Coded-aperture imaging is a powerful imaging paradigm that combines structured optical encoding with computational reconstruction to overcome the intrinsic trade-off between photon throughput and spatial resolution in conventional aperture imaging^[1–3]. By replacing traditional apertures with spatially engineered transmission patterns, coded-aperture systems can efficiently encode scene information into captured measurements and subsequently recover target images through computational decoding. Originally developed for imaging inherently unfocusable X-rays and γ-rays^[4,5], coded-aperture imaging significantly improves photon collection efficiency while preserving spatial resolution, thereby enabling high-sensitivity imaging under photon-limited conditions. With the rapid development of computational imaging, coded-aperture techniques have evolved into a versatile imaging framework and have been broadly integrated with compressed sensing, snapshot imaging, and computational reconstruction methods. Representative advances include compressed ultrafast photography (CUP)^[6,7], coded-aperture snapshot spectral imaging (CASSI)^[8–10], and coded-aperture polarimetric imaging^[11–13]. Meanwhile, the emergence of programmable spatial modulators^[14–18] and advanced reconstruction approaches, including deep neural networks^[19–22] and end-to-end optimization frameworks^[23,24], have further driven coded-aperture imaging toward higher flexibility, sensitivity, and reconstruction fidelity.

Extending coded-aperture imaging into the mid-infrared (MIR) is particularly attractive because the MIR spectral region contains rich molecular fingerprint resonances and important atmospheric transmission windows^[25,26]. These characteristics make MIR coded-aperture imaging highly promising for applications including non-destructive inspection, environmental monitoring, and biomedical diagnosis^[27–30]. However, realizing high-performance MIR coded-aperture imaging remains extremely challenging. On the one hand, high-fidelity spatial encoding in the MIR is fundamentally limited by the lack of suitable modulation devices^[31]. Conventional physical masks suffer from fixed coding patterns and poor adaptability, while programmable devices such as digital micromirror devices (DMDs) experience severe diffraction-induced degradation at long wavelengths^[32], significantly reducing modulation fidelity and encoding precision. On the other hand, MIR imaging detection is still constrained by the limited room-temperature sensitivity and pixel density of narrow-bandgap semiconductor focal-plane arrays, which typically suffer from strong dark-current noise and complex cooling requirements^[33,34]. Therefore, developing an MIR coded-aperture imaging framework capable of simultaneously achieving high-fidelity optical encoding and high-sensitivity detection remains an important challenge.

In recent years, nonlinear optical manipulation has opened new opportunities for MIR imaging^[35–39]. Among various approaches, frequency-upconversion imaging has emerged as a particularly powerful strategy by transferring MIR information into the visible or near-infrared (NIR) regime through nonlinear wave mixing^[40–45]. In the sum-frequency generation (SFG) process, the spatial structure of a shorter-wavelength pump beam can be optically transferred to the MIR signal, enabling indirect yet high-fidelity modulation of MIR radiation using mature NIR spatial light modulators (SLMs)^[37]. This nonlinear encoding mechanism effectively circumvents the scarcity of MIR modulation devices while simultaneously enabling sensitive room-temperature detection using high-performance silicon-based cameras. Various nonlinear MIR imaging schemes have consequently been demonstrated, including ultrafast temporal detection^[46], high-resolution spectral sensing^[47,48], single-pixel imaging^[37,38], and phase manipulation^[49]. In particular, the pump modulation scheme has been extended to lensless imaging architectures, where confining the pump beam to a single pinhole inside the nonlinear crystal achieves MIR pinhole imaging^[30]. However, a single aperture fundamentally suffers from limited photon throughput, and programmable multi-aperture spatial encoding strategies for MIR coded-aperture imaging have not yet been investigated.

Here, we propose and experimentally demonstrate programmable nonlinear coded-aperture imaging in the MIR at 3.07 µm. In our scheme, a nonlinear coded aperture is optically formed by spatially modulating a 1.03 µm pump beam with an SLM, enabling flexible and programmable spatial encoding. During the SFG process, the encoded pump pattern simultaneously performs optical encoding and frequency upconversion of the MIR signal, thereby realizing both high-fidelity spatial encoding and high-sensitivity detection within a unified nonlinear framework. The encoded measurements are subsequently reconstructed using the Richardson–Lucy (RL) iterative deconvolution algorithm. By optimizing the coding strategy using a Golay-7 array with near-delta autocorrelation, the proposed system achieves substantially improved signal-to-noise ratio (SNR), spatial resolution, and imaging robustness compared with conventional single-pinhole imaging, while maintaining the large depth-of-field advantage of lensless architectures. This work establishes a flexible and scalable paradigm for nonlinear MIR computational imaging and opens new opportunities for high-performance lensless imaging in long-wavelength regimes.

MIR nonlinear coded-aperture imaging can be regarded as an advanced extension of nonlinear pinhole imaging, where image formation relies on spatial modulation of the optical field. Figure 1(a) illustrates the principle of nonlinear pinhole imaging based on frequency upconversion^[30]. In this configuration, an optical aperture formed by the pump beam inside the nonlinear crystal acts as a spatial filter, enabling direct lensless imaging of the target object. A sufficiently small aperture enhances spatial selectivity and suppresses overlap between rays originating from different object points. However, strong spatial filtering inevitably blocks most incident photons, resulting in low light throughput and poor SNR^[3]. Increasing the aperture size can improve photon collection efficiency, as illustrated in Fig. 1(b), but simultaneously weakens the spatial filtering capability, causing severe overlap between adjacent object points and leading to image blur^[50]. Therefore, conventional single-aperture imaging fundamentally suffers from the trade-off between photon throughput and spatial resolution.

To overcome these limitations, we replace the conventional pinhole with a programmable coded-aperture array, as illustrated in Fig. 1(c). Compared with a single aperture, the coded array allows substantially higher photon throughput while preserving spatial information through structured optical encoding^[1]. The proposed imaging framework mainly consists of two key processes: nonlinear optical encoding and computational decoding. During encoding, a near-infrared pump beam is spatially modulated by an SLM to generate a programmable encoding pattern. Through the SFG process, the spatial structure of the pump field is optically transferred to the MIR signal, thereby realizing nonlinear spatial encoding of the target scene. This nonlinear optical encoding mechanism effectively circumvents the lack of high-performance MIR modulation devices while enabling flexible and high-fidelity spatial encoding using mature NIR modulation technology.

Under incoherent illumination, the imaging process can be approximated as a linear convolution model^[35]. Owing to the nonlinear imaging geometry, the object and image coordinates satisfy the mapping relation x′=Mx and y′=My, where the imaging magnification is given by M=−vλup/(uλs), with λs and λup denoting the MIR signal wavelength and upconversion wavelength, respectively, and u and v representing the object and image distances relative to the nonlinear aperture plane^[30]. The negative sign indicates image inversion. The forward imaging process can, therefore, be expressed as $$\begin{gathered} I(x′,y′)=O(x,y)*PSF(x′,y′) \\ =O(x′M,y′M)*PSF(x′,y′), \end{gathered}$$(1)where I(x′,y′) denotes the intensity distribution of the captured upconverted coded image, O(x,y) represents the object intensity distribution, and “*” denotes two-dimensional convolution. The point spread function (PSF) of the imaging system is determined by the nonlinear process and the coded-aperture distribution: PSF(x′,y′)∝|A(x′,y′)|2,(2)where A(x′,y′) denotes the amplitude transmittance of the coded aperture. Therefore, the spatial encoding characteristics of the nonlinear aperture directly determine the information transfer process and the subsequent reconstruction quality. More detailed derivations and discussion of the forward imaging model are provided in the Supplement 1, Note 2.

To recover the target image from the encoded measurement, we employ the RL iterative deconvolution algorithm for computational decoding^[51–53]. Based on the forward convolution model and Poisson noise statistics, the RL algorithm iteratively reconstructs the object through maximum-likelihood estimation: $$\begin{gathered} O(k+1)(x,y)=O(k)(x,y)·[I(x′,y′)O(k)(x,y)*PSF(x′,y′) \\ ⋆PSF(−x′,−y′)], \end{gathered}$$(3)where O(k)(x,y) denotes the reconstructed object after the kth iteration, and “⋆” represents correlation. As illustrated in Fig. 1(d), the reconstruction iteratively compares the estimated encoded image with the measured result and back-projects the error into object space until convergence is achieved. More details of the reconstruction procedure are provided in Supplement 1, Note 3.

By combining the high-throughput advantage of coded apertures with nonlinear optical encoding and computational reconstruction, the proposed framework effectively overcomes the trade-off between photon throughput and spatial resolution in conventional pinhole imaging, while naturally preserving the intrinsic advantages of lensless architectures, including large depth of field, compact configuration, and distortion-free imaging^[54].

Figure 2(a) illustrates the experimental setup of the programmable MIR nonlinear coded-aperture imaging system. The signal and pump beams originate from a common 1030 nm mode-locked laser delivering 174 fs pulses at a repetition rate of 20.25 MHz. A portion of the output is converted into a 3070 nm MIR pulse through an optical parametric process, while the remaining portion serves as the synchronized pump beam for subsequent upconversion imaging. This passive synchronization scheme provides a compact and robust system architecture while simplifying experimental operation. More details of the laser source are provided in our previous work.

In the imaging configuration, the MIR beam first passes through a rotating ground-glass diffuser to reduce spatial coherence before illuminating the target object. The transmitted object field is then directly projected into the center of a chirped periodically poled lithium niobate (CPLN) crystal with dimensions of 3mm×2mm×5mm (width × thickness × length). The poling period of the CPLN crystal varies linearly from 16 to 24 µm along the propagation direction, enabling efficient upconversion over a broad angular range and, thus, supporting a large field of view.

To realize nonlinear spatial encoding, we employ a programmable phase-modulation scheme based on a phase-only SLM. The SLM has a resolution of 1920 pixel×1080 pixel with a pixel pitch of 8 µm and a refresh rate of 60 Hz. As illustrated in Fig. 2(b), the hologram loaded onto the SLM consists of the target encoding pattern superimposed with a blazed grating. Owing to the dependence of first-order diffraction efficiency on phase modulation depth, phase-only modulation is converted into effective amplitude encoding of the optical field. The modulated pump beam is subsequently demagnified onto the nonlinear crystal through a 4f imaging system. During this process, a diaphragm positioned at the Fourier plane spatially filters the first-order diffraction component, thereby generating a pure encoded pump aperture inside the crystal, as shown in Fig. 2(c). Compared with conventional physical masks, this programmable encoding strategy enables flexible and high-fidelity spatial modulation. Moreover, it effectively mitigates the field-of-view degradation caused by inter-pixel phase discrepancies in DMDs, making it particularly suitable for ultrafast nonlinear imaging. More details regarding the pump encoding strategy and its characterization are provided in the Supplement 1, Note 1.

Finally, the encoded pump beam and the MIR signal carrying the object information are spatially combined by a dichroic mirror (DM), while their temporal overlap is precisely adjusted using an optical delay line to enable efficient SFG inside the CPLN crystal. The SFG process simultaneously accomplishes nonlinear spatial encoding and frequency-upconversion detection by optically transferring the structured pump pattern onto the MIR radiation and converting the MIR photons into the visible regime. After spectral filtering to suppress pump fluorescence and background noise, the upconverted coded images centered at 771 nm are captured by a silicon-based electron-multiplying CCD (EMCCD, Andor iXon Ultra 888) camera. The conversion efficiency from MIR to visible is measured to be 0.16%, which could be further improved by increasing the pump average power or the effective nonlinear crystal length. The recorded coded measurements are then computationally reconstructed using the RL algorithm to recover the target image.

We first characterize the programmable optical aperture of the system and investigate its pinhole imaging performance. In aperture-based lensless imaging, the imaging quality is critically determined by the aperture design. In conventional pinhole imaging, when the aperture is excessively small, strong diffraction effects lead to image blurring; conversely, when the aperture becomes too large, insufficient spatial filtering causes severe overlap between rays originating from different object points, also degrading image quality. Therefore, an optimal aperture size generally exists that balances diffraction and spatial selectivity to achieve the clearest image. More detailed discussion of the underlying mechanism can be found in our previous work^[30]. Consequently, flexible and precise aperture modulation is of central importance for high-quality lensless imaging.

In our system, the programmable optical aperture is generated through spatial modulation of an NIR SLM. The measured pump apertures formed inside the nonlinear crystal exhibit radii ranging from 0.10 to 0.28 mm, as shown in Figs. 3(a)–3(e). These optical apertures exhibit continuously tunable sizes while maintaining highly uniform intensity distributions. Such flexibility is achieved simply through hologram engineering on the SLM, significantly reducing the complexity and cost associated with conventional physical aperture fabrication and replacement. Beyond aperture-size tuning, the proposed nonlinear encoding scheme also enables arbitrary programmability of the aperture shape, spatial arrangement, and intensity distribution.

To evaluate the imaging characteristics of the programmable aperture, a transmissive mask engraved with “ECNU” is positioned at an object distance of u=20cm, while the image plane is located at v=12cm. The corresponding nonlinear pinhole imaging results are shown in Figs. 3(f)–3(j). To quantitatively characterize the imaging resolution for different aperture sizes, we employ the modulation transfer function (MTF), which describes the system’s ability to transfer contrast as a function of spatial frequencies. At a given frequency, the MTF is derived from the modulation contrast of the bar pattern in the recorded images. The intensity profiles extracted along the white dashed lines of the letter “E” in Figs. 3(f)–3(j) are presented in Figs. 3(k)–3(o). As the aperture radius varies, the image quality exhibits the expected trade-off between diffraction blur and spatial overlap. When the aperture radius is tuned to 0.18 mm, the resulting image achieves the highest sharpness, corresponding to an MTF of 0.52. In contrast, when the aperture becomes excessively small (r=0.10mm) or excessively large (r=0.28mm), the letter “E” can no longer be clearly resolved. These results verify that the proposed nonlinear aperture modulation scheme enables precise and programmable control of the imaging aperture in the MIR regime, while allowing rapid optimization of imaging performance through flexible optical-field engineering.

Next, we investigate programmable multi-aperture coded imaging based on nonlinear spatial encoding. Owing to the high flexibility of the SLM-based pump modulation, arbitrary coded-aperture arrays can be readily generated within the nonlinear crystal. In the following experiments, the radius of each sub-aperture is fixed at the optimal pinhole size of 0.18 mm determined above, while the number of apertures is gradually increased by expanding the rows and columns of the array under a uniform aperture spacing. The resulting encoded pump aperture patterns formed inside the nonlinear crystal are shown in Figs. 4(a)–4(d).

The corresponding upconverted coded measurements recorded by the silicon-based camera are presented in Figs. 4(e)–4(h). Owing to the structured spatial modulation introduced by the coded aperture, the captured images exhibit characteristic blurred intensity distributions determined by the encoding patterns, preventing direct visualization of the target object. To recover the original spatial information, we employ the RL iterative deconvolution algorithm for computational decoding based on the forward imaging model. Figures 4(i)–4(l) show the corresponding reconstructed images after 30 iterations for different coded-aperture configurations. In each case, the target pattern “ECNU” is successfully recovered, demonstrating the effectiveness and robustness of the proposed nonlinear coded imaging framework.

Notably, the nonlinear frequency-upconversion process plays a dual role in the proposed system. On the one hand, it enables high-fidelity spatial encoding of the MIR signal by optically transferring the structured pump field onto the target radiation. On the other hand, it simultaneously converts the encoded MIR photons into the visible regime, enabling high-sensitivity detection using silicon-based cameras. By combining programmable nonlinear encoding with computational reconstruction, the proposed scheme realizes lensless coded-aperture computational imaging in the MIR regime.

In the following, we optimize the coded-aperture design using a Golay array configuration with near-delta autocorrelation. In coded-aperture imaging, the encoding pattern plays a central role in both information acquisition and computational reconstruction. On the one hand, the spatial distribution of the coded aperture determines the optical transfer function (OTF) of the imaging system, thereby governing its spatial frequency response and information capture capability. On the other hand, the coded pattern serves as the physical basis of the measurement matrix in computational imaging, where its autocorrelation characteristics directly influence the ill-posedness of the inverse reconstruction problem. Ideally, the autocorrelation distribution should approximate a δ function with a sharp central peak and suppressed side lobes. Such a property minimizes spectral nulls in the PSF, thereby improving reconstruction stability, accelerating iterative convergence, and suppressing reconstruction artifacts and noise amplification. Owing to its near-ideal autocorrelation characteristics and broad spatial frequency coverage, the Golay array is theoretically well suited for high-fidelity coded-aperture imaging^[55]. Further descriptions regarding the Golay coding properties are available in the Supplement 1, Note 4.

To experimentally evaluate the influence of coding strategies, we compare the Golay-7 array with three other representative encoding configurations. The corresponding encoded pump patterns generated inside the nonlinear crystal are shown in Figs. 5(a)–5(d). For a fair comparison, all encoding schemes are designed with identical optical throughput and the same maximum spatial frequency range, indicated by the white circumscribed circles. The corresponding autocorrelation distributions are presented in Figs. 5(e)–5(h). Among them, Golay encoding exhibits the most concentrated autocorrelation energy within the central main lobe, while the surrounding side lobe energy remains weak and uniformly distributed, closely approximating an ideal δ-like response. In contrast, the other encoding schemes exhibit obvious side lobes, which are expected to introduce reconstruction artifacts and noise amplification during iterative decoding.

We subsequently reconstruct the coded measurements using the RL iterative deconvolution algorithm. The reconstructed results after 10 iterations are shown in Figs. 5(i)–5(l). Under the same iteration number, only Golay encoding clearly resolves the target pattern “ECNU,” whereas the other encoding schemes still exhibit significant reconstruction artifacts. When the iteration number is further increased to 30, as shown in Figs. 5(m)–5(p), all encoding schemes are able to recover the target object, although substantial differences in reconstruction quality remain. Quantitative evaluation using the structural similarity index measure (SSIM) further confirms the superiority of the Golay encoding, which achieves the highest SSIM value of 0.761, significantly outperforming the other coding strategies. These results demonstrate that the superior autocorrelation characteristics of the Golay array effectively improve reconstruction fidelity, accelerate convergence, and enhance noise robustness, highlighting the critical importance of coded-aperture design in nonlinear computational imaging.

Finally, we evaluate the imaging performance of the proposed MIR coded-aperture system under different illumination levels and compare it with conventional single-pinhole imaging. In traditional pinhole imaging, the strong spatial-filtering process inevitably blocks most incident photons, leading to limited photon throughput and low SNR. Although enlarging the aperture can improve light collection efficiency, it simultaneously introduces stronger spatial overlap and image blur. This intrinsic trade-off between photon throughput and spatial resolution fundamentally limits the performance of conventional pinhole imaging. In contrast, coded-aperture imaging mitigates this limitation by employing multiple apertures to simultaneously collect more signal photons while recovering spatial information through computational decoding.

To experimentally verify this advantage, we image the target pattern “ECNU” with an exposure time of 100 ms under progressively reduced illumination levels. The upconverted coded measurements acquired using the Golay-7 coded aperture are shown in Figs. 6(a), 6(d), and 6(g). After computational decoding, the reconstructed images shown in Figs. 6(b), 6(e), and 6(h) faithfully recover the fine structures of the target even when the incident optical power decreases to 0.4 fW/pixel. In comparison, the corresponding nonlinear single-pinhole images obtained under the same exposure conditions are presented in Figs. 6(c), 6(f), and 6(i). Although the pinhole configuration preserves recognizable image features under strong illumination, the image contrast and fine details degrade rapidly as the illumination level decreases because of the insufficient accumulation of signal photons.

Notably, under relatively strong illumination, the reconstructed coded-aperture images exhibit sharper edge features than those obtained from direct pinhole imaging. This improvement originates from the computational decoding process, which effectively compensates for the inherent blur introduced by finite pinhole filtering and enables better recovery of high-spatial-frequency information. Consequently, coded-aperture imaging not only improves photon collection efficiency and imaging sensitivity but also provides enhanced image sharpness compared with conventional pinhole imaging.

These results collectively demonstrate that the proposed nonlinear coded-aperture imaging framework effectively enhances imaging sensitivity while maintaining high spatial fidelity under extremely weak illumination conditions, thereby significantly extending the capability of MIR lensless imaging in photon-starved scenarios.

In conclusion, we have experimentally demonstrated programmable nonlinear coded-aperture MIR imaging based on frequency upconversion. The core innovation of the proposed scheme lies in the nonlinear optical encoding strategy, where a near-infrared pump beam is spatially structured by a programmable SLM and subsequently transferred to the MIR signal through the SFG process. This unified nonlinear framework simultaneously realizes high-fidelity spatial encoding and high-sensitivity frequency-upconversion detection, thereby effectively overcoming two major limitations in MIR imaging: the lack of high-performance spatial modulation devices and the limited sensitivity of conventional MIR detectors. Benefiting from mature NIR modulation technology, the proposed approach provides a flexible and highly programmable spatial encoding platform for the MIR regime.

Beyond the nonlinear encoding mechanism, the presented work also establishes a lensless computational imaging architecture in the MIR based on programmable coded apertures. Unlike conventional MIR upconversion imaging systems that generally rely on imaging lenses for optical focusing^[41–43,56], the proposed scheme directly records object information through structured coded detection and reconstructs the target image computationally. Consequently, the system naturally inherits the intrinsic advantages of lensless imaging, including compact configuration, distortion-free imaging, and large depth of field^[57]. A detailed discussion on the depth-of-field performance of the coded-aperture imaging scheme is provided in the Supplement 1, Note 5. More importantly, compared with conventional nonlinear pinhole imaging, the coded-aperture strategy effectively alleviates the intrinsic trade-off between photon throughput and spatial resolution by combining high-flux optical encoding with computational reconstruction. Through optimized coded-aperture design, the system achieves substantially improved imaging sensitivity and enhanced recovery of fine spatial details under weak-light conditions.

The presented framework also offers considerable flexibility for further extension and optimization. Since the coded aperture is generated optically through programmable pump modulation, the encoding pattern can be flexibly tailored for different imaging requirements, enabling adaptive spatial frequency control and optimized information acquisition^[18]. In addition, the current reconstruction framework can be naturally combined with advanced computational approaches, such as compressed sensing and learning-assisted reconstruction algorithms, to further improve reconstruction quality and robustness under low-photon-flux conditions^[20–23,58]. From the perspective of wavelength scalability, the proposed nonlinear encoding strategy is not restricted to the current MIR band and could potentially be extended to longer wavelength regimes by employing appropriate nonlinear materials and phase-matching conditions^[59,60]. Overall, by integrating programmable nonlinear optical encoding, coded-aperture imaging, and frequency-upconversion detection within a unified framework, this work provides a promising route toward flexible and high-sensitivity imaging in long-wavelength spectral regions.

The authors declare no conflicts of interest.

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Acknowledgment. This work was supported by the National Key R&D Program of China (No. 2025YFA1411700), the National Natural Science Foundation of China (Nos. 62505088, 62235019, and 125B2088), the Shanghai Pilot Program for Basic Research (No. TQ20220104), the Hainan Provincial Natural Science Foundation of China (Nos. 126ZD1019 and 126QN0836), the Postdoctoral Fellowship Program and China Postdoctoral Science Foundation (Nos. GZC20250545, 2024M760918, and 2025T180224), and the Fundamental Research Funds for the Central Universities.