurate, iteration of PSF measurements.

If I understand correctly, the movable assembly is first aligned with the optical axis of the microscope by repeatedly measuring the beads’ image position upon displacements, until a lateral displacement defocuses the beads’ image least. During this process, the dual PSD-based unit allows monitoring the movements accurately. Besides confirming the sample orientation and position, does the reported method feature other advantages?

4. “The cover slip acts as an emission filter that only allows the fluorescent particle’s emission light to travel into the microscope.” (line 85).

Is this filtering necessary here?

What type of filter is it? Absorption and/or interference?

If it is an interference filter, how does the reflected excitation light and the spread of incidence angles and polarizations of the fluorescence light alter the measured PSF?

5. Figure 7a shows a very small variation of the PSF diameter when the bead is axially displaced (line 260). Is tau_I0 shown here?

6. Figure 8 shows differences of PSF FWHM diameters versus the axial bead position (line 282). Why does the paraxial region contain different maximal values for the six measurements?

Author Response

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Reviewer 3 Report

In this manuscript, Mao et al. present a method to measure the point-spread function (PSF) of basically any microscope. This method comprises a device  that the authors have described earlier. Here, it is used to determine the pointing direction of a collimated laser beam.

The suggested device for the PSF consists of two parts. Part 1 (static assembly) is a collimated fiber-coupled laser that emits linear polarized light. A CCD camera is mounted next to the laser. In front of the CCD chip is a ‘plane-splitter’, which is probably a semi-transparent mirror. The authors use the term ‘refracted’ instead of ‘reflected’ which makes it diffivcult to understand.

The laser beam is then passed through a movable assembly (part 2 of the device) which is basically the ‘dual spot position detector’ that was previously described by the authors.

The two parts allow to monitor the z-position of the movable part and the orientation direction of the laser beam. The laser light is used to excite a fluorescent point emitter that is mounted on the exit face of the movable part of the device. The fluorescence emission of this emitter is then picked up by the microscope, of which the PSF should be determined. Scanning the movable part, allows to determine the PSF over the full field of view of the microscope.

The proposed device is mainly a method to align the plane of lateral scanning perpendicular to the optical axis of the microscope. As far as I can see, the alignment is dependent on the direction of the laser beam. I cannot see, why this alignment should be more accurate that the alignment of a classical sample stage on the microscope. A comparison of scanning the probe with the normal microscope stage may provide insights.

The parts that were used to build the device are not described in the manuscript. Therefore, potential users will have difficulties to adapt the method in their labs.

The method in total is not described accurately enough. For example, the quantities to compute the beam vector components are taken from the previous articles. However, there position sensitive detectors are used. In this manuscript, CCDs are used for this device and a rule for determination of the needed quantities is not given. A picture, which shows the real device integrated into the microscope would be insightful.

The wording and grammar of the manuscript need to be improved.

Author Response

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Round 2

Reviewer 2 Report

Firstly, I would like to thank the authors for some clarification of the equations, symbols and sample orientations. I understand that additional experiments cannot be done now – I am in home-office as well.

I keep my recommendation to discuss the manuscript with another scientist locally, preferably a native English speaker, to improve its readability and clarity. For instance, I have to guess what the “two parts at the central position” (Figure 5) really are. Maybe two projections along orthogonal directions that were fitted individually by one-dimensional Gaussian profiles? If that is the case, the term “curve surface fit” is confusing and I would ask if these directions were chosen as x and y axes; or based on the position of the bead with respect to the optical axis; or by the major and minor PSF extents.

Fit parameters that represent physical properties should be named accordingly instead of enumerating them.

To me, it is still unclear what the “polynomial combining logistic curve method” is. My best guess is a piece-wise logistic function.

Looking at the measurements, the measured PSF diameter is smaller (144 nm) than the diffraction limit (157 nm) and does hardly change with defocus. The added PSF profile shows a one-dimensional perfect Gaussian without any measurement noise, whereas I expected xy, xz and yz cross-sections through the measured 3D PSF. The emission filter sits in a strongly divergent beam path, which introduces serious shifts of the filter spectrum over the angular spectrum of the incident light and additional modulation of the excitation intensity near the filter surface. Emission filters are commonly placed in a collimated beam or paraxial beam. For this measurement, the filter could and should be placed after the objective or in front of the camera.

In conclusion, I emphasize again the need for discussing the report with an independent local scientist in English to check the understanding by a fresh mind. 

Author Response

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Reviewer 3 Report

The authors have considerably improved their manuscript according to the reviewers' comments. It now describes the method and results much more clearly and convincingly. I suggest publication in the present form.

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