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Abstract
Lensless imaging has recently become an alternative and cost-effective choice for many macro and micro applications, like wave-front sensing, fluorescence imaging, holographic microscopy, and so on. However, the polarized imaging, especially the cross-polarized light, has rarely been explored and integrated in lensless imaging methods. In this paper, we introduce the cross-polarized illumination into the lensless system for high-contrast and background-free imaging of plant samples. We capture a snapshot measurement and apply the blind deconvolution for reconstruction, obtaining the depolarized imaging of plant samples. Experiments exhibit the specific and sparse structures of the root system and vessel distribution of samples. We also build a corresponding lens-based system for performance comparison. This proposed lensless system is believed to have the potential in studies on the root development and water transport mechanism of plants in the future.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Lensless imaging scheme has been widely accepted as an alternatively computational imaging technique for both macro and micro purposes [1–3], mainly owing to its low cost, compact structure and high optical throughput (both high resolution and wide field of view). Recent progresses of lensless imaging focus on single-shot 3D imaging [4–6], pixel super-resolution microscopy [7–10], on-chip fluorescence microscopy [11,12], deep learning reconstruction [13–15], advanced algorithms [16–18], and applications like wave-front sensing [19] and lensless endoscope [20,21]. Among the many types of researches before, the polarized lensless imaging has rarely been investigated. Related works include using lensless polarization holography to quantitatively measure the polarization states of birefringent samples [22–24], and utilizing the interference of two light beams with a slightly different polarization direction to form a hologram for imaging reconstruction [25,26]. However, the cross-polarized light, a special polarized light which focuses on the detection of depolarizing signals from samples, has not been integrated in lensless systems yet for providing the high-contrast and background-free imaging within a single-shot.
Polarized light microscopy means a number of optical microscopy techniques involving polarized light, and has been widely used in imaging and characterizing the polarization characteristics of samples, such as the birefringent samples with crystal structures [27], and plant samples [28,29] like the root of Arabidopsis. Specifically, in the cross-polarized light imaging, two polarizers with a perpendicular orientation are used on the incident and transmitted (or reflected) lights. By blocking the transmitted lights with the same polarization direction as illumination, some transparent structures become apparent [30] and the glare and specular highlights can also be eliminated [31,32] under the cross-polarized light. This special kind of polarized illumination transfers the invisible depolarizing signals from samples into detection and visualization, allowing for an unobstructed view of subsurface pathology and a label-free imaging of some special structures of plant roots and vessels [33,34]. The cross-polarized light also shares the similarity with the dark-field illumination in the high-contrast and background-free imaging performance [35,36].
In this paper, we introduce the cross-polarized light into the lensless imaging system. We capture a single-shot raw measurement each time with depolarizing signals and apply a blind deconvolution algorithm for image reconstruction. Rather than using the traditional packaged polarizer, we put a commercially available and thin polarizer film (about 200 µm) between the sample and image sensor to block the transmitted lights and narrow the sample-to-sensor distance. Currently, researchers generally image fixed plant samples or microscopic slides for observation and study. However, the proposed method has the potential in the realization of a compact system for real-time observation of certain structures of plant samples, which are naturally growing in transparent culture dishes.
The contributions of our work mainly include:
- (1) We first introduce the cross-polarized light into the lensless imaging scheme. We use a thin polarizer film as the simple add-on into the existing lensless system for the high-contrast, label-free, and background-free imaging of plant samples.
- (2) We capture a single-shot raw measurement each time and apply a simple blind deconvolution for image reconstruction, which has a good potential for high-speed and computation-efficient imaging of dynamic processes.
- (3) The imaging performance of the proposed lensless scheme has a good consistency with the results of the correspondingly lens-based system, as demonstrated by the real experiments, which has good details in showing the sparse structures of the root system and vessel distribution of samples with depolarizing characteristics.
2. Methods
2.1 Schematic of system design
There are several optical structures for coherent and incoherent lensless imaging [1]. Among them, we choose the commonly used set-up with a LED light source and unit magnification. The sample is put as close as possible to the image sensor for a good imaging quality and resolution. We apply the single-shot acquisition and deconvolution imaging model in this work.
The optical schematic of the proposed cross-polarized lensless system is shown in Fig. 1(a), which mainly consists of the following parts: a white LED light source with a narrow-band color filter (could be substituted by monochrome LED), a linear polarizer, a sample to be imaged, a thin polarizer film and an image sensor. The only difference between our system and the traditional incoherent lensless imaging system is the two polarizers inserted in front and rear of the sample with a perpendicular orientation to each other. The two polarizers are used on the incident and transmitted lights respectively, as shown in Fig. 1(b). Under the cross-polarized light, the direct light through the sample will be blocked and only the depolarizing lights scattered from some special structure of samples can be detected by the imaging sensor. Without staining or labeling, these structures are invisible or unclear under the bright-field illumination, but our method can apparently distinguish these sparse signals. Besides, since the non-depolarizing light of the sample is blocked by the thin polarizer film, the detected image is with high-contrast and no background.
Fig. 1. (a) The optical schematic of our lensless imaging system. (b) The schematic of cross-polarized light, with a pair of polarizers in front and rear of the sample with a perpendicular orientation to each other.
2.2 Optical realization and imaging pipeline
The real optical structure of the cross-polarized lensless system used in experiments is shown in Fig. 2(a1). We first use a lens group, together with a narrow-band filter and a small pinhole, to produce the incident light, as the illumination path shown in the green box of Fig. 2(a1). A small pinhole is applied as the illumination aperture here to limit the illumination numerical aperture (NA) for a small enough defocus blur. The detailed analysis of illumination pinhole will be discussed in Section 4.
Fig. 2. (a1) The real optical set-up and (a2) the imaging pipeline of the proposed cross-polarized light lensless method are shown with the pseudo-color of hot green. We image the root of Arabidopsis as an example. (b1) We build up a corresponding lens-based system and (b2) capture images with the same field of view as the ground-truth.
The relay lens group in the illumination path decreases the diameter of light beam illuminating on the sample and improve the light intensity on each unit area. Then a pair of polarizers with the perpendicular polarization orientation is used to form the cross-polarized light for imaging. The detection path of the lensless system only consists of an image sensor, as shown in the yellow box of Fig. 2(a1). It should be noted that a thin polarizer film, rather than a commonly packaged polarizer, is adopted between the sample and sensor for a close sample-to-sensor distance. In addition, to build up a correspondingly lens-based optical system for performance comparison and ground-truth reference, we could replace the detection path of the lensless system by a simplified microscope (an imaging relay lens pair and the same detector), as shown in Fig. 2(b1).
We show the imaging pipeline of our proposed lensless method in Fig. 2(a2), while the lens-based ground-truth is presented in Fig. 2(b2). We image the root of Arabidopsis, a common model plant, as the example here. We capture both the single-shot bright-field and cross-polarized raw images by simply changing the polarized direction of the illumination polarizer. The captured raw measurements of the lensless system (both the bright-field and cross-polarized) are with certain defocus blurs, due to the sample-to-sensor distance (about 500 µm in our experiments). As labeled in Fig. 2(a2), we apply a blind deconvolution process [37] for the reconstruction of cross-polarized image, with an initial point spread function (PSF) based on the sample-to-sensor distance. As shown in Fig. 3(a), the main steps of blind deconvolution process include: (1) initial guesses of both PSF and object, (2) alternating iterations of PSF and object by keeping each other unchanged, and (3) obtaining of the deconvolved object image and restored PSF when reaching enough iteration times. For the bright-field lensless image, we can adopt a simple back-propagation of light wave (or other lensless phase retrieval algorithms [16–18]) to get the in-focus bright-field imaging. As shown in Fig. 3(b), we approximate the illumination as the normally incident parallel light in bright field lensless model and use the angular propagation equation in the near-field to recover the object image.
Fig. 3. Flowchart of reconstruction processes. (a) The blind deconvolution process of cross-polarized lensless image. (b) The back-propagation process of bright field lensless image, where $. \times $ means the dot multiplication of matrices, ${\cal F}$ and ${\cal F}^{ - 1}$ are the Fourier transform pair, j is the imaginary unit, ${k_0} = 2\pi /\lambda$ is the wave number, $\lambda $ is the wavelength of light, ${k_x}$ and ${k_y}$ are coordinate matrices in Fourier domain and ${\ast}$ is the conjugate operator.
The cross-polarized images are shown with the pseudo-color of hot green. Two parallel vessels of the root can be obviously distinguished under the cross-polarized light in both the deconvolved lensless imaging and lens-based imaging with no background, as shown in the close-ups marked by white boxes in Fig. 2. The structures are also well matched with the bright-field imaging, as shown in the merged images in Fig. 2(a2) and (b2). As experimentally demonstrated here, the sparse structure of signals under cross-polarized light makes a simple blind deconvolution efficient enough for a high-quality lensless reconstruction. Therefore, the imaging pipeline of our proposed method is easy to perform and computation-efficient. Our proposed single-shot lensless imaging method is more suitable for thin plant samples.
3. Results
3.1 Experimental set-up
We built up both the lensless and lens-based systems for performance test in real experiments. We use the image sensor (Image Source DMM 27UJ003-ML USB 3.0 monochrome board camera) with 1.67 µm pixel size and 3872(W)*2764(H) pixels for measurement acquisition. The white LED lamp in use has a wide bandwidth and thus we insert a narrow-band filter (532 nm central wavelength and 3 nm spectral bandwidth, Thorlabs) for providing the illumination. We use a lens group with a small pinhole in the illumination path. The illumination relay lens pair in use performs a 10:3 minification of the light beam. A pair of polarizers is also added to the optical system. Specifically, on the illumination side, we use a nanoparticle linear polarizer (Thorlabs, LPVISA050-MP2) for a high extinction ratio (over 106:1 at 532 nm wavelength). While on the detection side, a commercially available and thin polarizer film (Nitto Denko, about 200 µm thickness and over 104:1 extinction ratio at 532 nm wavelength) is applied in between the sample and image sensor for a short sample-to-sensor distance, in order to achieve an acceptable resolution and imaging quality. Our scheme can be used as a simple and cheap add-in to different kinds of lensless systems, since this thin polarizer film is very cheap (about 15 USD for 400 cm2 size). Compared to the lensless system, the lens-based optical set-up just applies an imaging lens pair (with 1:1 magnification, 25.4 mm diameter and 75 mm efficient focal length) before the image sensor, resulting in about 0.167 NA and 1.6 µm resolution under 532 nm wavelength light, as shown in Fig. 2(b1). It should be noted that we use different pseudo-colors (hot green in Fig. 2 and Fig. 7, and neon blue in Fig. 4 and Fig. 5) for cross-polarized imaging of different samples to ensure a high imaging contrast. Besides, for the cross-polarized lensless imaging reconstruction, we use the blind deconvolution function in Matlab [37]. The achievable field of view (FOV) of this work has about 3.13 mm diameter, which is determined by the size of light beam on the sample plane.
Fig. 4. Imaging of the fern stem cross section. The cross-polarized images are shown in the second column and colored in neon blue.
Fig. 5. Imaging of the fiber whole-mount. The cross-polarized images are shown in the second column and colored in neon blue.
3.2 Imaging of plant samples
We image some plant samples using our method, including the fern stem cross section in Fig. 4 and the fiber whole-mount in Fig. 5. These sample slides are bought from the AOXING Laboratory Equipment. As the images shown in Fig. 4, we can see clearly the vessel distribution of the fern stem cross section in the cross-polarized light images (the second column), with high-contrast and no background. The blind deconvolution step makes a good improvement to the lensless raw imaging. The sparse structures in neon blue also match well with the features in the bright-field imaging. The lens-based results (the first row) are presented here as the ground-truth. In Fig. 4, we can witness the similar imaging performance of the fiber whole-mount using our method. It should be noted that, compared with the correspondingly lens-based image, the deconvolved lensless image under cross-polarized light has a slight difference in some areas. An example is shown in the close-up images in Fig. 5, marked by arrows in white boxes. Some signals at other axial depths become faded off or even disappeared after lensless reconstruction, which we think may come from the reconstruction artifacts of blind deconvolution or because the imaging planes of these two methods are not completely matched.
From the above experiments, we can find that the recovered lensless imaging under cross-polarized light has a good imaging quality, and shares fine consistency with the ground-truth images provided by the lens-based system. We acknowledge that the recovered bright-field image of lensless system has a minor improvement from the raw measurement, due to the lack of phase information and the single-shot acquisition scheme. A commonly used multi-acquisition scheme can solve this problem, but it might be beyond the scope of this work. Besides, although the samples imaged in this work are all assumed to have a thin slice, the proposed method can be extended to 3D imaging of thick samples by capturing an image stack with axial movements of the image sensor at the cost of time resolution. Theoretical analysis of the 3D PSF of the cross-polarized lensless model under different illumination NAs needs to be studied in order to derive a 3D deconvolution algorithm for reconstruction, which can be a future research direction.
3.3 Resolution analysis
Our method is a new and specific lensless imaging technique, which shares some similarities with the lensless fluorescence imaging [12,38–40]. As an incoherent imaging model, its spatial resolution is mainly limited by the defocus blur, which is caused by the sample-to-sensor distance. In order to improve the resolution, we use a small illumination NA and a short working distance (less than 500 µm) to reduce the defocus blur, together with a deconvolution process. The resolution of our method can be further improved by accomplishing a more compact system with a narrower sample-to-sensor distance or a more advanced reconstruction algorithm.
To measure the achievable resolution, we image polystyrene beads with 9.51 µm diameter (Bangs Laboratories Inc.) for spatial resolution analysis of the proposed cross-polarized lenslss imaging. We dilute the beads 10000 times with water and put a small drop of the mixed liquid on the slide. We directly cover the liquid drop with the thin polarizer film and then start imaging. After capturing the single-shot measurement of beads, we first do deconvolution to 15 selected beads from the whole FOV. We normalize the gray values of images before and after deconvolution respectively and calculate the full width of half peak (FWHM) of these beads. We estimate the single point resolution by using the mean FWHM value of beads after deconvolution. As shown in Fig. 6(a), the achievable result is about 5.89 pixels, which is equal to 9.84 µm (5.89 pixels*1.67 µm/pixel). The average FWHM is consistent with the true size of the beads (9.51 µm) in use. As the examples of two selected beads shown in Fig. 6(a), the deconvolution step can improve the imaging resolution obviously. It should be noted that the actual resolution (or the resolution limit) of our method is hard to tell, since the sparsity of samples, sample-to-sensor distance (defocus blur), the efficiency of deconvolution, and the signal-to-noise ratio (SNR) all play important roles in determining the resolution. We use experiments of beads here to verify the achievable resolution is better than 9.84 um. The measuring of resolution limit needs smaller size beads, which, however, cannot generate strong enough signals for detecting. We can use more efficient methods in the future to measure the resolution limit of our system, like using an image sensor with higher photon efficiency and with pixel binning function or utilizing other quantitative samples with a small size instead of the beads in use.
Fig. 6. Resolution analysis using polystyrene beads with 9.51 µm diameter. We test both (a) the single point resolution and (b) the two-point resolution of the cross-polarized lenslss imaging. (a) The single point resolution is estimated by calculating the average FWHM of 15 selected beads after deconvolution. The result is about 5.89 pixels, which is equivalent to 9.84 µm and is consistent with the true size of the beads (9.51 µm) in use. Two selected beads are shown as examples here. (b) The two-point resolution is calculated as follows: (1) shift the raw image of each bead with different pixels (11∼14, with 0.1 step), (2) add the shifted image to the original image, (3) do deconvolution to the sum image, and (4) analyze the resolvable intervals of two beads using the Rayleigh criterion and record corresponding shifts. The average shift (for the resolvable two-point intervals) of 15 selected beads is about 12.58 pixels, equivalent to 21.39 µm two-point resolution. Two selected beads are also shown here as examples.
We also calculate the two-point resolution of the proposed method, by operating the following steps for all the 15 selected beads: (1) we shift the raw image of each bead with different pixels (11∼14 pixels, with 0.1 pixel each step), (2) we add up the shifted image and the original image to a combined image, (3) we do deconvolution to the combined image, and (4) we analyze the resolvable intervals using the Rayleigh criterion and record current shifts as the two-point resolution of beads. As shown in Fig. 6(b), the average two-point resolution of 15 selected beads is about 12.58 pixels, equivalent to 21.39 µm (12.58 pixels*1.67 µm/pixel). Detailed information of two certain beads are shown as examples in Fig. 6(b). The achievable two-point resolution is much worse than the single point resolution, indicating that the deconvolution model of lensless scheme in use is more suitable for imaging sparse structures. But for the dense distribution of samples, the imaging quality will rapidly worsen. Besides, the noises of the shifted image and original image are added up, which may be another reason for the drop of the two-point resolution.
4. Discussion
As mentioned before, the illumination NA greatly affects the imaging quality of the proposed method, since we use a deconvolution imaging model in this work. A larger NA illumination will introduce a larger blur kernel and result in a bad imaging performance after deconvolution, especially when the sample-to-sensor distance cannot be ignored here (about 500 µm). In fact, if we can further narrow the sample-to-sensor distance to accomplish the on-chip lensless microscopy [11,12], a large illumination NA applied in our method will have the advantages of high light intensity and high SNR without sacrificing the resolution and imaging quality.
We analyze the effect of illumination NA by imaging the lotus leaf tissue section (AOXING Laboratory Equipment) as an example in Fig. 7. We use different pinhole sizes to adjust the illumination NA at 0.033, 0.027, and 0.018 respectively. The different results of the cross-polarized lensless imaging are shown in Fig. 7(a), compared with the lens-based imaging result as the ground-truth in Fig. 7(b). We can find that the cross-polarized images (both the raw images and deconvolved images in hot green) become shaper with the decrease of the pinhole size. We note that we use different initial PSFs here for different illumination pinholes to perform the blind deconvolution. The sharpest deconvolved imaging can be obtained when the smallest pinhole aperture is in use, which matches with the details of the lens-based result best. The smallest pinhole aperture used here is corresponding to the quasi-parallel illumination applied in all the former experiments of this work.
Fig. 7. The effect of illumination NA. (a) The lensless imaging results of the lotus leaf tissue section with different illumination pinhole sizes. (b) The lens-based imaging result as the ground-truth.
In current lensless reconstruction, we use a guessed PSF (based on the sample-to-sensor distance) as the initial input and apply a simple blind deconvolution to process the raw image. The theoretical distribution of the cross-polarized PSF needs further analysis. A more precise solution to the inverse problem can then be derived with sparse constraints for a better reconstruction performance, even for a large illumination NA with a high light intensity. Besides, replacing the 3 nm narrow-band filter in use with a wide-band filter (10∼30 nm for example) could improve the SNR of imaging.
5. Conclusion
In this paper, we introduce the cross-polarized light into the lensless system for imaging plant samples. By simply using a blind deconvolution algorithm to the single-shot measurement, we obtain high-quality reconstruction with a high-contrast and background-free imaging property. The proposed method is suitable for label-free imaging and observation of specific and sparse structures of plant samples within a snapshot. It also provides a possibility for the multi-mode lensless microscopy by combing with other lensless imaging techniques, especially if we can integrate these different lensless techniques in a compact optical realization. We believe our method has the potential in real-time observation and study of plant development and water transport mechanism in the future.
Funding
National Natural Science Foundation of China (61627804, 62071219); Natural Science Foundation of Jiangsu Province (BK20190292).
Acknowledgments
The authors thank Bin Wang for sample preparation of Arabidopsis.
Disclosures
The authors declare no conflicts of interest.
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