Optical imaging with a large depth of field (DoF) has important applications in microscopic imaging, photography, machine vision, and satellite remote sensing^[1–3]. Traditional approaches for extending DoF typically involve reducing the aperture size or employing defocused image fusion^[4]. The former method significantly compromises system light throughput and degrades imaging resolution, while the latter demands extensive post-image processing, rendering it impractical for dynamic scenes. To address these limitations, on the one hand, focus engineering using specially designed phases emerges as a promising technique; structured focuses with Airy spots, optical needles, and multiple focal spots have been proposed to generate defocus-insensitive point spread functions (PSFs)^[5–12]. On the other hand, introducing scattering media into optical systems provides a new strategy. Due to the memory effect of the scattering media, the PSFs at different defocused positions are correlated, enabling image restoration using a stacked or modified PSF^[13,14]. Among these methods, an Airy spot generated by a cubic phase greatly simplifies the design process compared to other focus engineering methods and single PSF measurements without being stacked or modified^[5–8]. However, these methods can only capture the intensity information of the scene.

Since polarization is an important property of an object, decoding polarization properties of scattered light can reveal valuable information about texture, orientation, and even the constituent materials of an object^[15], while polarization-multiplexed dimensionality enables novel application scenarios^[16,17]. Polarization imaging systems are often based on focal plane division or time-domain multiplexing detection of polarization components^[18–23]. Planar liquid crystal (LC) optical elements have excellent properties such as large-scale fabrication, dynamic tunability, and efficient modulation of light fields^[24–34], and have been used for extending DoF systems^[35–40]. The phase modulation of LC elements is closely related to polarization, and a series of novel phenomena of optical spin-orbit interaction can be induced using the Pancharatnam–Berry (PB) phase conjugation characteristics of orthogonal polarization states^[41–48]. Thanks to these properties, LC elements are well-suited for the combined control of phase and polarization, enabling DoF extension and polarization imaging. The integration of extending DoF with polarization imaging brings about a wide range of applications across biomedical diagnostics, remote sensing, and industrial inspection domains^[49–53].

Here, we propose an LC PB-phase element that integrates cubic phase and tilted phase for extending the DoF and sensing the polarization ellipticity. Owing to the odd symmetry of the cubic phase and tilted phase, the LC PB-phase element can produce a pair of defocus-insensitive PSFs with orthogonal circular polarizations to implement DoF extension with a factor of 20. Furthermore, polarization ellipticity can be obtained according to the Stokes vector S3 from a single shot of two orthogonal polarized images, and thereby objects can be successfully recognized from an additional discrimination dimension beyond intensity profiles.

As illustrated in Fig. 1(a), the traditional 4f system can only generate a clear image of an object located at the front focal plane and cannot acquire polarization information. The defocus sensitivity of the system’s PSF causes it to degrade into a blurred disk when the object deviates from the focal plane, leading to significant deterioration in imaging quality. When adding an LC PB-phase element into the spatial spectrum plane, as shown in Fig. 1(b), it empowers the 4f system to extend DoF and acquire the object’s polarization information. The underlying principle is illustrated in Fig. 1(c). Due to the spin-orbit interaction induced by the LC PB-phase element, objects located in different planes will present coded images convolved with two orthogonal circularly polarized PSFs in the image plane of the 4f system. Because of the defocus-insensitive property of PSFs, two clear images with orthogonal spin states will be obtained by the Wiener deconvolution algorithm using the same PSF, and consequently, the DoF can be extended. The polarization ellipse information of the objects can be further obtained by the reconstructed spin component images.

To perform DoF extension and spin separation, two functional phase modulations are integrated into a single LC element. Limited by the phase conjugate locking of two spin components obtained from an LC PB-phase element, an odd symmetric cubic phase that can produce a non-diffractive Airy spot is used to achieve defocus-insensitive PSFs, of which the phase profile is ϕEDOF=α(x3+y3)R3,(1)where R represents half of the aperture length and α represents the attenuation factor used to control the non-diffractive characteristics and the shape of the focal spot^[54]. To achieve polarization imaging, a tilted phase ϕPI=ktanθ(x+y) is used to split the left-handed circular polarization (LCP) and right-handed circular polarization (RCP) PSFs. Because of the odd symmetries of these two phases and the conjugate feature of the PB phase, this LC element can transform the incident LCP and RCP components into opposite polarization states with spatially separated Airy spots, which enables the combination of extending DoF and polarization imaging.

The LC element was integrated into the spatial spectrum plane of a 4f system comprising two lenses with a 10 cm focal length and a 25.4 mm aperture diameter to validate its dual functionality. For this 4f system, we selected R=1.1mm and α=20π to ensure a defocus-insensitive PSF across a spatial range. The wavelength λ=633nm and θ=2.1° for splitting LCP and RCP were further optimized to achieve a suitable field of view. The LC element is shown in Fig. 2(a) with its local polarized micrograph in Fig. 2(b), fabricated using sulfonic azo-dye SD1-based photoalignment technology, and a digital micro-mirror device (DMD, 1080 pixel × 1080 pixel with each pixel size of 10.8μm×10.8μm) based dynamic exposure process. When adding the LC PB-phase element to the spatial spectrum plane of the 4f system, as illustrated in Fig. 2(c), light from a point source located at the front focal plane traverses this optical setup; spin-dependent PSF pairs are generated, exhibiting minimal variation as the point source shifts across different depths. For PSF measurement, a 50 µm diameter pinhole was employed to approximate a point source, illuminated by a 620 nm light-emitting diode (LED) with an optical bandwidth of 10 nm. As demonstrated in Fig. 2(d), the PSFs for LCP and RCP incident lights remained remarkably consistent across point source distances ranging from z=−5 to 5 cm wherein the correlation of the PSFs exceeded 0.9 as shown in Fig. 2(e), indicating that the same PSF can be effectively utilized for deconvolving the coded images. Furthermore, to demonstrate the robustness of our imaging system at different object distances and polarization states, we measured the imaging efficiency (IE) and polarization splitting ratio, where IE is defined by IE=(ILCP+IRCP)/Iinput. The imaging efficiency remains stable around 41% across varying object distances shown in Fig. 2(f), while the polarization splitting ratio aligns with theoretical predictions in Fig. 2(g).

We subsequently characterized this approach by imaging a 1951 USAF target (Thorlabs, R1DS1N, Newton, New Jersey, United States) to validate the DoF extension capability. The experimental setup is shown in Fig. 3(a), where an LC element is positioned in the spatial spectrum plane of a 4f system. The raw image is shown in Fig. 3(b), displaying the LCP component in the upper right corner and the RCP component in the lower left corner. The polarization component associated with the PB phase is strongly dependent on the birefringent retardation of the LC molecules, which can be modulated by adjusting the applied voltage to control switchable activation and deactivation of the LC element^[45]. Theoretically, we can modulate the voltage to the half-wave voltage, thereby suppressing the central zero-order image, which means we can achieve a larger field of view. However, due to the non-uniformity in the fabrication of the LC element, we only achieved a reduction in the zero-order image, but did not eliminate it completely. However, as the defocus increases, the intensity of the central image decreases, which means that we can still achieve a larger field of view. The first row of Fig. 3(c) displays the captured images when the device is deactivated, which rapidly blur as the focus deviates. In contrast, the second and third rows present the reconstructed images for the LCP and RCP components when the device is activated, demonstrating a significant extension of the DoF. The intensity profiles along the blue and red dotted lines in Fig. 3(c) are plotted in Fig. 3(d), where the blue (red) curve corresponds to the intensity distribution of the LCP (RCP) component under positive (negative) defocus conditions. Notably, we can clearly resolve the sixth element of the third group on the target, indicating a resolution of 35.08 µm for both LCP and RCP components, which indicates that the system achieves the maximum imaging resolution of the CCD camera without the need for additional microscopy components. Remarkably, a 20-fold DoF extension has been realized at this resolution, underscoring the exceptional capability for DoF extension in the system. Furthermore, leveraging the imaging properties of the 4f system, the lateral magnification of the image remains unity, ensuring minimal distortion and maximal preservation of the spatial information.

The system can also record polarization information, thereby enhancing the functionality of traditional systems. We tested the polarization imaging capability by observing an LC sample with a designed polarization state shown in Fig. 4(a), and the polarized micrograph of an LC sample under LCP light is shown in Fig. 4(b). Reconstructed intensities of LCP and RCP components are shown in Fig. 4(c), and mapped distribution of the Stokes vector S3 for this sample is calculated by S3=(IL−IR)/(IL+IR). We can see that compared to the previous work that only extended the DoF, we recovered both the intensity and polarization information of the object, which provides a good basis for polarization imaging with extended DoF.

Beyond the controlled sample tests, we further validated the system’s practicality by imaging real-world objects. In this part, we performed imaging experiments with a plastic ruler at z=−5, 0, 5 cm. As shown in Fig. 5(a), we imaged two areas, which have different polarization responses. Figures 5(b) and 5(c) are the raw images, which clearly demonstrate that the two parts have different polarization responses. Subsequent reconstruction of intensity profiles and Stokes vector S3 shown in Figs. 5(d) and 5(e) enable unambiguous discrimination of these areas through combined intensity and polarization state analysis.

Notably, our approach enables multidimensional discrimination capability in DoF-extended imaging by integrating polarization information. To demonstrate this advantage, we observed two objects with different defocus positions in the same scene. As shown in Fig. 6(a), two samples with ‘flower’ and ‘snowflake’ were located at z=−5 and 5 cm, respectively, both of which had different polarization distributions. The raw image is shown in Fig. 6(b), and the reconstructed intensity and Stokes vector S3 are shown in Fig. 6(c). This polarization-driven contrast provides an extra discrimination dimension to intensity profiles, overcoming limitations of traditional DoF-extended systems that rely solely on spatial features. Such multispectral-polarimetric fusion establishes the potential for target recognition in DoF-extended imaging.

Table 1 presents a comparative analysis of our method’s performance relative to alternative approaches, evaluating four key parameters: DoF range, resolution, processing speed, and polarization imaging capability. Intuitively, our method achieves polarization imaging while maintaining comparable DoF and imaging capabilities to other approaches. Furthermore, since both the geometric phase element and its spin-dependent separation are wavelength-insensitive, this architecture is suitable for broadband applications across various wavelengths. However, dispersion effects and spin-splitting efficiency must also be considered. In practice, our system is capable of microscopic imaging, where implementing extended DoF polarized microscopy could significantly enhance pathological diagnostics by providing depth-invariant polarization contrast. The integration of deep learning^[7,55–57] for image reconstruction could mitigate poor recovery caused by PSF distortion while accelerating processing speed. Although the 4f system’s fixed unity magnification limits field scalability, incorporating front-mounted imaging optics can expand the operational depth range from centimeter to kilometer scales. This capability facilitates high-value target identification in extreme-depth scenarios, including aerial reconnaissance and geological surveying. Furthermore, leveraging the multi-band response of the LC PB-phase element^[45] in conjunction with wavelength-specific filters enables multispectral imaging across various bands.

In summary, we demonstrated an LC PB-phase element that synergistically enables DoF extension and polarization imaging. By leveraging cubic and tilted phase modulation, the system generates defocus-insensitive PSF pairs for orthogonal circular polarizations, maintaining cross-correlation coefficients exceeding 0.9 over a 10 cm axial range. Furthermore, we achieved multiplexed imaging of multi-plane objects, where polarization-state divergence provided an additional discrimination dimension beyond intensity profiles. This breakthrough addresses the critical challenge of irreversible polarization loss in conventional DoF-extended systems. The proposed LC PB-phase element has broad application prospects and will play an important role in advancing machine vision, microscopic imaging, and optical detection.