Lateral resolution enhancement of confocal microscopy based on structured detection method with spatial light modulator

He Ni; Limin Zou; Qingyuan Guo; Xuemei Ding

doi:10.1364/OE.25.002872

1. Introduction

Breaking the diffraction barrier becomes the main purpose of the various optical super-resolution methods which have come up during recent years, including stimulated emission depletion microscopy (STED) [1], structured illumination microscopy (SIM) [2,3]. There are two major principles of these methods, respectively, narrowing the point spread function (PSF) and increasing the optical transfer function (OTF) bandwidth [4]. Besides, stochastic optical reconstruction microscopy (STORM) [5], and photo activated localization microscopy (PALM) [6] make the most of switching individual molecules stochastically and sparsely to distinguish two close molecules. All these the above methods lead to a huge breakthrough in fluorescence imaging resolution, yet each method has its due limitations. PALM and STORM take considerable time to switch the states of molecules, slowing down the imaging speed. Despite the fast speed, STED requires matching excitation and depletion wavelengths as well as a high-power-density STED beam.

The structured detection theory roots in the structured illumination principle and the concept of resolution enhancement is similar to the Moiré fringes. Through obtaining images with the illumination mask at different positions, it doubles the conventional microscopes cut-off frequency. Besides, it is greatly improved by resorting to other methods [7–10]. The structured illumination method can be applied in fluorescence imaging. However, the wide-field spatially structured illumination patterns require complex manipulation of the pattern generator such as grating and it is not suitable in confocal scanning laser microscopy. Lateral resolution of confocal microscopes should be better than conventional microscope [11], yet it is limited by the size of the pinhole. In a confocal microscope, reducing the size of the pinhole can enhance the resolution [12]. However, this also decreases the signal-to-noise ratio. In order to keep a balance of them, the size of pinhole is generally large and matches the laser beam Airy disk diameter, leading to a lower lateral resolution than the ideal result. Super-resolution laser scanning microscopy is realized by two approaches [13], respectively, scanning patterned illumination (SPIN) microscopy and scanning patterned detection (SPADE) microscopy. These approaches mainly use temporal and spatial modulations in point-scanning microscope. SPADE has already been justified by virtual structural detection [14, 15]. In this system, CCD is applied to obtain the spot images of every scanning position, and these images are processed on computer through adding a virtual pinhole and multiplying the detection function sequentially. Subsequently, the image of sample is reconstructed on the basis of the processed data [16]. However, the image of every scanning spot is necessary, resulting in a limited scanning rate.

In view of the above disadvantages, this paper attempts to propose a method of lateral resolution enhancement in structured detection confocal microscope (SD-CM) by using spatial light modulator (SLM). This method achieves higher resolution and faster imaging rate in comparison with the existing methods of the large pinhole confocal microscope system. According to the experimental results, it can be found that its resolution is 1.6 times higher than ordinary confocal microscope with the same scanning rate. In the present method, illumination arm is the same with the one in confocal microscope. The spot is modulated by the detection function displayed on SLM in detection arm and then received by the photoelectric detector and converted to a voltage signal proportional to the intensity of the modulated spot. The photoelectric detector, as well as SLM and pinhole, functions as CCD in virtual structural detection system. We reconstruct the image in accordance with the voltage signal. The system coherent transfer function (CTF) of this method expands, representing a higher spatial resolution than before and paralleling the spatial resolution of virtual structural detection system. In addition, the system processing rate increases hugely and it is not limited by CCD like in virtual structural detection system.

2. Confocal microscopy with structured detection

A conventional confocal microscope system is shown in Fig. 1. In a practical confocal system only one lens is used. As a result, a single lens works as the illumination and collection lens.

Fig. 1 The schematic of the basic confocal microscope system.

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Assuming that the distance between the objective lens and the source equals the one between the objective lens and the sample, indicating that the objective and collection lens magnification is 1. If a finite-size detector, is placed in the detection plane, the confocal microscope amplitude distribution in detection plane can be expressed as

A (r) = \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} h_{1} (r_{1}) o (r_{s} - r_{1}) h_{2} (r_{1} + r_{2}) d r_{1} D (r_{2}) d r_{2} .

In the Eq. (1), $h_{1}$ , $h_{2}$ is the amplitude point spread function (APSF) of objective and collection lens. The object function is denoted by $o (r)$ . $D (r_{2})$ is the detection function and $r_{s}$ is the scanning position. In confocal system, $h_{1}$ equals to $h_{2}$ , so both can be written as $h$ . When the object is a single point object, the microscope behaves as a coherent microscope with an APSF given by

A P S F (r_{s}) = h (r_{s}) \times [h (r_{s}) \otimes D (r_{s})] .

The point detector used in confocal microscopy system makes it possible to produce a 1.4 times enhancement in the transverse direction over the conventional microscopy [17]. However, the actual pinhole size cannot be infinitely small. In addition, the resolution is also limited by signal noise ratio (SNR) in the confocal microscope. In order to meet the requirement of SNR, the size of the pinhole cannot be quite small, leading to a reduced lateral resolution. The trade-off results in the marginal enhancement in lateral resolution. To solve the problem, structured detection is introduced to confocal microscope system in this method.

Different from structured illumination, structured detection multiplies the laser beam spot and detection function in detection arm instead of illumination arm, accomplished by SLM in our method. In VSD, it is realized numerically using images obtained by CCD. The image displayed on SLM is provided in Fig. 2 which is generated from detection function. Besides, the pinhole function of conventional confocal microscope is illustrated in Fig. 2(a). It is a circular pinhole mask whose radius is $r_{d}$ . However, the detection function of confocal microscope with structured detection is different, which modulates the spot in the circle in a way shown in Fig. 2(b). The transmittance fits the two-dimensional cosine distribution.

Fig. 2 Pinhole of conventional confocal system and structured detection system (a) standard pinhole (b) pinhole with detection function.

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When the defocus distance is 0 in confocal coherent system, the intensity PSF [16] can be expressed as:

I P S F (r_{s}) = {| h (r_{s}) \times [h (r_{s}) \otimes D (r_{s})] |}^{2} .

To lift the cut-off frequency, the detection function in this system is depicted as

m (x, y) = A + 2 \cos (2 π f_{0} x) + 2 \cos (2 π f_{0} y) .

If $A = 0$ and $f_{0}$ equals the cut off frequency, the detection function is

D (x, y) = circ (\frac{\sqrt{x^{2} + y^{2}}}{r_{d}}) \times m (x, y) .

In one dimension,

D (x) = rect (\frac{x}{r_{d}}) m (x) = {\begin{cases} 2 \cos (2 π f_{0} x), \begin{matrix}  \end{matrix} x < r_{d} \\ \begin{matrix}  \end{matrix} \begin{matrix}  \end{matrix} \begin{matrix}  \end{matrix} {\begin{matrix}  \end{matrix}}_{} 0 \begin{matrix}  \end{matrix} \begin{matrix}  \end{matrix} \begin{matrix}  \end{matrix} \begin{matrix}  \end{matrix}, \begin{matrix}  \end{matrix} o t h e r s \end{cases} .

\begin{matrix} ℱ {D (x)} = [\frac{J_{1} (2 π r_{d} f_{x})}{f_{x}}] \otimes [δ (f_{x} - f_{0}) + δ (f_{x} + f_{0})] \\ = [\frac{J_{1} (2 π r_{d} (f_{x} - f_{0}))}{f_{x} - f_{0}}] + [\frac{J_{1} (2 π r_{d} (f_{x} + f_{0}))}{f_{x} + f_{0}}] . \end{matrix}

In the Eq. (7), $J_{1}$ is the first-order Bessel function and $ℱ$ denotes Fourier transform operator. Because the spot is modulated by SLM on hardware, the detection function cannot take negative numbers. To obtain the modulated images when the direct current (DC) component is 0, we take two pictures through using two different detection functions separately and composite them together to reconstruct the images. In one dimension, the detection functions are as follows:

D_{1} (x) = rect (\frac{x}{r_{d}}) m_{1} (x) = {\begin{cases} 2 + 2 \cos (2 π f_{0} x), \begin{matrix}  \end{matrix} x < r_{d} \\ \begin{matrix}  \end{matrix} \begin{matrix}  \end{matrix} \begin{matrix}  \end{matrix} \begin{matrix}  \end{matrix} {\begin{matrix}  \end{matrix}}_{} 0 \begin{matrix}  \end{matrix} {\begin{matrix}  \end{matrix}}_{} \begin{matrix}  \end{matrix} \begin{matrix}  \end{matrix} \begin{matrix}  \end{matrix}, \begin{matrix}  \end{matrix} o t h e r s \end{cases} .

D_{2} (x) = rect (\frac{x}{r_{d}}) m_{2} (x) = {\begin{cases} 2, \begin{matrix}  \end{matrix} x < r_{d} \\ 0, \begin{matrix}  \end{matrix} o t h e r s \end{cases} .

The two different detection functions result in two images with different intensity distribution. According to Eq. (3), through taking the square root of the two images and subtracting the second one from the first one, we can reconstruct the modulated amplitude image without DC component. And then the intensity image can be obtained from a square operation. The reconstructed modulated amplitude image can be expressed as:

A (x) = h (x) \times {h (x) \otimes [D_{1} (x) - D_{2} (x)]} = h (x) \times [h (x) \otimes D (x)] .

Based on the IPSF, the simulation results of structured IPSF are presented in Fig. 3. In the simulation, the illumination wavelength $λ$ is 632.8 nm, the numerical aperture of the objective and collector lenses NA is 0.1, the frequency of the cosine structure $f_{0}$ is $N A / λ$ , and the detection $r_{d}$ is $0.61 λ / N A$ .

Fig. 3 Normalized IPSF of confocal microscope (CM) and structured detection confocal microscope (SD-CM) with same size pinhole.

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According to Fig. 3, the full width at half-maximum (FWHM) in SD-CM decreases to 0.57 times of the one in conventional confocal microscope. It is obvious that structured detection can be combined with confocal microscope to achieve higher resolution.

In frequency domains, CTF determines the highest frequency that can pass through this system. Low frequency stands for the contour information while high frequency represents details. To improve the lateral resolution, both of the cut off frequency and the proportion of high frequency should be increased. The frequency spectrum of cosine function refers to an impulse function at its corresponding frequency. SD-CM lifts the ratio of high-frequency information through taking the advantage of frequency-shift property of the impulse function.

Then, the CTF of x-direction is the Fourier transform of the system APSF. According to Eq. (2), in one dimension it is given as:

C T F (f_{x}) = C T F_{1} (f_{x}) \otimes {C T F_{2} (f_{x}) \times ℱ [D (x)]} .

The SD-CM CTF can be calculated as

C T F_{SD-CM} (f_{x}) = rect (f_{x}) \otimes {rect (f_{x}) \times [\begin{array}{l} \frac{J_{1} (2 π r_{d} (f_{x} - f_{0}))}{(f_{x} - f_{0})} \\ + \frac{J_{1} (2 π r_{d} (f_{x} + f_{0}))}{(f_{x} + f_{0})} \end{array}]} .

Here, $C T F_{1}$ and $C T F_{2}$ are the CTFs of illumination and collection arms. The collection arm consists of collection lens and SLM, which is presented in Fig. 4.

Fig. 4 CTF of system (a) CTF of wide field microscope (WM), confocal microscope (CM) and structured detection confocal microscope (SD-CM). The simulation wavelength λ is 632.8nm, NA of objective and collection lenses are 0.1. The frequency of structured detection function $f_{0}$ is $N A / λ$ , and the detection $r_{d}$ is $0.61 λ / N A$ . (b) CTF of illumination arm in SD-CM. (c) Fourier transform of detection function in SD-CM. (d) CTF of collection arm in SD-CM. (e) CTF of SD-CM system.

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The simulation results in frequency domains are presented in Fig. 4(a). According to the null point of CTF, the cut off frequencies of CM and SD-CM are equal. They are two times higher than wide field microscope, indicating that the theoretical resolution is enhanced by a factor of two. Despite the same cut-off frequency, the ratio of high frequency information in SD-CM is obviously higher than it in CM, which suggests that the greater ability of transferring high frequency information in SD-CM.

In the simulation result, Figs. 4(b)-4(e) account for how the CTF of SD-CM is obtained in the simulation. It is the convolution of the modulated CTF of collection arm and the CTF of illumination arm. The CTF of illumination arm remain unchanged. However, the CTF of collection arm becomes the product of its collection lens CTF and the Fourier transform of detection function which can be applied to the SD-CM. In our method, the Fourier transform of detection function is the sum of two Bessel functions, as shown in Fig. 4(c). The reason is that the detection function is a cosine function and it only exists in the circle shown in Fig. 2(b). It contributes to the improvement of high-frequency ratio.

3. Modulation of the light spot by SLM

In the VSD system, the application of CCD slows down the processing speed due to too many required images corresponding to every scanning spot. In the present method, SLM accomplish the structured detection in a hard-ware way through directly modulating the focused Airy disk.

The normalized structure detection functions are:

m_{1 D} (x, y) = \frac{1}{2} [1 + \cos (2 π f_{0} x)] .

m_{2 D} (x, y) = \frac{1}{2} [1 + 0.5 \times \cos (2 π f_{0} x) + 0.5 \times \cos (2 π f_{0} y)] .

The experimental results are showed in Fig. 5.

Fig. 5 The result of spot modulated by SLM. (a) and (d) are structured functions, (b) and (e) are modulated results by VSD, (c) and (f) are modulated spot by SLM.

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To obtain the Figs. 5(b) and Figs. 5(e), two steps are needed. At first, we display an image whose value of each pixel is 255 on SLM and use a CCD to capture spot image. Then the spot image is modulated by processing like VSD. And Figs. 5(c) and Figs. 5(f) are the images captured by CCD when the structured function is displayed on SLM. In this process CCD is placed in the detection plane. The correlation coefficient between the image in theory and experiment is close to 1. The correlation coefficient between Figs. 5(e) and Figs. 5(f) is 0.8619, indicating that the relativity is obvious. As a result, we can draw the conclusion that SLM achieves to modulate the spot in both directions. Another advantage refers to that the pinhole size can be changed without the adjustment of the hard ware. The pinhole radius is determined by the image displayed on SLM in Fig. 2(b).

Considering the non-linear property of SLM, it is essential to correct the imperfection in calculation with the support of the calibration data. Figure 6 shows how non-linear the SLM is in the experiment. In the calibration, the illumination intensity is maintained constant and the grey value of image sent to SLM ranges from 0 to 255. Besides, the transmission function f is introduced to express the relation of the transmission efficiency T and the input grey value g:

Fig. 6 Relationship between grey value and transmission efficiency of SLM.

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T = f (g) .

g = f^{- 1} (T) .

It is challenging to give the specific formula expression of f. However; there still remains a monotonic increasing relationship. Therefore, we establish a look-up table between T and g to amend the non-linear error.

4. Experimental system and result discussion

4.1 Experimental system

We illustrate a schematic diagram of the structured detection based on laser scanning confocal microscope in Fig. 7. A single mode He-Ne laser (25 LHP 991, Melles Griot), with wavelength λ = 632.8 nm is applied to produce polarized laser. Besides, a pair of galvo mirrors (GVS002, THORLABS) is used to steer the focused laser across the specimen in order to generate two-dimensional (2D) images. With the aim to control the vignetting effect, scanning lens (TSL-633-30-100, RONAR-SMITH) and tube lens (ITL200 Thorlabs) are applied to this system. The reflected light from the sample is descanned by the 2D (X and Y) scanning system, and is relayed to the modulating plane on SLM (RLE-CH04 Reallight). According to the image displayed on it, the SLM modulates the amplitude. The image is generated by the structured detection function. In the present experiment, the structured detection function fits cosine function and the pinhole radius equals to the radius of Airy disc. Through using a 4X infinity achromatic objective with numeric aperture (NA) 0.1, the diffraction limited imaging resolution is 6.33 μm. Linearly polarized light with specific polarization direction is required based on SLM and it is accomplished by polarizer 2. Optical attenuator and polarizer 1 aims at reducing the light intensity. The goal of 10x lens is to magnify the spot to improve the modulated performance because the SLM pixel size is too big. The sample in the experiment is standard optical target (negative USAF 1951 1X, Edmund) and the purpose of the aperture is to remove the natural light that may affect the output of PMT (PMM02 Thorlabs).

Fig. 7 SD-CM microscope. (a) The schematic diagram of experimental set up (b) The set-up picture of SD-CM. The SLM consists of 1024 × 768-pixels whose size are 26μm and its transmission efficiency is higher than 0.3. The theoretical resolution of this system without structured detection is 6.33 μm.

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4.2 Result discussion

The reconstructed images are shown in Fig. 8. The sample is standard optical target (negative USAF 1951 1X, Edmund) and the four images are obtained in the system shown in Fig. 7(b). The only difference between them refers to that the image displayed on SLM. To obtain the Figs. 8(a) and Figs. 8(c), we send the Fig. 2(a) to SLM, indicating that those two pictures are obtained in conventional confocal microscope. For Figs. 8(b) and Figs. 8(d), the image displayed on SLM is Fig. 2(b). The pinhole is determined by the image displayed on SLM and it is the same with the Airy disc on this plane. The comparison of the images in Fig. 8 reveals that a significant increase in image contrast is achieved when structured detection function is applied to the confocal system. Obviously, more details are resolved in SD-CM judging from Fig. 8.

Fig. 8 Implementation of the structured detection imaging on the resolution test target. (a) and (c) Image of the test target acquired by conventional confocal microscope. (b) and (d) Reconstructed super-resolution image by SD-CM.

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The period of the grating in rectangle 1 and rectangle 2 in Figs. 8(a) and Figs. 8(b) of this test target is 4.4 μm. And in rectangle 3 and rectangle 4 in Figs. 8(c) as well as Figs. 8(d), the period is 3.9 μm. In rectangle 5 and rectangle 6, it is 3.5μm. Conventional confocal microscope was not able to resolve these gratings, as presented in Fig. 9. By contrast, the bars could be differentiated in both x (Figs. 9(a) and Figs. 9(c)) and y (Figs. 9(b) and Figs. 9(d)) directions. However, the bars could not be distinguished in x direction in rectangle 5 (Figs. 9(e)) while the bars could be distinguished in y direction in rectangle 6 (Figs. 9(f)). This is the result of the different properties in x and y directions of SLM. The resolution improvement is confirmed by Fig. (9). In x direction, the resolution is improved to 3.9 μm. In y direction, the resolution is improved to 3.5 μm according to the results of the experiment. However, we can also see that the normalized intensity value of background is lower while the resolution is improved. This is caused by side lobe in PSF. Because this method decreases the FWHM at the cost of side lobe enhancement in Fig. 3.

Fig. 9 Normalized intensity curves of conventional confocal microscope and structured detection confocal microscope in specified areas. (a) Normalized intensity along x direction of the area specified by rectangle 1 in Figs. 8(a) and Figs. 8(b). (b) Normalized intensity along y direction of the area specified by rectangle 2 in Figs. 8(a) and Figs. 8(b). (c) Normalized intensity along x direction of the area specified by rectangle 3 in Figs. 8(c) and Figs. 8(d). (d) Normalized intensity along y direction of the area specified by rectangle 4 in Figs. 8(c) and Figs. 8(d). (e) Normalized intensity along x direction of the area specified by rectangle 5 in Figs. 8(c) and Figs. 8(d). (f) Normalized intensity along y direction of the area specified by rectangle 6 in Figs. 8(c) and Figs. 8(d).

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Briefly, the SD-CM has been experimentally proved to break the diffraction limit. The theory indicated that the SD-CM was able to enhance the lateral resolution through using a factor of two. Experimental imaging of optical target (Fig. 8 and Fig. 9) confirmed that the SD-CM demonstrated detailed structures that were not detectable in conventional confocal microscope.

5. Conclusion

To conclude, this paper proposes a new method to achieve structured detection through using spatial light modulator in confocal microscope. In the experimental system, the lateral resolution is 1.6 times higher than conventional confocal microscope. The microscope setup uses inexpensive devices and is a simple add-on to conventional laser scanning confocal microscopes. According to the achieved simulation results, the width of the CTF expands, representing a higher spatial resolution than before. In comparison with SIM in which the illumination is modulated, this method applies SLM to modulate the amplitude distribution of spot in detection arm. Compared with VSD, in which structured detection is accomplished by the reconstruction of a series of picture obtained by CCD, this method completes structured detection based on SLM and photoelectric detector. The system processing speed increases without the limitation of CCD. As a result, the detection rate of the system would be effectively improved. Besides, the rate of the system is 20 FPS while the image size is 250X250 pixels, reaching the video rate.

Funding

National Natural Science Foundation of China (NSFC) (51575142); Natural Science Foundation of Heilongjiang Province (E201423).

Acknowledgment

We thank Professor Zhengjun Liu for discussion and revision of the paper.

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Lateral resolution enhancement of confocal microscopy based on structured detection method with spatial light modulator

Abstract

1. Introduction

2. Confocal microscopy with structured detection

3. Modulation of the light spot by SLM

4. Experimental system and result discussion

4.1 Experimental system

4.2 Result discussion

5. Conclusion

Funding

Acknowledgment

References and links

Cited By

Figures (9)

Equations (16)

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