Parallel compensation of anisoplanatic aberrations in patterned photostimulation for two-photon optogenetics

Two-photon optogenetics becomes an indispensable technique in deciphering neural circuits recently, in which patterned photostimulation is generally adopted due to its low time delay and jitter, as well as its finely sculpting ability in space. However, optical aberrations in light propagation often deteriorates patterned photostimulation, leading to decreased intensity of patterns and thus reduced excitation efficiency. Considering anisoplanatic aberrations at different positions, only correcting aberrations at one position may aggravate aberrations at other positions. Here we propose a parallel aberration compensation based Gerchberg–Saxton (PAC-GS) algorithm for generating multiple holographic extended patterns with anisoplanatic aberrations compensated simultaneously. As an example, we demonstrate that PAC-GS is able to parallelly compensate anisoplanatic aberrations of multiple holographic patterns under gradient index (GRIN) lens, thus effectively improving the intensity of each pattern, promising for two-photon optogenetics in deep biological tissues with GRIN lens.


Introduction
To study function connectivity of neuronal circuits in vivo, the perturbation of neuronal activities is necessary.Optogenetics has attracted substantial attentions in the past 15 years, due to its capabilities in less-invasive and concurrent stimulation Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.compared to electrophysiology [1,2].In optogenetics, opsins are transgenically expressed on the membrane of specific neurons.When light stimulates the opsin, the structure of the opsin would change, which causes ions to move across the membrane and potentially generate or suppress spikes.Either excitation or inhibition response of neurons depends on the type of opsins.
In contrast to single photon optogenetics, two-photon optogenetics is more suitable to achieve photostimulation at single neuron resolution and higher penetration in scattering tissue, which is more promising in mapping neural connections.In recent years, two-photon optogenetics is widely used in neuroscience studies.For examples, Chettih and Harvey revealed feature-specific competition in primary visual cortex (V1) of mouse, using two-photon optogenetics to perturb individual neurons while observing the activity of peripheral neurons [3].Marshel et al realized the control of multiple neurons at different depths in the V1 of mouse in the order of milliseconds, and revealed that cortical layer-specific critical dynamics could trigger perception [4].Dal Maschio et al successfully identifed the set of neurons associated with tail bend control by iterative two-photon photostimulation strategy [5].Jennings et al found that there are interacting neural ensembles related to social and feeding behaviors in the orbitofrontal cortex through two-photon stimulation and recording of multiple neurons in the orbitofrontal cortex by gradient index (GRIN) lens [6].These exciting progresses suggest that, by combining with two-photon imaging, two-photon optogenetics plays a significant role in the study of neural circuits and behavioral regulation.
However, in two-photon optogenetics, the strategy of photostimulation affects the stimulation efficiency, as the neuron will generate spikes only when enough opsins are stimulated.A single focus at fixed points is usually not sufficient to photostimulate a neuron.In order to stimulate more opsins on a single neuron, serial [7][8][9][10] or parallel [11][12][13][14] excitation is usually employed.When serial excitation is adopted, a single focus is scanned on the whole cell by beam steering with galvanometers, where opsins at different positions of the neuron are stimulated successively.In this case, the accumulation of ion concentration variation is realized through time integration.For opsins with slow kinetic property, such as C1V1 [9,10], serial scanning can produce effective excitation.However, this method requires a long time, which causes the delay and jitter of action potential, and is not suitable for studying neuroscience problems that require high time fidelity.For opsins with a fast kinetic property, such as ChRmine, stimulating with extended patterns usually should be adopted [4].Extended patterns can cover the whole neuron, which could stimulate a large number of opsins simultaneously.Moreover, for highfrequency control of spikes in two-photon optogenetic [4,11], only patterned photostimulation can meet this need [12][13][14] as it can reduce the delay and jitter during stimulations.On the pattern types of photostimulation, disk patterns are the most widely used at present [5,[15][16][17][18][19], which are often combined with temporal focusing to improve the axial resolution [16][17][18][19].However, the introduction of a grating will increase the system complexity and introduce laser loss.Besides, we have proposed the beaded-ring pattern, which is able to maintain high axial resolution stimulation in living mice, with no additional gratings [20].
For the generation of patterned photostimulation, computer-generated holography (CGH) [21] is generally performed.However, conventional CGH algorithms fail in taking optical aberrations, from both optical systems and biological tissues, into account.The former is the result of design and machining errors of optical components and the misalignment of optical paths.The latter, resulting from the tissue inhomogeneity, should also be considered in in vivo twophoton optogenetics [22].For conventional lasers used for two-photon imaging (∼80 MHz repetition rate), the number of neurons that can be excited with extended pattern excitation is limited by the average power of laser.Under the influence of aberrations, the excitation power of each neuron needs to be further increased to achieve the same degree of excitation efficiency, which further limits the number of neurons that can be excited at the same time.In addition, increasing average power also increases the risk of thermal damage.Therefore, it is necessary to correct aberrations of extended patterns to restore their intensity and morphological distribution, and different aberrations at different target positions should be compensated parallelly.
However, most of patterned photostimulation schemes used for two-photon optogenetics have not compensated optical aberrations [14,19].For a few of works that consider aberrations [4,23], adaptive optics (AO) techniques are used to measure the compensation phase, as in two-photon imaging [24][25][26][27], in which the compensation phase detected at a single position is added to the hologram generated by the CGH algorithm directly.But, considering that optical aberrations at different positions are not identical, if only compensating aberrations at one position, the intensity and morphology of the extended patterns at other sites may be further deteriorated [28].
Here we propose the parallel aberration compensation based Gerchberg-Saxton (PAC-GS) algorithm and corresponding framework for aberration detection and compensation, for two-photon photostimulation based on extended patterns.The compensation wavefronts at different positions are introduced into the searching process of the hologram in PAC-GS, rather than directly superimposed on the hologram generated without considering aberrations.Compared with existing methods, the intensity enhancement ratio of patterns generated by our method is higher, as anisoplanatic aberrations at all target sites can be well compensated.We verify the performance of PAC-GS algorithm through numerical simulations and experiments of generating multiple extended patterns under GRIN lens.PAC-GS algorithm can simultaneously compensate aberrations at various sites and improve the intensity of each target pattern, promising for deep tissue two-photon optogenetics.

Principle of the PAC-GS algorithm
The GS algorithm is the most commonly used algorithm for patterned photostimulation in two-photon optogenetics [29].However, in the conventional GS algorithm [30], aberrations are not taken into account.The hologram generated without considering aberrations can reproduce target patterns under ideal optical conditions (figure 1(a)).Actually, the effect of aberrations is inevitable in in-vivo two-photon optogenetics.Utilizing the hologram generated without considering aberrations results in decreased excitation efficiency in real optical systems with aberrations.Worse still, aberrations at different target positions are anisoplanatic, causing various morphologies of different patterns (figure 1(b)).In the previous work for aberration compensation of holographic extended patterns The PAC-GS algorithm works as shown in figure 2. First, we define the intensity of the plane where the target extendedpattern S n is located as To start the iterative process, the initial hologram Φ 0 is generated as where F −1 denotes the inverse Fourier transform, Θ r is a random phase distribution, N is the number of target patterns, ϕ n is the aberration suffered by S n , and φ zn is the axial additional phase expressed as In equation (3), n is the refractive index of the objective immersion medium, k is the wave vector in vacuum, z ′ n is the axial depth of the target pattern, and θ is the deflection angle of the incident beam.In order to make the generated extended patterns more uniform, we introduce the weight coefficient corresponding to each pattern.The initial weight coefficient is defined as 1, that is, w n,0 = 1.Starting with Φ 0 , the intensity of the generated plane at axial depth z ′ n in the mth iteration is while the phase distribution at the plane is where F denotes the Fourier transform.Then, T n is used to replace I n,m to obtain a new hologram as where w n,m is the weight coefficient that changes in each iteration, defined as By iterating equations ( 4)- (7) for M times, the hologram Φ M is obtained.This process could compensate anisoplanatic aberrations when generating multiple extended patterns.In the following simulations and experiments, the iteration number is set to 50.The detailed codes about PAC-GS are available on Github (https://github.com/Jincheng-jcc/PAC-GS.git).
The calculation process of PAC-GS is can better simulate with the real transmission process of light in the media with anisoplanatic aberrations, so the hologram generated by PAC-GS can provide different corrections of each pattern at the same time.As shown in figure 2, in each iteration of hologram searching process, for each target pattern, the introduced aberration distribution is different, and the calculation process corresponding to different patterns does not affect each other.After some iterations, the hologram superposition of the aberrations corresponding to each pattern can just make the generated pattern best match the target pattern.It is difficult to achieve high intensity when an aberration inconsistent with the target position (such as ф 2 and S 1 in figure 2) is superimposed on the hologram, as this situation is not optimized by PAC-GS.Therefore, the hologram generated by PAC-GS can give each pattern a different correction, which exactly matches the suffered aberration.

Point-by-point numerical simulation model
To obtain an accurate simulation of the intensity distribution of patterns at different target sites in the same plane, we introduce a point-by-point numerical simulation model that dissociates the relation between the Fourier and image planes.Unlike traditional methods employing the fast Fourier algorithm to calculate the intensity of the same image plane, this model divides the image plane into multiple pixels and calculates the intensity of each pixel independently.As a result, the intensity of a target pattern is not affected by aberrations at other sites.
As illustrated in figure 3, when the pixel (x ′ k , y ′ k ) is located in the back focal plane, its corresponding position phase is set to If this pixel belongs to the target S n , it undergoes an aberration ϕ n (x, y), and the intensity of the pixel can be calculated as [31] where D denotes the pupil diameter at the Fourier plane and Φ M refers to the hologram.Hence, for any pixel at target positions, the intensity could be simulated based on equations ( 8) and (9).

The experimental setup and sample preparation
In the experiment, the aberration correction of multiple extended patterns generated simultaneously under GRIN lens are demonstrated.The optical system is shown in figure 4, consistent with that reported in our previous article [32].Here, a 0.5NA objective (Nikon, MRH00205) and a 0.486NA GRIN lens (Thorlabs, G2P11) are used.The GRIN lens is glued to a 0.17 mm cover glass with Loctite 401, and then the cover glass is placed on a dye pool containing SR101.The fluorescence intensity is captured by a sCMOS (Hamamatsu, Flash4.0V3) through backward detection.Imaging through GRIN lens will  cause aberrations [33].In addition, the GRIN lens is designed for imaging scenes where one end of the GRIN lens is in air and the other end is in water.Aberrations will be introduced when one end of the GRIN lens is glued to a 0.17 mm glass and then into water.Meanwhile, the GRIN lens is not adjusted to be coaxial with the objective, which would also introduce aberrations.

The process of aberration detection and compensation in experiment
Before executing PAC-GS for aberration compensation in real scenarios, anisoplanatic aberrations are required to test at all target positions.In theory, all methods about aberration measurement are applicable.The scanless AO method based on the Zernike mode is used here for simplicity [28,34].
The core idea of this method is to find the combination of Zernike polynomials that maximizes the intensity of the guide star at the target position.In the experiments, the guide star is the holographic focus generated by the GS algorithm with the position at the center of each target extended pattern.Before AO testing, set the Zernike polynomial bases and initial coefficient range, and set the initial compensation phase to zero.In each AO iteration, for each Zernike polynomial base, the coefficient is changed within the coefficient range.The phase obtained by multiplying the coefficient with the Zernike base is superimposed on the spatial light modulator while the camera is used to test the intensity of the guide star.Select the coefficient that makes the maximum intensity of the target, multiply it with the Zernike base and add it into the compensation phase.Three rounds of compensated phase iteration search are carried out for each target, and the searching range of aberration coefficient in each iteration is reduced to half of the last one.
After achieving compensation phases corresponding to all target patterns, the PAC-GS is applied to search a new hologram which could generated multiple patterns with aberration correction.Besides, aberration correction by superimposing single compensation phase or average compensation phase with original hologram generated by GS is also performed.The detailed codes for AO testing and aberration compensation with different methods are available on Github (https:// github.com/Jincheng-jcc/PAC-GS.git).

Complete compensation of anisoplanatic aberrations by PAC-GS
We simulate and analyze the performance of extended patterns generated by GS and PAC-GS algorithm under the influence of anisoplanatic aberrations.The disk pattern is selected as the target extended pattern.We define four disk patterns that are randomly distributed on the focal plane, with radii equal to 5 µm.The intensity distribution of disk patterns affected by different aberrations is simulated using the pointby-point numerical simulation model.Anisoplanatic aberrations are simulated using different Zernike mode bases multiplied by aberration coefficients.
In the absence of aberrations, the GS algorithm generates a hologram that accurately reproduces the target patterns, as depicted in figure 5(a).However, when the effect of anisoplanatic aberrations is considered, the intensity of patterns generated by GS algorithm decreases significantly (figure 5(b)).Under the same aberrations, PAC-GS can generate patterns comparable in intensity to those without aberrations (figure 5(c)).
To quantify the performance of the GS and PAC-GS algorithms, we perform a statistical analysis of the intensity of disk patterns generated under different degrees of aberrations.Under the same degree of aberration, we generate five different groups of disk patterns, each group containing four disk patterns randomly distributed on the focal plane.The wavefront aberration introduced at each position is a single term randomly selected in the first six order Zernike polynomial bases multiplied by an aberration coefficient.The Zernike polynomial bases applied to patterns are different from each other in each group, which simulates anisoplanatic aberrations.The equivalent aberration degree is expressed by the same aberration coefficient.Our statistical results confirm that anisoplanatic aberrations lead to a reduction of pattern intensity which worsens with increasing aberration coefficient, while the intensity can be restored to the no-aberration level by using PAC-GS for aberration compensation (figure 5(d)).Notably, in some cases, the intensity of patterns generated by PAC-GS with anisoplanatic aberrations is higher than that generated by GS without aberration interference.As hologram search process is not able to guarantee an optimal solution under all conditions [21], some of conditions are change when anisoplanatic aberrations are introduced into the searching process, which leads to a better solution.

PAC-GS is effective for higher-order aberration compensation
Though patterns are usually affected by low-order aberrations in practice.To verify the performance of PAC-GS, in this section, we demonstrate that the PAC-GS algorithm can effectively correct higher-order aberrations at different locations if the aberrations can be accurately tested under simulation results.
Four disk patterns are defined at z = −75, −25, 25, 75 µm respectively, as shown in figure 6(a).The position corresponding to each pattern is affected by random aberrations, and the aberrations are different at various positions, as shown in figure 6(b).Figure 6(c) shows the intensity distribution of disk patterns generated by the PAC-GS algorithm under the influence of extreme aberrations which have clear boundaries at target positions.During the execution of PAC-GS, both the total intensity and uniformity of patterns increase with the iteration going on, and tend to converge, as shown in figures 6(d) and (e).The definition of uniformity is where I min and I max mean the intensity of the darkest and brightest patterns, respectively.Random aberrations can be regarded as an extreme case of phase distortion introduced by scattering medium.Successful compensation for random aberrations can also demonstrate aberration correction capabilities of PAC-GS in real scattering media, such as brain tissues.

Anisoplanatic aberrations compensation under GRIN lens
In this section, we detect aberrations at different sites experimentally and use different methods to compensate aberrations for multiple extended-patterns generated simultaneously under GRIN lens.The target patterns are defined as three beaded-ring patterns with radius of 5 µm located on the focal plane, and the maximum distance between patterns is 240 µm.
To detect aberrations, we first use the GS algorithm to generate holographic foci at target positions.Then, the Zernike mode based scanless AO method is employed to test the compensation phase at each position.As shown in figure 7, the holographic focus under GRIN lens is well compensated when adding corresponding compensation phase detected by AO, and the intensity is increased more than 10 folds compared with the original one.After the whole AO testing at each site, we found there is a big difference among aberrations at different target sites (figure 8(a)(i)).Without aberration compensation, the morphology of beaded-ring patterns could not be clearly seen (figure 8(b)).Then, types of aberration compensation methods are applied to improve the intensity of beaded-ring patterns under the GRIN lens.Compensating only the aberrations at a single site can make the pattern at that location recover well, but cannot recover the pattern at other locations (figures 8(e)-(g)).To attain global compensation, we average the compensation phases at different positions and superimpose the mean phase on the original hologram generated by GS.The average compensation phase can restore the pattern intensity at all sites to a certain extent (figure 8(c)), but the recovery effect is not as good as that of PAC-GS (figure 8(d)).
Based on experimental results, the intensity enhancement ratio of the compensated pattern can be calculated as where I 0 and I x are the intensity of the extended pattern before and after compensation at position x.Besides beaded-ring patterns shown in figure 8, the intensity enhancement ratio of foci at target positions can also be obtained since they are used as guide stars in the AO measurement.We change the positions of target beaded-ring patterns and corresponding foci for three times and test the intensity enhancement ratio of different compensation methods.The statistical results are shown in figure 9. PAC-GS has the highest rate of increase in all mode.For multiple foci generation, PAC-GS has an increase ratio of 12.88 ± 4.35 (mean ± sd) for the 'Mean' mode, while the increase ratio of 'GS + C mean ' is 5.92 ± 2.32.The increase ratio of PAC-GS is significantly better than that of other methods.For multiple beaded-ring pattern generation, PAC-GS has an increase ratio of 1.82 ± 0.17 (mean ± sd) for the 'Mean' mode, while the increase ratio of 'GS + C mean ' is 1.18 ± 0.21.This result shows that only correcting the aberration at the center can effectively improve the overall intensity of the extended pattern.However, the foci have a higher rate of increase, indicating that the foci and beadedring patterns are not exactly suffering the same aberrations.By developing better aberration detection methods for extended patterns, PAC-GS can give a greater advantage in aberration compensation.
For statistical results, if only a single pattern is investigated, such as P1, P2 or P3 in figure 9(a), the intensity of the generated pattern by GS + C P1 , GS + C P2 , or GS + C P3 is lower than or not significant to that of PAC-GS.For beadedring patterns, the aberrations are similar but not exactly the same as that of the foci located at their centers, so the aberration compensation effect of PAC-GS is decreased.Compared with other methods, the number of cases with no significant difference increased.It is worth noting that in figure 9(b), PAC-GS is significantly better than GS + Cmean for the mean intensity of multiple patterns, which proves the comprehensive performance of PAC-GS is better than other methods when multiple beaded-ring patterns are generated.

Discussion and conclusion
It should be noticed that in the AO measurement, due to experimental errors, limited terms of Zernike polynomials, and discrete Zernike polynomials, etc the measured compensation phases may not fully compensate the aberrations.Even so, we demonstrate that the intensities of all target patterns can be improved by the PAC-GS algorithm.On one hand, this indicates the robustness of the PAC-GS algorithm.On the other hand, if the aberrations corresponding to each target pattern can be detected by more accurate AO methods [35,36], they can be better compensated by PAC-GS, and thus the excitation efficiency of generated patterns can be further improved.
Different from the aberration control method based on serial aberration compensation (SAC-GS) algorithm [37], our framework of aberration compensation is faster.In SAC-GS, the holographic phase searching process is integrated with the AO test, while it is carried out separately in our work.Generating 10 foci with aberration compensation under one AO iteration of Zernike modes Z3-Z14 takes 26 min in SAC-GS.In contrast, generating three beaded-ring patterns with aberration compensation under three rounds of AO iterations of Zernike modes Z3-Z27 (excluding defocus) takes 5 min in PAC-GS.If the parameters are converted to one pattern, one Zernike base, and one iteration, it takes ∼14.18 s for SAC-GS, and takes ∼1.38 s for our method.For the extended pattern generation where CGH algorithm is used to locate the spatial positions [18,19], the advantage of PAC-GS in phase searching time is apparent.Besides, SAC-GS uses the multi-spot model while PAC-GS uses the fast Fourier transform model.When generating an extended pattern containing tens of pixels, SAC-GS needs to split the pattern into multiple pixels and calculate their intensity one by one, while PAC-GS calculates the entire intensity distribution of the pattern during each iteration.As a result, PAC-GS has a faster computing speed than SAC-GS when generating disk patterns containing hundreds of pixels, even though SAC-GS combines compressed sensing methods [31].
In order to perform aberration-corrected two-photon optogenetics in biological tissues, it is necessary to detect the aberration of target positions at the excitation wavelength of twophoton optogenetics.In previous reports [3,10], in order to verify the expression of options for optogenetics, options and fluorescent proteins for indicating (such as mCherry) are transgenically expressed on the same gene sequence.On the basis of this method, if an indicator fluorescent protein with the same excitation wavelength as that of the option, the fluorescence protein can be used as the guide star for aberration detection in tissues.
In summary, we propose a parallel compensation method of anisoplanatic aberrations in patterned photostimulation and demonstrate its performance by the generation of multiple extended patterns under GRIN lens.Further work would be the application of our method in deep tissue two-photon optogenetics based on GRIN lens in vivo.

Figure 1 .
Figure 1.Effects of anisoplanatic aberrations on holographic extended-patterns.(a) Ideal holographic extended-patterns.(b) Holographic extended-patterns when anisoplanatic aberrations exist.(c) Holographic extended-patterns when one local aberration is compensated.(d) Holographic extended-patterns when anisoplanatic aberrations at all sites are compensated.

Figure 2 .
Figure 2. Hologram searching process of PAC-GS.Before hologram searching, target patterns S 1 −Sn are defined near the back focal plane of the objective.A 0 is the amplitude of the incident light on SLM.For each iteration, Φm −1 is assumed as the phase of the incident light.During the transmission of incident light to each target pattern, the defocus phase φzn and aberration ϕn corresponding to each target need to be superimposed respectively.After Fourier transform, combination of the phase Θn,m with the amplitude of the target pattern Sn is performed.Then the corresponding aberration ϕn and defocus phase φzn are subtracted from the phase obtained after the inverse Fourier transform of the light field near the back focal plane.The hologram Φm after the iteration can be obtained by adding the phase calculated from each target light field together.In the next iteration, Φm becomes Φm −1 .

Figure 3 .
Figure 3. Scheme of the point-by-point numerical simulation model.The hologram Φm, the aberration ϕn and the position phase σ k are defined in xy Cartesian coordinate system and target patterns are in x k ′ y k ′ Cartesian coordinate system.The incident light is decomposed into multiple discrete points in a circular aperture in xy plane.For each point (x k ′ , y k ′) in target pattern Sn, the relative intensity is obtained by integrating the light field propagated from multiple discrete points in xy plane and then take the square of the magnitude, which could be calculated simply from equation (9).

Figure 4 .
Figure 4.The optical setup to detect aberrations and generate multiple holographic extended patterns with aberration compensation by PAC-GS.BE, beam expander; L, lens; M, reflective mirror; ZB, zero-order blocker; DM, dichroic mirror; obj, objective; F, filter; TL, tube lens.The dye pool is mounted on three-axis translation stages.

Figure 5 .
Figure 5. Generation of disk patterns with or without anisoplanatic aberrations compensation.(a) Patterns generated by GS.(b) Patterns generated by GS, with anisoplanatic aberrations.(c) Patterns generated by PAC-GS, with anisoplanatic aberrations.Scale bar: 10 µm.Aberration coefficient: 0.6 wave.(d) Statistical analysis of mean intensity of disk patterns under different conditions.The color bar and scale bar are consistent in (a-c).

Figure 6 .
Figure 6.Simulation results of PAC-GS performance under random distribution aberrations.(a) Intensity distribution and position of target disk patterns.Scale bar: 50 µm.(b) Random aberrations of patterns at target positions in (a).(c) Intensity distribution of generated patterns, where the arrows point to the magnification diagram of each pattern.(d), (e) The total intensity and uniformity of all patterns increase with the number of iterations.Dot at each iteration: the average value, Error line at each iteration: the standard deviation, solid line connected all dots: the trend line.

Figure 7 .
Figure 7. Effect of AO aberration compensation under the GRIN lens.(a) The focus before AO compensation.(b) The focus after AO compensation.(c) Intensity distribution before and after AO compensation.(d) Compensation phase distribution.Scale bar: 5 µm.

Figure 8 .
Figure 8. Compensation of anisoplanatic aberrations under the GRIN lens.(a) Holographic phase distribution calculated by GS and PAC-GS algorithm, and compensated phase detected by AO at different sites.Cmean is the average of C P1 , C P2 and C P3 .(b)-(g) Beaded-ring patterns generated by GS algorithm without aberration compensation, by the GS algorithm with mean phase compensation, by the PAC-GS algorithm and by the GS algorithm with single pattern compensation, respectively.Scale bar: 50 µm.(h) Enlarged view of each pattern in (b)-(g).Scale bar: 10 µm.(i) Coefficients of Zernike modes corresponding to different sites.(j)-(l) The comparison of the intensity of the lines in (h) at different sites.

Figure 9 .
Figure 9.The intensity enhancement ratios of different compensation methods for the foci (a) and beaded-ring patterns (b) under GRIN lens.P1-P3 represents the foci (or bead-ring patterns) at different positions.'Mean' represents the average value of all target patterns.The ratio paired t test of increase ratio between PAC-GS and other methods has been shown.ns: not significant, p > 0.05; * : 0.01 < p ⩽ 0.05; * * : 0.001 < p ⩽ 0.01.