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Abstract
This research presents a coherent structured illumination single-pixel imaging scheme to image objects with complex amplitudes. By utilizing a phase-only spatial light modulator for phase modulation, we can efficiently generate the Hadamard basis structured light and the reference light that interfere with each other to form the coherent structured illumination. Using the 4-step phase-shifting, the spectrum of the object is acquired by detecting the zero-frequency component of the object light with a single-pixel photodetector. The desired complex-amplitude image can be further retrieved by applying an inverse Hadamard transform. The proposed scheme is experimentally demonstrated by imaging two etched glass objects, a dragonfly wing, and a resolution test chart. Benefiting from the phase modulation, this scheme has a high efficiency, a high imaging quality, a high spatial resolution, and a simple and stable configuration to obtain both the phase and amplitude information of the target object. The proposed scheme provides a promising complex-amplitude imaging modality with single-pixel detection. Thus it might find broad applications in optical metrology and biomedical science.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Single-pixel imaging (SPI) is an emerging computational imaging technique that uses a single-pixel detector to acquire the spatial information of an object [1]. In SPI, the object is sequentially measured using structured illumination or structured detection. The image is reconstructed by correlating the structured patterns with the signals recorded by the single-pixel detector. Compared to pixelated imaging devices, the single-pixel detectors have higher detection sensitivities, broader spectral responsivities, and more precise timing resolutions. Thus, SPI has a great advantage in low light environments [2–4], three-dimensional imaging [5–7], multispectral imaging [8–13] and non-visible wavelengths, such as terahertz [14–18], infrared [19–21], and X-ray range [22–25]. Meanwhile, orthogonal basis scan algorithms are well introduced into the SPI, which largely accelerates the data acquisition and improves the imaging quality [26–30]. Benefiting from these advantages, various applications of SPI have been proposed in the fields of optical microscopy [31,32], imaging through scattering media [33,34], and optical encryption [35,36].
Conventional SPI typically uses intensity modulation for structured illumination or structured detection, which can acquire the amplitude images. In order to simultaneously retrieve the amplitude and phase of an object, complex-amplitude modulation has been adopted for SPI in recent years. One way is to introduce complex-amplitude modulation in Mach-Zehnder interferometer or Michelson interferometer, and to image the object with complex amplitude by a single-pixel detector [37–42]. Another way is to introduce complex-amplitude modulation in common-path interferometric structure for complex-amplitude imaging [43–49]. This configuration is more compact and stable. It neither requires an external reference optical path nor introduces additional phase distortion. A number of SPI schemes have been proposed, all of which use complex-amplitude modulation but do not require any reference light. The complex-amplitude images are calculated by the phase retrieval algorithms [50–55]. Benefiting from the advantages of single-pixel detectors, the complex-amplitude single-pixel imaging (CSPI) is becoming a novel imaging modality in the fields of optical microscopy [45], optical metrology [49], and biomedical science [42].
To pursue an ultra-high modulation rate, digital micromirror devices (DMDs) are often used for complex-amplitude modulation. As an amplitude-mode SLM, to perform complex-amplitude modulation, DMDs require the use of binary hologram encoding techniques, such as Lee hologram [56], superpixel method [57]. However, this approach has the following drawbacks: (1) the diffraction efficiency of the binary-encoded amplitude holograms is very low, which severely limits the imaging system efficiency; (2) the binary hologram encoding techniques often come at the expense of individual pixels, which reduces the imaging spatial resolution; (3) the reference light introduction method and the phase shifting mechanism are both sophisticated, which increases the complexity of modulation. In cases where fast imaging is not required, a phase-mode SLM, such as the liquid-crystal-on-silicon spatial light modulator (LCoS-SLM), is more competitive than DMD for complex-amplitude modulation, which can avoid all drawbacks mentioned above.
Here, we propose an elegant and efficient CSPI scheme using coherent structured illumination. In this CSPI scheme, a phase-only LCoS-SLM is used to perform complex-amplitude modulation on the collimated laser beam. In the reflected light from the LCoS panel, the modulated part forms the structured light, while the unmodulated part serves as the reference light. The structured light and the reference light travel along the same path, resulting in common-path interference to form the coherent structured illumination. Unlike previous CSPI methods using phase-mode SLMs [38,44], which adopted an external reference beam or selected the field outside region of interest as the reference beam, our proposal utilizes the unmodulated laser beam as the reference beam which is elegant and efficient. To avoid quadratic phase factors, a $4f$ system is employed to image the coherent structured illumination onto the target object. The Hadamard basis scan technique is adopted to achieve high-quality imaging. Using the 4-step phase-shifting technique, the complex-valued spectrum of the object is acquired by detecting the zero-frequency component of the object light with a single-pixel photodetector. The desired complex-amplitude image can be further retrieved by applying an inverse Hadamard transform. Our experimental images for different etched glass objects and a dragonfly wing demonstrate that our coherent structure illumination idea provides a novel CSPI scheme with a high efficiency, a high imaging quality, a high spatial resolution, and a simple and stable experimental configuration.
2. Methods
2.1 Schematic of our CSPI
The schematic of our proposed CSPI system is depicted in Fig. 1. A He-Ne laser is employed as the light source to emit a vertically linearly polarized laser beam with a diameter of $2$ mm and a wavelength of $632.8$ nm. A round continuously variable neutral density filter (NDF) is used to adjust the intensity of the laser beam. A half wave plate (HWP) is used to rotate the vertically linearly polarized laser beam into a horizontally linearly polarized laser beam for phase modulation by a SLM. A spatial filter system (SF) with a microscope objective and a pinhole aperture is used to remove additional spatial noise from the laser beam to produce a spatial uniform spherical wavefront. A plano-convex lenes (L$_0$) is used to collimate the diverging spherical wavefront into a parallel light beam. The collimated beam passes through a 50:50 non-polarizing cube beamsplitter (BS) and is incident on the LCoS microdisplay panel of a phase-only SLM (Pluto-Vis, Holoeye). The LCoS panel has a resolution of $1920\times 1080$ pixels and a pixel pitch of $8$ µm. According to the displayed image which is generated by a personal computer (PC), the LCoS panel will modulate the phase of the reflected light to generate the corresponding structured light. However, because the LCoS has about $80\%$ modulation efficiency, there is still some unmodulated light in the reflected light that can be utilized as reference light. The structured light and the reference light travel along the same path, resulting in common-path interference to form the coherent structured illumination. Two achromatic doublet lenses (L$_1$, L$_2$) with a focal length of $30$ cm and an aperture of $50$ mm are used to form a $4f$ system. The coherent structured illumination light is reflected by the BS and enters the $4f$ system. An iris diaphragm (DIA) is used to remove the high order diffracted light from the LCoS pixelated panel itself and other stray light. The LCoS panel and the target object are located in the input and output planes of the $4f$ system, respectively. Thus, the $4f$ system can image the coherent structured illumination generated by the LCoS onto the target object without the quadratic phase factor. The transmitted light from the target object passes through a collecting lens (L$_3$) with a focal length of $30$ cm and an aperture of $75$ mm and then reaches the pinhole filter (PH). Since the object and the pinhole filter are located at the front and rear focal planes of the collecting lens, the Fourier spectrum of the transmitted object light is obtained at the pinhole plane. A suitable aperture size is selected to allow only the zero-frequency component of the object light to pass through the pinhole filter. A photodetector (SPD) (PDAPC2, THORLABS) as the single-pixel detector collects the zero-frequency light from the PH. The resulting output of the photodetector is fed to the PC via a data acquisition board (DAQ) (USB-205, Measurement Computing).
Fig. 1. Schematic of CSPI with coherent structured illumination. NDF, neural density filters; HWP, half wave plate; SF, spatial filter system; L$_0$, collimating lens; BS, non-polarizing beamsplitter; DIA, iris diaphragm; SLM, spatial light modulator; LCoS, liquid-crystal-on-silicon panel of the SLM; L$_1$, L$_2$, achromatic doublet lenses; O, target object; L$_3$, collecting lens; PH, pinhole filter; SPD, single-pixel photodetector; DAQ, data acquisition board; PC, personal computer.
To achieve high-quality and efficient imaging, the Hadamard single-pixel imaging uses a complete set of Hadamard orthogonal basis patterns for illumination. Since the Hadamard basis matrices are phase-only matrices, the corresponding structured patterns can be obtained directly by phase modulation under coherent illumination. Therefore, the Hadamard basis scan is adopted for the presented CSPI scheme.
2.2 Hadamard basis scan for the CSPI
The two-dimensional Hadamard transform pair is defined as
where $\boldsymbol {f}$ represents the spatial sampling matrix of the complex transmittance of the target object, $\boldsymbol {F}$ represents the Hadamard spectrum matrix of $\boldsymbol {f}$, $\boldsymbol {H}$ denotes the Walsh-ordered Hadamard matrix, and $N$ is the order. It is worth noting that $\boldsymbol {f}$ needs to be a square matrix which should be on the order of $N$.The complete set of Hadamard basis matrices can be generated as follows
Since the elements of the Hadamard basis matrix $\boldsymbol {P}_{uv}$ take either $+1$ or $-1$, it is a phase only matrix. When the LCoS panel displays the corresponding image, the complex amplitude of the reflected light from the LCoS panel will have the form of $E_0\boldsymbol {P}_{uv}$, where $E_0$ is the amplitude of the modulated light. In addition, the complex amplitude of the directly reflected light from the LCoS panel can be expressed as $E_re^{-j\phi _r}$, where $E_r$ and $\phi _r$ are the amplitude and the initial phase of the reference light, respectively. Therefore, the complex amplitude of the interference field can be written as
where $\boldsymbol {1}$ denotes a matrix with all elements being $1$ and the same dimension as $\boldsymbol {P}_{uv}$. When the target object is illuminated by this coherent structured light, the intensity of the zero-frequency component of the transmitted object light measured by the photodetector can be expressed as where $\eta$ represents the quantum efficiency of the photodetector, and $\ast$ denotes complex conjugate. Substituting Eq. (5) into Eq. (6) and then considering $\boldsymbol {P}_{00}=\boldsymbol {1}$, $D(u,v)$ can be expanded asA 4-step phase-shift method is used for the Hadamard spectrum acquisition. Firstly, by shifting the phase of the Hadamard basis matrix $\boldsymbol {P}_{uv}$ by $0,\,{\pi }/{2},\,{\pi },\,{3\pi }/{2}$, respectively, we obtain a set of phase-shifted basis matrices
Using the structured light modulated by the phase-shifted basis matrix $\boldsymbol {P}^{(\varphi )}_{uv}$ to illuminate the target object, the response of the photodetector is denoted as ${D}^{(\varphi )}(u,v)$. By differential calculation, we can obtain
2.3 Noise suppression in image reconstruction
As can be seen from Eq. (11), the acquisition of the Hadamard spectrum using a 4-step phase shift is essentially a differential operation. This can effectively remove the background noise. However, in practical experiments, the background noise cannot be completely eliminated due to the phase modulation error of the LCoS-SLM, the nonlinear response of the photodetector, low frequency vibrations, etc., which would greatly affect the reconstructed image quality. Therefore, we need to perform noise suppression during the reconstruction of the image. Here, we adopt the noise suppression strategy proposed by Xiao et al. [58]. In a practical case, the measured Hadamard spectrum can be expressed as
where $\boldsymbol {b}$ denotes the residual background noise matrix. If we directly perform inverse Hadamard transform on the measured spectrum $\boldsymbol {F}'$, we obtain where $\boldsymbol {B}=\boldsymbol {H}\boldsymbol {b}\boldsymbol {H}$ represents the Hadamard spectrum of the residual background noise matrix. Through extensive experiments, we find that the residual background noise is dominated by the DC component, accompanied by a slow and small fluctuation. Thus, the influence of the residual background noise on the measurement of each spectrum coefficient is basically uniform, but its influence on the reconstructed image is not uniform. The energy of the slow-varying background noise is mainly concentrated in the upper left corner of the reconstructed image. Therefore, when the target object has no energy distribution at the upper left corner, the background noise can be separated out as a reasonable estimate.For clarity, we take the estimate of the spectrum of the residual background noise as
Finally, the noise-suppressed image is obtained by performing an inverse Hadamard transform on the estimate $\boldsymbol {\hat {F}}$.
3. Results
We experimentally demonstrate the complex-valued imaging ability on two etched glass objects and a dragonfly wing. In all experiments below, we set the imaging resolution $N\times N$ to be $128\times 128$ pixels. In this case, to obtain appropriate spatial resolution and field of view (FOV) without adjusting the $4f$ system, we can represent the Hadamard basis matrices by using $m\times m$ LCoS pixels for each element. This operation can be called digital zoom. These digitally zoomed Hadamard basis patterns are imaged onto the object by the $4f$ system. Although this coherent imaging is affected by the effective aperture of the $4f$ system, the pixel size of the structured light fields does not change. Since the effective aperture is large enough in our experiments, all basis patterns in the whole set of the Hadamard basis patterns can be imaged onto the object by the $4f$ system. In this case, the spatial resolution of this CSPI depends on the pixel size of the structured light field on the object (see Supplement 1, Sections 2 and 3 for details). As the magnification of the current $4f$ system is $1$, the spatial resolution and the FOV are $md\times md$ and $mdN\times mdN$, respectively, where $d=8$ µm is the pixel pitch of the LCoS. For the two etched glass objects, we first take $m=3$ to cover the entire etched pattern. For the glass plate etched with a logo and the dragonfly wing, we further take $m=2$ to observe the local details of the target objects. In these experiments, we set $\rho _b=\sqrt {10}$ for noise suppression during image reconstruction.
3.1 Etched glass object imaging
In the first experiment, we use a glass plate (JGS2 fused quartz) etched with the letters HBU, as the target object. As shown in Fig. 2(a), the total width of the three letters is $2.6$ mm, and the etching depth for all letters are uniform as $715$ nm. The phase difference introduced by etching can be expressed as
where $h$ denotes etching depth, $\lambda$ denotes the light wavelength, and $n$ denotes the refractive index of the glass plate at the light wavelength. For a wavelength of $632.8$ nm light, the refractive index of the glass plate is $1.457$. If the phase of the white unetched region is $0$, the phase of the green etched region is $1.03\pi$ ahead. The complex transmittance of the phase object takes the values shown in Fig. 2(b), where $f_{\mathrm {G}}$ and $f_{\mathrm {W}}$ denote the complex transmittance value of the green etched region and the complex transmittance value of the white unetched region, respectively. The glass plate etched with letters HBU can be regarded as a simple binary phase object.Fig. 2. The glass plate etched with HBU. (a) Geometry diagram of the etched letters. (b) The values of the complex transmittance for a wavelength of $632.8$ nm light.
Since the phase of the complex transmittance is wrapped in $(-\pi,\,\pi ]$, during the calculation of the reconstructed image, we should choose an appropriate zero-phase reference point to clearly show the phase distribution of the object. For the glass plate etched with HBU, we choose the real axis and the imaginary axis as ${\textrm{Re}} ^\prime$ and ${\textrm{Im}} ^\prime$ in Fig. 2(b). In this case, the reconstructed real and imaginary images are shown in Figs. 3(a) and 3(b), respectively. The corresponding amplitude and phase images are shown in Figs. 3(c) and 3(d), respectively. The macro photograph of the imaging region captured by a CMOS camera (MER-130-30UM, DAHENG IMAGING) under white light is shown in Fig. 3(e). It can be seen that the reconstructed amplitude image agrees with the macro photograph. The phase profile along the highlighted line in Fig. 3(d) is shown in Fig. 3(f). From Figs. 3(d) and 3(f), it can be seen that the reconstructed phase image using our CSPI are clear and accurate. The values of all images except the phase image (curve) are linearly scaled to $[0,\,1]$ for display.
Fig. 3. Experimental results of the letters on etched glass plate with $3\times$ digital zoom. The (a) real and (b) imaginary images obtained with our CSPI. The corresponding (c) amplitude and (d) phase images. (e) The macro photograph captured by a CMOS camera. (f) The measured phase profile along the highlighted line in (d). See Data File 1 in Dataset 1, Ref. [60] for underlying values.
In the second experiment, we challenge this CPSI scheme with a multi-valued phase object with rich details, a glass plate etched with the logo of Hebei University. As shown in Fig. 4(a), the diameter of the logo is $3$ mm, and the etching depths in the red, green and blue regions are $372$ nm, $715$ nm, $1051$ nm, respectively. For a wavelength of $632.8$ nm light, the complex transmittance takes the values shown in Fig. 4(b), where $f_{\mathrm {R}}$, $f_{\mathrm {G}}$, $f_{\mathrm {B}}$, $f_{\mathrm {W}}$ denote the complex transmittance values of the red, green, blue, and white regions in Fig. 4(a), respectively.
Fig. 4. The glass plate etched with the logo of Hebei University. (a) Geometry diagram of the etched logo. (b) The values of the complex transmittance for a wavelength of $632.8$ nm light.
For the glass plate etched the logo, we choose the real axis and the imaginary axis as ${\textrm{Re}} ^\prime$ and ${\textrm{Im}} ^\prime$ in Fig. 4(b). In this case, the reconstructed real and imaginary images are shown in Figs. 5(a) and 5(b), respectively. The corresponding amplitude and phase images are shown in Figs. 5(c) and 5(d), respectively. The macro photograph is shown in Fig. 5(e). The phase profile along the highlighted line in Fig. 5(d) is shown in Fig. 5(f).
Fig. 5. Experimental results of the logo on etched glass plate with $3\times$ digital zoom. The (a) real and (b) imaginary images obtained with our CSPI. The corresponding (c) amplitude and (d) phase images. (e) The macro photograph captured by a CMOS camera. (f) The measured phase profile along the highlighted line in (d). See Data File 2 in Dataset 1, Ref. [60] for underlying values.
As seen in Fig. 5, the overall imaging quality is high. However, there is a loss of some details in the reconstructed images, for example, the Chinese characters in the central region of the logo. We zoomed in on this region with $2\times$ digital zoom, and the experimental results are shown in Fig. 6. Digital zoom makes it easy to translate between acquiring the overall structure images and acquiring local details images.
Fig. 6. Experimental results of the logo on etched glass plate with $2\times$ digital zoom. The (a) amplitude and (b) phase images obtained with our CSPI. See Data File 3 in Dataset 1, Ref. [60] for underlying values.
3.2 Dragonfly wing imaging
In the third experiment, we use a dragonfly wing as the target object, to test the imaging capability of this CSPI scheme for natural biological tissues. As shown in Fig. 7(a), the wing is mainly composed of veins and membranes. The membranes are thin films with high transmittance, while veins are much thicker than the membrane and with low transmittance. Thus, a dragonfly wing is a typical complex-valued object. The macro photograph of the dragonfly wing in the imaging region captured by the CMOS camera under white light is shown in Fig. 7(b).
Fig. 7. The dragonfly wing. (a) A photograph of the wing. The red box indicates the imaging region. (b) The macro photograph of the wing in the imaging region captured by a CMOS camera.
Figure 8(a) shows the reconstructed amplitude image of the dragonfly wing in the imaging region using our CSPI, which is consistent with the macro photograph displayed in Fig. 7(b). Figure 8(b) shows the reconstructed phase image, and Fig. 8(c) shows the three-dimensional surface of phase distribution. From the phase distribution, we can further infer the thickness change of each membrane. The phase distribution shown in Fig. 8 is wrapped, and further detailed analysis requires phase unwrapping operation, which also should take into account the continuity of the membrane thickness on both sides of the vein.
Fig. 8. Experimental results of the dragonfly wing with $2\times$ digital zoom. The (a) amplitude and (b) phase images obtained with our CSPI. (c) The corresponding three-dimensional surface of phase image (b). See Data File 4 in Dataset 1, Ref. [60] for underlying values.
4. Discussion
4.1 Spatial resolution of the CSPI
The spatial resolution of the imaging can be easily adjusted by digital zoom. However, in practice, when $N=128$, the size of the basis pattern display on the LCoS is only $1.024\times 1.024$ mm$^2$ with $1\times$ digital zoom. In this case, the utilization of the collimated laser beam is very low, which is unfavorable for the following photoelectric detection, and thereby reduces the signal-to-noise ratio of the imaging. One solution to this issue is to combine digital zoom with optical zoom. Here optical zoom refers to adjusting the magnification of the $4f$ system, by choosing an appropriate lens pair [42]. We replace the rear lens L$_2$ in the $4f$ system, as shown in Fig. 1, with an achromatic doublet lens with a focal length of $10$ cm and an aperture of $50$ mm. As a result, the magnification of the $4f$ system becomes $0.33$, and the spatial resolution could reach $5.33$ µm for $m=2$. Figure 9 shows the experimental results of the logo on etched glass plate with $2\times$ digital zoom and $0.33\times$ optical zoom, where (a) and (b) show the amplitude image and phase image of the local details of the middle region of the logo, respectively. It can be seen that the combination of the two zoom methods enables the CSPI with both high spatial resolution and high imaging quality.
Fig. 9. Experimental results of the logo on etched glass plate with $2\times$ digital zoom and $0.33\times$ optical zoom. The (a) amplitude and (b) phase images obtained with our CSPI. See Data File 5 in Dataset 1, Ref. [60] for underlying values.
It should be noted that the spatial resolutions given above are theoretical values. In practice, the achievable spatial resolution is larger due to lens aberrations, vibrations and noise, etc. We use the USAF-1951 resolution test chart as the target object to quantify the achievable spatial resolution of our CSPI experimental system. Figure 10 shows the experimental results of the test chart with $2\times$ digital zoom and $0.33\times$ optical zoom, where (a) and (b) show the amplitude image and phase image, respectively. As shown in the red box in Fig. 10(a), group $6$ element $1$ can be resolved at most. Thus the achievable spatial resolution is about $7.81$ µm, which is $2.48$ µm larger than the theoretical value. This gap can be narrowed by improving the experimental conditions.
Fig. 10. Experimental results of the USAF-1951 resolution test chart with $2\times$ digital zoom and $0.33\times$ optical zoom. The red box indicates group $6$ element $1$. See Data File 6 in Dataset 1, Ref. [60] for underlying values.
Different from the DMD-based coherent structured illumination imaging scheme [39,40,45,49], the $4f$ system has no spatial filtering function in this CSPI scheme. It simply images the structured illumination fields generated by the LCoS onto the target object without the quadratic phase factor. Therefore, we can replace the $4f$ system with a microscopic objective and then compensate for the quadratic phase factor from the microscopic objective by adjusting the collecting lens and the pinhole filter. This will make the imaging system more compact and stable, providing a promising way for complex-amplitude microscopy.
4.2 Imaging time of the CSPI
In above experiments, the imaging resolution is set to be $128\times 128$ pixels. The total number of the phase-shifted Hadamard basis matrices is $128\times 128\times 4=65536$, in which the factor of $4$ comes from the 4-step phase shift. For each basis pattern, a significant amount of time is required for the data acquisition. There are two major limitations: the response time of the LCoS-SLM and the data sampling duration. In our experiments, it takes about $0.1$ s from loading a basis pattern to its stable display. The sampling duration needs to be long enough to eliminate the fluctuation introduced by the LCoS-SLM phase flicker. Meanwhile, a sufficiently long sampling duration is also required to reduce the fluctuations caused by environmental changes. Taking into account all the above limitations, the actual imaging times for the images shown in Figs. 3, 5, 6, 8, 9, and 10 are $526$ min, $660$ min, $526$ min, $216$ min, $524$ min, and $523$ min, respectively. Such a long imaging time severely limits the practical application of the proposed CSPI scheme, especially for imaging active biological tissues. With the current experimental setup, a practical solution to this issue is to adopt under-sampling technique [29]. For less detailed objects, the number of the basis patterns to be measured can be greatly reduced by under-sampling, resulting in a significant reduction in imaging time. Figure 11 shows the experimental imaging results and the corresponding imaging times $t$ of the glass plate etched with letters at different sampling ratios $R$. To ensure high imaging quality while minimizing the introduction of noise, we use the hyperbolic under-sampling strategy [13], and set the highest spatial frequency of the background noise $\rho _b=8$ during image reconstruction. As seen in Fig. 11, the imaging time can be considerably reduced by reducing the sampling ratio without significantly sacrificing the imaging quality. When imaging at a sampling ratio of $4\%$, it takes $21$ min to acquire a clear phase image. If an LCoS-SLM with faster response speed and smaller phase flicker is used, the imaging time will be further reduced. In addition, this issue can also be tackled by efficient phase shifting techniques, such as the polarization phase shifting technique [59].
Fig. 11. Experimental under-sampling imaging results of the glass plate etched with HBU at different sampling ratios. See Data File 1 in Dataset 1, Ref. [60] for underlying values.
5. Conclusion
In conclusion, we propose and experimentally demonstrate an efficient CSPI scheme by utilizing a phase-only SLM to generate coherent structured illumination and a single photodetector to record the zero-frequency component of the object light. Our experimental results show that this CSPI scheme has a high imaging quality, and can accurately acquire the amplitude and phase distribution of the target object. The experimental configuration is very stable, thus ensuring image acquisition for up to several hundred minutes. The spatial resolution and FOV can be easily adjusted by digital zoom. Combined with the optical zoom, the achievable spatial resolution is up to $7.81$ µm in our experiments. This approach is universal for various wavelengths, and can be extended to other wavelengths, where array detectors are expensive or even unavailable, such as terahertz, infrared, and X-ray range. Our work makes an important step towards high-quality complex-amplitude imaging using a single-pixel detector. This CSPI technique might find broad applications in optical metrology and biomedical science.
Funding
Natural Science Foundation of Hebei Province (F2019201446, F2021201016); Start-up Research Grant of University of Macau (SRG2019-00174-IAPME); The Science and Technology Development Fund from Macau SAR (FDCT) (0062/2020/AMJ); Advanced Talents Incubation Program of the Hebei University (8012605); National Natural Science Foundation of China (11204062, 11674273, 61774053, 62105091).
Acknowledgments
The authors are grateful to Huan Zhou for her helpful discussions and suggestions. The numerical simulation was supported by the High-Performance Computing Center of Hebei University.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available in Dataset 1 (Ref. [60]).
Supplemental document
See Supplement 1 for supporting content.
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