Anti-laser interference methods for compressive spectral imaging based on grayscale coded aperture

Hao Zhang; Hao Zhang; Qing Ye; Qing Ye; Qing Ye; Ke Sun; Ke Sun; Yangliang Li; Yangliang Li; Yunlong Wu; Yunlong Wu; Haiping Xu; Haiping Xu; Haoqi Luo; Haoqi Luo; Haoqi Luo

doi:10.1364/OPTCON.504219

1. Introduction

Hyperspectral imaging collects a large amount of spatial and spectral information of a scene across multiple wavelengths [1,2]. It has found applications in a variety of fields such as environmental monitoring, geological exploration, biological chemistry, and so on [3]. Traditional spectral imaging systems, such as whisk and push broom scanners require a time-consuming scanning process [2]. To overcome this limitation, researchers combined compressive sensing with spectral imaging and proposed coded aperture snapshot spectral imager (CASSI), which captures 3D spectral data cube with just a single or several snapshots 2D measurements [2,4]. As shown in Fig. 1, the spectral scene is spatially encoded by the coded apertures and then different spectral slices are shifted by the dispersive prism and captured by the detector [4,5]. The detector receives encoded aliasing measurement data from different bands of the target scene. Subsequently, the 3D spatio-spectral data cube of the scene can be reconstructed from the 2D measurements using CS reconstruction algorithms [6,7].

Fig. 1. Sketch of the CASSI system under laser interference

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At present, there have been many researches on CASSI technology to improve the re-construction accuracy of CASSI system. A set of coded aperture optimization approaches and reconstruction optimization algorithms are proposed to improve the reconstruction quality for idealized conditions [8–12]. However, in order to apply CASSI technology to practical applications in the future, complex imaging environment must be considered. In addition to the light and dark brightness changes caused by various natural light sources, intense artificial interference such as laser has also existed [13,14].

CASSI system employs CCD or CMOS sensors to acquire hyperspectral compressive measurements. When CASSI system is irradiated by intense laser, the compressive measurements may exceed the sensor’s saturation level. Thus, sensor will inevitably be dazzled, leading to the loss of sampling information, thereby reducing reconstruction accuracy of spectral images. To avoid saturation of image sensor and reduce the impact of laser interference, the coded apertures can be used to modulate the incident light of the system. Traditionally, binary coded apertures are used in CASSI systems. However, their entries only can take two binary values 0 and 1, which limits the degree of modulation freedom.

In order to improve the modulation freedom of the incident light to avoid sensor saturation, this paper proposes grayscale coded apertures, which is designed according to the information of CASSI measurements. The entries of the coded apertures are updates in real time feedback according to the previously acquired measurements to reduce sensor saturation, thus improving the anti-laser interference threshold of the CASSI system which pioneering laser protection in CASSI system. This paper is organized as follows: first, the imaging model of CASSI system under laser interference is established. Then, the grayscale coded aperture design method is proposed. Finally, simulations are conducted to illustrate that spectral image reconstruction quality of CASSI system can be improved using grayscale coded apertures under laser interference.

2. Theoretical modeling

The laser interference under non-damage condition is manifested as the saturation of the area centered on the incident laser spot on the image plane, or the large area bright screen caused by saturation overflow of photoelectrons. This paper focuses on the non-damage scenario and establishes the imaging model of CASSI under laser interference.

Figure 1 is the sketch of CASSI system under laser interference. It images a target scene with spectral density ${f_\textrm{0}}(x,y,\lambda )$, and an interference laser field $U(x,y,\lambda )$ on the sensor. Suppose $f^{\prime}(x,y)$ is the two-dimensional superimposed signals of different spectral images detected by the sensor and $U^{\prime}(x,y)$ is the intensity of the interference laser incident on the sensor through the focusing of the lens. Then, the measured intensity distribution on the sensor of CASSI system under laser interference can be expressed as $I(x,y) = f^{\prime}(x,y) + U^{\prime}(x,y)$. In the following, we will analyze $f^{\prime}(x,y)$ and $U^{\prime}(x,y)$, respectively.

2.1 Imaging model of CASSI

Let ${f_0}(x,y,\lambda )$ represent the spatio-spectral density of the target. The target scene passes through the imaging lens 1 and is imaged on the coded aperture. The target scene is modulated by the coded aperture in spatial domain. Subsequently, the modulated spectral data is dispersed by the dispersion element, and then projected onto the FPA sensor through the imaging lens 2. Thus, the discretized compressive measurement in the kth snapshot can be written as [1,2,15]

(1)$${\textbf Y}_{i,j}^k = \sum\limits_{l = 0}^{L - 1} {{{\textbf F}_{i,j + l,l}}} {\textbf T}_{i,j + l}^k + \boldsymbol{\mathrm{\omega}}_{i,j}^k$$

where ${\textbf F} \in {R^{N \times M \times L}}$ is the 3D spatio-spectral data cube of the target scene with ${{\textbf F}_{i,j,l}}$ denoting the voxel at the spatial coordinate (i, j) of the lth spectral band in the data cube; ${\textbf Y} \in {R^{N \times (M + L - 1)}}$ is the measurement with ${\textbf Y}_{i,j}^k$ denoting the measured intensity of the (i, j) th sensor pixel at the kth snapshot; ${\textbf T}$ is the coded aperture with ${\textbf T}_{i,j}^k$ denoting the transmittance of the (i, j)th pixel on the kth coded aperture; $\boldsymbol{\mathrm{\omega}}$ denotes the noise on the sensor [2]. Equation (2) can be further reformulated into a vectorial form as [1,2,16]:

(2)$${\boldsymbol y}_{}^k = {\textbf H}_{}^k{\boldsymbol f} + \omega _{}^k$$

where ${\boldsymbol y}_{}^k$, ${\boldsymbol f}$, and $\omega _{}^k$ are the vectorized representations of ${\textbf Y}_{}^k$, ${\textbf F}$, and $\boldsymbol{\mathrm{\omega}}_{}^k$ in Eq. (1), respectively. ${\textbf H}_{}^k$ is the system matrix representing the effect of the kth coded aperture and the dispersion prism [2].

Taking into account K snapshots, the forward imaging model can be formulated as ${\boldsymbol y} = {\textbf H}{\boldsymbol f} + {\boldsymbol \omega }$, where ${\boldsymbol y = }{\textrm{[(}{{\boldsymbol y}^1}{)^T},{\textrm{(}{{\boldsymbol y}^2})^T},\ldots ,{\textrm{(}{{\boldsymbol y}^K})^T}]^T}$ and ${\bf H}{\boldsymbol = }{\textrm{[(}{{\bf H}^1}{)^T},{\textrm{(}{{\bf H}^2})^T},\ldots ,{\textrm{(}{{\bf H}^K})^T}]^T}$. Suppose the spectral data cube is highly correlated across spatial and spectral domains, and is sparse in basis ${\bf \Psi }$. Then, ${\boldsymbol f}$ in Eq. (2) can be represented as ${\boldsymbol f} = {\bf \Psi }{\boldsymbol \theta }$, where ${\boldsymbol \theta }$ is the coefficient vector with few nonzero elements in the basis ${\bf \Psi }$. Then,

(3)$${\boldsymbol y} = {\textbf H}{\bf \Psi }{\boldsymbol \theta } + \omega$$

In CASSI, the matrix ${\textbf H}$ has the structure shown in Fig. 2, It can be observed that the ${\textbf H}$ matrix is sparse and highly structured, which consists of a set of diagonal patterns determined by the coded aperture entries ${\textbf T}_{i,j}^k$, and repeated in the horizontal direction. Notice that ${\textbf A} = {\textbf H}{\bf \Psi }$ is the sensing matrix.

Fig. 2. Structure of the H matrices (K = 2, N = M = 6, L = 3) for the random coded aperture

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2.2 Transmission model for the interference laser

Figure 1 shows the transmission of interference laser through CASSI. The interference laser field $U(x,y,\lambda )$ is illuminated on the sensor. Suppose $U^{\prime}(x,y)$ is the intensity of the laser incident on the sensor through the focusing of the lens. The formation of $U^{\prime}(x,y)$ is formulated as follows.

• An interference Gaussian laser beam propagates to the front surface of imaging lens 1;
• The laser beam reaches the coded aperture through imaging lens 1 and then modulated by the coded aperture. The distance between imaging lens 1 and the coded aperture is ${l_1}$;
• The coded Gaussian beam propagates through imaging lens 2 and is received by the sensor with image distance of ${l_3}$.

Suppose the beam waist of the interference laser is ω₀ and the distance between the beam waist of the interference laser and front-surface of imaging lens 1 is d. The complex amplitude distribution on the surface of imaging lens 1 is [14,17–19]:

(4)$$U_1^{}({x,y} )= {A_0}\frac{{{\mathrm{\omega }_0}}}{{\mathrm{\omega }(d )}}\textrm{exp}\left( { - \frac{{{r^2}}}{{{\mathrm{\omega }^2}(d )}}} \right)\textrm{exp}\left\{ { - i\left[ {\frac{{2\pi }}{\lambda }\left( {d + \frac{{{r^2}}}{{2R(d )}}} \right) - \textrm{arctan}\left( {\frac{{\lambda d}}{{\pi \mathrm{\omega }_0^2}}} \right)} \right]} \right\}$$

where λ is the laser wavelength; $k = {\raise0.7ex\hbox{${2\pi }$} \!\mathord{/ {\vphantom {{2\pi } \lambda }} }\!\lower0.7ex\hbox{$\lambda $}}$ is wave number; $r = \sqrt {x_{}^2 + y_{}^2} $ is the spacial radial position; ω(d) and R(d) are the spot size and the equiphase surface curvature radius of the wavefront on the front-surface of imaging lens, respectively [20]:

Then, the laser beam reaches the coded aperture through imaging lens 1. Under Fresnel approximation, the complex amplitude distribution on the front surface of the coded aperture is [21]:

(5)$$\begin{array}{l} {U_2}({x,y} )= \frac{{\textrm{exp}({ik{l_1}} )}}{{i\lambda {l_1}}}\textrm{exp}\left[ {i\frac{k}{{2{l_1}}}({x_{}^2 + y_{}^2} )} \right]{\kern 1pt} {\kern 1pt} \\ \cdot {\kern 1pt} \int\!\!\!\int {U_1^{}({\xi ,\eta } )\textrm{exp}\left[ { - i\frac{k}{{2{f_1}}}({x_{}^2 + y_{}^2} )} \right]\textrm{exp}\left[ {i\frac{k}{{2{l_1}}}({{\xi^2} + {\eta^2}} )} \right]\textrm{exp}\left[ { - i\frac{k}{{{l_1}}}({\xi x + \eta y} )} \right]d\xi d\eta } \end{array}$$

where ${l_1}$ is the distance between imaging lens 1 and the coded aperture, ${f_1}$ is the focal length of imaging lens 1. Through the modulation of the coded aperture, the complex amplitude distribution on the rear surface of coded aperture is $U_3^{}({x,y} )= U_2^{}({x,y} )T({x,y} )$, where $T({x,y} )$ is the transmittance of the coded aperture.

Since the laser is monochromatic radiation light, it is assumed that the dispersion prism has no dispersion effect on the laser. The coded Gaussian beam is focused through imaging lens 2 and received by the sensor. The distance between the coded aperture and imaging lens 2 is ${l_2}$. Under the condition of Fresnel diffraction approximation, the complex amplitude distribution on the surface of imaging lens 2 is:

(6)$$\begin{array}{l} {U_4}({x,y} )= \frac{{\textrm{exp}({ik{l_2}} )}}{{i\lambda {l_2}}}\textrm{exp}\left[ {i\frac{k}{{2{l_2}}}({x_{}^2 + y_{}^2} )} \right]{\kern 1pt} {\kern 1pt} \\ \cdot {\kern 1pt} \int\!\!\!\int {U_3^{}({\xi ,\eta } )\textrm{exp}\left[ {i\frac{k}{{2{l_2}}}({{\xi^2} + {\eta^2}} )} \right]\textrm{exp}\left[ { - i\frac{k}{{{l_2}}}({\xi x + \eta y} )} \right]d\xi d\eta } \end{array}$$

Then, the laser is focused through imaging lens 2 and received by the sensor with the image distance of ${l_3}$. The complex amplitude distribution on the sensor is:

(7)$$\begin{array}{l} {U_5}({x,y} )= \frac{{\textrm{exp}({ik{l_3}} )}}{{i\lambda {l_3}}}\textrm{exp}\left[ {i\frac{k}{{2{l_3}}}({x_2^2 + y_2^2} )} \right]{\kern 1pt} {\kern 1pt} \\ \cdot {\kern 1pt} \int\!\!\!\int {U_4^{}({\xi ,\eta } )\textrm{exp}\left[ { - i\frac{k}{{2{f_2}}}({x_2^2 + y_2^2} )} \right]\textrm{exp}\left[ {i\frac{k}{{2{l_3}}}({{\xi^2} + {\eta^2}} )} \right]\textrm{exp}\left[ { - i\frac{k}{{{l_3}}}({\xi {x_2} + \eta {y_2}} )} \right]d\xi d\eta } \end{array}$$

where ${f_2}$ is the focal length of the imaging lens 2. The intensity distribution of the laser incident on the sensor is $U^{\prime}(x,y) = {|{U_5^{}({x,y} )} |^2}$. In conclusion, the measured intensity distribution on the sensor of CASSI system under laser interference is:

(8)$$I(x,y) = f^{\prime}(x,y) + U^{\prime}(x,y). $$

Equation (8) can be rewritten as:

(9)$${\boldsymbol i} = {\boldsymbol y} + {\boldsymbol u}, $$

where ${\boldsymbol i}$ is the vectorized representation of $I(x,y)$, ${\boldsymbol y}$ is the vectorized representation of $f^{\prime}(x,y)$, and ${\boldsymbol u}$ is the vectorized representation of $U^{\prime}(x,y)$. Substituting Eq. (3) into Eq. (9):

(10)$${\boldsymbol i} = {\textbf H}{\bf \Psi }{\boldsymbol \theta } + {\boldsymbol u} + \omega. $$

According to CS theory, the 3D spatio-spectral data cube can be reconstructed from the compressive measurements on the sensor using the CS reconstruction algorithm [22,23]. For the presence of laser interference, the sparse coefficients of spectral data cubes can be approximately reconstructed by solving the following optimization problem: $\hat{\theta } \approx \mathop {\arg \min }\limits_\theta {||\theta ||_1},s.t.||{{\boldsymbol i} - {\textbf H\varPsi }\theta } ||_2^2 < \varepsilon$, where $\varepsilon$ is a small constant to constrain the upper bound of the reconstruction error; ${||\cdot ||_1}$ and ${||\cdot ||_2}$ represent the l1-norm and l2-norm, respectively. The optimal solution $\hat{\theta }$ for the above optimization problem can be obtained using the gradient projection for sparse reconstruction (GPSR) algorithm. Finally, the data cube can be recovered as $\hat{{\boldsymbol f}} = {\mathbf {\Psi} }\hat{\theta }$.

3. Design method of grayscale coded aperture

When CASSI system is irradiated by intense laser, the compressive measurements may exceed the sensor’s saturation level. Thus, sensors may be dazzled thereby reducing the reconstruction accuracy of the data cube. In order to reduce saturation of the sensors, the entries of the coded apertures are attenuated according to the compressive measurements. Then, high irradiance incident light is attenuated before it is obtained by the sensor. Therefore, the entries of coded apertures will exist non-binary values, thus generating grayscale coded aperture.

Figure 3 shows the generation of the proposed grayscale coded apertures of the CASSI system under laser interference. The grayscale coded apertures entries are updates in a real-time feedback manner based on the previously compressive measurements. The computer records the measurement ${\textbf I}_{}^k$ from the sensor and remembers the previous compressive measurements ${\textbf I}_{}^{k - 1}$ and the previous coded aperture patterns. The entries of the coded apertures are attenuated in real time feedback according to the compressive measurements to reduce sensor saturation, yielding an adaptively generated grayscale coded aperture.

Fig. 3. Sketch of grayscale coded apertures of the CASSI system under laser interference

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Suppose $p_{m,n}^k$ is a weight matrix whose entries are the number of times that the (m, n)th pixel on the kth coded aperture induces saturation in the sensor.

(11)$$p_{m,n}^k = 1 + \sum\limits_{l = m}^{m + L - 1} {u[{{\textbf I}_{l,n}^k - sat} ]}, $$

where $u[{\bullet} ]$ is the unit step function. ${\textbf I}_{l,n}^k$ is the measured intensity of the (l, n) th sensor pixel at the kth snapshot; $k \in \{ 1,\ldots K\}$ and K is the number of snapshots. $sat$ represents the saturation level of the sensor. Assume that the attenuation in a pixel of the coded aperture is inversely proportional to the number of times that the pixel induces saturation on the sensor. Given the initially generated random coded apertures ${T^1},\ldots ,{T^K}$, the grayscale coded apertures are generated as

(12)$${\hat{T}^{k + 1}} = {\raise0.7ex\hbox{${{T^{k + 1}}}$} \!\mathord{/ {\vphantom {{{T^{k + 1}}} {p_{m,n}^k}}} }\!\lower0.7ex\hbox{${p_{m,n}^k}$}}, $$

where $A \bullet B$ is the Hadamard product.

When CASSI system is irradiated by intense laser, the measurements may exceed the sensor’s saturation level. According to Eq. (12), the first grayscale coded aperture remains as the original, ${\hat{T}^1} = {T^1}$, since the attenuation in the pixels of the coded apertures needs feedback. After the second snapshot, the grayscale coded apertures are generated according to the measurements. The amplitude of incoming scene disturbed by lasers are adequately measured due to the attenuation of grayscale coded aperture to reduce saturation levels.

Substituting Eq. (12) into Eq. (1), the imaging model of CASSI using feedback grayscale coding method can be written as

(13)$${\textbf Y}_{i,j}^{k + 1} = \sum\limits_{l = 0}^{L - 1} {{{\textbf F}_{i,j + l,l}}} {\textbf T}_{i,j + l}^{k + 1}/p_{m,n}^k + \boldsymbol{\mathrm{\omega}}_{i,j}^{k + 1}. $$

4. Simulations and discussion

4.1 Simulations

This section provides a set of simulations to assess the anti-laser interference performance of the proposed grayscale coded aperture. In addition, the performance of grayscale coded aperture is compared with that of random coded aperture. The simulation is carried out under the circumstance that the interference laser propagates through the imaging lens and modulated by the coded aperture and then detected by the sensor. The simulation parameters are shown in Table 1. The original spectral data cube is captured using a CCD camera exhibiting 256 × 256 of spatial resolution and 24 spectral bands. The wavelength spans between 450 and 650 nm. The resolution of the coded aperture is the same as that of the sensor. We use GPSR algorithm to recover the spectral images from the compressive measurements.

Table 1. The specific simulation parameters of interference laser.

View Table

Figure 4(a) shows the compressive measurement detected by the sensor without laser interference. Figure 4(b) shows the compressive measurement under laser interference when the laser propagation distance is 50 m. The distance between imaging lens 1 and the coded aperture is 100 mm. The distance between the coded aperture and imaging lens 2 is 200 mm. The distance between imaging lens 2 and the detector is 200 mm. It can be seen in Fig. 4(b) that the region on the image plane centered around the incident light spot is saturated.

Fig. 4. (a) Compressive measurement without laser interference. (b) Compressive measurement under laser interference when the laser propagation distance is 50 m.

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Figure 5 shows the reconstruction results using random and grayscale coded apertures when the interference laser propagation distance is 50 m, and the number of snapshots is K = 10. We selected equally spaced 6 wavelengths out of the 24 spectral bands to show the original and reconstructed spectral data cube for the length limit. The wavelengths of the 6 selected bands are shown in Fig. 5. The first row in Fig. 5 shows the 6 original spectral images out of the total 24 spectral bands. The second row shows the reconstructed spectral images using random coded apertures without laser interference. The third row illustrates the reconstructed spectral images using random coded apertures under laser interference. The fourth row illustrates the reconstruction results based on the proposed grayscale coded apertures under laser interference. In these simulations, we set the weight coefficients of the sparsity regularization in GPSR algorithm to be 2e-4. The peak signal to noise ratios (PSNR) of the reconstructed spectral images are presented in Fig4. Given a noise-free N × M monochrome image ${\textbf I}$ and its reconstructed counterpart K, it can be calculated as: $PSNR = 10{\log _{10}}(MA{X_I}^2/MSE)$, where $MSE = \frac{1}{{MN}}{\sum\nolimits_{i = 0}^{M - 1} {\sum\nolimits_{j = 0}^{N - 1} {[{\textbf I}(i,j) - {\textbf K}(i,j)]} } ^2}$, and $MA{X_I}$ is the maximum possible pixel value of the image. It can be seen that laser interference may reduce reconstruction accuracy. Because the compressive measurements exceed the sensor’s saturation level under laser interference leading the loss of compressed sampling information, thereby reducing reconstruction accuracy of spectral images. In addition, the grayscale coded apertures can improve reconstruction accuracy over random coded apertures in all spectral bands for the saturation is reduced between snapshots by using the grayscale coded apertures.

Fig. 5. Reconstruction results of the spectral data cube using 10 snapshots based on GPSR algorithm. From top to bottom, it respectively shows: (a) original spectral images, (b) reconstructed images using random coded apertures without laser interference, (c) reconstructed images using random coded apertures under laser interference, and (d) reconstructed images using grayscale coded apertures under laser interference.

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Figure 6 shows the RGB mapping of the original and reconstructed images for visualization purposes. A comparison between the original and recovered data cubes using the random and grayscale coded apertures can be seen in Fig. 6. The results show the grayscale coded apertures achieve an improvement of up to 1.72 dB of PSNR over random coded apertures under laser interference.

Fig. 6. RGB mapping of (a) original spectral images, (b) reconstructed images using random coded apertures without laser interference, (c) reconstructed images using random coded apertures under laser interference, and (d) reconstructed images using grayscale coded apertures under laser interference.

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Figure 7(a) presents the average PSNRs of the reconstructed spectral data cube using random and grayscale coded apertures in different spectral bands. In Fig. 7(a), the x-axis indicates the order numbers of the spectral bands, and the y-axis shows the average reconstruction PSNRs.

Fig. 7. Comparison of the average reconstruction (a) PSNRs and (b) SNRs of the spectral data cube in different spectral bands using random coded apertures and grayscale coded apertures.

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Figure 7(b) presents the average SNRs of the reconstructed spectral data cube using random and grayscale coded apertures in different spectral bands. Given a noise-free N × M monochrome image ${\textbf I}$ and its reconstructed counterpart K, it can be calculated as: $SNR = 10{\log _{10}}({P_s}/{P_n})$, where ${P_s} = {\sum\nolimits_{i = 0}^{M - 1} {\sum\nolimits_{j = 0}^{N - 1} {{\textbf I}(i,j)} } ^2}$, ${P_n} = \sum\nolimits_{i = 0}^{M - 1} {\sum\nolimits_{j = 0}^{N - 1} {[{\textbf I}(i,j) - } } {\textbf K}(i,j){]^2}$. In Fig. 8, the x-axis indicates the order numbers of the spectral bands, and the y-axis shows the average reconstruction SNRs.

4.2 Discussion

It is observed from Fig. 4 and Fig. 5 that when CASSI system is irradiated by intense laser, the compressive measurements may exceed the sensor’s saturation level leading to the reduction of the reconstruction accuracy of spectral images. However, existing research does not consider the impact of laser interference on CASSI imaging quality. This paper proposes grayscale coded apertures to attenuate the saturation of sensors to improve the anti-laser interference performance of the CASSI system. It is observed from Figs. 5–7 that the grayscale coded apertures can improve reconstruction accuracy over random coded apertures in all spectral bands. The entries of random coded apertures can only take just two binary values 0 and 1, which limits the degree of modulation freedom. Through the design of a reasonable and feasible feedback model, the grayscale coded aperture is adaptively calculated according to the measurements of CASSI system in real time feedback. The proposed grayscale coded apertures can improve intensity modulation and reduce saturation levels through modulation of the amplitude of the incident light. Areas affected by laser interference are adequately measured due to the grayscale coded apertures attenuation, thus improving the anti-laser interference threshold of the CASSI system.

5. Conclusions

When CASSI system is irradiated by intense laser, high intensity light that enters into the system may cause the compressive measurements exceed the sensor’s saturation level and lead to the reduction of the reconstruction accuracy of spectral images. This paper establishes the imaging model of CASSI system under laser interference and proposes a design method of grayscale coded apertures in real time feedback according to the information of measurements of the CASSI system. The proposed grayscale coded apertures allow to attenuate the saturation of sensors and improve the anti-laser interference performance of the CASSI system. The proposed method has advantages under the circumstance of intense artificial interference but also the high irradiance caused by various natural light sources. A set of simulations are conducted to verify the improvement of anti-laser interference performance of the proposed coding strategy. In the future, we plan to establish a testbed to verify the proposed grayscale coded aperture method in experiments and experimentally measure the anti-laser interference threshold of the CASSI system under different laser interferences.

Funding

National University of Defense Technology Youth Independent Innovation Science Fund (ZK23-49); the Director Fund of State Key Laboratory of Pulsed Power Laser Technology (SKL2022ZR09); the Young Doctor's Fund of Electronic Countermeasure College of the National University of Defense Technology (KY21C218); the Director Fund of Advanced Laser Technology Laboratory of Anhui Province (AHL2022ZR03); the Technology Domain Fund of 173 Project (No. 2021-JCJQ-JJ-0284).

Disclosures

The authors declare no conflicts of interest.

Data Availability

The data represented in this study are available on request from the corresponding author.

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Parameter	Value
Gaussian beam waist	1mm
Incident laser power	1W
Incident laser wavelength	532nm
Focal length of imaging lens 1	100mm
Focal length of imaging lens 2	100mm
Imaging lens pupil size	$\emptyset$ 50mm

Anti-laser interference methods for compressive spectral imaging based on grayscale coded aperture

Abstract

1. Introduction

2. Theoretical modeling

2.1 Imaging model of CASSI

2.2 Transmission model for the interference laser

3. Design method of grayscale coded aperture

4. Simulations and discussion

4.1 Simulations

4.2 Discussion

5. Conclusions

Funding

Disclosures

Data Availability

References

Data Availability

Cited By

Figures (7)

Tables (1)

Equations (13)

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