1. Introduction

Intense laser radiation can be used as an effective threat to an imaging system. High power lasers are widely available, affordable, and essentially unregulated. Such sources may be used to disrupt imaging systems by excessively illuminating the detector, even from large distances [1]. In scenarios where the threat of unwanted laser radiation is high, it is desirable to passively protect the detector from extreme irradiance levels.

If the wavelength of the laser or the state of a highly polarized beam is known, common optical elements such as notch filters and polarizers may be used to reject the laser light. However, a more desirable solution would be robust to many wavelengths, bandwidths, and polarization states. Another approach is to optically remove the light from a source based on its location [2]. Coronagraphs, for example, are commonly used in astronomy to image faint targets in close proximity to extremely bright sources such as exoplanets near to their parent star [3]. Although coronagraphs achieve remarkable suppression levels [4], prior knowledge of the source location and accurate pointing are required.

Over the past few decades, a large research effort has sought nonlinear optical limiting materials to mitigate the threat of laser damage [5 –8]. The goal is to fabricate an optical element with intensity dependent absorption to block intense laser radiation, while allowing for high quality imaging when a laser source is not present. Nonlinear filters are often focal plane elements that are limited by a high irradiance turn-on threshold, operate over a narrow bandwidth, or become permanently opaque after a hostile exposure. To our knowledge, a reusable material that allows for white light imaging and a few orders of magnitude of laser suppression over a large bandwidth has yet to be discovered [9,10].

The approach presented here protects a focal plane array in an imaging system from the damaging effects of intense laser radiation without prior knowledge of the laser source location, brightness, wavelength, or polarization and without the use of nonlinear optical elements. Rather, the risk of laser damage is reduced by modifying the point spread function (PSF) of the optical system with a linear phase element such that the peak irradiance in the image plane is reduced. The signal from the background scene is maintained and an image is recovered by computer processing. We calculate the peak irradiance reduction for a number of potential pupil-plane phase elements and assess the quality of the recovered background scene in terms of the National Imagery Interpretability Rating Scale (NIIRS) [11 –15]. Additionally, we numerically demonstrate the capability of the system to protect a detector against a powerful laser source and exemplify the strengths and limitations of using pupil phase elements for peak irradiance suppression.

2. Optical System

The scenario to be considered is illustrated in Fig. 1. The unwanted laser source is a bright, spatially coherent, monochromatic, quasi-point source described by the complex field $U(x_0,y_0)$. The scene, excluding the laser, is a relatively dim spatially incoherent background containing targets of interests described in terms of reflected spectral irradiance $b(x_0,y_0,{\lambda }_b)$, where ${\lambda }_b$ is the wavelength. Monochromatic illumination is assumed for simplicity. A single lens system is used to form an image of the $(x_0,y_0)$ plane at the $(x^{\prime },y^{\prime })$ plane. The laser source is distant enough that the beam width becomes large with respect to the aperture of the system and evenly illuminates the lens; that is, $z\gg z_R$, where $z$ is the distance from the source to the pupil plane, $z_R$ is the Rayleigh distance given by $z_R=\pi w_0^2/{\lambda }_L$, $w_0$ is the beam waist, and ${\lambda }_L$ is the wavelength of the laser light. Additionally, $w_0$ is small with respect to the targets of interest in the scene. The peak image plane irradiance owing to a laser source $I_{\text{peak}}$ is reduced by introducing a linear optical element at the pupil plane with complex transmittance $t(x,y)$. The image plane irradiance is approximated by $I(x^{\prime },y^{\prime })=I_L(x^{\prime },y^{\prime })+I_b(x^{\prime },y^{\prime })$, where the contribution of laser $I_L(x^{\prime },y^{\prime })$ and background scene $I_b(x^{\prime },y^{\prime })$ are described by the following convolutions:

 

Fig. 1. Diagram of the optical system with incident radiation from an unwanted laser source and background scene located at the $(x_0,y_0)$ plane. The object distance $z$ is large with respect to the Rayleigh range of the laser beam $z_R$. A phase element is placed adjacent to a lens with focal length $f$ and is bounded by aperture $A(x,y)$. Both the laser source and the spatially incoherent background scene are imaged at the $(x^{\prime },y^{\prime })$ plane.

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Laser damage thresholds for focal plane arrays depend on the architecture and materials that make up the device as well as the properties of the laser source, including wavelength and pulse duration. In each case, there are several damage mechanisms that occur at different exposure (fluence) levels [1]. For the purpose of this study, we use an estimated damage threshold based on typical morphological damage thresholds in charge-coupled devices (CCDs). The damage threshold of the Itek Optical Systems Model VLA577 E57D [17], for example, is ${\mathrm{\Phi }}_d\approx 1\mathrm{J}/{\mathrm{cm}}^2$ for a 10 ns pulse from a $Q$-switched Nd:YAG laser operating at $\lambda =1064\mathrm{nm}$ [18]. It is useful for our discussion to determine the ratio between the damage threshold and the saturation threshold of the CCD. Saturation occurs at an exposure of ${\mathrm{\Phi }}_{\text{sat}}=0.3\mathrm{\mu J}/{\mathrm{cm}}^2$ with white light illumination [17]. Thus, ${\mathrm{\Phi }}_d/{\mathrm{\Phi }}_{\text{sat}}\approx 3\times {10}^6$. We assume this value for the remainder of our discussion keeping in mind that the damage threshold may vary significantly for different detectors and laser sources.

A scenario where a focal plane CCD can be damaged is represented by the following example. A single 10 ns pulse from a laser at distance $z=1\mathrm{km}$ with divergence angle $\theta =w_0/z_R=2\mathrm{mrad}$, $w_0=1\mathrm{mm}$, and $\lambda =1064\mathrm{nm}$ incident on an $f/10$ imaging system with $R=50\mathrm{mm}$ is likely to damage the detector (i.e., $\mathrm{\Phi }>1\mathrm{J}/{\mathrm{cm}}^2$) if the output pulse energy exceeds 3 mJ. Here, the atmospheric extinction coefficient is taken to be $1{\mathrm{km}}^{-1}$. However, if the optical system passively reduces the peak irradiance, and therefore the peak fluence, by two orders of magnitude, the imaging system can withstand a pulse with energy up to 300 mJ. Lasers with such output power levels are commercially available [19].

We examined several different pupil phase elements designed to mitigate the risk of detector damage. A phase-only element is used to obviate loss to the desired image signal. Figures 2 and 3 show several example pupil phase patterns and line profiles of their corresponding PSF amplitudes, respectively. Note that each of the phase patterns shown reduces $I_{\text{peak}}$ by a factor of 100 relative to the peak image plane irradiance without a pupil phase element $I_0$. The phase patterns include low-order Zernike polynomials [see Figs. 2(a)–2(d)]. Also shown are a vortex phase element with complex transmittance $t(x,y)=\exp (il\theta )$, where $l$ is a nonzero integer known as the topological charge (see Fig 2(e)), and an axicon with transmittance $t(x,y)=\exp (ir/a)$, where $a$ is a constant [see Fig. 2(f)]. Even though these phase elements provide the same peak irradiance suppression, we show below that the vortex and axicon allow better image quality after postprocessing than the low-order Zernike polynomials.

 

Fig. 2. Several example pupil phase elements that yield two orders of magnitude reduction in peak image plane irradiance. The phase patterns shown are (a) defocus, (b) astigmatism, (c) coma, (d) trefoil, (e) a charge $l=18$ vortex phase element, and (f) an axicon with $a=R/28.3$. The phase is wrapped between $-\pi$ (black) and $\pi$ (white).

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Fig. 3. Horizontal line profiles (black) of the point spread functions (PSFs) corresponding to the pupil phase elements shown in Fig. 2. The PSF without a phase element (gray) is also shown in each case for comparison. The line profiles pass through the point of maximum amplitude and are normalized such that the maximum amplitude without a phase element is unity. We note that the functions shown in (c) and (d) are not circularly symmetric.

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3. Image Recovery

An optical system with any of the PSFs shown in Fig. 3 produces a blurred image. However, the background scene may be reconstructed by removing the effect of the phase element from the detected image via Wiener deconvolution. The detected image is a digitally sampled representation of the scene with dimensions $N\times M$ and may be written as

4. Optimizing Image Quality

In order to assess the performance of the imaging system described above, we use the general image quality equation (GIQE) to estimate the quality of the deconvolved background image resulting from various pupil phase elements in terms of NIIRS, a quantitative metric commonly used by the strategic intelligence community [11 –15]. The standard form of the GIQE is given by

Table 1. Coefficients of the GIQE [12]

View Table

The change in image quality caused by the introduction of the pupil phase element may be described as a change on the NIIRS scale

Figure 4 shows $\mathrm{\Delta }\mathrm{NIIRS}$ estimates for the pupil phase elements shown in Fig. 2 using each of the three versions described by Eqs. (10) and (11). The strength parameter of each phase function is varied to show the performance at all relevant values of peak irradiance reduction. We assume a 16-bit detector with an average signal corresponding to 16,384 digital counts and detector noise equivalent to $\sigma =5$ digital counts $(\mathrm{SNR}=128)$. The $\mathrm{\Delta }\mathrm{NIIRS}$ results are plotted against the reduction in peak image plane irradiance owing to a point source in the object plane. The calculations were performed using a $4096\times 4096$ computational grid with $0.083\lambda F\#$ per sample in the image plane and a detector sampling rate of $Q=\lambda F\#/\mathrm{\Delta }x=1.19$. $\mathrm{\Delta }{\mathrm{NIIRS}}_{4.0}$ yields the most optimistic results, whereas $\mathrm{\Delta }{\mathrm{NIIRS}}_{\mathrm{T}\text{-}\mathrm{F}}$ predicts the largest loss in image quality. For reference, $\mathrm{\Delta }\mathrm{NIIRS}=-1$ corresponds to approximately a factor of two in regards to the loss in resolution, while $\mathrm{\Delta }\mathrm{NIIRS}=-0.1$ corresponds to a barely noticeable difference [22,23]. In the most optimistic case, reducing $I_{\text{peak}}$ by two orders of magnitude is possible with $\mathrm{\Delta }\mathrm{NIIRS}\approx -1.255$. Discontinuities in the $\mathrm{\Delta }\mathrm{NIIRS}$ curves arise from the conditional definition of the edge overshoot.

 

Fig. 4. Estimated loss in image quality $\mathrm{\Delta }\mathrm{NIIRS}$ for the incoherent scene as compared to an unprotected system plotted against the relative peak image plane irradiance owing to a bright laser point source in the object plane. The results are shown for GIQE versions (a) 3.0 and (b) 4.0 [12] as well as (c) the modified version suggested by Thurman and Fienup [21] for aberrated imagery. $I_0$ is the peak image plane irradiance without a pupil phase element. The data for the vortex phase element are plotted at integer values of topological charge $l$.

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Among the pupil phase elements we have considered, the vortex phase element offers the best performance in cases where one to two orders of magnitude of peak irradiance suppression is required. The axicon performs slightly better than the vortex phase element near $I_{\text{peak}}/I_0={10}^{-2}$ according to all of the $\mathrm{\Delta }\mathrm{NIIRS}$ estimates. The comparable performance between the vortex phase and axicon pupil elements is attributed to the similarity between their PSFs, which appear as a narrow “donut.” This PSF shape is desirable because the light is spread out in the image plane while the PSF is narrow in the radial direction.

5. Computed Image: without Laser Threat

We choose a vortex phase pupil element for demonstration purposes, which yields a complex PSF generally given by

We numerically calculate the images generated by the system described above with an $l=18$ vortex phase pupil element, which affords slightly more than two orders of magnitude in peak suppression. The computed images (see Fig. 5) are obtained by convolving a discretely sampled test scene with the PSF of the optical system and the impulse response of the detector. The scene is then resampled from $0.25\lambda F\#$ per sample to $1.19\lambda F\#$ per pixel (i.e., $Q=1.19$). The diameter of the aperture is assumed to be 0.1 m, and the modeled exposure time provides an average signal corresponding to $S_{\text{avg}}=\mathrm{16,384}$ digital counts. Both Poisson and Gaussian distributed noise are added, where the Gaussian noise has a standard deviation of $\sigma =5$ digital counts. Kolmogorov random phase screens are applied at the pupil plane to simulate wavefront error caused by atmospheric distortion. The phase screens are calculated using a sub-harmonic Monte Carlo method [28,29] assuming a coherence diameter of $r_0=0.1\mathrm{m}$ and inner and outer scales of 20 m and 5 mm, respectively.

 

Fig. 5. Computed image with an $l=18$ vortex phase pupil element (a) before and (b) after Wiener filtering. The deconvolved image without the vortex phase element (i.e., the unprotected system) is shown in (c) for comparison. The image dimensions are $794\times 1112$ pixels.

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The detected image with the vortex pupil phase element [see Fig. 5(a)] appears blurry, but it is sharpened by deconvolving the PSF of the system [see Fig. 5(b)]. However, there is an overall loss in image quality in the recovered image that corresponds to $\mathrm{\Delta }\mathrm{NIIRS}\approx -1.63$ as compared to the image obtained with an unprotected system [see Fig. 5(c)]. Roughly speaking, this corresponds to a factor of $\sim 3$ loss in visual resolution.

6. Computed Image: with Laser Threat

The benefit of the pupil phase element is most obvious in the case where the peak irradiance due to a potentially damaging laser source is reduced to a safe level by the pupil phase element. Figure 6 shows a computed image of the test scene obtained with a bright laser originating from a window of the building. In the vicinity of the laser, the image becomes heavily saturated. As previously noted, a laser may cause damage if the image plane exposure is $3\times {10}^6{\mathrm{\Phi }}_{\text{sat}}$. In this scenario, the pupil element reduces the image plane irradiance from $3\times {10}^6{\mathrm{\Phi }}_{\text{sat}}$ to $<3\times {10}^4{\mathrm{\Phi }}_{\text{sat}}$, thereby protecting the sensor from damage. Line profiles of the image plane irradiance along the dashed line in Fig. 6 are shown in Fig. 7.

 

Fig. 6. Computed image with an $l=18$ vortex phase pupil element in the presence of a potentially damaging laser source (before postprocessing). Without the phase pupil element, permanent damage would occur on the sensor. Image plane exposure profiles along the dashed lines are shown in Fig. 7 with and without the protection provided by the pupil phase element.

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Fig. 7. Profiles of image plane exposure along the dashed line in Fig. 6. Without the pupil phase element ($l=0$), the detector may become damaged. The $l=18$ vortex phase pupil element reduces the peak exposure to a safe level by spreading out the laser light.

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In cases where the laser source is not bright enough to cause permanent detector damage, the detector may still locally saturate leading to a loss of information. A circular saturation region appears where the background information is completely lost, as shown in Fig. 8. Moreover, the local SNR may become too low for detection because of the noise associated with diffracted laser light. It is important to note that the saturated region will be larger with the pupil phase element in place, since the laser light is spread out on the detector. Figure 8 shows recovered images with a laser source of increasing brightness and the $l=18$ vortex phase pupil element in place. The saturation region becomes large for brighter laser sources, which obscures a substantial region of the background scene. Ringing artifacts also occur around the laser source after deconvolution and tend to appear near sharp edges in the image. Other saturation artifacts such as blooming have not been modeled.

 

Fig. 8. Computed images after postprocessing with Wiener deconvolution for ${\mathrm{\Phi }}_{\text{peak}}/{\mathrm{\Phi }}_{\text{sat}}=$ (a) ${10}^2$, (b) ${10}^3$, (c) ${10}^4$, and (d) ${10}^5$, where ${\mathrm{\Phi }}_{\text{peak}}$ is defined with the $l=18$ vortex phase element in the pupil plane of the optical system.

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In situations where critical targets appear near the laser source, additional postprocessing steps may be introduced to improve recovery of the background scene in the vicinity of the saturated region. We have implemented a two-step process for removing the laser contribution from the image prior to deconvolution. This prevents ringing artifacts that may hinder detection of objects near to the laser source in the image. First, we apply nonlinear optimization to estimate the contribution of the laser source from the detected image. Assuming a circular laser source with constant amplitude and phase, a Nelder–Mead simplex algorithm [30,31] is used to vary the size, location, and brightness until the expected laser contribution best matches the detected image in the region where laser light is present. We define the error metric as the squared difference between the detected image $G_{n,m}$ and the estimated laser contribution $\widehat{\mathrm{\Phi }}(n\mathrm{\Delta }x,m\mathrm{\Delta }x)$, which is calculated over the region-of-interest (ROI):

The images that result from the laser subtraction routine often have residual speckle due to wavefront error that, when significant, may also cause ringing artifacts in deconvolution. To remedy this, we have devised a gradient-based speckle suppression algorithm that iteratively reduces the image values in regions where the magnitude of the image gradient is high. Each iteration is computed as

 

Fig. 9. Computed, recovered images with the $l=18$ vortex phase element, ${\mathrm{\Phi }}_{\text{peak}}/{\mathrm{\Phi }}_{\text{sat}}={10}^2$, and $\mathrm{SNR}=128$. (a), (b) Recovered images using Wiener deconvolution with (a) the laser contribution subtracted and (b) after gradient-based speckle reduction. The ringing artifacts are reduced as compared to Fig. 8(a). (c), (d) Recovered images using Lucy–Richardson iterative deconvolution, where (c) is the recovered image using only the Lucy–Richardson iterative deconvolution algorithm (i.e., without performing the laser removal process) and (d) is the recovered image with the laser contribution removed. For this example, 10 iterations of gradient-based speckle suppression and 20 iterations of Lucy–Richardson deconvolution are used.

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Alternate deconvolution algorithms may also be less susceptible to certain types of artifacts. For example, ringing artifacts are less prominent when Lucy–Richardson (L–R) iterative deconvolution [32,33] is used instead of Wiener deconvolution [see Fig. 9(c)]. The L–R results are also improved when the laser contribution is removed as described above prior to performing L–R deconvolution [see Fig. 9(d)].

Using the additional postprocessing steps outlined above, the scene information may be recovered very close to the saturation region. However, wavefront error and noise are the ultimate limitation for recovering the background scene. In other words, the postprocessing routines fail when the actual PSF is very different from the expected PSF.

7. Future Work

Although the GIQE and NIIRS rating were used in this work, image quality may also be estimated using alternate metrics such as the mean-squared error (MSE), peak signal-to-noise ratio (PSNR), or perception-based image quality metrics including the structural similarity index [34], edge metrics [35], task satisfaction confidence scale [14], as well as others [36]. The image quality achieved using deconvolution algorithms, other than the Wiener filter, may also be assessed [37,38].

A phase element that operates over a large bandwidth is needed for the application presented here. With recent advances in the fabrication, high topological charge achromatic vortex phase elements are possible in a number of wavelength regimes including visible, near-, and mid-infrared. Broadband vortex phase transmittance may be achieved by use of holographic elements [39,40] with dispersion compensation [41 –43], subwavelength gratings [44 –46], liquid crystal elements [47 –49], and photonic crystal elements [50]. The most promising designs for achromatic, high-order topological charge vortex elements are liquid crystal vector vortex elements [51].

8. Conclusion

We have presented a novel imaging system design that mitigates the risk of damage caused by laser radiation. Optical elements for predetection processing and postprocessing routines have been developed to optimize the image quality. The main advantages of the approach presented here are that the system is compact, the optical technology is readily available, and prior knowledge of the laser source location, brightness, wavelength, or polarization is not required. This approach is particularly well suited for surveillance scenarios with high probability of incident laser radiation, but with the added assumption that light from the laser sources is unlikely to surpass the damage threshold by a few orders of magnitude. This may be the case for imaging crowd members with handheld laser pointers several meters from the imaging system. If more powerful sources are expected, a pupil phase element with further reduced peak image plane irradiance may be used at the cost of image quality. Alternatively, the technique presented here may be used in conjunction with other approaches such as nonlinear optical limiting materials in a focal plane.